So, hello everyone. I'm here to give a brief talk on our Jupyter.cs service, which is in use in the computer science department, mainly for courses. The point of this is sort of an internal talk to let people know how Jupyter.cs works for, basically let people know how it works so that way they can start working on it and developing it. But it's not just for internally. We also plan on posting it so that way other people can learn from us. Some notes about this recording. So there's a vertical screen share and yeah vertical screen share so that what you can have the other half of the screen open with HackMD please write on there to comment. So basically as I'm talking you can both use it to take notes along with me and to mention things which you'd like for me to say or comment on mention and so on. So if you work together we can have a good final set of notes here. The talk's recorded but I'm recording it with OBS and not with Zoom so if you say something it cannot appear in the final recording unless I unmute the desktop audio which I would say if you do. So that means well you can talk but please don't because then it will be a blank area. If I happen to show personal data like student user names or something in here let me know I put a note in the Zoom chat and I can ask that out. I think there shouldn't be many of those if my preparation is correct but who knows we'll see. So with that said here is the HackMD. Can people log in and make a note if you can connect here? So should we begin? This is basically a random walk tour so at any point interrupt via HackMD and let me know what you'd like me to mention. So let's start with the user interface. Or maybe what are the components here? What's the big picture? So this is built on open source software. There's Jupyter Hub which is the main piece. Jupyter Hub uses coopsponer in order to control Kubernetes. It uses the PAM authenticator to authenticate via PAM locally on a Kubernetes pod which is connected to the Active Directory of Alto. When things run then it starts the Jupyter single user server which runs inside a Docker image with various, how do you call it? Yeah, with the software installed inside. So my focus here is not the standard open source components but what makes the Alto Jupyter Hub special. So you'll see a little bit about the Jupyter Hub and images and single user server and all these things. But that's not the main point of this talk right now. Okay, should we begin? I don't see any other comments here. So please do interrupt anytime if there's something which I need to mention. Okay, so signing in. This is Jupyter.cs.alto.v. We arrive at this login screen. We log in with Alto username and password. So when I click sign in, this is basically a PAM local authentication onto the Hub pod. Yeah, okay, there we go. So this pod is connected to Active Directory. So yeah, the image is made with the necessary secrets in there. And then each time the pod starts, it does the connection, which is really sort of magic to me. So someone else has set this up and I, well, I just hope it doesn't break. Let's see. I know, should I be saying the names of people that have done all the other work on this because if it's posted, well, you can write the name of the person that did this in the HackMD if you'd like to give credit publicly. Okay, so once we log in, there's different server options. Well, there's these template messages here, which as you can see really needs updating. We can see where this is controlled via templates. So for server options, the first four here are generic. So they are usable by everyone. After that, we see things which are visible to me because I'm an administrator and otherwise are not public. So you see there's different courses and there are the way for an instructor to spawn it or a user to spawn it. And the user spawning methods may not be public. Okay, so if we keep scrolling down, there's a test course here. And I'm going to launch this as a student. So now we're doing the normal Jupyter mechanism. So it assigns it to a pod, it starts it, it pulls the image. Let's hope the image actually maybe this might be a problem if the image has to be pulled afresh now because we've been reinstalling some of these nodes. So this might take a little while, I guess we'll just wait. So after we log in, we're in the student environment here. So what are the properties we'll see? There are user IDs and groups. There are... Okay, so one of the most interesting things about the way we've set up the Jupyter Hub is that there are real user IDs and groups in here. So basically, we'll log in and the username will be Darstar1, which is my Alto username. And the user ID, the numeric user ID will be whatever my real Alto UID is. And this is important because... Well, maybe we can talk about this some. So I see most people running Jupyter Hub in Kubernetes or really anything in Kubernetes. It always seems to be arranged as a everything runs with a fixed UID. As in everyone, all the students pods will be running as user 1000 or something. But we need to match up these pods with the Alto storage system because the file systems here, well, home is temporary, but all of these other ones here are mounted via NFS from an Alto NetApp export. And this NetApp export uses the real user names and user IDs. So it's exported to the pod using NFS v3 with sec equals sys. So that way it's a network control inside. But as a user, whenever I make a new file stored in one of these, it gets stored under my Alto UID because that's what's running inside the pod. The advantage of this is that whenever I can come to the Alto system, which is open here, let's see. Why show when we can tell? Do I need to gain it? Probably. So if we look at Jupyter U04. So this is my files. This will be the same as the notebooks directory mounted in there. And if I list it, I can see all of my Jupyter files. And yeah, so that means that both as students and instructors, we have seamless access to the data from many other many other ways. It's not just locked behind the Jupyter. And we get free things like multi-user notebook grader, which is a problem for other people. We get data storage handled by someone else as big as we need. We get quotas. We get snapshots. We get all these other amazing things. Okay. Yeah. So the home directory is temporary. So every time it restarts, this gets it's recreated inside the image. Notebooks is stored. So there are some links here from home. So these things get linked into the home directory. So there's some things that are persisted locally. Okay. Let's see. Okay. It says it started. Hopefully we will get the environment soon. HackMD. So for questions, HackMD is best. But what you just said will not end up in the recording. So please, whatever I'm talking about, just write the question in here in the actual agenda. Like, there. Maybe someone can paste this in Zoom again. Okay. So the question is coming. So while that's coming, now that this has started, I'm going to make a new terminal. And let's take a look. ID. So I see, yeah, here's my alt or user ID. Here's my notebooks directory, which as you notice is the same as we saw on the Cosh shell server. There's a question. Can you copy the data from Jupyter to AltoHome easily? So from Jupyter, there's not an easy way from Cosh here. Yeah. You basically can use any of the normal tools to copy it. Yeah. And the reason the home directories themselves aren't mounted here is security. So will the security policies allow us to mount the home directories in here? Probably not. How long is personal data persisted on J to NAS? So what I wrote in the privacy policy is it would be the same length of time as the home directory data. So once the alt accounts expire, then we would start removing the data once the AltoHome directory gets removed, which still needs implementing. Okay. Let's see. So when we look in here further, let's see. This was the test course data. We noticed that here we have access to the whole file system. So if we scroll up one, we see there's the Linux system. And I did this on purpose. So I didn't want to hide the Unix system from the students. First off, because it gets them more familiar with the students. And second off, sometimes they might need to go to things like the other course data directory. Or you might need to go to the course directory and so on for instructors. Okay. So we see there's course data, which let's look at, look at that here. This is something that is mounted in all the student pods. And the students should not have right access here. Why do I have right access? So I guess I have right access because it's by my user. Although I thought this should have been mounted read only, like at the mount level. Yeah. So there's these questions about mounting Alto home with SMB. Well, if someone wants to look at that, please do. It would be an interesting thing to try. Okay. Let's see. So what else did I say? The default working directory. So the default working directory of Jupyter is the root of the file system. And that's because Jupyter working directory is what's browsable, the default starting directory students would see it's a notebooks directory. And there's some bash magic that makes a new terminal start in the notebooks directory. That's like in the bash RC or a bash hook or something like that. Okay. Oh, let's see. Yeah. So kernels. So if we do new, we see there's the different notebooks available. And if we go to the terminal, we can probably see where those come from. Jupyter kernel spec list. So these are included in the image. And we see the kernel runs from opt conda. And we'll get to this in the image later. So this is, yeah, I'm just showing you the effective user connection. Umask. So the Umask is set. So it's not group or things are not group writable by default, except when you're an instructor, then they should be group writable. Yes. So the image, yeah, we see the Jupyter image, which the variables, this is configured via the spawner. It's like this will get to the images later. We can get things like the limits. Yeah. And these are all controlled by coop spawner at the Jupyter Hub level when things are starting. Okay. So most of the user environment is configured in this Jupyter prespawn hook. And all the software inside is configured in the image itself. So before we go to this prespawn hook, let's go to the control panel and I'll stop my server. And it takes a little while. There's no response. If we start, it still says it's still stopping. So the instructor is pretty similar, except there's a course directory also mounted in there. And the Umask is set so that things are group writable by default. Let's see. I'm going to start this as an instructor now. So let's hope this starts a little bit faster. I wonder if it's pulling again. Okay. So as some background, in notebook grader, most of the people that use it haven't figured out how to run notebook grader in a multi-user setup, like with multiple instructors. So what they will do is they will have one dedicated instructor user, basically, which everyone blogs in as. So it's actually a bit more complicated in running as a Jupyter Hub service, but still there's not like this multi-user management in there. It's basically user account sharing. So here for the instructors, it's actually shared with separate user accounts. So I made a modification to notebook grader that would write the instructor files as group writable and group writable. So that way it's reasonable to have multiple instructors log in. So there's still some different UNIX problems, such as if one user makes something that's not group writable, then other users can't modify it. But well, that needs to be solved with UNIX stuff. There's an extra file system slash course, which is mounted in there. So let's see. Core, yeah, here we go. Test course. So in this path, there's two different, this is the course data directory. Although really we call this data the course data directory, this data gets mounted as course data inside the pod and files gets mounted as course. So course is instructor data, like the student submissions and all that stuff. Course data is the shared data, like the big data, which is shared via NFS instead of copied for every student. Let's take a look. Okay, test course data. This should look familiar. This is what we saw inside Jupyter. And if we look at files, we see all these files here, which people have made. So if we did LS-L, we would probably be seeing the, we would be seeing the people that have made this. So it would not only be my user ID here, but we would see other real Alto UIDs. How do I have access to this? So, well, you will notice that my ID includes a group Jupyter test course, Jupyter test course. So it's controlled via completely normal UNIX mechanisms. So, okay, here we are again. We're, we now started this as an instructor. If we go up, we see the course data here, just like I was showing. No, the course files, which is the instructor files, course data, which is the same as the student, except the instructor should be able to write to it. If we make a new terminal and we look at my ID, well, yeah, so I'm an instructor. So that means that I get added to the test course group ID. But you notice I'm in all these other courses. So why is this? So if we look at MJHNAS Jupyter course, we see all these other things. So I'm an administrator here, which basically means I'm an instructor of every course. So I get added to all of the groups of all the other courses, and all the other courses get mounted in here. Only the courses that I'm actually a part of would be mounted in here, not others. We don't, we assume that the users could have root and wouldn't be able to access anything else. And that happens because it's not, we wouldn't mount the other stuff. So basically as an instructor, I can copy data from previous years into my current year and access things across different courses seamlessly. This is all due to the magic of NFS and UNIX groups. Okay, so there's one other interesting thing to consider, and that's the exchange directory here. So if we look, if we go to the course directory, and if we look at, well, let's go through the flow of things. So source is the origin of assignments. It gets translated to release in the instructor directory. Where is the exchange directory? So it says serve and be greater exchange test course. And here we see the way that notebook grader communicates between the different pods. There is outbound, which means outbound from the instructor to the students. And if we list this, we see the different assignments that have been released to the students. So notebook grader fetch would copy this to the student's directory, which would be notebooks, test course here. So for example, A2 got copied locally here. And then when something gets submitted back to the instructors, it gets copied to this directory. And this directory's permissions are set so that, uh, let's see. So others have execute permission so they can access things, but they don't have read permission so they can't list it. So basically other students can put a new directory in there, which is their submissions, and they can't list it to see other students submissions, which get protected with a random hash in there. And that's the way notebook grader gets submissions back. So it uses Unix permissions to keep this secure. And then it gets fetched back to the instructor pod. Okay. Uh, I don't see any other questions here. But if you want to ask questions about instructor stuff, now's a good time. Okay. Uh, oh, let's check my UMass. My UMass is 0007 now. Okay. Uh, yeah. So if you notice everything I'm saying here, it's not really specific to Jupyter or notebook grader. It's, I try to make it look like a completely normal Unix system. And that is by design. Okay. Should we start taking a look at the course management then? So, okay. Here we are on my work computer. Get a course meta. So this is where all the courses are defined. So I have recently made a demo demo YAML file. So I basically copied another course and removed the personal data from it. So we see there is, well, metadata here. There's the name, which is what we see in the spawner list. There's the user ID and group ID. So these have to come from Active Directory and get, uh, yeah. And this is used so it can create the file systems with the right user ID and group ID so that people can access it. And then there's the supervisor, which is supposed to be basically the teacher in charge. There's the contacts and there's managers. So manager is who can control the group via the domestic service. So they can do the self-service adding of other TAs to there. Let's see. There's a, we say we want a data directory. We can give it important dates, which, so these are not currently automatically used anyhow. So it looks like this would tell it that, okay, the course should become public automatically on this date. It should become private again on this date. It should be archived on this date and deleted on this date. In reality, there's no automation. It will just show us in a report what needs to be changed and what is old. Here's the actual dates of the courses. Um, this is what actually controls the course setting. So if I change this to private true, then it would no longer appear in the public list. If we did archive equals true, then it would not appear in the instructor list either. But the data would still be there and would be mountable read only in other courses. And here we see the image. So it uses the standard image, which basically meets Python, and it uses the image as of this date. So if I make a newer image, it won't automatically get updated. But until that date, if I updated the image, they'll get all the latest changes. So another option here would be to specify the exact Docker tag of the image. So it would only use that one image. This is a point that we'll be considering next week. Okay, then there's the course script. Courses.py. Let's hope this doesn't show personal data. Okay, it doesn't. I need to make this smaller. So when I run courses.py, it parses all the YAML files, and it gives us a report on everything. So it tells us what is archived, private, and public. These tags mean things like it's missing the contact, it's missing the instructor, it's missing the public date, it's missing the hide date, it's missing the archive date. So all of these old courses, we see that they didn't have good metadata being stored with them. Note to others, don't make the mistake I made and start setting up things without collecting very good metadata on it. The later courses do have the different things in it. So we can see the currently active courses are not private or anything. This course says delete here, which means that it's past the delete date, so it should be deleted now. If it says something like archive, that means it should be archive, although it's already archived. So basically what I would be doing is running this and seeing, okay, what maintenance do I need to do, and then I know to go and contact those instructors and say, okay, this course is now old, can I go and delete it for you? And hopefully they say yes. There's also things you can do like... So courses.py also does things like validates all the YAML files and validates that it has all the necessary data and so on. Python 3. So we could do... So for example, we could have it print out all the contacts of a course or supervisor. Really this was made so that it prints out the contacts and supervisors of all courses so they can be emailed and contacted. Let's see. How's it actually updated? So there's an update script here. So this basically... First it runs the check on it and then it pushes it, pushes the git repository to jupyterhubmanager.cs.ulta.py. So let's not go over the details here, but let's just say it's a little bit of a hack. So you would have to commit it to git, then you would run update which pushes it to a local git repository on jupyterhubmanager. And then it would run on jupyterhubmanager, it runs the course script again, and it runs setup and makes the missing courses and so on. Maybe let's not go into details because it doesn't really make a lot of sense, but through the scripts in here and through running locally for checking and then the remote end and checking, we can get all of the... It can make the courses. If we ssh to the jupyterhubmanager... This is where all of the files are managed. So this is the computer that has root access sec equals sys to all of the jupyterhub files. So if we need to go deleting data or changing permissions or so on, this is where we would do it. Let's see. Yeah. So we see the other different data here. There's the course directory, which is what we've seen. There's u for users, which is what we've seen. There's software, which has some shared Python files like this MyCoursesExporter and some other things that could be installed globally. There's some other... There's a shared bin directory here. We have shared data. I missed this from the file system list up above. So this is data, which is shared among every single image that's bond. So for example, there was a course from the engineering department and they wanted to share some data but didn't need the notebook grader course. So I put it here and then it's available to every student via... This is probably how it's available inside of the pod. Let's take a look. Yeah. There we go. Okay. What else is in here? There's the exchange directory. And this is what is mounted at the serve notebook grader exchange. There is admin, which has the hub data, test hub data, last login timestamps of users. If we look at hub data, this includes the Jupyter Hub SQLite database, which can be deleted and then sessions are lost but nothing else important gets lost, like the secrets and stuff like that. Oh, user and course hooks, if needed. Okay. So how is this protected? So on the auto shell servers, things like admin and exchange should not be mounted there. So that others cannot access it. At least I hope that's the case. So group management. Let's come back to here. Wonder where it's stored. So one thing that should happen whenever this processes all these YAML files, it makes another YAML file which gets copied to the domestic service. And then that is used for domestic so that way the group managers can add and remove data from there. So it has to be run and it has to be manually copied. Let's see how this is done. Oh, yeah. So here it is. So it's told to write it here. I guess I won't open this file because it will have all of the instructor usernames in there. But then we see it gets rsync to domestics and put in the right place. There could probably be a better way than manually running this. So let's look at the image next unless there's any questions. If you have questions now would be a good time to ask. Okay. So the image. Here we go. So this is a huge mess and this is what we have a hackathon on for later. But since it's Docker maybe we don't need to go in too much into here. So this repository is on GitHub. The build system is via a make file which you can look at later if needed. The make file first builds the base image which is derived from the upstream Jupyter image, the sci-pi image. So it already has some Python in there. It has the Jupyter stuff. But we upgrade and make sure all the Jupyter stuff works. And from there it builds the standard image which is Python. It builds an R image which is R and a Julia image. Maybe let's quickly look at these Docker files. So we see it derives from an upstream image. There is a clean layer script which will remove temporary files. Here we see it's pinning some versions of things. It installs some Debian packages. It installs Jupyter at a proper version. It installs even more content and pip stuff that might commonly be used. It installs the bash kernel and widgets and other stuff. It installs a specific version of Jupyter lab.  It tries to enable this for integration with Google Drive which doesn't actually work. And it updates more. Let's look at the standard. So this derives from the base image. It tries again to pin the stuff that's installed here. Here's all the stuff that installed. I tried to indicate it by course. And then some giant install commands. So first let's content install a ton of stuff, pip install stuff. Then let's install TensorFlow and Keras. Then let's install even some more stuff. And here we're upgrading Notebook Grader because I needed to upgrade it and the old version. If I updated in the base image it would have to update all the images which I didn't have time or effort to do. Even more stuff. So at the bottom we start installing stuff. Okay. So around here. These are things which needed to be installed but I couldn't add it to the above layers because it would break the existing stuff. So I have to just keep adding more layers at the bottom. What I would normally do is once a year or twice a year go and copy this from the bottom to the upper installs and then regenerate everything from scratch. But well, that's another story. Let's discuss that later. And some permission fixing. And then hooks. So these hooks get run whenever it is run. Let's look at hooks. So there's, for example, like there's before Notebook, yeah. And this handles things like making ContaCache, setting an editor, various stuff. Okay. This could be a whole other talk so maybe I won't dig too deep into here. Yeah. Yeah. Okay. Yeah, there's a question. What's the philosophy of a few big images of many smaller ones? So I don't know. It really might not be. So I think the reason they get so big is that I can't go and update them. And I have to keep adding more layers. The image for just a single course is not that big. It's quite convenient that I don't have to ask instructors every single thing they need installed. And then they'd probably keep coming back to me and say, oh, can you install this now? Can you install this now? If I give them everything, well, people are generally happy. But this is something which I hope that we will discuss in the hackathon that happens next week. It's really a good open question for me. I think if the mega image was actually maintainable and it could be regenerated from scratch, it wouldn't be that bad. The problem is it gets big and since it's used by so many people, it can't be easily regenerated. Actually, no. The size means that it can't be regenerated, which means that it keeps getting bigger because I keep adding layers. Okay. Like for example, if I ask every course, please send me an environment YAML file, which will work for your course. It sounds really great, except when you have people that don't use YAML files and don't get it right and so on. Okay. So let's go to the back end. So this is the real thing. This is where everything runs. This is the Kubernetes repository. So this repository is public, so that way others can use it, except secrets is a submodule, which is secret. There is a Docker file, which is used for Jupyter Hub itself. And this is a much easier thing to make. So it's actually a reasonable looking Docker file. But in there you saw the connection to Active Directory. Let's see. We see scripts, which is scripts like scripts which are used inside of the Hub itself. We see bin and this has shortcuts like bin create hub, which will take the hub down and up, remake hub, which will take the hub down and up, shell, which will get a shell on the hub. These are all basically wrappers around Kubernetes. So here we see it finds the Jupyter Hub pod and runs kubectl exec on it. Okay. The crazy thing is Jupyter Hub config. So this gets mounted inside of the Hub pod and this controls everything. And we see it's 800 lines here. So it's not a short thing. It sets some default images. It sets the default limits and all that stuff.  But it also contains a lot of executable code. Here we see the default profile list, authentication config, spawner config, config is boring. Here we see a file that executable code that runs Git courses. So every time that the I've seen every time the spawning page is listed, like someone goes there to spawn courses, it will refresh the courses from the YAML files, which are stored on NFS. And it will render only the courses which are available to that user. So this is how it limits it to limits it to the images that should be visible for any given users. I wonder where is this configured? Like I said, it's configured down below. Select image. There's no point in even trying to go over this code. Oh, here we go. Git profile list. So this is what handles the public, private archive, that kind of stuff. And then it gets set as a property of kubectl spawner. So all of this code gets run on every every time it gets rendered. And we see it does think like it's setting the font color and so on. Okay. And now we have the pre spawn hook. And this is the really crazy stuff. So every time a user tries to launch a particular image, it goes and will try to... Let's see. What does it do? So it configures all the different things inside of there. Like it will configure the volumes. It configures the volume mounts. It configures the notebook path, which is here. So basically all of the different properties of Kubernetes, which got set and we saw inside of the single user image, they start getting set here. Okay, we see environment getting set. This is interesting. These commands can be configured in the pre spawn hook and then it gets assembled into a shell command and used as part of the spawning process. So all of these commands can be run before the notebook runs. So I can do lightweight configurations of the image without rebuilding the image based on shell hooks. Okay. So here we see, for example, if it's a GPU node where adjusting stuff, it just goes on and on and on. We see this is if you're part of a course or if you're not part of a course. So all of this happens if you're part of the course and then there should be a hook here. If you're an instructor, do this stuff. Again, there's no point in even trying to understand this right now. You can come back and read and we can go over it together. So yeah, there's all kinds of hooks there. There's a stopping hook. There's some sort of remembering of the state. This is what removes pods which have been running for too long. So there was no way that someone should try to understand all the contents of here based on what I've said. But the point is, this is where a lot of the configuration happens. Maybe it could be rewritten, quite honestly. Okay. There's also a test environment, which someone has set up. But I've actually never used that. But it's run via this somehow. Yeah. Maybe what do you like for me to unmute and then the person who set this up can talk about it and say who you are or not comment on it if you want. Okay. I unmuted it. So you'll appear in the recording if you talk now, if you want. Okay. So there is a test environment that is currently currently have been set up, but it hasn't been really touched in a while. It's basically more or less identical copy of the current deployment, but running in a different Kubernetes namespace. Currently, it doesn't have the PAM or AD authentication. So it only uses local accounts. But the plan is to integrate the ALTO authentication using OAuth in the future. And it would basically, the idea would be that we can have a separate test environment, which we can use for testing new features or testing courses or everything like that. Because right now we have had to basically do all the testing in production, which is not very ideal. Yeah. Okay. Thanks. I'm muting the audio again. So, well, we're coming up to an hour. This has taken longer than I've hoped. I hope it wasn't that boring and repetitive. I guess we can use the HackMD for some final discussion before we go. But this is basically a tour of the user side and the key places to configure it on the other side. I hope that once you know the user side, then the configuration will make a little bit more sense. And then we can, and then you can start to understand where the configurations are. There's documentation of this in our internal wiki. Perhaps it should be improved. Well, documentation should always be improved. Well, I don't see much other discussion. So maybe I would say thanks and stop the recording. Okay. Thanks a lot. Bye.


Studying John A. God's poem, Half-Cost, let's discuss how you can analyse this poem. He repeatedly asks, explain yourself what you mean and this is an imperative sentence.  He uses the words light, shadow, sky and weather, which belong to the semantic field of nature to ask if things mix naturally in nature. Is this unnatural? In similar ways, we are triggered to wonder if the mixing of races is also unnatural if this already happens in nature. Although the tone is overall one of disgust, he does have some humorous reference. He says, England weather nearly always half-cast. Here he's talking about how the English weather is always grey, a mix of light and darkness. Bear in mind, he uses words like them till D. This means he writes phonetically. He writes exactly as the words are pronounced using what is called patois dialect. The speaker shows his anger by saying arras, which is an expletive. It's a swear word in patois.


So I always start with Yolanda Kakabatze She is president of the WWF International in Switzerland Then we have Takishi Ninami chief executive officer and representative director Lawson from Japan We have Atsu Toshi Nishida Chairman of the board Toshi for cooperation, you know all from Japan as well And we have James T. Reidy chief executive officer lipo group Indonesia a warm welcome to all of you And ladies and gentlemen, you all know the mission of the World Economic Forum Committed to improving the state of the world and We were here the last two and a half days Because of our mission for East Asia And that is committed to improve the state of East Asia And now at the time the clothing session to ask if We have something achieved and if yes, what Have we achieved and so please? imagine Next Monday morning, we are all back in office It's hard just before the weekend, but and one of your colleague will ask you Okay, now you are back from Manila What was what is your major takeaway from the 23rd World Economic on East Asia? And so I will ask a question to our ambassadors of This year our forum and we start with your lander. What was your major take away from the last two and a half days? You know that I won't give you just one takeaway. Yes She negotiates because she is the president of a WWF. She knows how to negotiate And should we use ten minutes to talk about only one major takeaway or two major takeaway and she was a porphy She an expert. She started with three major takeaways. So now maybe she's allowed to make two major takeaways your lander The most important one I think is recognizing that The problems today are completely different than the ones last week then the ones of a month ago and a year ago and Will be totally different from the ones coming next week next Monday and next year therefore that we cannot think and Close our discussions into a box We do need to be permanently renovating our way of thinking looking into new options new technologies new actors and Because the problems will be different today. We do need to involve more young people The the young people who are looking at us and how we respond and how we react to be on a path of Evolution and rethinking our responses to create their own responses. So that would be I think my my main takeaway Get them more involved is not talking about them for Is future actors that is present actors for future problems or future expressions of the problems the the second one is We need more to Shiba chairs of the boards You are an amazing man, you're an amazing individual who from your position of such an important company of the world is integrating Sectors actors dynamics Technologies options and that is fantastic. You you have given me a lesson and I only think that We need more like you In the in the third I have to say the third is thank you to the Philippines For sharing with us the lessons that they have learned especially in this last year It has been a very difficult period for the Philippines But also a wonderful moment to demonstrate to us the rest of the world that you can do it that you can bring sectors together that Governance is absolutely important that the dynamics cannot be Improvised if there is not a Solid ground on which to build a response and the response to the crisis in in the Philippines has given us a fantastic lesson and and I hope we can Replicate that or imitate that dynamic in in our own sites of work. Thank you very much. You're not. Thank you very much Take Jinny Nami Thank you, Phillip. I Like to say thank you to the friends of Philippines This time I felt the energy and Hospitality of the Philippines a lot. That was a big big Impressive thing I experienced at this time. Thank you very much Not only the economic growth in this area Now what is my major take away? I found as a mr. Reddy mentioned This region has been transforming into the second stage of the economic growth But to make it successful definitely this region has to go through the assignment challenges and first of all I think how to deal with the fair distribution of wealth and and this leads to the Eventually emerging Middle-class emerging middle-class is a very important to have a sustainable growth of this region and definitely I believe This emerging middle class will play a key role To lead the this region to be sustainable in terms of economic growth That deals with the lots of social issues Education we discussed in the Equitable employment that is very important and the health care to the people People is asset. How do you let them feel we are you know having the equitable? Growth so I think health care is very important and I think I Think of this region should have the structural reform. I Think of this region needs more entrepreneurs To have more entrepreneurs definitely the government has to implement the structural reform so with the idea regulation and I Think a second the challenge that I would address is Geographical challenge. I mean issue whether you like or not this happens and To to sustain Peace and the solidarity. I mean that peace and stability definitely in this region Solidarity and Collaboration of ASEAN countries has become increasing more important. I found that in The third challenge of this region is how to deal with the natural disasters If because of the climate change, I think we have to be more Where are aware of it's it's the the resilience the resilience is very important But how to deal with the natural disasters is we have to collaborate Making use of our expertise. I mean our know-how our experience our technology to challenge this this I mean the natural disasters and Especially we want to bring in a more NPO energy to this region to tackle these issues. I am sure that This region and together with the rest of the world We'll be able to go through this these challenges and we'll be able to Have the sustainable growth but people is The the most important at that we have to think about Thank you for much for that Mr. Nishida I Would like to express a few words about my impression of the meeting and what I couldn't tell As my message during sessions because of time limitation Over two days this meeting has offered talented people mainly from East Asian countries and from many sectors of business government and academia the opportunity to discuss and debate and offer food for thought on the theme of Liberaging growth for equitable growth. I Am pretty fortunate Enough to have participated in several fascinating sessions With prominent opinion leaders such as the session of climate smart growth and on a range of topics a climate Resilient future and innovation among them As I mentioned in the session We have to prepare for natural disasters and reduce greenhouse gases by deploying concept of smart frugal city For future river rural cities soft power to Enlighten people as to the importance of the environment Could become of vital importance In addition to the hard power That provides cities with social infrastructure We live in an age of increasing social political and economic uncertainty in a global hyper-connected economy driven by exchanges of information Capital and human resources as a consequence the impact of natural disasters and economic crisis Can surpass over us at a faster more destructive pace than ever before to achieve sustainable development incessantly creating innovation and Continuously increasing productivity are and will remain vital Beyond this two new capabilities might be necessary detection and prevention of anticipated risk and quick judgment and the implementation of appropriate damage control in the event of the appearance of unanticipated risk along with the capability to recover from a crisis with agility and flexibility as if That were not enough Companies today must also successfully address the issue of sustainability In order for the entire world to enjoy long-term economic growth I think this meeting has allowed us to define some new directions and to develop new solutions for achieving sustainable and moreover Risk resilient East Asia. I'm sure that it has been a fruitful meeting that have that has provided us with some degree of enlightenment as to how the world can realize smart flu girl so Let me close On a positive note with confidence that The 23rd World Economic Forum on East Asia Provided great opportunities for leaders from industry academia and government to cooperate and Interact with each other as a human cloud a Vital network to stimulate the discussion and cultivate insight among participants and to further Achieve a resilient and the sustainable prosperity. Thank you. Thank you very much for that Mr. I.D The world GDP today is about 60 trillion dollars That's the amount of business that's being done a year over the next 30 years that GDP is going to be 250 trillion dollars and Wealth is about two to three times the GDP growth So that means there'll be another 500 to 700 trillion of new wealth to be created over the next 30 years And I think this is quite exciting because there are plenty of opportunities But I think what comes out During this forum is the whole issue of inclusiveness It is a big issue It is going to be very difficult. It is not easy We see all the indications In terms of the Gini ratio in some of the developing countries And in the last two to three years actually have deteriorated That reflects the gaps that we have income gaps wealth gaps Geographical gaps infrastructure gaps We have all those issues that are in front of us at the same time if you look at the sectoral Agriculture is huge in ASEAN and yet in this area you do not have the inclusiveness at the farmers level They're not there yet so You know you go on and on and on again unemployment, especially in the among the youth so On the one hand, we live in an exciting world. We all have this opportunity over the next 30 years Yet on the other hand the issue of inclusiveness. It's a real issue and May and danger all the progress that we have made so I think this forum has been successful in not in the sense that Specific actions might have been done because if that's the case it would have been very limited But changing the mindsets because actions is determined by belief system By value system by our thinking so together during this forum. I see that People are talking about it. So you cannot leave this forum without getting that impression that hey, you know You know, we really have an issue So I think the belief system must be changed So the belief system will determine what is of value that we must do together And I think we in it together if there's one take away is to go back and say that each one of us will do something Continue on with our with our with our business of of growing economies We do have tensions. We do have tensions in Asia today. We do have nationalism But each time when we see problems I tell my people that focus on the job that we are doing and it is a private sector That needs to rise up to get involved in education to get involved in health care at the at the core of all this would be Developing the human capital the human talent. So with that, I think I think we've achieved our our goal and On behalf of all the co-chair we want to thank you for for coming out here We hope that all of you will become very active in the future and the next time we meet a lot of actions That would have been done in your own companies in your own communities as well. Thank you So thank you, Mr Righty, so I think we saw the the whole broadband of all the issues we tried to raise in the two and a half Days this week and we start with solidarity with the people education health care agriculture geopolitical situation and Flexibility agility. So thank you very much for that. But maybe last question to the whole podium Do you miss something because you you you you mentioned that is and we realized the same while I will run up for this session That the issues change is very fast In terms of agility flexibility. So do you miss some issue? We could raise maybe the next region somewhat on this Asia Missing missing in terms of the discussion of this forum. Definitely. Yes. I don't think there is enough emphasis on the Recognizing the value of the natural capital on on which we depend and on which every single Production system depends on There is nothing from technology to food to any sort of good That doesn't depend on a natural resource and that is not being valued enough It is an externality that it's not considered Nor in the price nor in the Evaluation of the process of development and I do think that unless we get that right unless that capital is paired in terms of Importance in terms of value in terms of relevance of any development system We won't be able to tackle the problem at the root Mm-hmm Okay, so maybe next time much more about resources and the value of resources But I think we talked about in the question of agricultural food security, but not with this focus You mentioned but maybe for the next so we can have some takeaways for the organization. I'd love to see that great Okay, ladies matter because we are very short in time so as you know the the way to To improve the state of the world of the World Economic Forum is we tried to create some Community of interest that means interest on East Asia and I think in this question. We were very successful because we have had a similar successful world economic Forum on Africa two weeks ago and look only under social network activities It was very high because of all the events we have had in Africa But on the first day of this event. We were much stronger in all the social network activities than in Africa and Latin America together so that shows your engagement in the social network Particularly the younger generation you mentioned it here in other region the second is after having a community of interest To create a community of purpose that means we promise together that we want to commit We are committed to prove the state of East Asia So to motivate the people not only the participants, but the whole people at at the end and Mr. Righty said it to create a community of actions So that is my last call to you on Next Monday in your office That is not only a gathering of business leader public figure science and younger generation that is community to have some actions and So that is not the end of two and a half fruitful discussion and meeting That is the beginning of the next 12 months hard work on all the actions we committed in the last Two and a half days. So something missed as We know from your lander, but I have an idea what missed as well That is a huge Very huge. Thank you to our four Ambassadors for this year's World Economic Forum in East Asia. Thank you to our four co-chairs for an outstanding job. Well done Thank you. Thank you very much And now ladies and gentlemen, I can hand over to Sushant Sushant is as you know our head of East Asia in the World Economic Forum and you will now make the closing remarks for the World Economic Forum and let me say before That is his last World Economic Forum because he will leave the World Economic Forum So a big hand at the beginning for Sushant Sushant. It's your lecture and I never leave in spirit I will always be there your heart will stay Ladies and gentlemen, these have been three days of invigorating discussions developing action plans setting the priorities for making a difference and We've been serving our commitment to improve the state of the world and I would like to describe our sense of purpose here in one short quote of Harold Kushner What cannot be achieved in one lifetime will happen when one lifetime is joined together This year's East Asia meeting reflected the many connections we have But also the many connections we need to create stronger communities of purpose To ensure that there is economic growth with a purpose for a future of equitable progress as They say in the Philippines. They don't only say that it's more fun in the Philippines They also say and I hope you will forgive my Tagalog pronunciation Valang Mahiratna Gawapa Dinansa Thiaga Nothing is hard to do if you pursue it with through perseverance and the success of this year's meeting is because of a lot of hard work and perseverance and That's why it's the moment for me to extend a very strong vote of thanks to All of the speakers in the program The government of the Philippines in particular the office of president Aquino Secretary Purissima secretary Domingo and your respective departments Undersecretary and treasurer de Leon I'd also like to recognize all of my colleagues for the hard work and commitment You have shown after an intense diverse from the run-up to this meeting and in particular two people if I may a Joach who is a Gentleman and diplomat by every definition and to Clara whose heart can't be more golden Than it is I'd also like to thank our partners at publicist live and the very gracious stuff of the Shangri-La hotel here So now I'd like to wish you all a very safe journey home And we are looking very much forward to seeing you all next year at the 2015 World Economic Forum on East Asia in Indonesia. Thank you


In our previous lecture, we discussed about the various conservation principles and let us briefly recapitulate what we discussed. So, we started with the Reynolds transport theorem. Then I mean we first derived the Reynolds transport theorem. I am just recapitulating what we have done. So, we will not get into the details. So, in the Reynolds transport theorem what we essentially did is we expressed the change in the system in terms of change in the control volume. We applied the Reynolds transport theorem to the principle of conservation of mass that gave rise to the continuity equation. Then we started considering the Reynolds transport theorem for momentum conservation and typically linear momentum conservation. So, we have not entered into the linear momentum conservation as yet but we tried to basically express various forces acting on the control volume. So, we tried to express the forces in terms of the surface force and the body force. So, we define what is the traction vector and we express the traction vector in terms of the various stress tensor components by using the Cauchy's theorem. So, that is what we did and we will take it up from there. So, it is important to understand that we are going to apply the conservation of linear momentum by expressing the rate of change of linear momentum for the system by relating that for the system with that for the control volume. Once we do that question remains that what happens with the angular momentum because when we write the equations of conservation very common equation that we write is equation of linear momentum conservation where does or where goes the consideration for angular momentum conservation. So, we will consider that in a moment. So, if you look here you will see that we are considering a rectangular element in the rectangular element the dimensions along x and y are delta x and delta y and what we are trying to see is a basically rotation of a 2 dimensional element. So, the 2 dimensional element is in the x y plane and we are interested to characterize the rotation of this element with respect to the z axis. So, when we want to do that we will express various forces acting on the element. So, what are the forces acting on the element? The forces acting on the element are surface forces and body forces. This is not a complete free body diagram we have not shown the body force simply because we want to find out the moment of all forces with respect to the centre of mass of this element and because I mean the body force will pass to the centre of mass in this particular case it does not have any net moment with respect to the centre of mass. So, therefore we are if we consider an axis a centroidal axis which is basically coincident with the centre of mass in this case because it is considered to be a homogeneous body. So, this may be considered as an element of fluid or an element of solid. So far we have not distinguished between fluid and solid. So, let us try to identify various surface forces we have already discussed that the body force has no contribution towards creating a net moment with respect to the centroidal axis but surface forces will have. So, what are the surface forces? So, if you consider the right surface for example you have a normal stress which is tau 11 the first index just for recapitulation first index is the direction normal of the surface. So, tau 11 here means that the direction normal of the surface is 1 that is x 1 direction or x direction and the second index 1 indicates that the force itself is along x 1 direction. So, this is tau 11 is force per unit area. So, the total force is tau 11 times the area area is delta y times the unit width along the z axis. So, tau 11 into delta y into 1 similarly you have the shear stress which is tau 12 the first index 1 for the direction normal along x 1 the second index 2 for the force itself being directed sorry I will put the cursor properly the force index force itself being directed along the x 2 direction. So, that makes it tau 12. So, tau 12 into delta y. So, similarly on the opposite phase you will see similar expressions like tau 11, tau 12 only they are all in the negative x 1 and negative x 2 direction. The reason is that the outward normal to the left phase is actually minus x 1 not plus x 1. So, similarly we consider the upper phase upper phase the normal stress is tau 22 and the shear component of stress is tau 21 and the lower phase the normal component is tau 22 and the shear is tau 21 same thing but their positive senses are just opposite because their direction normal 1 is positive x 2 and another is negative x 2. So, now we are interested to know what is the net moment because of with respect to the centroidal axis of the element. So, the net moment usually if you see here the moment is contributed by the forces tau 12 into delta y and tau 12 into delta y they are acting in the anti-parallel direction. So, they are from giving rise to a couple moment. So, the couple moment is given by tau 12 into delta y times the distance between these 2 forces that is the couple arm that is delta x. So, tau 12 into delta y into delta x and this is a anticlockwise moment. So, we consider the anticlockwise moment to be positive then the tau 21 into delta x on the upper phase and tau 21 into delta x in the negative x direction in the lower phase that will form another couple moment. So, that is tau 21 into delta x times the distance between these 2 forces that is delta y. So, this is acting in the clockwise direction because this is acting in the clockwise direction it is negative. So, minus tau 21 into delta x into delta y. So, this is the net couple moment the normal stresses tau 11 tau 22 these all these forces due to these stresses will pass through the centroidal axis and therefore will not give rise to any couple moment. So, net couple moment is the moment of inertia with respect to the same centroidal axis times the angular acceleration. So, the moment of inertia is proportional to the mass which is rho into delta x into delta y that is the into 1 1 is the width that is the mass into delta x square plus delta y square into some constant that constant for a rectangular element is 1 by 12. But I mean let us not so much bother about the constant the some constant say k into delta x square plus delta y square times the angular acceleration alpha. Now, if you take the limit as delta x delta y tends to 0 see you look at this expression carefully in both sides if delta x delta y tends to 0 delta x into delta y will be cancelled because they are tending to 0 they are not equal to 0. So, you can cancel that from both sides and then in addition in the right hand side you can substitute delta x and delta y both as tending to 0 in the limit. So, you will get tau 12 equal to tau 21. So, we can generalize that by considering all possible rotations and write tau ij is equal to tau ji. So, we write this expression not explicitly in the equation of motion that we usually describe but we write it implicitly because in the Cauchy's theorem when we write t is equal to tau i tau ji into nj or tau ji into eta j if you consider the previous slide. So, t is equal to tau ji into eta j this is what we had derived in the previous lecture. Now, we will substitute in place of tau ji we will write tau ij. So, we will write t with the ith component of t basically is equal to tau ij into eta j remember that because j is a repeated variable there is a summation over j from j is equal to 1 2 3. So, eta 1 is the x component of the unit normal vector of the surface eta 2 is the y component and eta 3 is the z component. So, to summarize the contribution of angular momentum we are not writing an explicit separate equation for angular momentum in terms of differential equation but in the differential equation of linear momentum we are going to substitute tau ij equal to tau ji that is where we are incorporating the consideration for angular momentum. Now, a very important question is tau ji equal to tau ij always valid. Now, this is a very critical question because see while deriving this tau ij equal to tau ji we considered a body force but no body couple. So, no there is we even if we consider a body force the body force will not give rise to a net moment with respect to the centroidal axis but if you have a body couple that is a some couple which is acting over the entire volume of the body then that will give rise to a moment a couple moment and that moment should add to this. Therefore, in presence of a body couple you will not have tau ij is equal to tau ji but normally we write tau ij equal to tau ji for fluids the reason is fluids will normally not sustain body couples but if fluids contain particular type of matters like if the fluids contain engulfed particles which by virtue of their own rotation can introduce body couple in the fluid then it is possible that the fluid can fluid the equation of motion for the fluid has to be written by taking the body couple into account and that kind of fluid is there in the in the in the study of fluid mechanics and that type of fluid one such example is micro polar fluid. So, we will not be discussing about micro polar fluids in details because I mean we do not have enough scope in this fundamental course to talk about that but these are special types of fluids you know which can sustain couple body couples. So, it is possible that for such a fluid you do not have tau ij is equal to tau ji and you write separate differential equations for angular momentum conservation just like we write differential equations for linear momentum conservation we need to write separate differential equations for angular momentum conservation. Now, micro polar fluids are very much important in the context of microfluidics research because there are certain examples when micro polar fluids are used to model some biological fluids like for example there are instances when micro polar fluids have been used to model blood and you know biological fluids are very important in microfluidic applications. Therefore, I mean we cannot rule out those possibilities where you will have tau ij is not equal to tau ji but if the fluid is not sustaining any body couple it is true that tau ij is equal to tau ji and we will consider that kind of example for the remaining part of this course. Now, maybe for little bit of the remaining part of the exercise we will go to the board and do it because some of the algebra is little bit involved and that is not worked out in details in the slides. So, what we will do is that as I told you earlier that we will like switch over from the board to the slide whenever necessary and for some detail working out we will use the board rather than the slide. So, let us say that so what formalism we have come across is that we have surface force, we have body force. The surface force we are writing in terms of what? So, the other ith component of the surface force what we are doing if we have a control volume like this you consider a small area dA, the surface force per unit area is ti along the ith direction and that you multiply with dA and integrate this over the entire control surface. So, now this ti what we can write? We can write as the Cauchy's theorem gives it tau ji into eta j but from angular momentum conservation since tau ji equal to tau ij we can write this as tau ij eta j dA. Now we will try to express this in terms of dot product of 2 vectors why we are interested to express this in terms of dot product of 2 vectors is because we can then express it in terms of a volume integral by using the divergence theorem that is what is our motivation. See I will try to give you a big picture in all the derivations using Reynolds transport theorem we have some surface integrals and some volume integrals. You will find that the terms in the Reynolds transport theorem in general forget about the complexity at the end it will be either surface integral or volume integral. Now to derive the differential equation from the integral form what we do we convert the surface integral into volume integral by using the divergence theorem. So, the first requirement is express the surface integral in terms of a dot product. So, that we will be in a position to convert it into volume integral then all terms will be converted into volume integral and you will get integral of something into dv equal to 0 because that dv the choice of the control volume is arbitrary. So, that something integral of which is 0 that something is 0 that will give rise to the differential equation. So, that is the basic philosophy by which you derive the differential form of the conservation equation from the integral form of the conservation equation. So, we will be expressing this in terms of what we will be expressing this in terms of a dot product. So, what we do is that see let us maybe use a different color to highlight this. So, what this is? So, this is tau i1 eta 1 plus tau i2 eta 2 plus tau i3 eta 3 right. So, that expression this one we can write tau i1 into i cap plus tau i2 into j cap plus tau i3 into k cap dot eta 1 i cap plus eta 2 j cap plus eta 3 k cap where ijk are unit vectors along x, y, z. So, what we do out of here? We you can see that this is essentially a vector right. It has a 3 components tau i1 tau i2 tau i3 as a some numbers scalar components. So, let us give it this vector a name tau i this is just a name that we give often in the books in some books this is called as stress vector just a name given. So, and this is what? This is the unit vector eta with 3 components. So, this integral is nothing but integral of what tau i dot eta dA. So, this is nothing but divergence of tau i dV integral is over what? The volume that bounds the control surface the volume rather the control surface is the surface that bounds the control volume. So, this is the control volume. So, we have got the surface force the body force. So, the surface force we have written in terms of what? The surface force we have written in terms of a volume integral the body force anyway is normally written in terms of the volume integral. So, the body force if Bi is the body force per unit volume along i. So, what is Bi? Small Bi is the body force per unit volume along i. So, if you just multiply it with dV and integrate it over the control volume then this is the surface force. So, by these 2 we have represented the surface force and the body force. So, we have represented the force in the Reynolds transport theorem for linear momentum conservation. Let us recollect. So, maybe let us go through the slides. So, that we can go a little bit quickly because we have already represented the forces the remaining part is trivial. So, if you look here. So, the resultant force acting on the control volume we have just shown in the board how to do the Reynolds how to find out the resultant force acting on the control volume. So, the resultant force now the right hand side the right hand side is like this is the change within the control volume the first term and this is the outflow-inflow term. So, here again it was the surface integral or area integral we have converted it into volume integral. So, that is how this the last term in the right hand side is divergence of rho ui into v what is ui? ui is the ith component of the velocity v v is the velocity vector it is ith component is ui. So, you have divergence of rho ui v dv. So, how has this term come let us quickly look into the board and figure out that how this how this particular term has come let us switch over to the board. So, you have this particular term is equal to what rho ui is small n that is capital N is m into ui per unit mass is ui this is the last term outflow-inflow term. This v is v relative but we have considered the control volume to be stationary. So, that the relative velocity is same as the absolute velocity. So, here the vector field f is nothing but rho ui into v. So, this for the control surface is as good as integral of divergence of rho ui v dv. So, that is very straight forward this is using the divergence theorem. Let us go get back to the slides. So, as you see here that so the right hand side we have written in terms of the volume integral left hand side is also written in terms of the volume integral because both the forces are expressed in terms of the volume integral. So, the forces one of the forces so one of the forces this is what is written in the right hand side of this equation is actually the left hand side just we have switched the right hand side and the left hand side. So, this is the surface force term del dot tau i that is what we worked out in the board just now. This is the surface force term and this is bi is the body force term. So, everything this term plus this term minus this terms into dv integral of that is 0 because all the terms we have expressed in terms of the volume integral. So, in the volume integral individual terms will be appearing like this is the unsteady term within the changing within the control volume. This is the outflow minus inflow term this is the surface force term and this is the body force term. So, all these terms together multiplied by dv integrated over the control volume is 0. Now, since the choice of the control volume is arbitrary we can write the corresponding differential form like this. Now, we have expressed the divergence in terms of the index notation to write the equation in terms of the index i and j. So, again I will go to the board to explain that let us go to the board to explain that just for those who are like little bit out of touch with this nabla operator. So, this is i del del x plus j del del y plus k del del z.   So, the dot product of these 2. So, what is this del f 1 del x 1 plus del f 2 del x 2 plus del f 3 del x 3. So, here you can see that there is a summation. So, you can write this as del f j del x j I mean this could be instead of j k l m n whatever does not matter because it is the repeated index. So, there is a summation over that. So, when you write del dot tau i. So, you can write this as del tau i j del x j just tau i is like f. Similarly, when you write this expression del dot rho u i v this v has components what this v has components u with a subscript we cannot use the subscript i again because that has already been used to represent the component along i. So, we can use the some other subscript j. So, this is as good as. So, u j is the component of this velocity v. So, this is as good as del del x j of rho u i u j. So, with this sort of notation let us get back to the slides. So, we can see that these two terms one is del del x j of rho u i u j and this term del tau i j del x j. So, we have represented all the terms. Now, I mean can you tell I mean what are the restrictions of this equation like I mean this I always tell in all classes that I teach that is it is important to know the equations which you need which you require to solve problems and we will solve problems using these equations. But it is more important to know what are the restrictions under which or assumptions under which those equations are used. So, if you recall that when we derived starting from the Reynolds transport theorem we made two important assumptions that the control volume is stationary and the control volume is non deformable. But you can see later on that if the control volume was not stationary and if the control volume is non deformable that will what effectively it will do it will just give rise to some extra forcing terms. For example, if the control volume is not stationary if the control volume itself is accelerating or rotating we will talk about the rotating control volume in the context of microfluidics the lab on a CD that you have the device a rotating device in which you have microfluidic channels. So, a rotating control volume is a very practical example that we will consider in microfluidics and then we will revisit these equations. You will see that for those cases what you essentially require is basically you have to account for some pseudo forces which you experience in the accelerating reference frame those are so called inertia forces. So, that will give rise to extra forces in the forcing term. So, if you have a deformable control volume and if you have a accelerating control volume all that will boil down to some modification of the force term you will have additional force terms. But if you take all those forces into consideration then this equation is very generic it does not have any restriction provided that whatever is the additional force to take care of the special nature of the control volume that you take care of by modifying this bi term. If you do that then this is pretty general and this should be true for all fluids. So, this is a very important equation because here we get an equation with which we can start as an equation of motion for all fluids does not matter whether it is a special type of fluid that will satisfy certain law or it is some other special type of fluid that will satisfy a different law. Now before proceeding further we will look into the equation try to see that if we are solving this equation then what are the number of equations and the number of unknowns. So, if you look at this equation so let us note down the number of equations and the number of unknowns may be let us do that in the board. So what are the equations that we have derived so far first the continuity equation. So, let us write that this is the continuity equation the momentum equation also known as the Navier or the Cauchy equation this equation Navier equation or Cauchy momentum equation I mean again like these equations are given such names to honour the famous scientist or mathematicians who have contributed very significantly towards the development of the modern fluid mechanics. Now let us look into the number of equations and number of unknowns. So, let us list in general rho may be a variable so you can consider rho as a variable. Now you can have a special case when rho is not a variable so but that special case we will consider later on but we consider the general case when rho can be a variable then u1, u2, u3 the velocity components and the tau ij's how many tau ij's are unknown see ideally i is from 1 to 3 and j is from 1 to 3 there are 9 components but because tau ij is equal to tau ji you have basically 6 unknowns. So, this is a symmetric tensor with tau ij is equal to tau ji so there are 6 such so 6 this is 1 these are 3 so in totality you have 10 so you have 10 unknowns how many independent equations you have this is one equation and then 3 components this is just the ith component so i equal to 1 i equal to 2 and i equal to 3 so 3 components so 3 equations here and 1 equation here so 4 equations or 4 independent equations with 10 unknowns so it is an enclosed system of equations and unknowns you have to match the equations with the unknowns that means you require a closer model that means you require a sort of modeling a mathematical paradigm that will invoke more equations that relate some of these may be tau ij with some of these. Now question is with what tau ij is related that is where now you have to appeal to the special case of a fluid when you consider a fluid tau ij is dependent on what? See a great distinction between a fluid and a solid though I must give you a caution that there are very weak distinctions between fluid and a solid for some substances which are partly fluidic and partly solidic type of behaviour so what I am giving you is not a strict definition of what should be the characteristic of a fluid or what should be the characteristic of a solid but in general think of some limiting cases if you think of a elastic solid in elastic solid the stress is related to strain right and we know that the stress within proportional limit the stress is linearly proportional to the strain right it is not within elastic limits because elastic limits may be beyond the limit of linear proportionality there can be non-linear elastic behaviour so it is better to say within proportional limits you have stress is proportional to strain right so that is the Hooke's law. In general stress is related to strain it may be linearly proportional it may be non-linear whatever for fluids if you want to relate stress with strain the problem is that fluids are what fluids are continuously deforming even the under the action of a very small shear stress so fluids can be non-deforming or under rest only when it is subjected to a pure normal stress and that pure normal stress that in that situation that pure normal stress can be described by a hydrostatic state of stress expressed in terms of the pressure of the fluid but if the fluid is continuously deforming then what happens if the fluid is continuously deforming and if you relate the stress with the strain then the strain will be tending to infinity as you allow infinite time so a time factor will come into the picture but in reality because the fluid is continuously deforming it is not the strain itself that is important but the rate of strain that is important that is how fast or how slow the fluid is getting strained or the fluid is getting deformed so for fluids normally you relate stress with the rate of strain or rate of deformation so when we write tau ij this tau ij we are relating to what this tau ij we are relating to one situation where the stress in the limit boils down to the hydrostatic condition that even if the fluid is at rest some stress is shown if the fluid is at rest what stress appears that is the normal stress because of pressure so we represent that I will explain how why it is represented like that first this delta ij this delta ij is called as Kronecker delta I have not yet written the full tau ij expression so please keep some space for writing that this is Kronecker delta so delta ij is equal to 1 if j is equal to i and is equal to 0 otherwise maybe it is not capturing the frame so I will write a little bit on the other side so delta ij is equal to 1 if j is equal to i and is equal to 0 otherwise so you can see that tau ij when is it normal stress and when it is is it shear stress it is normal stress only when j is equal to i and then only it will be minus p and if j is not equal to i that is shear stress pressure cannot give rise to a shear component of stress pressure can give rise to only normal component of stress and why minus minus is because the positive normal component of stress is by sin convention considered as tensile whereas pressure by definition pressure means it is acting compressively so that is what is pressure so minus p delta ij this is the hydrostatic component that means if the fluid is at rest this is what is the component of stress that is acting one very important point is there is a distinction between something called as mechanical pressure and something called as thermodynamic pressure so here we are trying to express this through thermodynamic pressure we will see when thermodynamic pressure is equal to the mechanical pressure the thermodynamic pressure is the pressure that will satisfy the thermodynamic equation of state for example for an ideal gas it is pb equal to nrt that p we are talking about as thermodynamic pressure whereas mechanical pressure is simply a manifestation of the average of the normal component of stress negative average of the negative of the average of the normal components of stress in the 3 directions so tau minus of tau 1 1 plus tau 2 2 plus tau 3 3 by 3 so this is the hydrostatic but very importantly even if the fluid is under dynamic condition this is acting but there is something beyond this that is acting when the fluid is under dynamic condition so that is called as tau ij deviatoric so the deviatoric component of stress is acting when the fluid is under deformation when the fluid is under motion under motion fluid under motion means fluid under continuous deformation now what will be the relationship between tau ij deviatoric and the rate of deformation or the rate of strain see this is the part of the stress that is responsible for deformation therefore for fluid this must be related to the rate of deformation now the rate of deformation if you if you recall the kinematics of fluid flow you can recall that the rates the deformation the linear deformation angular deformation volumetric deformation all those are expressed in terms of some gradient of velocity right the linear strain the angular strain the volumetric strain all these are expressed as collection of terms with some gradient of velocity so the velocity gradient is an implicit indicator of the deformation but we have to isolate a deformation from rigid body motion because rigid body motion is also represented by these types of terms right so to do that we can write this as half of see this is nothing but very trivial we can write as half of a plus b plus a minus b right so here this is what is a and this is what is b you can look into the special features of this this term remains the same if you swap i and j right the first term which I have shown by this curly bracket this term remains the same if you swap i and j therefore this is the symmetric tensor right on the other hand the next term it will become minus of this if you swap i and j so that is a skew symmetric tensor or an anti symmetric tensor so this is something which is very obvious because every tensor can be written as a sum of a symmetric and a skew symmetric tensor just like in matrix algebra you have learnt that every matrix can be written as a sum of a symmetric and a skew symmetric matrix and you have to remember that matrices are nothing but some systematic ways of representing tensors of say a 3x3 matrix is a systematic way of representing a second order tensor so matrix algebra will follow very close to the tensor analysis so with this understanding now let us try to look into the physics of these terms so what this term relates to this term with a half at including a half I mean you forget about the half this del ui del xj plus del uj del xi is an indicator of the deformation if i is not equal to j it talks about angular deformation if i is equal to j it talks about linear deformation so this is deformation. So remember that the deformation can be both linear and angular many times we have the perception that deformation means it has to be angular deformation not really deformation could be related to both angular deformation as well as linear deformation and this is what and this is related to what this is related to rotation of the fluid so the rotation of the fluid you relate to what the rotation of the fluid you relate to what you do not relate the rotation of the fluid with the stress because rotation is a rigid body type of behavior. A rigid body will not be subjected to stress, it is a deformable body that is subjected to stress. So rotation is not something about which we will bother for the time being. So tau ij will be related to deformation. So when we say that it will be related to deformation, the deformation, how many indices does it require? So if you want to represent this term, let us call it eij. So eij is half of del ui del xj plus del uj del xi. Maybe I will write again in a separate place because the computer monitor is blocking it. So eij is equal to half of del ui del xj plus del uj del xi. So now what we can see that tau ij is a second order tensor. It is related to another second order tensor which is the deformation tensor and a second order tensor should now be expressed as a function of another second order tensor basically. So one second order tensor is the stress. It should be expressed as a function of the rate of deformation tensor which is a second order tensor. Now question is how they are related? There can be any arbitrary relationship between the stress and the deformation. But the stress and the deformation may be also mapped linearly. So the linear relationship between the stress and the deformation exists for some special types of fluids which are called as Newtonian fluids. So for Newtonian fluids the stress is linearly related to the rate of deformation which we simply call as deformation for fluid because for fluid by deformation we always mean the rate. So stress is related to the rate of deformation for fluids for special types of fluids called as Newtonian fluids the stress is linearly related to the rate of deformation. So there must be a linear transformation that maps the stress with the rate of deformation. So what maps the stress with the rate of deformation in terms of tensor theory it is a transformation it is a mapping that maps a second order tensor on to a second order tensor. We have earlier seen through Cauchy's theorem that a second order tensor is such which maps a vector on to a vector like the if you recall that the Cauchy's theorem when you couple it with the angular momentum conservation principle it is originally tau ji but if you consider tau ij equal to tau ji it becomes this. So you will get tau 11, tau 12, tau 13, eta 1, eta 2, eta 3, tau 21, tau 22, tau 23, this is T1, T2, T3 okay. So this is just the matrix representation of the Cauchy's theorem nothing very special. See the power of writing in the index notation is that such a big thing we could condense in the small expression that is the power of writing it in the index notation. So you can see that this is nothing but the stress tensor. What it has done? It has effectively mapped this vector on to another vector, mapped the normal vector to the traction vector. It is a linear transformation that has mapped the normal vector to the traction vector. So it is a second order tensor that has mapped a vector on to a vector. Vector is a first order tensor. Similarly you now require a second order tensor instead of this now you have tau ij related to the deformation on this side there must be a mapping that maps this second order tensor. This is again a second order tensor. This is also a second order tensor. There must be something that maps the second order tensor on to a second order tensor that is nothing but a fourth order tensor. Just like a second order tensor maps a vector on to a vector, a fourth order tensor maps a second order tensor on to a second order tensor. So we can write how many indices we will require for a fourth order tensor, we will require 4 indices. For a second order tensor, we require 2 indices i and j. So for a fourth order tensor, we require 4 indices. So tau ij, we can write a fourth order tensor Cijkl into Ekl, where we have defined what is E. So this is the fourth order tensor. This is the generalized Newton's law of viscosity. But the problem is that this is too cumbersome to be used for solving a practical problem in fluid mechanics. The reason being that how many such constants you will require, the i will be from 1 to 3, j will be from 1 to 3, k will be from 1 to 3, l will be from 1 to 3. So 3 into 3 into 3 into 3 total 81 constants. Of course, you can immediately reduce those 81 constants to 36 constants by using the symmetry that is tau ij is equal to tau ji. And even those are very large number of constants. So you remember that in practical examples like when we deal with water or air, we do not require 36 or 81 constants to specify the property of water or air. That means things can be boiled down to something which is somewhat more simplistic than this by appealing to some special considerations. What are those special considerations? Special considerations are isotropic fluid and homogeneous fluid. We have already considered this as a Newtonian fluid. So Newtonian fluid is a fluid that will obey the Newtonian's law of viscosity. So if we have isotropic homogeneous and Newtonian fluid, we will be in a position to show that this 81 number of constants will boil down to 2 effective constants, 2 material constants, 2 properties of the fluid, 2 independent properties of the fluid. So briefly what is isotropy? Isotropy means that it is direction independent. That means if you have a fixed set of coordinate axis to represent a particular property, then if you have a rotation of the coordinate axis, so that the orientation is changed, you will get, you will still have the same representation. The representation does not depend on the rotation of the coordinate axis. Homogeneous means it is spatially uniform. That is the property does not vary as you go from spatially one position to another. So you can use one particular material property for the entire volume of material or maybe one sub-volume of the entire volume of material. You do not have to consider point to point variations that is inhomogeneity. So isotropy and homogeneity are two very common characteristics which again are not satisfied for all engineering fluids but some common engineering fluids which we encounter not just in the classical fluid mechanics but also in microfluidics based applications. So we will be seeing in the next class that how we relate this isotropy and homogeneity with this but remember that this is not the complete tau ij. This is tau ij deviatoric. So the total tau ij is the hydrostatic tau ij plus the deviatoric tau ij. And in the next class we will see that how we can relate the deviatoric tau ij with e ij with e kl basically and that we will do for homogeneous and isotropic fluid. So that we will be able to express tau ij in terms of the pressure and the velocity gradients that will give rise to a constitutive law which we can use for homogeneous isotropic and Newtonian fluids. And that we will substitute in the Navier's equation and we will invoke another hypothesis which we call as Stokes hypothesis. So in the next class our agenda will be to discuss about how the generalized form of the Newton's law of viscosity boils down to a special form for homogeneous isotropic fluids and then how that can be incorporated in the Navier's equation in addition to the considerations of Stokes hypothesis and that will eventually lead us to the derivation of the celebrated Navier's Stokes equation. So that we will take up in the next lecture. Thank you.


Salesforce has so many products, I didn't mention it yet, sales cloud, service cloud, CPQ, industry clouds. So I knew my not as a professional, even though you may be in another industry for five years, 10 years, you may not get opportunity to work on all of these products. So how do you learn new product? Like, suppose you have never worked in CPQ, how can you learn? One of the easiest way I recommend is get a certification, right? So go to trailhead, find the trailhead for the CPQ, go to the trailhead, create a sandbox, complete those hands-on exercises and then appear for the certification. So these certifications help you to get a decent, I will not say it's like complete knowledge, you'll become an expert when you need certification, but it gives you that head start where you, from nothing to you have decent amount of knowledge about a product so that when you are putting a project, you can apply that knowledge and you'll be able to perform with minimum assistance.


What is popping guys today was an unexpected dunk session wanted to keep it Documented just wanted to get this quick recap up started with the usual of the drop step one step dunk attempt 99.5 rim ask any questions that you have about your journey how I can help any questions about my journey as you can see as This video goes on I get more and more Aggressive that aggression is coming back that nice little one-step right there, and I'm feeling fantastic. So stay tuned Excited to be jumping higher than ever. Let's go


For a long time, church art tended to depict the translation of the Book of Mormon as Joseph Smith and Oliver Cowdery sitting around a table, sometimes with the gold plates out on the table. But that's not really the best match for what we know about the translation process. What do the historical sources from those involved around the time tell us about the translation process? Well, first of all, Joseph Smith explained that he translated the Book of Mormon through the medium of the Urim and Thummim by the gift and power of God. But he didn't explain further than that. So what about the seer stone, for instance? What was its involvement in the translation process? So Emma Smith, Joseph Smith's wife and Martin Harris, his friend and David Whitmer, his friend who were around during the time of the translation of the Book of Mormon, said that he used a seer stone to translate parts of the Book of Mormon as well as the Urim and Thummim. And Martin Harris explained that Joseph Smith started using the seer stone instead of the Urim and Thummim for convenience. Wait, so what might that mean for convenience? Well, that's a really good question. We're not really sure what that means. But if you think of the Urim and Thummim, the descriptions that are given of the Urim and Thummim, it's described as two clear stones in a rim like glasses. And the Book of Mormon says that these stones are what constitute seers. Having and using these stones are what constitute seers. So the Urim and Thummim actually is this special pair of seer stones. And we have these descriptions of the Urim and Thummim connected to the breastplate and that they're large and that they don't fit on Joseph Smith's face. And we even have accounts that he takes the lenses out of the rim and puts them in a hat, which is the way he uses seer stone. So if he uses his own seer stone, rather than the Urim and Thummim, he can put the Urim and Thummim and the breastplate away somewhere safe and just use his seer stone. And that's more convenient. Okay, that makes sense. But it also sounds a little bit strange to then think of it as Joseph Smith looking at a stone in a hat. Yeah, that's an image that we're unfamiliar with, but actually it's not that strange. He's just trying to block out light. That's the point. So it's like on a really sunny day, if you get a text message and you pull out your cell phone and you can't see it because of the sun and you make shade, you block out the light so you can see what it says. It's the same kind of idea. So in the stone, he sees the translation in light and he puts his face in the hat so he can block out light and see what's on the seer stone. Can you make the Book of Mormon translation process visual for me for a moment? If I were an artist and to come to you and say, hey, I want to do a depiction of the translation that's more accurate, how should I make that look? Well, we would actually need two different images. We would need one depiction where Joseph Smith is wearing the breastplate that was connected to the Urim and Thummim and he's looking through the Urim and Thummim and he can be looking at the plates. And then we also need the other image where Joseph Smith is with a hat looking into the hat at a seer stone. The Book of Mormon wasn't just translated in one way. It was translated in different ways at different times. So the seer stone was integral to the translation of the Book of Mormon, but for some people it's still a little bit uncomfortable to think about that seer stone. Why do you think that is? That's a good question. I'm not sure exactly why that is. I think a big part of it is just that when Joseph Smith wrote about this in 1838, he talked about the Urim and Thummim spectacles that he found with the golden plates and he didn't write about the seer stone. And that history became canonized as part of the Pearl Grape Price and that is what Latter-day Saints are familiar with. And we have much less familiarity with other sources that talk about a seer stone. I think that's part of it. It may be that we want things that are miraculous to be ancient, like the Urim and Thummim in the Bible. It may be that a seer stone is too much like an ordinary rock. It's something mundane. But the idea of Joseph Smith using a seer stone to translate, this is an idea that we can get used to. We believe in modern miracles. We believe in a God that can work through small and simple things and God can speak to Joseph Smith however he wants to.