Hello and welcome to the session. Let us discuss the following question. Question says, find the local maxima and local minima, if any, of the following functions. Find also local maximum and the local minimum values, as the case may be. Sixth part is, function g is defined by gx is equal to x upon 2 plus 2 upon x, and x is greater than 0. First of all, let us understand that if we are given a function f defined on interval i, c belongs to interval i, such that f double dash c exists. Equal to c is a point of local maxima, f dash c is equal to 0, f double dash c is less than 0. This is equal to c is a point of local minima, if f dash c is equal to 0 and f double dash c is greater than 0. In this case, value of fc is the local maximum value of function f, fc is the local minimum value of function f. This is the key idea to solve the given question. Now, let us start with the solution. We are given gx is equal to x upon 2 plus 2 upon x, where x is greater than 0. Now, differentiating both the sides with respect to x, we get g dash x is equal to 1 upon 2 minus 2 upon x square. We can differentiate this term by applying quotient rule. And this term also by applying quotient rule, now we will find out all the values of x, where g dash x is equal to 0. So we can write, g dash x is equal to 0 implies 1 upon 2 minus 2 upon x square is equal to 0. Now, adding 2 upon x square on both the sides, we get 1 upon 2 is equal to 2 upon x square. Now, multiplying both the sides by 2x square, we get x square is equal to 4. Now, taking square root on both the sides, we get x is equal to plus minus 2. Now we know x is greater than 0. So we will make it the value of x is equal to minus 2. And we get x is equal to, now we know g dash x is equal to 1 upon 2 minus 2 upon x square. This we have already shown above. Now we will find out g double dash x by differentiating both the sides of this expression with respect to x. Differentiating both the sides of this expression with respect to x, we get g double dash x is equal to 0 minus 2 multiplied by minus 2 upon x cube. Simplifying, we get g double dash x is equal to 4 upon x cube. We know derivative of constant term is 0. And we can find the derivative of this term by quotient rule. On simplifying, we get g double dash x is equal to 4 upon x cube. Now let us find out value of g double dash x at x is equal to 2. So g double dash 2 is equal to 4 upon 2 cube, which is further equal to 1 upon 2. Clearly we can see this value is greater than 0. Now we get at x is equal to 2, g dash 2 is equal to 0. And g double dash 2 is greater than 0. So we get x is equal to 2 is the point of local minima. And we know local minimum value is given by g2. g2 is equal to 2 upon 2 plus 2 upon 2. Now simplifying further, we get g2 is equal to 1 plus 1, which is further equal to 2. So we get local minimum value is equal to, so our required answer is local minimum occurs at x is equal to 2 and local minimum value of the function is equal to 2. This completes the session. Hope you understood the session. Take care and have a nice day.


Good afternoon, ladies and gentlemen. This is probably the biggest audience I've ever seen on the stage. Cool Same with me. My name is Jörg Dürre and this is Yeah, my name is Gunnar Tölle We'll show you how to power stuff without paying Wattenfall, Ion, the National Grid, whatever value from and without paying anything at all basically.  First things first. Where's this? It's not the moon. It's not Mars. It's Iceland. You might have heard of Iceland. It's a country full of ice and There's no sun in winter, but still they power their gadgets like this one This photovoltaic power Seems to work. So why not make it work for you? It's a bad quality of that photo anyway. The photograph isn't too good. I'm sorry for that. Let's see if this thing works Yeah, wonderful Who came by train or by car? Show of hands, please. Oh Wow, that's a lot You might have seen loads and loads of square kilometers of solar panels in Brandenburg around Berlin You might have seen loads of windmills You can have some too. One of those costs at least one million euros, if not more To generate enough electricity for a village. So you don't need a big one. Well, we'll show you a small very short introduction into physics we'll keep it short and What's more important? We'll show you how much power you can actually get from the sun or from wind or whatever and Then we'll make you calculate how much power you need Who of you have got laptop with you? It's quite a lot. Wonderful. It's a cash computer club and Did you bring your power brick? Your net style in German? Cool, we can do it and Then we'll show you what you need Then we'll tell you to Google for the schematics and What's much more fun how to put power into the electricity grid? because you're what the Sun shows the Sun and Very little. This is our Sun. It's a 500 watt Baumarkt Sun We intend to actually put electricity into the Berlin grid right on stage. Let's see if this will work Yeah, nobody, please tell anybody because it's not really correct, but we tell you later I don't know if it's actually illegal. Is it? later You've heard of renewable energy before I suppose do you read newspapers? Yes, you do There's a lot of sources You've heard of photovoltaics. It's what what you can see here You've heard of wind power and then there's a lot of strange other stuff There's in France. There's a place which makes power from the tides Or you could actually drill down into the ground and get electricity from that That's loads and loads of opportunities most important one is the Sun and If you think about it Most of the other stuff you can use that's the Sun Water flowing down rivers can be turned into electricity easy That's solar energy Can you tell me how? Well, I'll tell you it's because the Sun evaporates water from the sea and gets transported to the mountains rains down you've all seen that in elementary school and Flowing water gets electricity You could actually use the kinetic energy of moving planets Sounds weird, but that's what those plays in France does it makes electricity from the movement of the moon around the earth Yes Are there physicists here? I know at least one and You will notice that Generating electricity from the movement of planets should slow down the movement of planets Yes, it does but also what What's really quite funny is You can even use atomic power and it's called renewable energy It's when you drill down into the ground three or four kilometers deep you get one hundred or one hundred twenty degrees hot water Okay, turn into electricity That's actually made from radioactive decay of metals in the earth core and From residual heat from the big bang So it's 5050 I would love to do that privately But we have to invent a real cheap drilling machine then so if anybody feels Motivated go ahead, please then we make it green This light will show you and clear and easy to remember colors green and red What's good for you at home, and what's not good for you because it's too expensive Too difficult too big Our recommendation is use the Sun Easy cheap Doesn't make any noise. No dirt Wonderful you can use wind at home Do you have a garden or balcony? Yeah, so you can use wind power and In theory if you're living near stream you can actually use Flowing water, that's a rare occurrence, but some do You know Next slide now engineers are creative This is one wonderful power plant here It actually runs on the difference of salt concentration in water.  Water with different salt concentrations meet It's where river flows into the sea and It can be done through a process called osmosis and It has been done once If you know how to make a good osmosis membrane, please come forward and have a talk here next year So we can turn all over with our mouse into electricity generating machines Then a strange idea of Gona again just build a very small dam here and then the water evaporates here in the Mediterranean And then we have a good power plant here, but maybe maybe later Well, it's not actually my plan, but it could it could be done because say the Mediterranean It loses more water than its rivers put in If you damage here The Mediterranean Sea will evaporate You'll get huge amazing beaches You will get well you might probably get earthquakes due to the missing rate of water And you will get a really really high difference of water levels at this point Can be turned into electricity, but we shouldn't do that quest question Sounds good, doesn't it? You should you should repeat the question the question and it wasn't really a question But it was 200 meters for some 10,000 square miles of desert sounds good Let's do it tomorrow Well, there's some more physics left What's energy? Energy is the ability to do work That's all do you like club matter you probably do that's a form of stored energy Why because if you drink it you can do work Question for the audience, please calculate the energy content of club matter in kilowatt hours It's it can be measured like all physical variables Well in kilowatt hours That's what your electricity company Bills you kilowatt hours go look it up It has to be There's a difference between kilowatt hours and what What what What isn't energy it's power the more power you need some more energy per time You need the last line is from gunna for the technical it audience that kilo actually means 1,000 not 1,024 So you are all set aren't you Next slide Well, that's enough physics for now About the Sun the Sun is shining all day all night not always in Berlin, but so what And it's shining at a very constant rate of 1.361 kilowatts per square meter That sounds like quite a lot you compare that to your laptops power requirements later And there are quite a few problems The clouds and there's the problem is the more the newer you get to the poles the less Sun you get in winter Well, there's winter and Then there's the thing about efficiency those photovoltaic panels over here They only convert about 10 to 15 percent of the Sun into electricity that's old stuff and About the longitude and the solar constant basically wherever you go you can just move the Solar panel according to the Sun to get the maximum input then as we are now based in Berlin You can calculate how much Sun you get in a year and What's a quite realistic number is 100 kilowatt hours per square meter in year in Berlin? most of that is in summer and Only a few kilowatt hours in winter. We'll talk about storage later But we won't tell you too much about how to calculate how much Sun you get because there's the Internet have you heard of the Internet? Yes In Germany follow this link choose the place you are living at and You can even enter the Form of your roof on your house, and it will calculate how much power you get Easy don't need to do it yourself and some Some cities have something called a Zollacher Taster Is there anyone here who doesn't speak German? Yeah, that's not too much. You're left out now. Sorry and But We've got imagery so you can understand what it is a Zollacher Taster is a pretty fancy Measurement technique. What you do is you fly over a city You measure the roof And you make a map of which roof in your city is Good to get solar power from let's see for bullet Ravi Well, you don't have laser pointers we're here in this Every photograph of Berlin area around Alexanderplatz red is It's very good for solar power yellow means it's not so good and I would have picked green That's Berlin for you Go look that up if your city has one and your roof is perfectly suited to solar energy usage do it If there is no solar caster for your place Please go upstairs Find those people with those small drone like helicopters with those four rotors. I don't know how they are called and Just ask them Yeah, we learned something else today. Maybe social hacking could also work Just ask your local politician and demand something like that Get it who knows Yeah, then there's wind if the Sun isn't shining at your place, who knows the wind might be blowing How do you find out how much wind is at your place you could go out and stick your finger into the air That's not very scientific and it doesn't actually get you any numbers. Okay. No, and you get you get you try this now How much wind is this? Not too much. Sorry and Can you fix it here? And this be Sorry doesn't work That's a problem with wind it's different at every place you can't calculate it You have to actually measure or at least forecast wind speeds As you know from traveling to Berlin the wind is now a commercial commercially interesting resource This poses problems for us Is anyone of you rich? No So we have to get to wind data for free There's one source in the internet right here What it gets you is wind maps like this The resolution isn't too good if you are researcher if you are employed at the university Go and try the British Atmospheric Data Center. They are really good They have wind data from all over the world But they'll only give it to you if you research with wind data Who if you can do this? Nobody too bad Well, I forgot to talk about fluctuations, sorry You might have noticed that the Sun isn't shining all day at a constant rate Let's go back and If the cloud is passing you don't want your laptop to turn off do you? You have to deal with fluctuations For photovoltaics fluctuations happen on our order of one minute, maybe You all have witnessed clouds passing over your place They go by in one minute Deal with it For wind it's easier Wind is a bit more constant. You have fluctuations on the order for about 15 minutes more or less You have to deal with that too, but it's less difficult We'll talk about energy storage later How do you actually get electricity from wind? I'll use one of those if you've got money those are So so horribly expensive this thing produces about 50 watts You'll know what what says now and it costs more than 800 euros or 1,200 US dollars It's too expensive. Sorry. So build it yourself. It can be done from car alternators Google for it Actually, that would be interesting somebody have Has to do it because those small wind machines are extraordinary Expensive even though if you ask in China the small wind machines you can't pay So if anybody feels like it, please go for it Really there was a market niche here do it please well Now you know how much energy you can get or at least you can look it up How much energy do you need to power your stuff? That's a question We've got a microphone, but it doesn't if you're interested in wind energy. There's actually a small book I think or maybe to know by a guy who's actually called a care huck here in in German and They are very good background material and he also has some nice statements about the quality of these wind machines that you can buy from China And then you'll probably wait a little bit more for before you get one yourself That was our conclusion. So we left out went for the rest of the speech if I may add There's a series of books. It's called a Einfälle statt abfälle invention instead of Waste and he describes windmills up to I think 700 watts or so and he builds them from waste you all you need is an old car and Some more stuff you can actually visit that guy. He lives in Kiel That's about 400 kilometers from here They are great and very cheap Well, now you've got your power. What can you do is it? Remember those calculators from school? They don't really need any power this is Indeed a solar panel you can power them with mother match maybe There's quite a few numbers on this slide you can read them yourself If you want to power an Arduino, did I pronounce it correctly? cool Well, you maybe I think you already know how much power it needs. It's not much We found out how much power a Kindle needs it only needs power when turning pages and it's a pretty small amount You can read lots of ebooks with solar power. It's not true Is this a Kindle with You've got better numbers than us wonderful I will repeat that for the stream listeners They've got an expert here who is much more knowledgeable than us, which is good and Kindle will lose all its power in three weeks Can you calculate how much that is? Could you calculate how much water was that is let's meet afterwards The iPad seems to use about half a watt more or less Depends on what you do with it and let's go to the much more interesting stuff like you But it's definitely not true if you do something with it Yeah, wonderful questions our numbers are questionable. Yes, definitely Well Some more interesting numbers. They are as questionable as the others But at least the rain should be all right human beings like you sitting here each one of you is about 80 watts of heat not electricity, of course Have you been on those? They use about 16 million watts when accelerating at full speed Comparison to the iPad 16 million iPads And a pretty impressive number is the energy consumption of Germany Down here, that's only electricity not the energy Can you actually pronounce that number the energy consumption of Google 260 million watts not too bad your homework now is Try to power Google from your town. How many square miles do you need? It should be quite a lot. Wow Now build it yourself you need parts lists you need schematics and instructions, but you're smart enough, so we left it out Is it all right? There seems to be all right and Well, what you need is some sort of electricity generator solar panels wind whatever You need a charge controller You probably don't You need at least a diode Why do we need it? solar panels Will discharge your battery at night? If you don't put a charge controller at least a diode Into the circuit don't do that You need a battery our recommendation currently is lead acid batteries They are cheap. They are very heavy But they work You need you probably need some kind of voltage converter. There will be another exercise in this lecture now Turn out your laptops and see if you can spot the requirement Voltage your laptop needs. It's probably not 12 volts So you need to converter And you need some cables of course When shopping at a at an expensive place the Germans no Conrad, don't they? You can get by with about 100 euros and shopping at a cheaper place like eBay or the scrapyard or wherever it's cheaper It's the easy way and you could actually go large scale By a few square meters of photovoltaics and it adds up to this Do you care to explain this? It's a bad slide, but we just put it in Half an hour ago because we wanted to have money calculation in there We looked up what Wattenfahl charges at the moment for electricity and that is 22.56 cents per kilowatt hour as of today for really bad energy from Yeah coal and lignite and Well, it's basically it's brown and it stinks And then we took the lead acid basseries and Looked how much that would cost if we want to store and we came up with 20 cents per kilowatt hours So that would add up for any stored kilowatt hour There are quite a few assumptions in here one of What did you see? Okay Well, there's a question microphone place is a difference between Car battery and solar battery there are technical differences, but for the easy assumptions we just took car batteries Car batteries are optimized for some other usage because they have to stand the cold and have to have the big Currents to start the car which you would not need for solar batteries, but their price too high So we took the very cheap approach. They will so there would be better batteries for that purpose Car batteries will break earlier. That's a dot cheap. So you said That's another question isn't there so in the numbers that you've got here, I mean my euros to US dollars is slightly Isn't the best that it could be but when I'm looking at this I mean, so this is this is kind of like the cheapest that you were able to get it because I mean, I'm not familiar with European power grid and you know in the US Yes, we're wasteful and you know we do all kinds of stuff But I mean the our cost for power like just all in all the taxes everything comes out to normally 11 to 12 us cents. We know So we are being tricked by the electricity companies and that's why we're here to tell you that's not necessary I'm very sorry, but this talk will probably not be too interesting for you Bad luck. It's just based on really strange You have to put market in What's it called in English? It's not really a free market. It's kind of state-run Republicans would say communism or something That's what we get here in Europe. I calculated for myself for the Percentage of the net cost that I pay is 45 percent of total cost. So We have to do it on our own and then we force the big companies to come down with the prices and then we proceed on How close we are to this? Well, let's let's go to our assumptions now our assumption was for this calculation You could actually disconnect your home from the electricity grid. It's possible. It's not too expensive What you need is Batteries we chose car batteries. How many you need? Well depends on what you need and We have we've got the assumption that you use most of your power at breakfast and in the evening Because as a fellow hacker you go to work. So you don't need electricity during the daytime This assumption comes through when That we need to store 70% of our electricity and batteries and can use 30% of the electricity we make from our roof directly It's just an assumption. It's as questionable as all our numbers are and With some technical Optimization you can of course change it, but that's later and There's another assumption which we just kind of picked from Wikipedia, which is a wonderful source as you all know that's If you buy solar panels you Get a loan from your bank for 25 years You can actually produce electricity from your own roof for 13.8. You will sense per kilowatt hour See for yourself or edit it and flame us afterwards. So we have to Say a few words more in Germany if you use a renewal energies law They annoy a bar and a gene gazette then you would get the fixed compensation for 20 years But after 20 years the photovoltaic system is not broke. You see your Scientific calculator the solar panel will stay on forever. So after 20 years, you still have 80% power left So what we did is calculate was 25 years and not with the 20 years that are always in the papers so next time you read something about The cost of photovoltaics they always calculate was 20 years not a year more because in the 21st year The cost of photovoltaics would be almost nothing Yeah, you already pay back your loan. You get free electricity Great Well, what we came up with is Electricity from your own roof costs 27.8 euro cents per kilowatt hour. It's more expensive than now But the German energy agency just said electricity prices will rise 20% next year No, we're moving closer and if you want to be On a cheapskate deduct 5 euro 90 fixed fee per month and it pays you nearly well Your investment costs Did you all understand that? Let's sum it up It's not expensive anymore compare that 27 cent 22 cent not too bad Well Where to buy you get PV cells everywhere even at Conrad That's kind of the most expensive place you could buy them the cheapest place seems to be China If you don't want to go to China go to eBay we just Which is China basically yes, but Um Actually it gets delivered to your doorstep. That's cool and It seems like currently prices are at 1 euro 20 per What you measure photovoltaic cells not in square meters, but in what because that's what's actually interesting Go buy your led batteries from a cheap car shop you all have one next door and Well, we've talked about wind generators build your own or If you are rich you can buy one of those ready-made things The company I named here. That's not our company and they don't pay us And you need your charge controller or at least a diode which you get from your local radio check or whatever for Next to no money Take care with those batteries. They contain sulfuric acid Please don't pour it over your hands or other body parts. So it doesn't look nice and it doesn't feel very good please don't and Definitely take care if you are experimenting with lithium batteries They don't contain sulfuric acid, but if you Charge them incorrectly they might ignite Burn melt your house down. Don't do that, please Now we've said that let's put power into the grid Okay, I'll entertain you in between and he will do the real thing If you insist mr. Cameraman, how far can you come to the stage? How near can you come to the stage story from my English actually about the lithium batteries? It's not all that dangerous. It's not ready for home use yet, but I have talked to some German companies that are ready with lithium isom lithium ferrum phosphate batteries with titanium Anodes or and they will have cycles far better than actual batteries now So that we come down for our last forever basically basically yeah by one Use it for the rest of your life and once we are there and we have the photovoltaic system. We have an amazing future I'm so putting your own power into the public grid Usually at home it can't be done. We show you how it can't be done In Germany, we have the anoyabara energine gizettes renewable energies law Anything about one kilowatt one thousand watts Gonna how much is this what you have there? 50 watts Those those are 30 watts each 30 watch each far too tiny for a new apache energy gizettes So you need a few of those or a little more better ones like five of the big panels Then you can use the renewable energy law, but you have to fill out a lots of papers Once we put this on the grid theoretically Then the meter would go backwards so we don't tell anybody and Once the grid company recognizes what we do then Most likely you will have a digital meter and not a Ferrara's counter as it is in the most household at the moment This is a magic box the grid tie inverter When we really do a bigger installation at home, then we have to take care that the local Electrician does not get electrocuted. So there have to be some Rules to be followed. It's a German faude ear rule zero one two six That defines what this little box has to do that actually on the power plug Hmm Where's the power plug plug anything like here? It's absolutely not allowed that electricity comes out here, but with such a box it does so Yeah, make make very sure you include this in your own circuits There's a good reason for that if your power grid at your place goes down which happens and The Sun is shining You miss your own power parts are delivering electricity into a grid that your local technician is trying to repair Don't try him Really don't You'll die So what you really do is just fix it to the grid with an approved Electrician because you're required to by law to use one so once it's Attached to the grid then there's no danger anymore if you do that in Germany or if you buy electricity in Germany usually you have Your local supplier the grid supplier in this case we took the example of Wattenfall in German it says You have to Take care and sich erstellen das von seiner eigenanleih keine schädlichen rückwirkungen an das elektrizitätsversorgungs netz möglich sind und der Anschluss von eigenanlagen ist mit dem Netzbetreiber abzustimmen so We have to take every measure that there's no danger and We have to talk to the grid company before we do this what we don't do of course So that's a photo from inside Really cheap. Can you turn us around or we can't see anything anymore? So that's the Chinese box cheap thing from inside which actually is conformed to faulty e is 0126 So we could attach this Okay, maybe the show is over It's over I'm sorry, we aren't prepared Yes, we put the coin for a scale in there just to show you how how small you could do that So that yes, that's five cents I put in here to have an idea of how much air is in the box. So basically we could fit it into Cigarette box, I think if some real technicians go for it So connections are you ready? So should we try the Sun? Oh, we've got stage some is enough. No, it's not enough Your son's cable is too short What I think we need help from the audience Would you care to shine the Sun onto the photovoltaic cell? Here is an electricity meter in case you're wondering those are the cheap crapper ones from your local Baumarkt, they can count backwards But not all of them. Yeah, it's already on and the Sun isn't shining. It's working Well It's right here That's a good. There's a green light blinking on our magic box. Can the camera show it? Which actually indicates that we are now putting electricity into the public grid and There's another problem which we didn't anticipate. Well, I did and Those counters only started About nine or ten watts So we are putting less than nine watts into the public grid now I'm sorry What if there is no camera with that? It doesn't make sense anyway anyway Okay, we go on then. This works since As you might have noticed It didn't take much time most of the time I spent because I'm not well prepared If you are prepared in a good and wonderful way It will work in about two minutes It's easy But it's still not enough Sun So this little machine has a maximum power point tracking in there It would adjust to the power that shined on there and does an optimized feed-in But this technology exists since years and nobody develops this very small scale gadgets so there is from our perspective a good market because we're so close to Grid tariff that you could actually use it at home on your balcony Which I do Well, now we've entertained you. I hope we did that in a sufficient fashion Now it's your turn as a lot missing from well, basically from the internet and That's a lot of information missing We need open solar map dog What does it do? Well, we've talked about that it takes one of those wonderful flying helicopter things and you need a laser pointer and a camera and some fancy software and Finally you get a solar catastrophe for every place For much cheaper currently it's done with a real plane and commercial software Basically, we need the same for wind and Then there's fun to be had with hardware solids and maybe even with fluids You need one of those boxes as open hardware so everyone can have fun if thousands and thousands and thousands of people have one well Nothing file has to be convinced. They will allow it because you are you know, it's reality and basically this Grid tie inverter is nothing else if you have the Taha the thing for your car you put in 12 volts you get 230 volts for your laptop in the car That's the same thing. It's only the synchronization to the net That's different and the box for the car costs only 40 euros So this should not cost too much more and then No, that's another thing you shouldn't do you shouldn't take your car Alternator which turns your secret ladder into real electricity and connected to the public grid That won't work. It will melt and burst into flames Hopefully because that's interesting, but please don't do that You need the special box which currently can only be gotten in China and There's definitely a need for energy storage technologies Yeah, let acid batteries are cheap, but they are heavy They don't work too well They contain sulfuric acid which is bad and they contain that which is bad for the environment In my dream, I will come here next year Not be on stage, but in the audience and some of you will Show you of your new Redox flow battery. Have you heard of that? Oh Wonderful. How many of you have heard of that? Okay, so I have to explain it.  It's recharged wonderful If you want to enlarge your redox flow battery Well, you get another few bottles of fluid off you go sounds good and We definitely need a way to get very cheap solar panels If you care to ask downstairs in the heck center, there's some guy with a 3d printer I asked him today if he can make solar panels. He said yes, but We didn't do it today because you would Need to make a vacuum in this room Which we can't Go ask him so it gets cheaper So there are other things for cheap Electricity generation that was in the papers last two days ago That there's some paint being invented that gets you 1% of the light that falls in To electricity so 1% efficiency So to wrap it up. This is our future. It's dark It's black Oh, it's not green For my opinion because this 1% is Photosynthesis that's the efficiency you get from light that is being transferred to biomass and that's only the theoretical Usage that you can get out of this. This is practical photo Voltaics that you can buy off the shelves 15% of the light that falls in has been converted to electricity and that Should be a chance. Yeah, that leaves 85% of light wasted Do something with it, but at least it's 15 times more than plants can do Sounds good So next time you read the papers think about these numbers well, why not make use of networks your love networks, don't you and What we need is kind of and well, I've called it energy server.  I'm sorry, and If you produce your own electricity, you need to match it up with what you need It's interesting if you turn on the washing machine while the Sun is shining But you shouldn't need to think about this for yourself your home server can do that So you need a control pot you need a washing machine with some kind of Web server in it, which can turn it on and off You need a toaster which can be turned on and off from your home server Doesn't this sound like fun? And you need fancy server-side software This is a job for you And if you've done all of that go and disconnect yourself from the grid team up with your neighbors because it's easier And you get to meet people And use the Sun because it's shining and it's good for people If you live in the European Union, you will get to know those You probably know those from your basement The old Ferraris counter It's not a Ferrari counter because they can't actually go that fast but See you want us to have fancy digital electricity counters Well, what can you do with it? I've been told those things Can do communication two ways But I've got no idea what they actually communicate I've been told those things can actually turn off electricity to our soul. This sounds like a denial of service attack to me Impress us next year, please I don't think so No, I just want to mention some communication protocols that are not really good documented, but there's really good chances to integrate different Renewables in your home if you have your photovoltaics if you have your wind Maybe you have a CHP a combined heat and power plant and you want to have that communicate with your Actual demand so that would be work for guys like you and for now Well, ask questions either now or wire email You have to follow this algorithm. So to prove you aren't a spambot, but shouldn't be too bad There's time for questions now. I think where's our angel? Is there any time left? There's time left isn't there? First question. I'm on well my remark If you go more global, there's a good book. I read a couple of months ago called renewable energy without the hot air I don't know if you've read that it's free You can just download it on the net just Google renew renewable energy without the hot air and it basically Makes a whole assessment for whole Europe about Running all Europe and renewables. So it's quite a good read and it's also very well-founded Next question More questions. Oh Lots of questions. Yeah. Yeah, actually. It's not a question It's an answer because you asked how much energy there is in club matter and it's 1.2 million kilowatts if you bring it together with anti-matter Wonderful that's a question right down there Thank you so much. That's impressive Hi, I just a remark concerning your talk. I mean, thanks for the talks. It's very nice I just want to contrast powering your own gadgets with the Vocabulary you use to describe a bright future with renewable energy and the rather Stark vocabulary you use to describe the current coal and fuel energies, but Just to be clear.  So I'm just worried about This will not scale this is very nice to power your own gadgets But not enough power to make the gadget and certainly not enough power to run all the computers that this gadget is Usually connected to so just I just wanted to have your thoughts about this very quickly. Thank you actually We looked on how much energy there is theoretically in some battery materials and this lithium sulfuric battery is described was theoretically 3200 watts per kilo and What hours kilowatts kilowatt hours kilowatt hours per kilo so You would have 10 kilowatt hours per kilo in diesel and If you want to make electricity from diesel you only have like 30 or 40 percent Efficiency so Interrupt but can I ask everybody to stay seated because it's really interruptive during the Q&A So, thank you very much. Okay. My point is Batteries and in theory should do almost the same electricity storage like diesel does at the moment. So I don't see too much of a problem That's another remark from me actually the energy you need to produce one of those panels can be Produced by the actual panel in about six months. That's called erntefaktor in German. I don't really know in English Word for it and they pay off after some time the energy you need to Build a wind turbine as you see in Brandenburg Is being produced by that same winter by no in about a week after one week it's free and Usually you don't need to store that much energy like you used to if you Had an old heating system at home. You might have had two cubit meters of heating oil there So that would be lasting for the whole winter But for the future you would only need so much electricity To cover the need until the next wind has come and filled up your storage. So that would be quite a bit less Yeah One two three four questions now five. Yeah, you first. I'm I'm quite a bit disappointed from this talk Because what I what I really looked for was a lot less Some vague allegations about the fact that not only there was solar power but that you could actually use it but rather Concrete experience how to construct a small scale installation of either solar or wind power and and the and the very nuts and balls of How that actually does work because not only is it not trivial but there is also a patent lack of of Purchasable and and reliable electronics Doing doing the work in the background and I would very much like to to have at least at this stage Some some answers to these kinds of questions Okay Please people else is disappointed show of hands. No, I'm I'm not really this point No, we want to ask the answer this question because basically we a little bit expected this but With a gadget like this, which is only be accessible at the moment in China It's trivial. You just plug plug into the wall and it works.  I had some bought an eBay from German companies. They don't produce it anymore So I bought these from China and plug it into the wall and they work so the the thing is you have the grid tie Inverter it's the same thing like you have in your car I said you plug in 12 volts that come out of your car Or either or you take the 12 watts that come out of this photovoltaic thing and it changes this to 230 DC power and Then you have to have the synchronization and the mechanism that cuts it off the net so that they don't get electrocuted And that's basically it. That's one What's that shelter switch switch one switch away and one part of an electronics that does a Synchronization you have the official net that goes with 50 Hertz And you have to synchronize it that you don't disturb the net and that does the machine and everything else is just peanuts Yeah Question going I Want to answer? I actually go ahead. I want to have a similar demand I'm also trying to live off the grid for a couple months and I do use a small solar system and I have the need to Find other guys who are actually working on getting a small Structure together like you said because it is missing. There's nothing for below thousand euro or bucks where you can buy a Solar setup. It's not there. You have to get the solar panels. You have to get the diode, which is kind of Okay, you have to get the thingy and and connect everything, but there is nothing like a package or something anyway I would love to share also Okay, we'll set up my question where where we Collect this I actually reserved one called Piraten strom dot de so maybe we set up as a as a website for that Why not? Would be great to have a package anywhere my question is I'm messing around with the 12 volt and my ideas not to use To put it back into the system because 12 volt is more efficient because that's what you have and when you you lose power Anyway, I use the batteries, but there are Nasty and break and I thought about using a pump to fill up a thousand liter Whatever tank water tank basically and use the try to use the power back. Is that reliable? Do you think it is in a small scale? Usable because I'm not too good with calculating that would it be useful for like 50 watts or something? I'd like to offer you that we should meet after this talk We need to do some number crunching on this. It's just a rough scale Would it make sense to play around with water as a basically energy? As a battery basically no to be honest no no Hi, I wonder how photovoltaics really compares to photosynthesis Because you said it's 1% and 15% Evolution had a few million years. I think to optimize this technology called tree and on one square meter I can grow a really huge tree which has perhaps billions of little solar panels these leaves and I can just I can make this solar power plant out of dirt literally and I can burn the wood and generate electricity and To have these photovoltaic panels I think there's a lot of ancient sunlight which is stored in oil and gas which is necessary to produce these things and My question is do you have numbers? If I have one square meter and I grow a tree or I put a photovoltaic cell on it What is what are the what is the real efficiency of these come both technologies compared? That's that's a good question The photovoltaic thing one square meter of photovoltaics gets more or less 15% efficiency. We've seen that before one square meter of tree Regardless of tree size, that's the interesting part gets about let's say 1% might be true more or less and The thing about trees is if you use a larger tree By having it getting it to grow bigger you don't get more Sun So you don't actually get more energy I Increasing the tree doesn't help Because it still needs Sun and the Sun doesn't increase with it Yeah, but yeah, the problem is if if you use the vertical space and you get all your sunlight in your tree up here There's none left for the below. That's the constant We only have so so much Sun for one square meter and at the moment we Can collect 15% with a off-the-shelf solar panel and in the laboratories We have systems that go up to 40% Collection and that's just a fact photovoltaic photosynthesis look it up in Wikipedia There's a link for a big study for photosynthesis in general you would get like point six or point eight percent Efficiency and that's only the energy that is stored in biomass if you want to transfer biomass again to electricity You lose again 50% so we would not use that numbers because that's good thing too amazing then The tree is interesting because it produces chemicals. That's a good thing Which you can use for building like furniture medicine Whatever we're not against biomass you can eat it I'm very sorry, but I've got to end it because it's the end of the talk Where can they find you right now if they want to talk a bit more about this? Well, I'd say right outside this dog Yeah, it's very busy. So that's not gonna happen Okay, oh, that's too bad suggest the place You tell it. I don't know where I can find you Maybe in the restaurant or where you're sitting see In front of the speakers room, but not inside the speakers room because that's for us. That's okay Okay, so if you want to talk to them, please


Let us start our today's lecture for NPTEL video course on Geotechnical Earthquake Engineering. We are going through now module 8 of this course that is site response analysis. Now, let us have a quick recap what we have learnt in our previous lecture like we started defining what is called transfer function. It is nothing but a filter or a multiplier which changes input ground motion to an output at another level. So, we have seen various cases how to estimate the transfer function like for uniform damped soil. This is the way we calculate the transfer function and this is the transfer function expression which is nothing but the ratio of the displacement function at ground to that at the rock level that is the interface between the soil and rock. Then we have seen what is the expression for this transfer function which is a function of the frequency and the damping ratio expressed in this pattern. So, which is nothing but can be mentioned as amplification factor in terms of k h. So, we can see as the damping ratio increases the amplification factor will decrease and so on with number of cycles. Then we have talked about uniform under soil on an elastic rock. Earlier we talked about rigid rock and then we came to consider the elastic rock which is more practical. For that we have seen even though we do not consider the damping of the soil that is the material damping or the viscous damping of the material we had considered. But even then because of the impedance ratio of non-zero value between this elastic rock and the soil you will get the non-infinite value of the transfer function at the particular value of k h like this. So, this is the expression for transfer function when the specific impedance ratio between the soil layer and the rock layer is considered that is considering the elastic rock. Then we have talked about most generalized case of layered damped soil on elastic rock. So, for that we have seen that the displacement compatibility and the stress equilibrium between the layers has to be maintained which by known boundary condition will give us the values of various coefficients. Then we have also discussed how to carry out the equivalent linear ground response analysis. This is how the modulus reduction curve or G by G max ratio over the cyclic shear strain varies when we are talking about G second that is second modulus and the how the damping ratio varies with respect to the cyclic shear strain. So, we need to choose initially one initial value of the cyclic shear strain to start the analysis and until the results of assumed strain and the final output strain after using the chosen value of G and eta we get matches those two strain we have to repeat this. So, this is a trial and error procedure or iterative procedure by which finally we will get that gamma effective. However, for non-linear approach we cannot use that modulus reduction curve. We need to then use the equations solve the wave equation incrementally that is a small steps of the backbone curve of that shear stress versus shear strain into a small time interval steps. Now to do that these are the steps we have seen we have to start with initial tangent modulus which is nothing but G max then use small time step of delta t that time step has to be chosen based on the entire time duration of the input ground motion or input seismic motion wherever level we are considering that time has to be subdivided into number of small time segments. Then you have to compute the shear strain amplitude at the each end of time step that will give the corresponding G tangent that is individual tangent modulus for each and every time step that finally will lead to the shear strain amplitude at the end of each time step and it has to continue for the entire time duration. So, by using this incremental procedure of analysis we will get this backbone curve of non-linear response which automatically considers the material damping by this hysteretic response. And this approach requires a good model to understand the behavior of this stress strain. So, what are the good models? Two major types of models one is cyclic non-linear model another is advanced constitutive model. Now, cyclic non-linear model one can get very easily from a lab test on a particular soil by knowing the backbone curve unloading reloading rule and the pore pressure model whereas, for advanced constitutive model yield surface hardening rule failure surface and flow rule all this information should be available. So, we have seen also in our previous lecture a comparative study between the use of cyclic non-linear model and the advanced constitutive model. We have mentioned that obviously the cyclic non-linear model is a simpler model to use, but there are difficulties like exact soil behavior or dilatancy effect etcetera may not be captured. Whereas, advanced constitutive model is the best that way there because it considers all the dilatancy effect yield behavior failure behavior everything, but the disadvantages it is a complex model and it requires longer time also it is difficult to calibrate with respect to a particular soil model that is unless for your soil you have your constitutive model known then otherwise you cannot use this advanced constitutive model for your analysis. Now, in today's lecture let us now start with the comparison of this equivalent linear and this non-linear site response analysis. So, inherent linearity can lead to spurious resonances in equivalent linear method. What inherent linearity we are considering if you look at this curve once again which we have already discussed in previous lecture this is the inherent non-linearity which we are considering right. It is actually non-linear, but we are taking assuming this linearity that inherent linearity which is used in equivalent linear method may lead to some resonances spurious resonances which is not actual. So, use of this effective shear strain can lead to over damped or under damped system depending on the nature of strain time history. Equivalent linear analysis can be much more efficient because it is more faster right than non-linear approach whereas, non-linear analysis can be performed in terms of effective stresses and non-linear analysis can predict the permanent deformation because it is exactly capturing the final cyclic shear strain which the material is undergoing through for that time duration of input motion. So, what will be the suggestion for a practical use of this equivalent linear or non-linear approach when we are dealing with very important problem let us say design of any earthen dam or design of some nuclear power plant foundation system. In those cases where the importance of the structure is very high in those cases non-linear ground response analysis is a must whereas, for medium important structures or medium important analysis like for buildings etcetera. If you want to do the ground response analysis what you can use equivalent linear approach why because equivalent linear approach will save a lot of computational time which is necessary in case of non-linear approach because you are doing incremental small time interval and repeating the method of analysis. So, that is why non-linear approach takes much longer time of computation than equivalent linear analysis also non-linear approach is complex than equivalent linear approach. Whereas, I am telling that linear approach where only g max is used should be avoided for any type of ground response analysis because we know earthquake response is a high strain phenomenon. So, in that case if somebody is using linear ground response analysis that will be absolutely wrong because that does not capture the high strain phenomenon it will be only a low strain phenomenon where g max is valid or linearity of the model is valid. Now, let us look at this comparison one further that is non-linear analysis require reliable stress strain or constitutive model which we have already seen. So, this is one complexity in the analysis differences in computed response depend on the degree of non-linearity in the actual soil response what it is having. So, suppose if we are handling with stiff soil site that is these are all relative terminology of course with weak input earthquake motion in that case non-linear and equivalent linear will result almost the similar output that is for a stiff soil site and subjected to weak input earthquake motion you can either use equivalent linear or non-linear in both the cases similar results you will get. So, obviously it is better to use equivalent linear which is less time consuming also which is simpler to analyze. Now, but for soft soil site where chances of licky faction is there and the soil site is subjected to strong input motion in that case non-linear analysis is always preferable because that will capture the actual displacement of the soil material which will help you to further which will help you to further calculate the displacement related to this licky faction and which will lead to lateral spreading etcetera. So, those things for those type of soil site and that type of input motion strong input motion non-linear approaches preferred over equivalent linear approach. So, some practical aspects of this site response analysis what we can say that equivalent linear much more commonly used why those are commonly maximum used than non-linear because of its first widely available method because it is pretty well known and widely available greater range of experience many people have done. So, people have experience handling with that performance is well documented how they perform with the equivalent linear approach those are available in literature it generally runs faster because less computational time than non-linear. It allows deconvolution what is deconvolution we will see that convolution is nothing, but when we are approaching from the ground to from we are approaching from the bedrock to ground surface and deconvolution is the reverse one that is from the ground surface to the bedrock level. Material property characterization is easier in case of equivalent linear why because only you are considering the G second at whatever strain level you are interested to that value of G sec you can consider right. Wherever we are mentioning this advantages of equivalent linear over the non-linear what are the other side of it is probably these are overused for the case of very soft site and liquefiable site which should not be we have already seen for these type of site non-linear approach is better non-linear site response analysis or non-linear ground response analysis is a better option. Now, practical aspects of the site response analysis are convolution what is convolution as I said just now bedrock motion is applied at bedrock level and outcropping motion is needs to be obtained motion within the profile has to be obtained and motion propagated upward through the soil profile. Whereas what is called deconvolution in this case motion is applied at the ground surface and then that motion propagated downward through the soil profile and bedrock motion corresponding to surface motion is computed in this case of deconvolution. So, for the case of convolution we need the transfer function to be used whereas for the case of deconvolution we need to use the inverse of the transfer function to be used right. Now, as we have already discussed these common situations to major common situation and how to find out now after having the complete knowledge of this site response analysis let us look at it once again that is common situation one is say ground surface motion on the top of some soil layer needs to be determined. So, at this point we want to obtain that is the problem statement let us say. So, determine the soil profile characteristics we need to know what are the material property of this soil layer by subsurface in investigation or the field or laboratory testing program. Then determine the design motion characteristics how we can get that design motion characteristics either using deterministic seismic hazard analysis or probabilistic seismic hazard analysis right and site conditions must be recognized what type of site then obtain the input motion obtain input motion means for which earthquake motion you want to analyze you want to carry out this ground response analysis like actual input motion you can download from the website that is for the authentic data as I have already mentioned USGS database or IMD database or PR database there are various other database where actual ground response or actual earthquake response at different depths are available. So, you can use that motion as an actual motion or one can use the synthetic input motion synthetic ground motion is nothing but it needs to be generated you generate the is synthetically design it is not the actually happen and this actual is where some earthquake has really happened in some part of world and then using this input motion whether it is actual or synthetic out crop or within the profile that needs to be determined that needs to be known whether it is a out crop motion or it is at the bedrock right. So, then once we get all this information and what we do say this out crop motion you are getting from some website if it is an actual earthquake from some reliable source or you are applying some synthetic motion you can do that also because when you are doing site response analysis at a particular site for your design you do not know in future what earthquake will come. So, probably I either you can use the historical earthquake in the nearby region or you can use some synthetic motion which will justify the seismic zonation of that area. So, that way the synthetic motion has to be chosen at out crop. So, this is known now this motion and this motion should be different are this motion at two points identical no they cannot be identical because it is a free surface and this is a underline by a soil layer right. So, in one dimension analysis input motion is applied at a point directly below the ground surface of the point of interest. So, you can apply if the bedrock motion is known you can apply it here also, but that should be different you remember that then you apply all the soil properties etcetera do the either equivalent linear or non-linear analysis to get the known value over here. So, that is what it says here it is zero stress free boundary condition whereas it is non-zero stress. So, that is why they should not be equal as I said already. So, bedrock motion will be slightly different than the rock out cropping motion because of it is related through that transfer function using that boundary condition and equivalent linear programs allow specification of rock out cropping motion bedrock motion automatically gets computed. So, this bedrock motion once you put it then you compute the free surface motion by using this equivalent linear or non-linear programs. So, for that as I said either shake or deep soil can be used. For common situation number 2 where free surface motion at one soil site is known suppose just now we have computed at this soil site one the ground response analysis right then in another soil site number 2 we need to find it out. So, soil site number 2 we need to find it out. So, how we can do that? We need to transfer from point A to corresponding bedrock motion point B and that bedrock motion you have to take at the out crop motion C. That C you have to take if the rock profile is same at out cropping at the 2 different places at ground surface also because rock material is same and both are out cropping. So, you can use that data. Once you use that data at C then from C D you equate that is assume that rock out crop at site of interest D is equal to that of measured at C. Then once you get D you can get it at E again using transfer function. Once you know at E then use the ground response analysis and get this unknown at soil site 2 F. So, compute the desired free surface motion at F. So, these are the steps how we carry out the ground response analysis or site response analysis from one site to another site clear. So, the deconvolution how we can cross check it is helpful to check the results carefully before using because it may be unrealistic sometimes like soft soil profile. High frequency components are getting deamplified whereas for consistency with surface accelerations unrealistically large high frequency bedrock accelerations may be required. So, in that case to check the deconvolution you can use the synthetic time history also that is what it means. Instead if you do not have a real earthquake motion to check the deconvolution for your soil layer you can use a synthetic time motion. So, it can filter surface motion below 15 hertz frequency to reduce the potential for this effect. Now, let us start going through the example problems on this ground response analysis from 2 case study. These 2 case study the first example is the case study on the seismic ground response analysis for Mumbai city in India. This is a part of the Ph.D. thesis work by Dr. V. S. Funnican who completed Ph.D. in the year 2011 at IIT Bombay. Under my supervision he is a scientist at BRC and Dr. G. R. Reddy was external supervisor from BRC. So, from his Ph.D. thesis work on this ground response analysis this journal paper has been published. So, one can go through this paper for the detail discussion about how this ground response analysis using the equivalent linear approach has been carried out for some typical sites in the Mumbai city of India. This is in journal Geotechnical and Geological Engineering of Springer publication volume 29 issue 6 page number is given over here year 2011.  One is Mangalbadi site near Girgaon. There are 2 borehole data typical borehole data. Mangalbadi site borehole number 1, Mangalbadi site borehole number 2 were used. Valkeshia site, Valkeshia borehole number 1, Valkeshia borehole number 2 and B.J. Marg near Pandhari Chowl site with B.J. Marg borehole number 1, borehole number 2 and borehole number 3. Typically, this soil data from collected source of reliable sources of soil data this information has been first taken care of. So, this is the typical borehole data for the Mangalbadi site number borehole number 1. You can see the layer thickness over here given depth below the ground level that is beyond 9.8 meter below the ground level the hard rock is available at that site you can see over here. So, corresponding SPT values are given over here as recorded at the site. Based on this input motion what next step we need to do this is the bed rock we have several layers of the soil as we have seen. So, that multi layered site response analysis we need to carry out what we have just now we have seen we have seen how to carry out for individual layer. So, to do that next is we should know what is our input motion we are using. Now, for the input earthquake motion Dr. Funnichanth had chosen these four input motion 2001 Bhuj earthquake motion 1989 Loma Priyatama earthquake motion 1989 Loma Guillory earthquake motion and 1995 Kobe earthquake motion. These are the various parameters which are obtained like date of occurrence of this earthquake magnitude MW recording station distance from the source that is MHA predominant period mean period bracketed duration and significant duration. So, all these data have been taken as input value of this earthquake motion for further ground response analysis at those borehole locations or soil site. So, once again the pictorial representation of this acceleration versus time history of the input motion. So, this first one is for the Bhuj motion of 2001 earthquake then Loma Guillory this is Loma Priyatama this is Loma Guillory this is for Kobe. Now, input parameters for this borehole number 1 has been further extended to the shear wave velocity. Why we need shear wave velocity? We need shear wave velocity because unless we know the individual layers of soil shear wave velocity we do not know the initial tangent modulus or the maximum shear modulus G max right. Because G max we can calculate from rho V s square. Now, this V s either it can be estimated from the site using M S W or S S W or other field test or in absence of that one can use the available empirical relationship between SPTN value and V s value and obtain these values. Then starting point of damping ratio is considered as 0.5 percent all these are 0.5 percent for all the layers you can see 6 numbers of layers for this M B H 1 as we have already seen has been considered. So, this is individual initial values of damping ratio for an initial cyclic shear strain. So, this is reference strain in percent initial values reference stresses and other coefficients beta s and so on. So, you can get the details in this paper as I have mentioned where you should know the equation for the backbone curve that is tau versus gamma which is expressed in this form. So, G m o is nothing but initial tangent modulus that is maximum shear modulus. Beta is a coefficient s is another coefficient gamma is cyclic shear strain and gamma r is reference shear strain that is you select a reference strain at beginning and then do this iteration until this selected reference strain and the converged finally, obtain reference strain matches. After doing that what output you will get. So, this analysis was done using the software deep soil deep soil version 3.5 beta of 2008 version was used. So, one can always use the latest version to do the analysis at that time 2008 was the latest version. Final output one can get this acceleration versus time history at any layer. So, finally for any structural design we will be interested to know the ground at ground level what is the output acceleration time history. So, this result shows the at ground level this is the acceleration time history of that 2001 Booge input motion which was given input as the bedrock level at that borehole number 1 at Mangalwari site. So, using that soil property using this we got this one. So, this was your input motion you can see the maximum value was 0.106 g whereas, the output came more than 0.2 g can you see that. So, there is an increase in the maximum value of acceleration from the bedrock level to ground level in that borehole number 1 considering the local soil parameters or properties. So, the response spectra acceleration response spectra if in that fashion we want to express because why we are interested to know about response spectra all the design codes they talk about the response spectra versus period right that we have already seen even in our IS code also. So, this is acceleration response spectra with respect to this period for different earthquake input motion for Booge motion this dark color solid line for Kobe this dotted one for Loma Prieta this one for Loma Gilory this one. So, depending on different input motion your output is also different as you can see for the same borehole location MBH 1 at ground level. So, this response spectra is at ground level considering 5 percent damping at the soil side because you remember whereas, you are getting this acceleration time history result at ground level here you are getting the exact damping ratio, but for spectral response spectra you have to assume some damping because it is for the equivalent single degree of freedom mass spring dashpot model right you remember for response spectra how we determine. So, that is what it is mentioned 5 percent damping it is nothing related to actual damping of the soil. You can see the result that A max value the maximum value at ground level for MBH 1 what we got it was about more than 0.2 g how higher than 0.2 g. So, that if you compare with respect to your input value of 0.106 g what is the increase or amplification of peak value amplification is nothing, but we can see A max in terms of g at ground level divided by maximum horizontal acceleration at bed rock level that will give you nothing, but the values of amplification with respect to depth. So, for different earthquake input motion and for all different borehole all the borehole number 1 of all these 3 sites are reported over here. You can see in Mumbai city typically considering all this soil site we got a range of soil amplification ranging between 1.22 above 3.5 that is the range of soil amplification when we are considering a bed rock to the ground surface level clear. So, that shows a typical soil amplification of earthquake acceleration at various soil site in Mumbai. This is in the tabular from the exact values are computed the same thing MHA at ground surface by MHA by bed rock at different input. Motion and at different borehole site. Now, we can see acceleration response spectra at different layers. Can you see layer 1 is nothing, but your ground level which we have already discussed, but if somebody is interested to know that other layer say layer 2, layer 3 or layer 6. Why it is important? It is again for MBH 1, but for different input motion this figure A is for Booge motion, figure B is for Loma Priyatha motion, figure C is for Loma Guillory and figure D is for Kobe earthquake motion. Why this response spectra is important? Let us look at very carefully. Suppose, if we take this Booge motion for MBH 1 at the ground surface see where the peak is occurring at this time period. So, corresponding to this time period whatever buildings or structure will be there that will be more vulnerable or will be subjected to maximum damage. Am I clear? Now, if you are considering your structure say you are constructing a foundation or underground structure, let us say close to your layer number 6. For layer number 6 you see here where the peak came here. Can you see over here? This is the peak for layer 6. So, when you are designing corresponding value of time period that will be more critical that is a structure having time period of this value will experience maximum damage when we are constructing any structure at layer 6. So, that way individual layer wise data also very much helpful to us. So, this is about layer variation. Now, let us compare Booge motion with respect to Kobe motion. What we can see? For Booge motion the major damage will occur or the peak value of spectral acceleration we got at the period of say about 0.2 seconds. Whereas, for Kobe motion the peak came same at top layer ground surface is about 0.5 second. So, that means it is not that all the means the same structure will be subjected to same amount of damage irrespective of ground motion. But it will be subjected to damage depending on what is your input motion that is Booge motion will make maximum damage to a structure which is having a period of 0.2 second whereas, Kobe motion if it comes to Mumbai at that site that will damage a structure which is having a period of 0.5 second. Is it clear how we are using these things for further design? Hence, it is very important instead of generalizing one should do site specific ground response analysis like this depending on various input motion at that particular site or using a logical synthetic motion at that site to get the data for further design. This is the Fourier amplification ratio that is we know the response of amplification or acceleration we can express in terms of spectral response or Fourier response. So, this is in terms of Fourier response. Now, let us come to the values of this frequency what we can compute using the simple formula of this sum of 4 h by V s that we have already seen. So, using that simple formula that fundamental frequency what we can get that comes out to be this knowing the values of V s and individual layer value of h for all your site. Now, deep soil software also will give you the corresponding values of frequency now equivalent ground response analysis values of frequency output we got like this and non-linear ground response analysis we got like this in all the cases Bhoj motion is used. So, if you want to see what is the percent error or percent difference I should not mention it as error. So, it is within the about 20 percent in case of equivalent ground response analysis whereas, if you use the non-linear ground response analysis it is still lower it is within 13 percent. So, non-linear result will be obviously closer to the actual values as it is expected. Now, let us come to the next example of ground response analysis that is example number 2 which is the case study on the seismic ground response analysis for 4 port sites ports in Gujarat state of India. This is the part of the PHD thesis work of Dr. Jayakumar Shukla who completed the PHD in 2012 at IIT Bombay under my supervision and this is the journal paper which describes about the details of this seismic ground response analysis of 4 port sites in Gujarat that is seismic hazard and site specific ground motion for typical ports of Gujarat it is published in the journal natural hazards springer publication volume 60 issue 2 page number is given over here in 2012. Let us look at the major 4 ports which for which the study was carried out these are the 4 ports Kandla port, Mundra port, the Hedge port and Hazira port these are the 4 port sites and these are the fault map already we have discussed it in the seismic hazard analysis problem. What are the steps followed like fault map and seismicity parameters are known logic tree framework is already used then we have developed UHS at bedrock level for the synthetic ground motion then geotechnical characterization is now necessary for each of the port site to carry out the site response analysis which will finally give us the result for this site response or ground response analysis. So, to do that this is the UHS or uniform hazard spectra which we have already seen for different return period of 2475 72 and 2475 and we have compared that with respect to IS code recommendation for zone 5 when we are talking about Kandla port which is in zone 5 of seismic zone as per IS code. So, as we have mentioned IS code value is matching close to our return period of 475 years. Similarly, you can use that for Mundra port site this is the spectral acceleration versus spectral period and as we have already mentioned MCE has been used for rock site and DBE design basis earthquake is 50 percent of that MCE. Now, we should know that geotechnical properties or geotechnical characterization at that site. So, various borehole data were collected only the typical borehole 1 and 2 are shown here for Kandla port. Similarly, for Mundra port also borehole 1 and 2 have been shown over here you can see majorly it is a silty clay followed by stiff clay then silty sand then stiff clay then sandy gravel at Kandla port site whereas, so up to 30 meter depth it is mostly a soft to stiff soil and mostly clay in between a very thin sand layer. Whereas, for Mundra port site it is mostly silty sand followed by stiff clay and then dense silty sand all the SPTN value recorded at the site also are available using these values one can get the shear wave velocity with respect to depth at this Kandla port site or Mundra port site. As I have mentioned one can measure it using MASW or SASW or other field test or in absence of that equipment one can use the available correlationship between SPTN value and shear wave velocity to get this shear wave velocity values at those site fine. Now, once it is known next step is the synthetic ground motion which ground motion we are going to use for our ground response analysis. So, this is the synthetic ground motion one can use the Booge earthquake motion and the match spectra is shown over here which is recorded at the passport office of Amdabad 2001 Booge earthquake data and that program this is a software program RSP match developed by Abrahamson in 1998 which is available is used to generate that synthetic ground motion which will be compatible with that generated UHS at all levels of ground motion that is you have to select such a input motion for your analysis which is compatible to that site that is either you use from the earlier historical earthquake data at that site or use that synthetic ground motion or that synthetic motion which will be compatible with respect to that site based on this UHS clear. It is not that you can intake any arbitrary any arbitrary value of this input ground motion clear. So, input properties are very important first of all geotechnical property as well as which ground motion you are going to use further. So, this is the mapped one the previous one we have seen over here the Booge time history and next one shows us the design time history based on 2475 we are of return period at Kandla port can you see a similar match right. So, this is exaggerated form you can see the Booge earthquake which is the black line then level 3 ground means 2475 which is the red one green one is level 2 which is 475 return period and the blue one is level 1 that is 72 years return period that is the spectral acceleration versus time response. Now, we carried out this ground response analysis at this site Kandla port with the level 3 ground motion I have already mentioned what is level 3. So, for different layers layer 1, 2, 3, 4 these are the layer you can see how the layers has been divided and what are the average value of the SPT and what are their description. Now, in this process equivalent linear analysis was carried out and for doing that the computer program shake has been used shake 91 version which is developed by scramble et al in 1972 at UC Berkeley it has been further modified now latest version of shake 2000 is also available. And you can see for doing the equivalent linear model you should have known what is the modulus reduction curve or the damping ratio behavior for individual soil layer which you are analyzing. So, either you can use the proposed or available design curves which are available with this shake like we have used for this shake analysis of equivalent linear model the model of sun et al 1988 which is valid for soft clay sun et al has given for soft clay what is the G by G max versus gamma behavior and what is the damping ratio versus gamma behavior that model we have used. For stiff clay we have used Busetic and Dobri's model of 1991 which is already embedded in that shake software. Also in deep soil software you will find these standard or these well known available literature modulus reduction curve and damping curve are available. But if you want for your own site it is better to develop it through the actual soil property and use that modulus reduction curve and damping curve in your input model. Then Idris curve for medium silt sand and Busetic Dobri's curve again for stiff clay were used and for 4 different layers by considering 5 percent damping for the case of pseudo acceleration or spectral acceleration versus period plot we got the result like this clear. So, how the amplification ratio can be obtained amplification ratio is nothing but at ground level divided by the bedrock. So, that is what for different 4 layer you can see this different amplification ratio versus frequency. You can see the black one is just line horizontal line with value 1 because layer 4 is nothing but at bedrock level. So, layer 4 is at bedrock level that is why there is no amplification, but other layers shows significant amplification whereas layer 1 is a ground surface. You can see red color for ground surface amplification is this much, but in between the amplification ratio raises up to about 2.25, can you see that whereas at ground surface it is only about 1.3. So, it depends on what type of material you have in between depending on that site response you will get different amplification ratio at different level. So, somebody is founding or planning or proposing a foundation 2 in this layer number 3 then they have to be very careful about this amplification clear. So, what are the important observations we got from this analysis important observations like for Kandla port the contributing faults we got like F 13, F 25a and F 14 whereas for Mundra port it is F 25a and F 13. For the H port the responsible faults are contributing faults are F 33 and F 30 whereas for Hazira port it is F 34. How you will get those things because at the beginning we have mentioned this fault map are available you are using seismic hazard analysis and corresponding UHS coming from that. So, that will give you which fault is responsible as I said this F 25 and F 13 are responsible for Kandla port and Mundra port. So, as per IS code of 1893 part 1 of the year 2002 version it underestimates the seismic ground motion for the two port sites. So, why it underestimates let us look at this comparison table ground motion level 1 2 3 level 1 means return period of 72 years level 2 means return period of 475 years and level 3 means return period of 2 475 years. We know at which level needs to be used for which type of structure that is known to us. Now, for Mundra port site the peak ground acceleration we got these values whereas, IS code recommends for zone 5 which ports are in zone 5 this Mundra and Kandla these two are in zone 5 whereas, this Hazira and Dahesh these are in zone 3. So, when we are comparing the level 2 PGA as per the IS code the recommended value is 0.18 G and what is the value we got from the analysis for Mundra port site considering the soil properties at Mundra port 0.19 which is very close to IS code recommendation when we are designing it for 475 year return period remember that. So, IS code we can safely use for Mundra port site when we are designing for 475 year of return period, but the same IS code is underestimate this value when we are considering the design for Kandla port. For Kandla port the site response analysis gives us the value of 0.25 G which is much higher than the IS recommended value even for the 475 year return period whereas, for IS code recommended value for 2 475 years of return period is for zone 5 it is 0.36 G. Whereas, for Mundra port site we got 0.33 G which is very much comparable with respect to IS code. So, if we use basically IS code recommended values for Mundra port site design is perfectly fine, but if we use the IS code recommended values for the Kandla port site as shown over here using the local soil properties and the input motion it seriously the IS code seriously underestimates. So, we should design for this higher values. So, using this comparative study or table one can easily find out what is the need to carry out the site response analysis before going for a particular design or important design at a particular site because port sites are very important, port structures are very important that has to be built for several years that should not get damaged by any earthquake. So, that is why it is mentioned underestimates the seismic ground motions for two port sites of Kutch region. However, for the Hedge and Hazira port they are very much in good agreement. What are the other important observations we got from this case study that is for Kandla port site the ground amplification factor is observed to be around 1.37 for frequency range between 1.37 to 2.1 hertz. Remember this amplification also depends on your input frequency that is what earthquake input motion you have used what frequency it was having. If you use different earthquake motion obviously this amplification factor also will change and layer 1 has the higher value compared to other layers at all ground motion levels. Whereas for Mundra port site the value of amplification factor is ranging between 1.94 to 1.74 when the earthquake input motion is in the frequency range of 1 to 2.5 hertz. For Hazira port the amplification factor is 1.86 to 1.91 and the input frequency range is between 2.22 to 2.74 hertz whereas for this the Hedge port site the amplification ratio is 1.59 to 1.61 with an input frequency range between 2 to 1.6 hertz. So, with this we have come to the end of our module number 8 that is site response analysis or ground response analysis we will continue further in our next lecture.


Hi, gweithio. Yn Gweithio, Alberto Fernandedd yng Nghymru, Ffobieddol. Fy oeddwn i'n ddod i'r ffawr i'r ffordd yma. Mae'n 11 july 4 o'n oed, mae'n Cwenca. Fy oedden i'r ffawr i'r asturiau, felly rwy'n gweithio yma, ac mae'n fawr i'r ffordd. Felly mae'n golygu i gyfathio ac yn unrhyw boll yn ei funud hyn. Felly, nid oedd y cwestiynau gyda'n siarad ddiwrnod ddim yn un darlofodfod ddiwrnod. Felly, rwy'n gweithio i'r gweithio gyda'ch meddwl sy'n un roi. Rwy'n gweithio'n gweithio ar gyfryd, rwy'n gweithio'n gweithio. Mae hynny, dyna'n gweithio'r ddiwrnod o'r Readucation Cymru. Rwy'n gweithio hyd yn ei ddod. OK. I have been thinking about this presentation for the last weeks. When I was preparing this talk, I was very happy because I thought I was going to be with teachers. When you prepare these things, I was thinking about something which was new for you, something which could be useful for you. Ne gasgwch fy fidesgwedd, gy→der, ryefoddiad na ddeachel bassiau mae yma eich bilgo buralau Fewf dyn amlwyr, fell broadbandu hyد yn cyfligio. Y holl fyddwch wedi nawblygu, yy momentumau gyda bod y pleiddiad i pellcau iaol bydditatw yng Nghyl Herm. That means how to use, how to apply Audio-lingual translation in language teaching, okay? And I'm going to divide this talk into three parts. Very simple parts. Oops, sorry. First I'm going to talk to you about subtitling and clip. Then we are going to have an example. I'm going to show you a project we developed a couple of years ago. And finally, we are going to have some hands-on activities. So practice, okay? Now, before that, I would like to start with a story. I'm going to tell you a story about translation and language teaching, okay? Which is not exactly a love story. I worked in translation for some years. I was a conference interpreter and a translator. So translation is fascinating, believe me. You have an idea, but you have a message, and you have to transfer that. You have to convey that message into another culture, into another world. That is really interesting. So when I was working in translation, I got many interesting ideas. Many inspiring techniques and strategies and things and insights. And I thought that perhaps these could be used and applied in the classroom, in education. In primary education, in secondary education. However, when I joined the university and I started with language teaching, CLEAL, bilingual education and all these things, I very soon realized that translation, bless you, wasn't at all popular. Translation is not popular in language teaching. In fact, it is very, very stigmatized. It has a bad reputation. Most teachers do not like translation. Probably there are several reasons for that. But I think one of the most important is, I think, the influence of a very old friend of ours, which is the grammar translation method. It has grammar translation method, okay? The grammar translation method, as you know, is one of the oldest, and everyone hates the grammar translation method, because it led to very dark times in language teaching. No interaction between the student and the teacher. No interaction among students. No nothing. No use of the language. No language to learn. No nothing, okay? Now, if I ask you now, think about translation in the classroom. Perhaps you have had some experience of being a student, perhaps a teacher at one point he or she used translation in the classroom. If you close your eyes, you don't need to do that, okay? But if you closed your eyes and you thought about translation in the classroom, what would you think about? Think about it for a moment. You would probably translate in songs. Yes? Okay, well, that's okay. But I was thinking about you. When you were studying on the teacher's years' translation, you would probably visualise something like this. Probably you cannot read it very well, but this is a typical text. So you've got final absurdo, absolute ending. And it says, era en las uchu media de la tarde, it was 8.30 in the afternoon. I el detectivo y Lorenzo Fresnos, and detected Lorenzo Fresnos and so on and so forth. This has been so for many years. So this was the use of translation in the classroom. This, inevitably, leads to that. It is almost impossible not to fall asleep with that kind of thing. And this, as you know, this is the worst thing we can do in the classroom. So when I started thinking about translation in the classroom, and I went to some schools of primary education in Asturias, and I contacted friends of mine and I told them, I have a project. Would you like being part of it? Would you like to try something about translation in the classroom? They told me, no, thank you. Because it has such a bad reputation. However, translation in the classroom is not only parallel texts. This is what we know as literary translation. Word for word translation. You take one text and you translate that into another text. That's where when I studied Latin in high school, that is terribly boring. And if I may, I'm useful. I'm not exactly useful for communicative purposes, for the language we need today, for the kind of language that your students need. In any case, translation, believe it or not, can be funny. It can be funny. You're looking at me like, no, no, it can't. It can be funny. It can be funny. I mean funny, you follow me. I'm not suggesting that you are going to do this on Saturday night. I'm suggesting that this can be used in the classroom. That's funny as this can be. And more importantly, translation can be useful in Clil. OK? 15 min. Rapidito, ia casi a cabes. OK? Not really, not really. Now, think about the following things. I'm going to ask you two questions. And I would like you to tell me first, what do you know about translation? Do you know anything about it? This is something you have used in your lessons? No? What else do you know about translation? Anything else? OK, no problem. Have you ever used translation in the classroom? Yes, no, only on Thursdays. Tell me. Have you ever used translation in the classroom? OK, so yes. OK, so drills, so translating drills. OK, that is translation, yes. What else? And you use Spanish for that? I'm just checking, OK?  OK, but yes, we are as teachers, we are asked to translate in many occasions, aren't we? OK, you are translating all the time. I'm going to do a very simple activity. Because you know that this is one of the best, one of the most relevant principles in Clil. You learn by doing. OK? In Clil you have to do things by yourself to learn how to do them. So this is what we are going to do. Activity on translation. OK? Now, this is going to be the first one. For this I'm going to... Which was your name? Mariangeles, Mariangeles, me bai yw dda? Si, si, si, si. Mariangeles is hyperventilating right now. OK, I'm sorry about it. I'm really sorry. OK. Well, that's it. What was your name? Antonio, would you help me for a minute? It's very easy, very easy. I'm going to explain it to you. I'm going to explain the activity in Spanish. Antonio is going to translate it into English. Very good, very good. You could put it the other way. Alberto is going to explain the activity and I'm going to... OK, very good. Sorry, I said I was going to speak in Spanish. Is it difficult? Why? I can't... I can't promise. I haven't thought about that answer. It is not good to believe me. Very, very good. Now you are going to ask all the teachers because you play. You know that the worst thing a student can do is to somehow, in any way, call the teacher's attention because then he is going to ask you. No, I'm not. I'm not.  I have tried this with many people, believe me. So this is what I would like you to do. I would like you to work in small groups, three, four people, no more, no less. OK? One of you is going to talk in Spanish for one minute. The second student is going to interpret everything into English. Everything the first one says. He has to interpret into English. And the third one can just be a mediator, if you want. He or she can ask questions. You can talk about anything. Quenca, Clil, the weekend, Game of Thrones, Donald Trump, anything. In fact, believe me, the less academic, the better. I mean, if you are talking about your hobbies, your husbands, whatever, it would be great. I would like everyone to interpret for one minute. This is, by the way, for those of you who don't know it yet, this is the difference between translation and interpreting. So translation, sorry, is written. Interpreting is when you transfer the message orally. You have consecutive interpreting, which is what we were doing now. You talk, you stop, and the person renders the message. And you have simultaneous interpreting, which is when you need, of course, a headset for that, and you are listening to the person. So just relax. This is just a game. I'm not going to ask anyone to bring. You can relax. I just want you to talk. In Spanish and in English. Three, four people, right? Five minutes or so. Have you finished, more or less? Thought off. This simple exercise was just an icebreaker. I just wanted you to relax a little bit and use it. So tell me, how was it? Was it easy, difficult, boring, extremely boring? Extremely boring, you say? No, difficult, difficult. How many of you think it is difficult? The rest, you don't think it's difficult? I mean it should be, it should be. And it does not relate to your language competence in English. You can have a very good level of English. You can command English and still find it very difficult. Why? You interpret and get the idea, but if you want to translate every single word or every expression, that's the difficulty in the expression. Remarkable. That's very interesting. When you translate, when you interpret, like the exercise you have just done, you do not have to transfer every word. Word for word. You have to convey a message. You can change things. It doesn't matter. You are not professional translators. You are not going to be translating a book. So you can change things. The important thing, the objective, is that you convey, you transfer the message. It should be difficult. Because we are not used to it. So you are not used to this code switching. Perhaps if you have experienced the typical situation where you've got some foreigners in your city, you have to go to a restaurant, you have to order the menu, that is exhausting really. If you spend one or two days with people from abroad at the beginning, that is very tiring. You feel tired because English is not your native tongue. It will never be. So you have to change and you have to translate. Now, when we go into audiovisual translation, which is what I wanted to do today, you would probably think about this, a television set, audiovisual translation. But this picture is no longer useful. Because audiovisual translation today is more like this. So you have computing, you have tablets, you have phones, et cetera. You have digital information. In audiovisual translation today, you do not translate films, you translate everything, video games, Netflix, everything. And this is the world of your students, as you know. The other day, let me tell you, it has nothing to do with it, but I want to tell you this story. The other day I was at the faculty and I listened to girls, they were talking. One told the other, es que seros tan del 2013? So yes, films and all that things, they live in a different world. They live in a different world. So they use, we are dealing with audiovisual multimedia products. This is nothing new to you. It shouldn't be. It's no surprise for you. We should use audiovisual multimedia products. Why? In the classroom, why? First, because they are motivating the video. But all these things, they are very motivating for your students. That is the first thing. They love it. They like it. And Donnie Tromsky, many people said that. A teacher has to keep motivation. That is our primary goal. If they are motivated, they learn. If they are not motivated, they don't. So motivation. Second one, they are close to the students. They love these frozen and all these things. They love it. So it is very close to their world. Third, it is real language. Yes, it is an adaptation and all that. But it is real language. Videos and all that. And something which is close to CLIL, it is full of cultural elements. Bless you. Full of cultural elements. OK? Now, when we come into subtitling, I'm going to show you a definition which is provided by Jorge Diazintas, who is from Albacete, very close from here. He's the most. Are you from Albacete? OK. That's right. I'm not going to read that. But the thing is that subtitling is a written representation, representation, not the actual thing, but the word, of the dialogues in a film. OK? So you have to try to capture the message.  OK? Now, if you want it, if you become crazy one day and you want it to know about subtitling, there are two books that you have to read. One of them, you don't need to copy anything because you will have this available in five minutes. One of them is Translations, Subtitling by Jorge Diazintas and Alain Remael. And the second one is probably more didactic is by Noah Dallavan from the UNEF, OK? Who used subtitling for teaching purposes. OK? So you can just read these two books and you will know a lot about translation and subtitling. But I'm going to tell you a couple of things that you need to know. First, you know that there is a split, there is a separation between subtitling and dubbing, OK? We have been a dubbing country. Everything in Spain was dubbed, OK? Doblaje, just in case. In Spain everything is dubbed, OK? Subtitling countries, for instance, Sweden, the Netherlands have normally a much better command of foreign languages. Dubbing countries don't. That's a problem, OK? Nowadays they do not have an excuse. They do not have an alibi. They have Netflix, they have YouTube, they have everything. When I studied, I didn't have such a thing. I didn't. You needed to go to England and, yeah, well, speak up. Yes, yes. Or you had to go to the UK. Many years, well, not many years ago, a few years ago, OK? So dubbing versus subtitling countries. Which countries you think are dubbing countries? Apart from Spain, Italy


The first s*** I went on, I was able to participate in the cleaning process. It was gunshot situation, but there's also that component of, wow, like this was a person and they're no longer here, and this is what basically what's left of them for me to encounter. It's a very strange feeling because you really don't know what you're walking into, you don't know what you're gonna see, and you certainly don't know how your body is going to process it. This time around, because I was physically participating, it was a little bit different. I did feel a sense of gratitude because we were able to help the family to process this a little bit better. It was great to see Laura in action. She was such a resource for the surviving members of the family. She was able to give them so much information, and because she was in law enforcement prior, there were details that Laura was able to give them and letting them know that, hey, like we're here, we're going to take care of this for you. Now you can start on a new clean slate.