Tezal Barcelona At our Tezal course in Barcelona we endeavor do everything possible to ensure that you will have an enjoyable and rewarding time in the wonderful city of Barcelona. Our Tezal course center here is home to a small and friendly team of staff which offers all course students a warm welcome and a wide variety of social and leisure activities. Our staff can arrange evening excursions to the top as bars and cafes, sailing trips and other watersports activities, skiing, in winter, wine tasting and trips to many beautiful beaches. We arrange a welcome dinner at the start of the Tezal course in Barcelona to help you get to know the other students on your course at an early stage. The Tezal course is intensive but we do everything possible to make sure that you ample free time to make the most of your time in this lovely part of the world. Barcelona is perfectly located between the warm waters of the Mediterranean Sea and the Tibor d'Abo Hills. The idyllic Balyric Islands are to the east of the city, the famous resorts of the Costa Brava, Wild Coast and the towering mountains of the Pyrenees, are to the north, the wine growing region lies to the west, and the lovely Roman city of Tarragona and the beach town of Sitges are to the south. There is something to door somewhere to explore whichever way you turn in this charming city. Barcelona is home to the works of many of the most famous artists and architects of recent times, including the modernist spires of Gaudí's Cathedral, Picasso's Cubist art and Dali surrealism. The distinctive Catalan perspective has had an impact that has felt way beyond the region. If you stroll down the most famous street in Barcelona, the Rambles, which leads right down to the sea, you will witness grand opera houses, beautiful churches, street artists and mimes, cafes and bars galore, and of course great shopping at and around the market. The centerpiece of the Gothic Quarter is its fine cathedral. The Picasso Museum, which houses the best collection of Picasso's work in Spain is nearby. It has justifiably also famous for its nightlife. It sometimes appears that every other building is a club, cafes or bar. Nightlife is Spain and in Barcelona in particular tends to start and finish late and dinner is usually served after 9pm. After dinner you can pick from a huge range of bars or cafes to continue your evenings, entertainment and those with plenty of stamina can then move on to the open-air nightclubs in the Tibor Debo Hills amongst other options. With all this to offer, Barcelona is a great place to take your Tezal course as well as having a great time outside of course hours, whether you like beaches or mountains, art, or history, cafes or nightclubs, Barcelona does offer something for everyone. The home of our training course in Canada is the city of Toronto, the capital of Ontario and the most populous city in the country. This important global city is at the very heart of the country's business and finance sectors and also leads the way in terms of its arts and culture. Although Toronto is undeniably large in size, countless polls and surveys would suggest that it has avoided the fate of many North American cities by being rated as one of the world's most livable urban areas. Add the welcoming nature of the local people and you can see why the cosmopolitan city of Toronto has become a popular destination for completing our Tezal course. Toronto has steadily grown on waves of immigration since its initial founding and this continuing trend means the city is one of the most diverse in the entire region. The city's multicultural population hails from all corners of the globe which has led to a unique blend of cultural attractions to enjoy. The Art Gallery of Ontario has a fascinating collection of works from across the world which highlights the multiple influences on the city's development while the Royal Ontario Museum boasts one of the largest and most varied collections in North America. Another popular attraction in Toronto is the city's most famous landmark, the CN Tower. The views from the observation deck make this one you won't want to miss. If you find yourself in Toronto during the winter months you can participate in the city's love of winter sports. A night out at a Toronto Maple Leafs game, one of the founding members of the NHL, offers an exciting way to mix with the local fans. For those who prefer to get more hands-on, the variety of public skating rinks, ski slopes and cross country skiing, and skating trails that appear across the city every year are sure to be a highlight of your stay. Of course, there is more to the city than winter sports, why not sign up for our course in Toronto and find out for yourself. Tezal San Francisco San Francisco is a city that needs no introduction, its use in a huge number of Hollywood movies means that much of this Californian city is instantly recognizable to people from all over the world. Whether it's the iconic Golden Gate Bridge or the infamous Alcatraz Island, nearly everyone has an image of this city in their mind. San Francisco has a long history of ethnic diversity, and this can be seen in its inclusive atmosphere and the many distinct neighborhoods that make up the city. San Francisco's unique and iconic attractions, blended with its a sigoing atmosphere, make it a great place to earn your Tezal certificate. Despite being first settled by the Spanish in the 18th century, San Francisco did not start to really grow until the famous Californian gold rush in the middle of the 19th century. Since then the city has grown and grown, and while the days of the gold miners are long gone, the city still draws visitors from all over the world. For anyone visiting San Francisco for the first time a trip across the famous Golden Gate Bridge is a must, as is a visit to the world famous prison on Alcatraz Island. In fact, there are so many well known landmarks your whole trip could be taken up visiting them all. You could head to Pate Ashbury to recall the heady days of the summer of love and soak up the bohemian atmosphere that still infuses the area. San Francisco is also home to the largest Chinese community outside of Asia and the city's original Chinatown is well worth the visit. When you consider all the attractions that San Francisco has to offer from its rich cultural history, iconic landmarks, modern infrastructure and inclusive atmosphere it is easy to see why the city remains a popular destination for visitors from all over the country and the wider world. It is also easy to see why our San Francisco TEFL Tezal course is such a popular choice with students of all ages and backgrounds. Tezal New York City New York City is justifiably one of the most famous and popular cities in the world and is the perfect location for taking a Tezal course. Spend just five minutes in New York and you will understand why it's like nowhere else in the world. Only in New York City will you see everything that is the spirit of the USA in one city. The diversity, the culture and the style of the USA are all here in one fascinating place. There are so many things for the visitor to see and do. See the Empire State and Chrysler Buildings, the Statue of Liberty, Rockefeller Center, Times Square, the Bronx Zoo, Staten Island Ferry, Brooklyn Bridge as well as many other well-known attractions. There is also a wide variety of restaurants, shows, museums and sporting events to visit. New York in reality is a city of islands. Manhattan and Staten Island are islands and other famous areas such as Queens and Brooklyn are on Long Island. All in all, with the wide variety of attractions and activities and the cosmopolitan feel of the city, New York is a great choice for your Tezal course. Tezal Boston Boston is not only home to exciting historic attractions but also holds a great number of concerts, exhibitions and festival during the year. Because of the many tourists flocking to Boston each year, there are countless comfortable housing options both for long-term and short-term visitors. One of the most popular accommodations we recommend tour our trainees is the Berkeley YMCA residence. The comfortable rooms are offered at low rates tour all our trainees. Another housing option we are happy to suggest is the Hillside Durant House with comfortably double rooms. The hotel also features free internet and a laundry service. Both accommodations are located within minutes of our training center. Upon successful registration to our in-class course in Boston, we will submit further information on housing and room bookings. Tezal Wisconsin Located in the Midwest of the United States Wisconsin is a state blessed with breathtaking nature. The state is often referred to as America's Dairyland due to the booming farming industry that produces some of the finest products in the country. As well as being famous for producing high quality cheese, Wisconsin is also a premier vacation destination due to its as beautiful location in the Great Lakes region. You can always find the cozy cabin in the woods where you can take a hike around forests, lakes and waterfalls. Wisconsin is a true outdoor paradise. The shoreline of Lake Superior offers spectacular options for outdoor fun. In the Chippewa Valley area you will find some of the finest biking and hiking trails in the country while the Apostle Islands make for the perfect place for kayaking and fishing. The northeastern region of Wisconsin is truly a wonderland for water sports enthusiasts. Whether it is boating, whitewater paddling, swimming or even water skiing, you will find a place to do it here. At the end of the day, you can watch the sunset at the lake while having a BBQ or bonfire. Wisconsin makes everything possible. South Wisconsin leaves nobody's wishes unfulfilled either. Here, you will find some of the most beautiful valleys in the country. The Mississippi River also runs through this part of the state, creating spectacular landscapes and thriving wildlife. Small towns along the Mississippi are especially charming and always a great place to visit. This part of the state is also influenced by nautical themes and you can find some of the finest seafood restaurants as well. Lake Winnebaco is the perfect place to take in all that Wisconsin's natural beauty has to offer. Relax at one of the many spa resorts, have fun at the racetrack or try some golf on one of the many courses. Wisconsin's south central region also offers some great attractions. At Wisconsin Dells, you can experience a collection of water-themed amusement parks that gave Wisconsin the title water park capital of the world. Besides the water parks, you should also visit some historical sites, including the iconic state capital building. Other interesting attractions in the area include Sylvanna's Wade House, Madeleine Island Museum, Stonefield and Old World Wisconsin. Not only does Wisconsin welcome millions of tourists each year, it is also a popular destination for thousands of national and international students. You are drawn here by renowned universities such as Concordia University, Marquette University and the University of Wisconsin. When you complete our in-class TEFL Tezal course in Wisconsin, you will graduate with an internationally recognized teaching qualification that enables you to work right across the globe. Tezal, Massachusetts Massachusetts is the state with the largest population in New England, the northeast of the United States. Its convenient geographic gave it the name the Bay State as it bordered the Atlantic Ocean in the east. Due to this exciting coastline, Massachusetts is a wonderful destination for outdoor lovers with tall mountains, deep valleys and the best beaches in the region. Add to that, Massachusetts' rich history is it was the place where the pilgrims landed and the Revolutionary War started. As you can see, Massachusetts truly is a wonderful place to explore. In fact, visitors can enjoy the beautiful natural landscapes of Massachusetts during all four seasons. The mild weather in spring is perfect for camping, hiking, biking and even fishing. On top of that, people love to start of the new season by cheering for the Red Sox at a game at Fenway Park in Boston. Soaking up the sun is one of the best ways to unwind in the summer. The many beaches also invite visitors to surfing and even whale watching. One of the most exciting times of the year is fall in Massachusetts. The famous Indian summer allows for leaf peeping at the foliage when the trees shine in hues of red, orange and yellow. In fact, people come from all over the world to experience this famous natural spectacle. Even in wintertime, there's a lot to do in Massachusetts. The state has 12 premier ski areas, making it possible to engage in all kinds of different winter sports. Besides skiing, many also love tubing and riding down the slopes while others, seeking more adventure, try out dog sledding or ice fishing. No matter what your heart desires, you will find it in Massachusetts. It is true that Massachusetts is among the most popular destinations for summer vacations in the country. This is mostly due to the spectacular 1,500 miles of beautiful coastline on the Atlantic Ocean. Families especially enjoy Coast Guard Beach and Chatham Lighthouse Beach, where you can watch and even feed wild seals. The annual sand sculpting festival is held at Revere Beach Atmatic at Beach is said to be the best place for sunsets in the state. Upscale vacationing takes place in Martha's Vineyard in Nantucket with countless relaxing hotels for any budget. Ever since the pilgrims landed here in 1620, Massachusetts has been of tremendous importance in US history. The locals are keeping the history alive by providing state-of-the-art museums and exhibition halls throughout the state. Plymouth Plantation, for instance, is a perfect example. Here, visitors can explore what life was like for the pilgrims when they first arrived. The famous Freedom Trail in Boston perfectly showcases the Revolutionary War, Lexington Green marks the beginning of this war, and the abolitionist movement is displayed in the African American House. Massachusetts offers beautiful natural landscapes, outdoor fun and history, but there is more. Some of the best schools and universities were founded right here in Massachusetts and are amongst the best in the country today, such as Harvard, MIT, Boston College and Berkeley. Therefore, you can be sure that our TEFL TESOL courses in Massachusetts will get you far in the ESL world. Upon graduating from our training course, you will find international job positions in the field of English education.


I'd like to take a moment to thank everyone who comments their code, taking time out from instructing a processor to explain your actions to fellow persons. It's like you're looking at the inner workings of a machine, and suddenly the person who made it turns around and goes, Oh hey, I know it's strange that there's a bunch of nested conditionals here, but everything else crashed. It's very much appreciated. Of course, the process benefits the author a lot too. I'm a big fan of the reverse commenting before the code. Basically, you write an outline, and then just fill in the functionality later. That top-down view early on exposes a lot of potential problems, redundancies. It's nice.


So, we have a linear device, the output is a linear function of input and the gain of this device is negative and it is given by R 2 by R 1. This is called an inverting configuration or inverting amplifier. This is not new, this is something that we had in fact we had tailored the specification of this op-amp to produce this kind of op-amp. Let us look at something which is different from that. This time we want a configuration in which the input provides no current at all. In the previous one, V in provided a current which was V in by R 1, but we do not want to draw any current from the input at all. That means we should not connect anything other than the input of the op-amp to that point. So, we connect and therefore we use this point and this is my V in. I can draw any amount of current from the output, that is not a problem. So, I can connect my R 2 here and so that current flows provide a path to that current by connecting R 1 here and grounding this. It is very similar to the previous circuit. However, the input is now directly applied to the positive input. The feedback is still the same through R 2, but the R 1 resistor rather than going to the input is going to ground. Let us work out what is the output voltage now. So, this is V out and we will make use of the virtual shot. You can do it without that then you will have to assume infinite gain and do similar kind of algebra that we did earlier, but now we have this powerful tool in our hand. So, therefore, we already know that the voltage here is how much that is equal to V in. So, now let us find out what is the output. Essentially, you are saying what is that value of V out which when goes through this potential divider it produces an output equal to V in right because this value is V in and no current is flowing through this. So, if you look at this circuit it is just a potential divider. So, the V out divided by R 2, R 1 should give me V in to provide the virtual shot. So, what is the value here in terms of V out and R 2 by R 1? The current is V out divided by R 1 plus R 2 and into R 1 and that should be equal to V in. That is quite straight forward and therefore, V out divided by V in that should be R 1 plus R 2 divided by R 1 times V in and that is 1 plus R 2 by R 1 into V in. Notice a few differences from the previous configuration. The previous configuration the gain was negative. In this configuration the gain is positive. The output swings in the same direction as input. There is no negative sign. Therefore, this is called the non-inverting amplifier. The output is not inverted with respect to input. The gain is a little higher in this case. Earlier the gain was minus R 2 by R 1.  So, now the minimum gain is in fact 1. We cannot have gain less than 1 in this case. In the other case it just dependent on the ratio. We could have a gain less than 1. We could have a gain greater than 1. So, that configuration could have been used as an attenuator as well as an amplifier. This configuration can only be used to amplify the output. That stands to reason because the fraction of the output given by this potential divider has to equal to be in. Therefore, the output has to be greater than we begin with. So, that when it is divided down by this potential divider it is still equal to be in. So, the gain is higher and third point that we are now drawing no current from our input source. The input source is connected directly to this input and nothing else is connected to it. So, the input source is providing no current. Very often you have situations like this. For example, the old times you are probably not exposed to this. Music used to be played on records using a piezoelectric pickup right. So, the piezoelectric pickup has very high impedance. It produces charges in response to a crystal being distorted. So, there are very minute distortions of this crystal because the needle vibrate and that results in charges being generated. But if you take away those charges then it will produce nothing at all. Therefore, you must draw zero current from it. Only notice the voltage changes. Similarly, a capacitive mic. Suppose you have some charge placed on a mic.  The two plates will vibrate. The capacitance will change. The total charge is the same. But the corresponding voltage must change because the capacitance is changing right. What do you have? This charge must remain constant and as the capacitance changes the voltage must change. As long as I do not take away this charge I am fine. I shall now be able to use this condenser microphone right. And therefore, I need a configuration in which I draw no current from the input and this configuration is the appropriate one for you. Because now if I connect it to an infinite input impedance that charge will not be taken away. That charge will remain where it is and those voltage fluctuations how so ever small they are they can be amplified by choosing appropriate values of r 2 by r 1. So, there are many configurations in which you do want to make use of the infinite impedance. And for those configurations it is better to use the non-inverting configuration. Also the gain is a little higher. However, its range is limited. You cannot make the output smaller than input. You can only make it larger than input. The inverting configuration is good because it has a direct ratio of 2 resistors as its output. It can be used for amplifying as well as attenuating the output. The output can be more than input. It could be less than input. However, it does draw current from the input. The source has to provide current. So, depending on the situation that you have, you can have an amplifier which is either inverting or non-inverting and you choose depending on what the conditions of the input and the output are and the gain that you require. These are the two major configurations of this. But these are not the only two ones. These are only resistive combinations. Let us just for the sake of argument see what happens if I replace one of these resistors in the inverting configuration just for the sake of argument that is simpler. Suppose, I replace one of the resistors by a capacitor. So, let us draw that configuration. I am referring to this configuration. I have replaced R 1 by C and because we have only one resistor, we will just call it R. So, R 2 is now called R. But R 1 has been replaced by C. Suppose, I have a voltage here which is a function of time. As this voltage changes, what is the amount of current which flows in this branch? Remember there is a virtual shot. There is negative feedback. Therefore, this potential must be maintained at 0 because of the negative feedback. So, this point is held at 0 and this point is fluctuating as a function of time. V of t has some dependence on time. It could be sinusoid. It could be much more complex. Some function of time. So, how much current will flow through this capacitor? What is current? It is d cube by d t and that is equal to d by d t of C times V where V is the voltage difference across the two plates. One of the plates is maintained at 0. The other plate is at V in of t. So, the voltage difference between the two plates is nothing but V in C times V in of t. Now, C is a constant. It can be taken out from the differential. So, the current which is flowing here in this path is C times d V in by d t. Rate of change of the input. If the input is changing faster, there is more current through the capacitor. If it is changing very slowly, then there is less current. If it is at d C, there is no current at all. Now, what should the output voltage be? This current cannot get into this op-amp. Input impedance is infinite. The only way for this current to flow is through this resistor and as we had seen earlier, the output makes it possible for that much current to flow. It adjusts itself such that precisely that much current will flow. If it did not, then this point will not remain at 0. Therefore, to keep the virtual ground at ground, the output must adjust its value such that this much current flows through this R. Therefore, that is only possible if out is negative because this is 0. What is the value of the output? R times this current. Therefore, V out should be minus R times this i which is equal to minus R C d V in by d. So, I have got a differentiator here. I can produce a differential. Indeed, it is possible to just take this output and you can take it. You know that op-amps do not disturb you or at least not too much. You take your output and feed it to another differentiator and then you will get the double differential. Indeed, you could actually make differential equations using op-amp and indeed, they used to be computers which made use of it which solved differential equations by making circuits. Those were called analog computers and complicated differential equations could be solved just by making an analog circuit using op-amp.  Just set up a circuit and voltages at various nodes will be the solution of that problem. So, you can solve in fact differential equations using this because you can have any number of differentiators following one to the other. This R C time, this is the normalizing factor of this differential. Output is not equal to the differential. It is R C times that differential. That stands to reason because R C has dimensions of time. So, we have divided the dimension of time here by T. Therefore, I must multiply by T to get back a voltage. So, this time must be multiplied. So, rate of change of input voltage, this is essentially tells you the rate of change of input voltage average not really average, but normalized by the R C time constant of this circuit. If R is large and C is small for the same time constant, then you will get the same output voltage, but now you will draw less current from your source. So, if you are worried about drawing current from your source, you must use a small value of C, but to get the same output it correspondingly large value of R that you can do here. Now, quickly let us say that if I had connected them in another way before we go away from here. Suppose, this V of T was a sinusoid. It was some sine omega T. What will be the output? Suppose, V in of T is some A times sine omega T. So, this will be output, it will be minus R C times A into omega cos omega T. We are taking the differential with respect to time and the angle here is omega T. It tells us something, it says that the output amplitude will increase with increasing frequency. That makes sense because higher frequency means greater rate of change. Therefore, the differentiator should produce a higher output, because the differentiator measure the rate of change and the rate of change is higher at higher frequency. So, it produces an output which increases linearly with the frequency and such a circuit is called a filter. It is called a high pass filter. That means, it prefers high frequencies versus low frequency. Indeed, if the frequency goes to 0 that means you have a DC, the output will be 0. Therefore, low frequency is blocked, indeed DC is blocked completely. If you have only a DC output will be 0, but otherwise you have a frequency which is linearly increasing with omega. Such things are called filters and these are called linear filters, because I have a linear amplifier. I have just replaced the R 1 by R 2 by that figure. That is only V out. That is right. We will make the correction. Here I have written V out by V in, whereas I am writing V in here. So, in fact, this should actually be removed. I have already carried the V in on this side, difficult to align. This V in should not be there. Thank you. We put the R here and put the C in the feedback path and let us see what happens. We are grounding the positive input again. Therefore, this point is at 0. So, how much is this current and how much is this current? This is equal to the differential current. So, that is again d by d t of C times output. The potential difference between these two, but that is equal to, so it is d by d t of C into 0 minus V out. This is the potential difference across this capacitor. This plate is at 0, held at 0. This is held at V out. Therefore, this output will be minus C times d V out by d t. Therefore, what is d V out by d t equal to minus V in divided by R. Therefore, V out is the integral of V in d t. Now, I have got an integrator. This will integrate the input. Notice that this will do naughty things if the input is at d c, because the integral of a d c is not 0, unlike a differential. The integral of a d c is a ramp. It will continuously increase. That makes sense. If you look at this circuit, suppose I put a d c here, then I am forcing a steady current into the input. That means the output should be a ramp whose differential is that steady current. So, the output must continuously change to produce a current which cancels this steady current. Therefore, this output will continuously charge up or charge down. In a practical case, it will stop when it hit either the positive supply or the negative supply. So, I must make sure that it does not happen. It does not saturate. We will see later what practical steps are taken for doing that. However, again suppose I was to give a sinusoid to the input. What will be the output? Integral of sine omega t. What is the integral of sine omega t? Minus 1 by omega cos omega t. So, you will get omega in the denominator. So, you will get 1 by omega r c amplitude divided by cos into cos omega t. If the input was a sin omega t. That means the amplitude of the sinusoidal wave is now divided by omega. Higher the frequency, lower is the output. That means this one is a low pass circuit. It does not allow high frequencies to pass. It allows only low frequencies to pass. Indeed, as omega goes to 0, you can see that the output goes to infinity eventually and that is what we had seen. That if we give it a d c, it will continuously ramp up till it goes to infinity or till it is brought short by practical consideration. So, this has very high gain at low frequencies and low gain at high frequencies. Therefore, it is a filter and this filter will then pass low frequencies preferentially over high frequency and this is the property of an integrator. An integrator essentially if the frequency changes here, then at very high frequency the current will just pass through this capacitor without requiring too much voltage across it at high frequency. So, the corresponding voltage difference from 0 will be very small and the output voltage will be very small. So, essentially this integrator and this differentiator can also be alternatively used as a filter and it is a linear circuit. As you can see, if the input is changed linearly, the output will change linearly. This amplitude just comes here as it is. If I change the amplitude or if I mix two waves, then the output will be just the superposition of the output. So, that is the next thing to be understood that in case of complicated configuration, this is actually a linear circuit. In one configuration, when you had both resistors, the output was minus R 2 by R 1 into V in. That is a linear circuit. If V in is 0, output is 0. In the other case, it was 1 plus R 2 by R 1 times V in again linear. What would happen if you had inputs at both? That is to say, I have a configuration like this and I applied two inputs V 1 and V 2 and I have my familiar R 1 and R 2 connected there. How do we analyze a circuit like this? So, first let us do it the painful way. There is negative feedback here. Therefore, this voltage must be V 2 because of the virtual short because there is net negative feedback. This voltage must be V 2. Therefore, how much current is flowing here? V 1 minus V 2 divided by R 1. That much current is flowing. So, V out must be such that the same amount of current flows through R 2. That means, V 2 minus V out divided by R 2. This end of the resistor is at V 2. This end is at V out. Therefore, V 2 minus V out divided by R 2 should be the same current which is equal to V 1 minus V 2 upon R 1. So, now I can take V 2 by R 2 to that side. Just collect all V 1 and V 2 terms on one side and V out on the other. So, if I now multiply by minus R 2, what I get is V out equal to V 2 R 2. Sorry, one of these should be R 2. V 2 by R 2. So, it is R 2. I have multiplied by minus R 2. So, these minus signs will go for V 2.   So, it appears as if the inverting amplifier and the non-inverting amplifier are acting independently. Suppose V 1 was not there. Suppose V 1 was grounded. What would be the output? V 2 into 1 plus R 2 by R 1 namely this. If V 1 was there, but V 2 was not there was grounded. Then, the output will be minus R 2 by R 1 V 1. So, therefore, principle of superposition applies. It is a linear circuit. If you have two independent inputs, you can assume that the other input is 0. Calculate the output. Then, make the first one 0 and calculate the output and now you can just add it as in linear circuit. Indeed, notice that instead of this R, it could be j omega c or anything. So, these are linear circuits and the corresponding filters are called linear filters. Because they use active devices like amplifiers and so on, they are called active filters. So, we can make active filters using simple op amp circuits and these are linear circuits. That means if I have inputs impressed on both the inputs, then it is as if you analyze one, then analyze the other and just add them. Assuming the other input is reduced to ground. This is the hallmark of linear circuit and that makes the analysis of these circuits quite easy. Just as an interesting circuit, let us look at this somewhat symmetric looking circuit. All resistors are equal. Can we quickly calculate what the output will be? So, we are going to apply superposition. So, how do we apply superposition? You make one of the input 0 and calculate with respect to the other and then the other way round. So, let us make V 2 0. If you make V 2 0, the potential here is 0. So, it is like an inverting amplifier. What is V out? Equal to minus r by r times V in. So, it is equal to minus V in. Now, ground V 1 and see with respect to V 2. Now, notice what is the voltage at this point? This is a potential divider. No current is going into the op amp. So, the voltage here is V 2 by 2 and this is grounded. So, it is like the non-inverting amplifier. The voltage here is V 2 by 2. What is the gain of this? 1 plus r by r. That means the gain is 2. So, 2 into half overall the gain is 1. So, it is minus V. I am calling V 1 and V 2. So, it is minus V 1 plus V 2 as simple as that. It is a true difference amplifier with a gain of 1. That extra factor of 1 plus r 1 by r 2 is nullified by attenuating this using the same. Therefore, you can make all kinds of interesting difference amplifiers where the two inputs never look at each other. One input arrives at the positive side, the other input arrives at the negative side. Now, the virtual shot assures that both these inputs are at V 2 by 2. Now, this is a very flexible device that we have, this op amp. We can make all kinds of amplifiers, all kinds of linear filters, all kinds of frequency dependent circuits and indeed it is such that it is not bothered what is connected to its output and it bothers its input either not at all or very little. As a result, it is possible to design simple modules and just stack them up one after the other. This is the kind of example that I had talked about where you have a differentiator and it is followed by another differentiator. Now, you can get the second differentiator. So, very complicated systems can now be mimicked in analog fashion by using this versatile device that we got out of our wish list and therefore, it is quite a popular device indeed and it turns out that it is not so difficult to make. The insides of this are quite horrendous looking, very painfully made, but it sells in such large quantities that the prices of ordinary op amp are quite small. If you start demanding perfection, then of course, these can be quite expensive. If you say that the offset voltage should be truly 0 or that it should go to very high frequencies or indeed that its input bias current should indeed be truly 0. So, if you start asking for total perfection, then they can be quite expensive, but for ordinary run of the mill work, they are very convenient and very cheap. So, you choose your op amp which work appropriately for the signal range, choose the configuration which provides the gain and behavior that you want and now you can make, if that is too complicated, you can break it up into modules and each module provides a function that you want and these functions then just can be stacked together and now you can have a system. That means, analog design has been elevated to the level of analog system design which earlier we did not see through. We thought that system design was possible only with digital components, where you have a complicated system and now you could break it down finally, we make it as a combination of logic gates and so on. Similar things can now be done with analog, where filters and adders and gain stages and attenuators, subtractors all of these can be constructed and just stacked together to perform it and give you the functionality of the system as you desire. So, that is the big thing about op amp and in the subsequent lectures, we will see that how these op amps can then be used to make many useful functional blocks. So, we will stop this lecture here.


Here, let me start by thanking the organizers for inviting me and giving me the opportunity to give a talk here about one of our latest pieces of research. So what I would like to talk about today are quantum fluctuation relations, but not in the case where you start from a thermal state of the system, but rather it's off again. My mic seems on. Can you hear me now? No? No? All right. One, two, one, two. It's OK? So should I start again? Can you hear me now? No? Higher. Doesn't seem to be better now. No? Nobody can hear me, it seems. Very sorry about that. One, two, three. One, two, three. No? If I speak a bit more loudly, is it better then? OK, I'll try to speak up. So let me start again by thanking the organizers for inviting me to come here and give a talk about one of our latest research topics on quantum fluctuation relations. And I would like to actually use these quantum fluctuation relations, not to relate to as usually a kind of thermalized states, but to different kinds of states which might be pre-thermalized states or more like generalized Gibbs ensembles. And I'd like to look at how can we do non-equilibrium dynamics to find out a bit more about those types of states. Now the reason why this is a topic for us of interest is that in co-reactant physics as well as in condensed metaphysics, we more and more have experiments that actually take systems far out of equilibrium and try to induce by dynamically induce useful properties into these types of systems. And I've shown here two different kinds of non-equilibrium dynamics that are particularly promising and interesting for that purpose in the left-hand column. I got on the top an optical lattice experiment where basically a mirror is shaking. And through the shaking of the mirror, one tries to reduce the hopping rates and induce a kind of mod-insulating state from a superconducting state by shaking the lattice. So this is what you'd get here through a shaking mirror. You would induce a mod-insulator from a superfluid. And similarly, in condensed metasystems, and here I show some alkali-adopted fullerites. An experiment has recently been carried out where through shaking these buckyballs, so basically by driving the buckyball oscillations, one could induce a superconducting state into the system. So turn it from a conductor, from a normal conductor into a superconductor at very high temperatures just through driving. Both of those types of experiments have one thing in common. They take the system far out of equilibrium, and they induce some kind of interesting properties that make a macroscopic difference to those types of systems out of thermal equilibrium. And the second type of experiment is shown here, again, a kind of coratum implementation, and here a condensed matter implementation, where rather than driving a system periodically with some kind of laser excitations, what we can also do is do a sudden quench of the system. So in this upper example here, that's an experiment from 2012 in a Manuel Bloch's group. What they did was suddenly quench an optical lattice to see a density wave melt, and this melting dynamics was then followed as shown here, and we could in real time see how a density wave melts in an optical lattice. Similarly, here in the thin NIO3 film, what was done was a fast laser pulse that would basically excite here the interface between these two types of materials to induce the melting of anti-ferromagnetic order. And again, both of those experiments have one thing in common. There was a sudden quench of the system, and the sudden quench led to, in one case, the melting of a density wave or the melting of anti-ferromagnetic order. So I would like to do today with not exactly those examples, but with some simpler examples, is I would like to discuss how one could use these types of non-equilibrium states and characterize them through quantum fluctuation relations and whether it's maybe possible to use these types of fluctuation relations to detect symmetry-broken states. So some kind of conserved quantities that might take on non-zero value in these systems when they're driven out of equilibrium, whether those can be detected through these types of fluctuation relations. Now, fluctuation relations are, of course, a very kind of intriguing concept in that they take thermodynamics a step further and make some equalities out of what we usually know from thermodynamics as inequalities. So in particular, what we have in thermodynamics is that if we do work on a system, then the only thing we know is that this amount of work that we need to do needs to be bigger or equal to the change in the free energy of the system and that the entropy needs to always increase as we do such kind of quenches or work on the system. And that, of course, those relations are fundamental to the operation of all kind of heat engines, fridges and so on and so forth. But what remains is that we always have to deal with inequalities and then optimize those. What we don't have in traditional thermodynamics and what was only discovered in the early 90s are that we can turn these types of relations into equalities. And if instead of just looking at the work, we look at the expectation value of this e to the minus beta times the work, so where beta is the temperature of the system and we average this over many runs, then what we get is an equation here that equates this expectation value to the change in the free energy. And this is termed the Yashinsky equality and turns basically something that up here is an inequality into an equality if we average over many runs. And similarly, one has the so-called Krug's relation which relates the amount of work that is needed in a forward process. So we drive the system out of one state into the other to the work that is needed to drive the system back from the final state to the initial state in this so-called Krug's relation. And those types of equalities were first invented and derived for classical systems. And for instance, we're used here in this beautiful paper in 2005 to do some sequencing of DNA. So basically what people did there was they measured the force it takes to tear a DNA apart and from the fluctuations in the forces that are needed to do so, they could, via these Krug's relations, find out what the sequence of the different pairs in this DNA would be. Now, if one takes these types of equalities to the quantum regime, one can do so. But basically, considering the dynamics of a system that is described by a certain Hamiltonian is coupled to a Bartha temperature of beta and then is taken out of this thermal equilibrium by some kind of process that here for simplicity, I assume, is a process that is unitary. And if we take such a unitary process and work out how much work is needed to take the system out of this thermal equilibrium to some other state, then again, what we find is that this expected amount of work here in the exponent is equal to the change in the free energy in the system. So exactly the same thing as we had for the classical case. And similarly, for these systems, also the so-called the Saki Krug's relation holds that again relates the work needed to take a system out of equilibrium in a forward process to the system in the backward process and those two things are again related in exactly the same way as before for the classical system. However, all of those types of processes assume that we start from a thermal state. So the assumption is that the system is fully thermalized and we have here only one parameter, the parameter, the beta, the temperature, the inverse temperature of the system that characterizes this type of system. And what I would like to look at now is, oh, sorry, and also this kind of quantum Yasinski equality has been tested experimentally in an experiment in 2015 in a single ion trap experiment and one can see here that the agreement between the kind of theoretical predictions here in these color bars and the actual measurements agreed extremely well. So both the classical and the quantum version of these equalities have been tested and used in experiments. Now, what I would like to do today is actually to look at what happens if instead of having a thermal state, we start out with a state that is characterized by some Hamiltonian again, but in addition, a set of observables that commute with this Hamiltonian and are conserved initially. So basically that means that our initial state is now not described just by a quantity beta, but also by a set of more Lagrange multipliers beta k that are kind of constraining the average values of these observables mk. And so rather than having a pure thermal state, what we now look at is a state that has the typically to the minus beta h term here, but then a set of more Lagrange multipliers constraining these mk's. And so basically this so-called generalized Gibbs ensemble here is a state that will actually be the one with the most entropy under the constraints that we have a fixed average energy and we have a fixed average of those types of quantities mk. And what I would like to look at now is how do fluctuation relations relate the work that is done on this system to these types of generalized Gibbs ensembles and can this be used to detect say if such a conserved quantity exists and what its value might be. And in order to do this, what needs to do is extend the kind of meaning of work a little bit. So rather than just having the work defined as the difference between the initial energy and the final energy, we need to add to this all of these kind of initial values for the observable mk and for the observable ml with the corresponding Lagrange multipliers here. And so what we need to do is we need to replace the work that we initially had without these conserved quantities by the difference in this final value of this property A and the initial value of this property A. And if we do so, then indeed what we get is a generalized Yashinsky equality. This generalized Yashinsky equality will now relate this e to the minus w. So this generalized work that I just introduced to the difference in the generalized Gibbs ensemble free energy. And we'll also get generalized the Saki-Crux relations which relate the forward process to a backward process again in the same way as before. But now relating these generalized works to the change in the free energy where this change in the free energies or the free energy is now defined as the logarithm of this partition function of the generalized Gibbs ensemble state. And so basically what we now have is a set of equations that relates kind of work type quantity in any out of equilibrium process to properties of the generalized Gibbs ensemble in this system. And we'd like to look at what the meaning is of this in some simple examples that I would like to discuss now. And the first example is just take the Dicke model. So the Dicke model basically couples a bosonic field to an ensemble of spin one half systems. So what we have here is a Hamiltonian where we have the bosonic field. So this is typically a cavity field described by field operators a and a dagger and some energy omega a. Then here we've got the energy of the spin ensemble. So the J set basically is just the set component of this kind of sum over all the spins. And those two systems interact with each other. And the way they interact with each other is that they can basically exchange quantum between each other with a coupling G times here's a parameter one minus alpha where we basically create an excitation in the spin by destroying an excitation in the field or the other way around. And if we have a non-zero alpha here then also the opposite process can happen. And this is the two excitation are created one in the field and one in the spin ensemble or two can be destroyed at the same time. Now this type of Hamiltonian can be realized in iron traps. So basically if you have here an iron trap these irons would constitute the spin ensemble. And if we take two lasers one reticent one blue detuned then this type of model can be realized. And by changing the properties of this laser driving we can change these parameters G and alpha here. And now the interesting thing about this model is that if we choose alpha to be equal to zero then we have a conserved quantity here. So the total number of excitations in the spins and in the field is a conserved quantity and will not change as long as alpha is equal to zero. And so what we now assume is that we start from such a state with alpha equals zero then we turn alpha on for a while to some non-zero value and turn it back off again. And at the same time we increase this strength G to such a value then we would expect this M the number of total excitations to change with time. And if we now look at what that type of evolution would, how that type of evolution would look like in the standard the cyclic nucleation what we find is that actually there's a big difference in the work distributions between the forward process and the backward process. So here in blue is the probability distribution of the work needed to affect this type of change, this type of evolution here in the forward direction and in white is how this work distribution would look like in the backward direction. And so what we can see here is that these two probability distributions do not agree. And because they don't agree, we can actually conclude from this that some kind of conserved quantity we have missed out. So there's something that tells us this system is not yet thermalized and in particular this system was not really in a thermal state initially with no conserved charges. If however, we instead take the generalized the cyclic Rooks relation and relate the forward direction with this generalized work to the backward direction. What we find here is perfect agreement between those two probability distributions. So basically by identifying this quantity M, this conserved quantity as something that takes the initial system out of thermal equilibrium. We can again use this the cyclic Rooks relation in a generalized way to relate work in a non-experiment dynamics to properties of a generalized Gibbs assemble here. Okay, similarly if we want to take the Sinski equality we get a similarly interesting behavior. The first thing that you notice is that this expected sorry this exponent of the standard Gibbs free energy and the generalized Gibbs free energy they do not agree. So basically if you were to now measure the work to identify what is the change in free energy when we get a wrong result because we would always get the change in the generalized Gibbs assemble free energy and not in the Gibbs assemble free energy here. So those two differ and thus we will get a wrong result if one were just to assume that there is no conserved quantity here. If one then now measures the work for again a similar process as I've shown before. So we start off with alpha equals zero that is M is a conserved quantity turn this into something non-zero and then back into something zero and similarly increase this coupling G here. Then we'll be fine this that for very short time so if we turn this change it is quenches on for just a very short amount of time both types of your Sinski equality disagree with one another. So here we have got the triangles, the blue triangles are the standard your Sinski equality and they give exactly the same result as this generalized Sinski equality. So both of those terms agree and the reason for this is that if this quench is done very very short and quickly then there's not enough time for this conserved quantity to dissolve itself and to turn into some and to basically become thermalized. So that means there's hardly any change in this value of M and all these different types of works give us the same value for the free energy change. However, if we make this time longer then we see some market difference between the two types of work functions and in particular we see here that the generalized work remains exactly where it should be it's constant it is independent of the duration of this protocol so how long it takes to turn this on and off and the two agree as they should. However, the kind of standard work will actually deviate massively from what we've had before and the reason for this is that after about this kind of length of the protocol the kind of conserved quantity starts to get messed up it starts to thermalize and this leads to a change in the work that is needed to drive the system out of equilibrium. So basically in this case the Asinski equality can be used to kind of track the dynamics of non-equilibrium quantities and conserved quantities in the starting state over time and here for instance get that the lifetime of these types of M the lifetime of this M in a quench would be about 0.1 microseconds for this particular value that we've chosen if the protocol takes longer they will just scramble and thermalize. Okay, now a second example is now not one where we do a quench but I would like to do a second example where we look at what happens if we drive the system and whether again we can use these types of ideas to characterize driven states of quantum systems. Now in order to kind of do this in a concrete example I'd like to take the Hubbard Hamiltonian and the Hubbard Hamiltonian in this driven in the limit where the interaction energy U is much larger than the kinetic energy T so the hopping between different sides is small and we have a the system is dominated by the interaction energy and in this particular case what we can do is can get rid of double occupancies in the system and what we are left with is basically a Hamiltonian is mostly described by this hopping between or fermions between different sides and so we have fermions moving along a lattice if they sit on top of each other a large energy that repels the two. Okay, and now we turn on some driving and this driving that we would like to turn on is a driving that basically shakes the individual lattice side up and down so we basically want the system to wobble around in time and then we look at what happens to this system if we do this so if we drive this system and make the driving amplitude stronger and stronger how does this system change in time? In fact if we remodel this by just having an onsite energy that oscillates in time so we add to the Hamiltonian sinusoidal modulation here of the onsite energies and we do this in an alternating way so if one goes up the other one goes down basically all oscillating phase nothing much happens. Now in this particular situation where we find this and this is well known from a number of experiments is that as we increase the amplitude of the driving what happens is that the bandwidth and hence the hopping amplitude between different lattice sides goes down with the driving strength like a vessel function and so if we start out here with a band that is brought that has approximately 40 width in a 1D system then this bandwidth will get smaller and smaller and here at this point the driving is so strong that any kind of hopping between different lattice sides is suppressed and we basically get all the band collapse into one point. This happens if our driving's frequency is large compared to all other quantities in the system so we have now a driving that is much faster than any kind of interaction strength than any kind of hopping and then basically we just suppress the tunneling of particles between the different sides. If instead we take this driving frequency below you then the behavior is slightly different so what we get is we do not get really compression of the band width to one point and thus kind of stop any type of dynamics but instead what we are left with is a certain bandwidth here that is determined by four times the exchange interaction so the T squared over U here and that never goes away so there's always some residual dynamics going on in the system and what we're interested in is in this limit how does the system behave close to this point here and in order to study this we first did some numerics and just turn on the driving strength in a slope as you see here and look at what are the properties of this system if we take a hubbub model and do this oscillation with ever increasing modulation strength and then we look at different types we look at different types of correlations particularly the density-density correlations spin-spin correlations and pair correlations and I'd like to focus here on the pair correlations so the pair correlations would tell us how two fermions pair together and then move together through the system and this is captured by this correlation function here that basically correlates a pair that is located at sides i and i plus one to sides j and j plus one and if we turn on this driving what we find here is that indeed this system turns from one that has a hubbub like ground state into one that looks completely differently and instead of having a peak here in the structure factor at four times kf has two peaks at two times kf and basically turns from repulsive Latinx liquid into an attractive Latinx liquid if we just look at the slope here so here is the slope at q equals zero and what you see is that for weak driving this Latinx parameter always stays below one so we have a repulsive Latinx liquid but if we drive the system very strongly we get an attractive Latinx liquid and it seems that the system moves from metallic state into a superconducting state we looked at that also through the spin structure factor and again conclude the same thing because what we get is in the structure factor two peaks at two kf turn into one peak at pi and this indicates a doubling of the wavelength of the spin wave so rather than having here a spin wave with two kf here seems to indicate that we get pairs and those pairs have a different types of spin wave and we conclude that this might be due to undeterminatically bound pairs in the system if we then look at the pair correlations this picture is corroborated even more so we turn on the systems driving and find that the pair correlation peak increases massively at q equals zero and seems to indicate that again pairs are formed and these pairs in the system would then bind together and move together through the system and that is what we find from the numerics but now I would like to use this type of fluctuation relations to find out whether one can say a bit more about those types of pairs and in order to do this what we do is we write down a low energy TGA model so basically we now assume that this driving can be effectively described as adiabatic motion or as dynamics in a low energy TGA model where we have as the first term the hopping again where single particles hop from one lattice side to the next with the hopping amplitude that is suppressed by the driving according to this zero sort of Bessel function the other terms it turns out are totally unaffected by this driving so if we now have here a bare energy here so we are basically a pair of binds together and that gives you the reduced energy J then that single bare binding is unaffected by the driving and remains the same as what it was without driving similarly we here have terms where the bears hop from one side to the other and that hopping goes like alpha times J with alpha is one half and again this type of hopping of pairs is unaffected by the driving so it turns and finally what we do is we protect out any double occurrences because they are still high up in energy so it turns out that in this low energy model the only thing that really depends on our driving strength is the hopping of individual pairs and if we now basically change the driving strength all that will happen is that this hopping term here changes and in particular if we go to residence where the hopping term is zero what we'll have is the number of nearest neighbor pairs that are described here by those two terms in the Hamiltonian will be a conserved quantity and what we're now going to look at is what happens if we start from the situation where the system is described by this low interaction, sorry by this low energy Hamiltonian in the case that driving is such that the hopping term is switched off this number of nearest neighbor pairs should be a conserved quantity and if this number of nearest neighbor pairs is zero so this means if our driving has not induced any nearest neighbor pairs then the evolution of our system should be perfectly aligned with the standard, the Sarkich Rooks and the Ashinsky equations if our driving has actually induced non-zero number of pairs then our evolution should violate the Ashinsky equality and instead agree with the generalized Ashinsky equality and so what we did in order to study this is we looked at an initial state that is just like a GG state that I introduced before so we here have a temperature Hamiltonian with zero hopping and then some kind of chemical potential here for the pairs that fixes our average number of pairs we start dynamics at t tilde equals zero so no single particle hopping and turn this towards one and then we look at the standard work so basically if we do the standard work what we should get here is that the expected amount of work that is needed to drive the system from this from this value of zero to 0.1 is just zero on average and the fluctuations are shown here so the W squared is shown here so this means that our standard Ashinsky equality would predict zero work is needed to do this if instead of course we take the generalized work then what we find is a very different behavior so the generalized work goes like the number of pairs in the system and hence by just measuring this generalized work in this quench of t from zero to some finite value we will see a change in the amount of generalized work that is needed and now of course this measurement of the work needed to drive the system from t equals zero to t equals 0.1 could therefore be used to test whether or not we have produced some pairs in our driving process and similarly of course we can then work out all sorts of higher moments of the generalized work and of the magnetization and constrain the probability distribution of our pairs produced in the driving by measuring generalized work of that system now I should add that all of these results are still preliminary we haven't really published any of this yet but what we can see here is actually if I go back is a very good agreement between the generalized work and the number of pairs that we've produced here between the two cases so it seems that this is actually already working very well now with this I would like to come to my summary what I hope I've shown today is that it should be possible to use extended quantum fluctuation relations to track the formation and destruction of charges in quantum quenches so if one has some conserved quantities that have produced some non-zero value for conserved quantities then one might be able to track their evolution and their lifetime and their destruction and creation through measuring the work that is needed to drive the system out of this kind of pre-thermalized state one can hopefully use this also to detect pre-thermalized states because if there's a pre-thermalized state then the standard of the Szynski and the Sarkic Rooks relations will not hold anymore and that means it should be possible to identify them through measuring work needed to drive the system and also to identify conserved degrees of freedom that one might not know about so if one measures actually English faith and assumes that the system is thermalized and then finds that there is a discrepancy between the Iazinski quality and the Sarkic Rooks relation and the experimental results then one can try to start thinking about maybe there are some conserved quantities that one needs to include into the consideration to make this work and so hopefully be able to identify some of them and then of course by doing the same thing it should also then be possible to indirectly or at least observe dynamically induced symmetry breaking like I showed in the last part of the talk in the last example if we basically take this system and create pairs and they start to form a condensate of pairs then again this should constrain the system even further and violate even this generalized Iazinski qualities that I've shown but we haven't really shown that yet here are some references and I'd like to conclude by thanking the people who have been working on this in particular Jordi Moopetit who has been the leading senior poster from this Jonathan Coulthard who has been doing all the calculations all the numerical calculations and our collaborators Amanda Rilano and Rafael Molina in Spain and of course I'd also like to thank all the other members of my group postdocs and PhD students and of course most importantly all people who give us the money to do what we do every day alright then with this I'd like to thank you very much for your attention, thank you


Something's not right here, something's not right here, look at the size of our donuts and look at the size of the boys donuts. Wait a minute, that's bigger than you. Can you tell you like my new coffee pot? It worked, it got me out the door today and it was a big way. Just finished a 20 mile run, boom, crushed it. Now, need some food. There it is, yeah. Okay, the boys and I are ready. 21-7 donkeys up on the cowboys. Oh, that feels good. Alright, a little halftime playing in the backyard with the boys. Here we go. Only issues, we don't have a football, oh no. We'll have to get a football for these boys. That's on me, that's on me. Two sacks for Miller.  Get them, get them. Anyway, two minutes left, we got this. Good job, Broncos. I love the Broncos, alright, time to go eat some pizza. Yeah, sorry. Touchdown! Oh, thank you hon for the pizza. Not from last night's party with Josh and Maggie. What a weekend, I hope you guys had a good weekend.


Welcome to All Hands Update, I'm Petty Officer Tony Rosa. Chief of Naval Operations released a plan August 19th detailing the Navy's fiscal spending over the next five years. The new plan lays out future spending, training and the direction of the fleet. The plan describes how the Navy will deal with budget constraints while increasing operational tempo and balancing the fleet's current readiness. More submarines, patrol aircraft and newer classes of warships are coming to the fleet. Warships and their crews will continue the Asia Pacific Rebalance to increase presence in the region. Ten more ships will be forward deployed to the Middle East by 2019 and 15 ships will be added to the Asia Pacific region. The plan calls for investments in quality of service initiatives like more use of tactical trainers and simulators, improved barracks and more travel in schools. To read CNO's navigation plan visit his leadership page on Navy.mil.


So I'm going to pause it real quick. So this is Druid Lock games. And generally our strategy here is to run after the Druid, get fears on him, shatter him out of it with a sheep on the wallock, roughly around the same time to stop him fearing me or stopping me. And then I'll burn the Druid, try and force CS from the pet. So yes, either CS the burn or CS the shatter from the mage. And if these games go a bit too long, the Druid Lock ones, as they have a tendency to, I'll skip through them a little bit because obviously it's just us doing setups and you don't need to see that over and over. Here we force the Druid's trinket because the wallock's down the bottom, Druid's in a bad spot. And obviously he doesn't want us creating pressure on him. Now we're just chilling at the top, waiting for fear cooldown, maybe looking to sniper burn, gets resisted, now he bears. So if we force bear, we're still forcing some mana out of the Druid. Druid's positioning was poor here so he got casted on a lot and was so we're creating some pressure on him. So this actually makes him use quite a lot of mana. I get feared here, a trinket, unfortunately you get feared again. Maybe he wasn't a good trinket, now he innovates, but he just runs straight into me. So this is a lower team. This is one of our earlier games, as you can see. But the strategy remains the same. We're essentially trying to do the same thing over and over, here we get a fear on him. Majors usually trying to keep some sort of stacks on him, whether it be winter's chill or like a slow, obviously he can shift it, but if I get it, when, if he slowed at the same time as I fear him, then potentially the pet can remove some other random bullshit instead of the fear. Obviously if the pet removes the fear, then he can't dispel himself from She-Beaver. So right now there's no reason for me to drink with Majors ahead on mana. Druid is in a lot of trouble, has no inner vein, we're just chasing him down now. And when I have this much of a mana lead, I can just play really aggressively on him and it makes it really difficult for him to kind of get away and survive. Warlock actually gets a full fare on me here, so this is gonna save him for another go, most likely. But Druid is starting to get real low. And right now we just need to stop him drinking. That's the main goal. He's looking for it here, but I don't think he's gonna get anything rivers onto it.  I'm just gonna get a little safety drink in here, just in case while waiting for my fear cooldown. Might try and mount up at the top here. Probably the play here. Maybe he didn't need to go for that renew. Looking for some cheeky damage on him. Using Chastai is obviously to get onto the Druid as decent as well. Okay, I actually managed to force the Druid to drink it again on that one. And yeah, again, most likely he's gonna die on the next fear if we get a shout. Yeah, as you can see, this is a lower team. Warlock hasn't been mana draining at all. He's trying to just put out pressure with damage, but he's not getting that much off. There's a mana drain very late in the day for that. But yeah, mostly he's obviously been trying to create pressure, but obviously river's out playing him. We get the fear on the Druid here.  Just delaying it a little bit because I want river to get a shatter. Burn goes off, trinket the fear. Try and, oh, feel what the next actually, he lost it anyway, feel what doesn't get removed. And I just dropped Fiend on him here just to create a little bit of added damage pressure. And honestly, at this point, if it's not Blades, it's Druid is long dead. Only reason he's still going is because it's Blades, but I think he dies here. Probably looking to remove the blooms on three stacks rather than two. Getting a big gray healer on river just to be safe while he's in the fear. Boy uses bark skin, gets a burn to spell, and I think he just dies now. He should do. It's annoying, you can only go forward 30. It's okay, I've edited it a little bit. So we've got another Druid Warlock game. So the way I've set it up is I've got all the Druid Warlock stuff in the same segment so that we can kind of see the improvement or any mistakes from the games in a row and see how the teams kind of progress a little bit. So obviously the games that are more recent will be at the end of each segment, which is where obviously we're like fine tuning mistakes more so.  And we're not on Blades at just time, so it's a lot easier to harass the Druid. And we're using the rank one Blizzard as well, sometimes if I need to get a fear. Right now I have the pet on me so I can't man up to fear, which is annoying, but at least it keeps it off river. So I'm just running at him. I should try and commit to a certain way more and then let river just Blizzard the other way. We'll have an easier time catching him because right now he's just running. See like this, this is what we want and I'll get the fear here. Get the PI on river and just drop my fiend on the Druid. And actually we're going for the pet here. This might be, no, I don't think it's gonna go down. As soon as it gets a heal from the Druid it's pretty much gonna survive. It's like he needs like one maybe two life blooms and we're not gonna kill it due to resists. Unlucky tornado there. Try to run through it and get it to bounce me to the Druid, but it doesn't always work out. And right now we're actually winning mana, but it's gonna come down a lot so if I can get the innovate off will be quite important. My strategy is to spell the fear. Trying to force the Druid round to the tornado. Unfortunately it despawned the exact same moment but we still get a fear due to the Blizzard. Dropping a burn, breaks the fear. Pet spell locks too late so we get that off and he bears so we force a good bit of mana out of the Druid here. He's cloning me. River has no dots so this is fine. Not too scared of this. Actually unlucky tornado despawned for the Druid there. And Druid is leaving it really late to innovate. If he innovated a little bit, it's like there was a few times where I'm in CC and I can't really remove it. But if he leaves it this late, then because of how high my mana is, the Warlock's putting out double dots, right? So it allows me to palm bounce all the time rather than just like solo dotting river and forcing me to use more mana to heal him. I can just palm bounce every time I go near him and it's gonna top us. Druid went for a little drink there. I don't think he got a tick. Gonna probably palm bounce here since we're in the open. He has a shield so it's not bouncing which is a bit annoying. You need to be careful of that. But when I palm bounce, I should palm first and then shield. This Warlock's draining more. I managed to get the triple fear even. Warlock trinkets into a sheep. So misplay from him there if you will. He could have trinketed the sheep and we managed to get the Druid in him. He can't innovate. Trying to get the Barkskin off is resisting every despawn. Finally get it off like three quarters all the way through the duration. Trying to get the fear off river there. And I'm not too worried here. The Warlock has no spell lock, no coil. So it's not the end of the world. If I take a little bit of damage, Druid invades way too late and we take him out. It'd be interesting to see what I'm amar. This one's at the Warlock healthstone for no reason. We won't get to see it. So this is a more recent game actually. This was the other day. This is a much better team. But we've also improved since then. Get a good shot on the pat actually. And I actually misplay here. This was a misplay trinketing this. I shouldn't have trinketed the bash. The Druid's like lagging all over the place, making it very risky to just go for a fear on him. And I think he devours the Fjord. No, I fjorded the river actually. So yeah, I get feared here instead of getting a burn on him. But the Druids used a lot of mana, which is nice. I got full darts, which have been powered up. So this is a bit risky for me. I've played that quite aggressively and the trinket was poor, which is why it got so scary. So I had to desperate prayer in the room. And I believe River locked the Druid on NS. Otherwise I would have received an NS wrath and we could have lost the game there. But this was a nice save.  Now I'm just gonna run at him. The Warlock's used a lot on that last go. He's committed pretty hard for that. So we're okay to go offensive for a little bit now. If everyone is charged, gonna pom bounce. Warlock gets CS'd. And I'm looking to do a little bit of damage if he's in bear, if he's in cast and then I'll look to burn him as it's more efficient in the way of, you know, forcing the Druid to play more defensively due to low mana, putting a little bit of damage on the pet. I'm staying in the pillar here because Druid not crossing, River doesn't have CS yet. And we're generally trying to cross more with CS so that the Warlock can't fear me because if the Warlock fears me, then we can fall behind and it's really bad in this matchup. We need to maintain pressure on the Druid like all the time.  I could have waited with that. There was no reason to rush it. So Warlock somehow doesn't get that fear. Maybe I resisted that one. I'm not sure, it didn't land on anyone. River gets full fear and I'm stopping the Druid drinking.  And I think I'm late here to fear. No, I actually get the fear. I thought I might be late, but managed to get it. My bangle just came back up.  So he barks, managed to just bow the bark, just bow the fear, pop the fiend. And here actually we managed to rush him down before he zoomed due to that really nice shatter. I guess he got some crits on that one. So it was a solid executed go from us, but we were actually behind on mana.  Mainly due to the start from me, I think. So again, same team, same map. Little bit later. And I'm fully dispelling the Warlock at the start just to make sure he has a little bit less, you know, less mark of the while, less chance to resist major stuff. Dispelled the pet as well so that we can start on it. Forces the druid out. And instantly I'm trying to burn him, forced the bear form so he's using some mana on that. And I believe here I use a glow wall and he charges past me. So I need to be more careful with that here. I think I just positioned poorly. I overcommitted on my positioning. I didn't need to go down the stairs and I was a bit concerned that the stairs would lost my fear. So I didn't fear him. So we missed an opportunity there. Warlock is already draining. It's gone behind the hill so I can't get it, which is unfortunate. I know the druid wants to clone me here so I'm just being a bit careful. This team likes to do an all in with coil and a full line of dots. So being very careful of that. Snipe the fear on the druid here. Druid actually hasn't been dispelled yet. This is something I could maybe do better if I fully clean him at the start. And druid takes a fair bit of damage so he's got a lot to heal up now. And I pot fiend on him actually because of that. Let's see if it actually works out. The fiend is sitting on him pretty well getting hits off so it's not too bad. Druid risking going for a clone but he doesn't land it because River has CS. If River gets the CS, Son of Me is gonna be in a fair bit of trouble I'd say. And I'm just constantly staying near to the tomb. I don't wanna stray too far away from the tomb because then the Warlock can fear me for free. I wanna make it as hard as possible for the Warlock to fear me and we're actually really ahead on mana this time. And I really like the early fiend for me as well. I think fiending nice and early in this matchup to keep my mana top is definitely a decent play because it comes back up then and we get maybe an opportunity to kill him between the first two innervates. But if I do it late then I don't get the second fiend and I end up being really behind on mana and having to play it defensively. But here we're miles ahead. I actually pop an early bangle as well. This is the second bangle but yeah. And Druid is in a rough spot now because he's left it really late to innervate. He has no buffs and obviously it's ruined so it's a lot easier to actually get fears on him because he runs into that dead end you know. Try to get the boxing off to resist so far. Get it on the third. And he actually doesn't have mana to use his NS. I'm trying to dispel it. I should have probably just chastised him to be honest, I think it would have killed him. But I dispelled River on fear. It resisted and then he blocked and then I dispelled the NS and it resisted. So standard Druid gameplay there. I think that was the last Druid lock game. This was quite a high one.


Have you ever been sitting around just having a really rough day and then something happens that completely flips it around? Well today we're going to be talking about J-Hope aka Hobie I think his name is from the band BTS and how he did something amazing today. What is up everybody? This is Chris from The Rewired Soul where we talk about the problem but focus on the solution and if you're new to my channel, my channel is all about mental health and I try to pull different topics from pop culture or music to try to teach you how to improve your mental and emotional well-being. So if you're into that stuff make sure you subscribe and ring that notification bell. So yeah I don't know if you got the memo or not but I am not a huge K-pop fan but it's something insane going on where the fans and yesterday Blackpink just broke a record for most views on a music video and I'm like I need to understand what the heck is going on right? So anyways I was browsing around on Twitter today right before my beautiful girlfriend and I went and saw Pet Sematary thinking about doing a video on that but anyways also follow me on Twitter if you're not yet at The Rewired Soul and I saw this hashtag trending right and it was hashtag curious about army and I'm like excuse me I'm a 33 year old man I'm not down with all the link I'm like curious about army like people like thinking about enlisting in the army the armed services like what's going on today so I'm sitting there I'm looking at it I'm like what the heck is going on there's just thousands and thousands of tweets of people doing the hashtag curious about army so I go and I do some more research and it turns out that J-Hope from BTS actually sent out a tweet today and it looks like it was a couple tweets but the next one the second one after the hashtag curious about army said I've read all comments I will show you a great show soon after I practice combo choreography today good night my amy I don't know I don't know I'm using I'm using the translate feature on here but holy crap like I'm looking at this and as his hashtag was trending like here's some of the tweets that I saw alright so Hosea arc and I apologize I apologize if I mispronounce these names like let me learn a little bit and I'll figure it out let me know if I'm saying it wrong down in the comments but anyways says Hosea went online just to ask how our day was we don't deserve him he is too good for us hashtag curious about army I love how sunshine hobby legit asked how our day was like OMG he actually read all the comments he's so sweet who needs a boyfriend or girlfriend if you have BTS to check on you or to know what you're doing at least there's nothing more beautiful than the relationship BTS and armies have don't fight me on this and this last one says the fact that no one today asked me about my day but Hosea did is enough to make me feel loved I don't know what this is about I was really having a bad day hope he made it better I am working as a nurse nurse later my shift starts 7 p.m. so wish me luck Opa all right so like like this like something I just want to talk about is is like first off like kudos to J hope and kudos like to BTS like I feel like they're really like good down to earth guys trying to learn more and understand it but like I'm all about like you know we need to balance like the negativity with the positivity and there's such little things that all of us can do to you know send out this like positive message or just vibe in the air so it's awesome that somebody like J Hope can do that with just a single tweet like think about that like think about that for a second just a single tweet made somebody's day like that's absolutely phenomenal and I want you guys to just start thinking about that and seeing or ask yourself like what can you do to make somebody else's day so many of us get caught up in this thought trap of this person or that person completely ruined my day right maybe someone cut us off on the freeway or somebody said something to us or maybe we got a crappy email at work or a call or a text or something we how many times do we say that ruined my day right well if it was that easy to ruin somebody's day wouldn't it be just as easy to make somebody's day and that's why I wanted to make a video about this tweet from J Hope showing that you can make somebody's day as well like okay just for example for example something I like to do something that I have fun with is whenever I go to the DMV like the DMV is just a place of misery right and every time I go to the DMV like I know I know a lot of the employees there aren't happy to be there either no more happy that I am to wait around all day for whatever it is so like I have a goal every time I go in there to try to make the DMV person smile or laugh right I have like a 93% success rate on this right but like it's just little simple things like think about what you could do today or even tomorrow like it's a good daily practice to see what can you do once a day to make somebody else smile right like think about that just for a second like negativity spreads right like if I have a bad day it's easy for me to snap at somebody else make their day bad then they can snap at somebody make their day bad why don't we try to reverse that thing right and say something kind of nice or check in on somebody do something nice and maybe that'll encourage them to do something nice as well you see what I'm saying so anyways like I'm gonna learn more about BTS and K-pop in general like I am just I'm fascinated by this like worldwide phenomenon so if you guys want to educate me or send me some video links or articles or whatever help me help me out help me to learn but it's absolutely amazing what BTS and J-Hope are doing just impacting people's lives on a day-to-day basis see what you can do as well today all right but anyways that's all I got for this video if you liked this video please give it a thumbs up if you're new make sure you subscribe and ring that notification bell because I make a ton of videos and a huge huge thank you to everybody supporting the channel over on patreon you're all amazing and in case you missed it all of you wonderful patrons out there make sure you go check the patreon page I just posted the answers for the last Q&A all right thanks again so so much for watching I'll see you next time