Without any further ado, I'd like to hand it over to our associate director of the DC office, Mr. David Barbell, as he's going to take us to a world beyond doctor. So I'd like to start off by just pulling the room. Who here has used doctor? Who here has heard of doctor? Okay. So before I talk about doctor, I'd like to start by just talking about computers. This is a basic computer. You've got hardware. This is your CPU and your memory and your USB and all of your stuff. And then you've got an operating system that kind of controls all of those things. It provides this really nice abstraction layer above your hardware. And then above that, you've got your applications. And so your application talks to your operating system. The operating system talks to hardware. And what's really interesting about this is that nothing really cares about anything except the layer below it. So application only cares about the operating system. Operating system only cares about the hardware. So now let's talk about virtualization. Back in the 60s, somebody at IBM figured out that you could take that basic computer and run it all in software. You could simulate that hardware in software. And so you could spin up these virtual computers. And it looks kind of like this. You have the actual hardware. And then you have the hypervisor, which is a layer that could spin up these virtual machines, virtual computers. And then you have these virtual machines, which have hardware. It looks a lot like hardware to the operating system, but it's actually being run in software. And then you've got the same operating system. You've got the application running on top of it and all the application stuff running on top of the operating system. So from the perspective of the application, the OS, everything is the same. But what you can do is you can run multiple computers, virtual computers, on one actual computer. What's also cool is you can take each one of these virtual computers and you can write it out as a file. You can save it down to a single file, which you can email around. You can FPP it around. You can also have a website. Do whatever you want with files. So this is virtualization. It really started to come to the forefront back in the 80s when it hit the PC market. And then when computers got big enough and cheap enough to effectively run a lot of computers on one piece of hardware, probably early 2000s, companies like VMware made a lot of money selling virtualization technology to allow you to consolidate all sorts of things onto a single server. But each one of these is isolated. Each one is completely isolated from the other. This one thinks it's alone in the world and can't directly touch anything in any one of these. So it's really good for security members too. So what is Docker? Docker is containerization. And this is the important to talk about. Let me talk about what Docker is before I talk about what it isn't. And talk about what's beyond Docker. So Docker and containerization is very similar to virtualization except you don't have the hypervisor and virtual hardware. Instead you have the same underlying computer. You only need to have one of those. And then you have an operating system that can run containers above that. And then it creates little virtual operating system spaces. It can simulate for the application you have your own file system, you have your own username space, you have your own things the operating system provides. And so from the application's perspective, it has complete control of computers. It provides the same kind of isolation. It provides the same kind of boundaries as the virtualization. But each one of these is really, really fast to spin up. It's really cheap because you don't have that virtual hardware. You don't even have an additional OS in the virtualization. You have full OS for every single virtual machine. This is just a basic OS process. So it's very, very lightweight, very, very fast to spin up. You can spin up one of these things under a second. And what's cool about this is you can also save these off so that you have your application and it has its own view of the world and all the supporting libraries and things like that. You can save one of these off into a file. Same as you would a virtual machine. You can share it around just like you would a virtual machine. Now, one important note here is really, if you look at it this way, containerization in Docker is just really cheap virtualization. It allows you to save off your application and all of its state and all of the things that support that application and share it around as a file. Virtualization provides exactly the same functionality. The difference here is this is dramatically cheaper. It's dramatically faster. You have a lot less overhead. And that's one of the reasons it's so popular right now is because with virtualization you can only run three or four of these things that don't forever start up because we're starting up a full computer every time you're starting a virtual machine. But these, you can spin up incredibly fast and they're really, really lightweight. So let's look at the procedure for Dockerizing an application and then putting it on to another computer.  That's what you're generally trying to achieve is you have an application and you want to get it on a computer and they can do all the things it needs to do. So you write your code. You put your code into a Docker container or any other kind of container using a different container-based technology. You configure it.  You probably need to add a web server. You need to add supporting OS libraries, language libraries, things like that. You might need to configure the web server. You might need to set whatever permissions you need to make sure the security is okay. And once you feel you're done, you save it. And you save off an image. That's the file that is your container. And you push it up to some really major repository. Somewhere, hopefully, on the Internet where you can then pull it down to another computer. And then it has everything it needs. It just spins up everything that's in that file and you can run it. So it makes deployment of that Dockerized application very, very easy. It's just pulling down a file, opening up and running it. Now, this is really, really cool and incredibly useful. However, it doesn't solve all of your problems. One of the first problems it doesn't solve is scheduling. So what is scheduling? So let's imagine a world where we have three servers. I may use myself. So you have 12 application instances of application A. And it's pretty easy to divide that among three servers. So you say four per server, okay. Four, four, four. All right, great.  This one has some capacity left. This one's full. It's usually all the memory and disk space and all the things. So it can't really fit any more applications on it. So say now we want to run a couple instances of application B on this. Well, where do you find them? Well, you can put one here and one here. You've got capacity. Okay, now say you want to spin down a couple instances of application A. Okay, at 12 you want to drop to nine. Where do you start taking those away? Do you take two here? It starts to get very confusing. Especially you start adding and removing applications and scaling up and scaling down. Keeping track of all those things is a very complex problem. And one of the things you'll probably want is a piece of software called Scheduler that will oversee all of that, all of this. Who puts what where? It's one of the first problems that we tend to run into when you're running dockerized infrastructure, which is why there are a lot of task schedulers out there. The big ones are Mesos, Diego, which is Cloud Foundry's task scheduler for Kubernetes. So what's another problem that docker doesn't solve by itself? External services. External services. So this is a web app. Say you've got your web app here. This could be a Ruby web app, a Spring web app. You've got all these web apps running in these containers on your web server. And they need to connect to a database in order to store some application state. So you could herd code the address of your database here. But then what happens if the database moves? What happens if you need to change something? Well, then you'd have to rebuild your docker. You'd have to find out what it is, rebuild your docker, and just redeploy them. What you really want is you want something that can dynamically tell all of these things where this external resource is. Tell all of these things in this container where this database is. And this is true for all sorts of things. This could be login services. This could be all sorts of external services that you might want to find in your application. And docker doesn't solve this for you. You have to have something that points all of your containerized applications to that database, to that external resource. Another problem, routing and load balancing. So say we've got three applications, A, B, and C. They're all at example.com. So A.example.com, B.example.com, C.example.com. So you want to go to B.example.com. So the web request comes in. And then you need to have something that then routes those web requests to the containers that have application B. So that B.example.com will get B rather than A or C. It's pretty easy to describe. It's really hard to solve, actually. Because each one of these things needs to continually register this thing needs to know somehow which applications are where and be able to wrap things directly, not just to a server, but to specific containers on a server. So this is actually a fairly sophisticated problem to solve.  Hopefully your applications are doing things. They're taking web requests. They're tossing off error messages. They're showing access logs. They're screening access logs, things like that. You want to be able to capture that in some way. And you can't just have the logs inside the container. You need to be able to get at them in some consolidated way. Also, these containers are bouncing up and down. Like if the logs are in the container, what happens when the scheduler moves it, when a container gets destroyed? You really want to have some kind of mechanism for automatically streaming things that are happening in here out to some centralized logging service and then aggregating together all of those logs. Now, it gets even more sophisticated when you're running different applications streaming those things, this log service, because you want to be able to see what is my entire cluster doing? What is application A? Doing one of the events for application A. So it needs to be able to know that log events from application A and application A should go together somehow so that you can get a unified view of what's happening with application A rather than having all of your applications mixed together. So your logging service needs to be container aware. It needs to know exactly what is streaming into it and be able to parse all that stuff apart. There's another problem with Docker business law. So what do I mean by packaging? So let's look at our web app again and web requests are coming in to say application B. Let's dive in on this container for application B. And inside this container, inside each one of these containers, there's going to be several pieces. There's going to be a web server so that you can actually handle web requests. It's going to have libraries. It's going to have OS libraries. It's going to have programming libraries, Ruby gems, Java jars, whatever. And then you have your application.  What happens if there's a security vulnerability in one of your libraries? But what happens if you want to tweak the configuration on your web server? Say you want to increase the amount of RAM available through your web server. What you're going to really do that is to rebuild your Docker image, make the change in an image, push that image up, and redeploy it through using Docker to standard fashion. So that means in this case, any time you want to make any change to, say, the web server that application C uses, you would have to rebuild and redeploy all of application C. And if it's a web server that all of them use, like say you're using Tomcat for everything, you're going to have to rebuild all of the images for all of your applications and then redeploy all of those images. What you really want is you want to have something that just allows you to worry about this, this application code.  And have that change independently. So you want to be able to say, hey, I've got to change my application, rebuild all of the containers and build a new image for all the containers that have that application on it. Hey, we need to do a patch for the Tomcat web server, rebuild all of the images for the applications that use the Tomcat web server and redeploy those. So packaging is actually one of the big pain points with managing a large, dockerized infrastructure. So all of these needs, these things that it doesn't do, so what's beyond? What's beyond? What's the next step? What we're seeing now is we're seeing a lot of platforms, a lot of software projects that solve these problems using containers. There's a ton of schedulers, there's routing services, there's logging, and a lot of these things are being consolidated into unified platforms. Mesos and DCOS is one that's very popular. Kubernetes is another. Cloud Foundry is a really big one. And all of these solve these things at various levels of abstraction. Most of them do all of them except packaging. Cloud Foundry solves the packaging piece as well. What's interesting about these platforms is as they get more sophisticated, these are container management platforms. But as they get better at what they do and dealing with all the issues with containers, the unsolved problems, you find yourself worrying about the actual containers less and less. Because you have all of this automated logic that is rebuilding your container images, it's scheduling your container images, it's pushing things up and pulling things down and managing it for you. And so the future of ops and the data center and containerization is not having to worry about containers because you have platforms that will solve for you. And that really is what I see as the next frontier. So with that, I'll open it up to questions. I guess somebody who owns a business that has a technology product that we do, if I am a non-technical person, why should I care about this? Why does this impact my bottom line? I guess why do I care about this? Is this just an engineering thing or is there a big product or business thing? That's a good question. The big pain point that any business that writes software has is not writing the software but running the software. And if you look at a lot of companies that run a lot of software, there's a lot of overhead to running that software.  You have to do all of these things anyways. You have to figure out where are my applications going to run, which computers are they going to run on, how do they connect their web server, how do they connect their login service, how do they connect their database, how do they do all of the things that we're talking about. And it's largely been a manual process. It's been very labor-intensive in the past. Containerization is a huge step forward for deployments for actually putting something on a computer. It makes it very, very easy and very cheap. What all these other things do that the projects like Cloud Foundry and Kubernetes do is they make it really cheap to do all the other stuff. So we're removing all of the manual labor of actually running your software company. And it frees up your people rather than worrying about, I'm going to write my application and then I'm going to write all the configurations for the web server that will run my application and I'll worry about how to configure the operating system so that I can write a run book. So the ops team knows how to manage my application. It takes all that stuff away and it makes it so you can just worry about writing your application and focus on the things that are really important and value-generating for your company. So does your company design a custom solution for each and every client? Or are you offering certain pre-package systems or people to sort of pick A to your C? How does that work? So our company has a product called Cloud Foundry or Pivotal Cloud Foundry. And Pivotal Cloud Foundry is a platform that solves all of these problems. It actually goes a step further and it spins up hardware. It generates virtual machines and then runs containers on those virtual machines and manages those virtual machines and containers and provides all the routing and the logging and the external service binding and scheduling and all of those things that I talked about. So by the end of the day, you just push up your application code and it just runs. It's pretty cool. Cloud Foundry is pretty distinctive in that it is one of the few platforms that allows you to just push up your application code and not have to worry about configuring your container and pushing that up. There are some posted solutions like Amazon, Google Black Engine, RR proprietary where you write it for a particular cloud and you can also run it that way for Roku as another one. But Cloud Foundry is one you can install on virtually any data center, virtually any cloud hosting provider and get that just to worry about your application functionality. You mentioned Amazon for an application that's not really posted on AWS. Does it replace? Go back to this. AWS is really good at providing servers. If you look at EC2, it provides you with... Let's go. It provides you with this, the hardware and operating system. But you still need to manage all of the application state and all of the configurations on top of those services. So you need to configure your web servers. You need to manage system libraries. You need to figure out what deploying your application on that server looks like. It's really not from a functional perspective. It's not very different than running your own physical data center. The advantage is, rather than racking hardware, you just push a button. It really manages the EC2 provides. What a platform like Cloud Foundry or Kubernetes provides, is it provides this automatic scheduling and logging and routing and all of these other problems.  So as you have these more sophisticated platforms, not only do you get containers, but you get automatic container management. And you'll want to layer that on top of the EC2 or Azure or Google Computing or OpenShift or things like that. And I think that's really where the future is. We're moving to these cloud-based infrastructures, but we're also finding people layering things on top of those cloud-based infrastructures in order to help them manage all of their applications. Containerization is a great raw component, but you also need these intelligent systems to help manage all of your containers on top of that infrastructure. So it's potentially cheaper and can offer automation of a lot of things that I actually manually. There seems to be a lot of pros to it, but it doesn't... It feels like, to me, if I am running a technology organization, there's a lot of magic that's happening. What are the possible drawbacks or other considerations to going this type of approach? Where it's like, I'm used to having all of the control of doing everything myself, and now it's like, there's like, I'm trusting this other thing. What other considerations are there for maybe why I'm not going to use one of the plug-ins? It's pretty hard to argue against something like this at this point. You could say that manually tweaking everything can give you slight savings on memory. Maybe you could manually configure all of your machines and all of your applications. You could get a little bit more consolidation, a little bit more efficiency out of your servers. But it's a lot like the old days of the assembly language programming where people said, well, why would I use a higher level language like C or Java? I can manually do each opcode and optimize the heck out of things. What we found was not only was that laborious and you were way too slow in doing it, but it wasn't worth it, especially with computers and memory and everything getting cheaper. A little bit of overhead is effectively free, especially in comparison to the human cost. What you're really doing is removing the human manual component out of all of this. For almost all infrastructure and computer things, anything you can automate is a big win from a cost perspective. You also get portability. You get the ability to arbitrage between various providers. If you're using containerization, you're using these platforms, my containers will run the same as Google Compute Engine or Azure or EC2. If Amazon is offering a Super Tuesday deal on compute, then I can take my application, move it over to Amazon running one of these platforms. I don't have to change my own thing. I don't have to change my application. I don't have to reconfigure anything. I just move it over to the low cost provider. While these huge cloud computer providers are on a race to the bottom for pricing, it allows you to arbitrage between them. Thank you very much.


OK, so I'm going to be talking today about a topic which is really intimately connected with turbulent mixing in this sort of theme of this conference. And I'm going to try to show you some very unique experiments we're trying to do in plasmas where we can study thermal mixing, for example, very controlled conditions. And I want to acknowledge my collaborators, a couple of graduate students that are involved in the project from my institution, Scott Karpiszewski and Matt Paulus from UCLA. And we're also working together with Professor Morales and Dr. Juan Campernello. So first of all, I'm just going to try to motivate this by trying to explain what we mean by filaments, plasma filaments. Magnetize, we'll be looking at magnetized plasmas. So the filaments will be in the regime where charged particles in the filaments are basically guided by magnetic fields and involving electric fields. And so I'll try to go through some of the basic physical processes, the transport physics. Essentially, we're trying to understand transition from classical transport to anomalous or transport driven by collective processes. And then we'll try to go into the new regimes we're trying to access. And that's situations where you can have actually filament-filament interaction. And we can build structures that are basically complex, can generate quite complex patterns. And we can study, for example, things like chaotic heat flow in quite a bit of detail. So here's the working definition of a plasma filament, is that it's a coherent mesoscale plasma structure that's strongly aligned to a magnetic field. And so mesoscale here would be plasma, magnetized plasma typically has scales like the gyratius of the electrons, say gyratius of the ions, collisionless skin depth, CO omega p for the species. And so we'll be studying mesoscale structure so that we're talking about plasma filament structures that are sort of on the order of the collisionless skin depth or gyratius of the ions or a little bit larger. So that's what we call mesoscale. Microscale would be subscales below the electron inertial, the CO omega p collisionless skin depth scale. So filamentry structures are typically observed in boundary layers of plasmas. As George McGee was explaining, that you have core turbulence, for example, but you also have boundary turbulence. And some of the boundary turbulence observed in magnetically confined plasmas contain these filamentry structures, which I'm going to be talking about. And of course, filamentry structures are found in many plasma environments, for example, stellar atmospheres. I'll try to show you some example. And so we would like to basically study the transport physics associated with filaments because they can often carry large amounts of heat and particles, and their transport theory is not just simply dictated by a fixed law. So the transport theory for these could be much more involved and involves non-local effects. So just through a couple of examples of the types of filamentry structures we're kind of interested in studying, why are we studying magnetized plasma filaments? So I just pulled out of the literature just a very couple examples that these structures have been imaged in quite a bit of detail with very, very high-speed cameras, for example. So here's an example of a magnetized toroidal plasma more spherical-like plasma that is at the Princeton Plasma Physics Laboratory called NSTX. And there's a similar toroidal device called Mast in the UK, which has very similar characteristics. And both of these are experiments that are studying filamentry structures in particular and the transport associated with them. So that's why I kind of use those as examples. So for example, here's a high-speed video image of one of these sort of spherical-like plasmas which evolves and then there's a formation of so-called ELMS, edge localized mode. So these are kind of occurring near the boundary of the plasma. And you can see this filamentry structure kind of winding around the plasma device sort of toroidally. And here's kind of another picture of it, sort of the time evolution sequence of the development of these filamentry structures. And then here is some modeling of those using fluid models to describe sort of the characteristics, the length scale. As they wind around, many times around the device, these things could be many meters long, for example. And they're fairly highly aligned with the magnetic field as I was trying to explain earlier. And here's another example from the NSTX Plasma Princeton. For example, they can image the formation of the filaments at the boundary layer of the plasma. And so you can see a time sequence here of the development of it. They call it a blob, but it's actually more what we call a blob filament because actually this thing has very elongated structure. But if you look in a plane, it looks like a blob, right? So sometimes they're called blob structures. But basically, they have a lot of dynamics. And you can imagine these blob filaments, they will be carrying heat and particles out as they sort of shed away from the boundary layer of the plasma. So these structures are quite important in terms of the overall transport of heat and particles from the edge region to the outer boundaries of the plasma. And just one more example, this is kind of connected with experiments at General Tomics. For example, you can sort of see the development here of these so-called edge localized modes, which are essentially filamentary structures in both density and temperature. So we're sort of looking at profiles across the boundary, the edge of the plasma. And you can see here sort of structures. So the elevation of the density above the background is quite significant here. So here's a filament density. And then if you look at the temperature, you also see temperature filaments as well. So you could think of this as being a lot of fluctuations that involve filamentary structures of temperature and density. And of course, we can go to the solar surface, for example. And we can see beautiful images from extreme ultraviolet light. We can see that also the plasma structures, the magnetic arches, have very kind of filamentate structures. And these things are very dynamic. And the main thing here is that the luminosity along any of these arches is very non-uniform. So there's a lot of possibilities that the distribution of the heat and the particles is very non-uniform in the magnetic arches, for example. So these are just some examples of filamentary structures. And here in this case, there'll be multiple filaments interacting. OK, so what we want to do is take that sort of background of filamentary structures in the magnetized plasma. And we want to see if we can actually isolate filaments. So we would like to make the filament in a linear device so we don't have the effects of curvature as we have in the toroidal plasma. So we want to make long filaments, linear filaments. And just study, for example, the fluctuations and waves internal to those filaments and then see how we can characterize the transport physics and also the modes. Because you can think of filaments as sort of like an antenna. If you can actually develop modes, internal modes through gradients, for example, this thing will be radiating. We want to know the near field of this filament antenna, if you will, and also some of the far field effects. So to see how much non-locality effects come into play. So here's a cartoon of what we want to set up. And it has been studied in the lab since the late 1990s, early 2000s, in the large plasma device at UCLA, which Walter Guckman gave an excellent introduction to. So what we'd like to do is create a filament that's far away from the boundaries. And also the filament should be isolated. And so it should not be in contact with, say, the anode where you're sort of biasing. If this is your cathode source, we would like to have the filament have a finite length, for example. So what we're attempting to do is basically create a filament which has an elevated temperature above a background. So typically we work with a background plasma which is cold, like a quarter of an electron volt. So that's almost the energies that you'd find in a solid, for example. And then we would have a heated region which is about, say, 20 times larger so we get a very good contrast. And this filament would have the very large gradients if we could localize it in space. And then we could study, for example, the normal modes associated with that filament. So here we study in plasmas which have a density of like 10 to the 12 particles per cubic centimeter. And this is, say, studied helium, but we could study these in hydrogen or other plasmas. And so this is the kind of thing that we set up. So what we first need is a heat source, a good heat source that's very controllable. And so what we're gonna show you now is basically how we actually make the filament from a particular heat source which provides us with a kind of electron beam. And if the plasma is of this density, the mean free path of the particles, electrons, for example, it's rather short. It's about like 10 to 15 centimeters. But this filament is like 10 meters long. So what'll happen is if we have a beam launched into that plasma, the beam will slow down and thermalize and the energy will basically be transported classically along the field line if there's no like a wave processes. And so then we'll get a very nice sort of, very clean sort of temperature filament. This is what we're attempting to do here. So just the pure energy transport. So the gradients of density will be very, very mild and we'll have just everything from, coming from mostly the thermal components. Okay, so Walter has already explained the large plasma device and others in Chris Neiman's talk as well. So we do the experiments here in the, and length here is very important. And this motivates, this work will motivate the reason why we need to do this in a very long chamber. You think, well, why don't we just do this in a very small plasma? Why do we have to have such 18 meter long plasmas? So I'll explain that in a moment why we do need that very, the length and also the very large diameter. So the main plasmas created in this barium oxide cathode and it's pulsed every one second. And plasmas are again magnetized, so one kilo gauss magnetic field, as I told you the density. And the electron, the beta, the ratio of electron, the thermal pressure to the magnetic pressure is rather small, it's like 10 to the minus four. So it's considered low beta plasma. And we work in a particular phase of that discharge. So when the plasma is turned on, that barium oxide source is turned on, you have this background plasma. And then the main plasma source is turned off and then what happens is you get what's called an afterglow. And in this afterglow region is the region we wanna work in because we can then turn on a heat source in this afterglow region when the plasma is very cold. So here's the kind of profile of after the main plasma source is turned off, then there's a slow decay of the density and almost no decay, well very little decay of the temperature, okay? And so we have basically about 15 milliseconds of time to actually put in a heat source and study the waves in which are processes which are occurring on microsecond time scales, for example. So this is the important point. And so we get basically this one quarter of an electron volt. This is electron temperature versus time in units of electron volts, so it's here. And we also have to pay attention that the density is changing over the time scale, but we want to work over time scales where the density changes is rather modest. Okay, so the heat source. So now we've got our background plasma that's really cold and now we have to make it warm, heat it up. And so what we use, so there are a couple of different ways we can introduce the heat source. So the heat source, we could make very small heat sources using these so-called Lantium hexaborate crystals which give us a heat source that's a scale of about a few millimeters. And then we could also use another larger, say 10 centimeter diameter Lantium hexaborate source to actually make filaments that are actually much larger in scale. But we're gonna talk, mostly I'll talk today about the small, very localized heat source. And so what we do is we introduce this crystal into the plasma at some region and then we bias it relative to some anode. Now, Walter described flux rope experiments. Now those biases are like 100 plus 200, or 100 to 200 volt biases. So here we want to make the filament a finite length so we have to do low biasing and the biases on this crystals are typically like about 10 to 20 volts in that range. If you bias above 20 volts, then you start ionizing helium and so then you have to worry about the density changes in the discharge. Okay, so when you actually introduce that Lantium hexaborate crystal as your heat source, again, as this explained the thermalization, then you get this nice kind of thermal filament and I'll explain like how we can control the length. But basically here's the, this looks like a kind of Gaussian looking thermal profile. Here's the, this is taken at a plane, a few meters away from the source. And so in a plane, we kind of use probes to kind of create a map of the saturation current and saturation current is actually proportional to density and square root of electron temperature. But the density here, we can separate these quantities and actually this, when I show these maps, you can think of these as almost purely coming from the temperature, not so significantly varying from, the density's almost a constant over this size of the filament. So here's a nice sort of localized Gaussian filament that we, and these kind of experiments were like as I said done before and we're building upon them. Now the other way we can make larger filaments is to actually use a larger land theme hexabyte source. So this is a disc about 10 centimeters or so in size. And so that can actually be used to make temperature filaments where we're working more in the centimeter scale, not the millimeter scale as I've been explaining. And so the nice thing about this technique with masks, with this larger source is you can put a mask in front of it and then you can actually make controlled sort of thermal structures. So for example, I'm gonna show you here. And the result of you put a mask and you drill three holes and then you can vary the spacing so you can make multiple masks. And here you can see that we can form three filaments. And this kind of idea came from Walter Gecklman's experiments in flux ropes where they use a similar technique to create multiple flux ropes. Walter showed some nice examples of two flux ropes, but he's done three flux ropes. And so here the mask method, we can drill an arbitrary number of holes, and well, not arbitrary, but some finite number of holes and we can actually make dozens of filaments. Of course, depending on the size of the hole, the size of the filament can be like small scale or larger scale. So this is another second method that we can use to create filament structures. And we also built masks where we can actually make a ring shape heat source. So this is some work that we did with Bart and creating a ring shape to hollow profile of the temperature. And so we were studying various kinds. We observed very interesting phenomena associated with intermittent transport and also avalanche type thermal avalanches. So I won't go into those, but I'll just to show you the capability that you can make more or less designer filaments. Okay, so previous work was using these, localized like these Lanty Maxwell crystals. They were used previously for studying fundamental transitions from classical collisional transport in a plasma to anomalous transport where we had from the gradients, they drive the fluctuations in the waves and those would be in addition to the classical effects. And so the other element of this work is that if you have like these steep temperature or pressure gradients in the plasma, you can actually drive alphane, shirofane modes. And just to remind you, shirofane mode is basically a perturbation that is perpendicular to the main magnetic field. So it's driven by a parallel currents, but these induce perturbations in the magnetic field perpendicular to the main field. This is so-called line bending perturbation, which propagates just like when you pluck a guitar string, you can think of that as a shirofane mode equivalent in a plasma. So yeah, so this is the kind of physics we've been investigating with these experiments. So first of all, let me just explain to you a single filament and then we'll just discuss the situation of multiple filaments. So if you have a single filament, how can you sort of characterize it through sort of classical transport theory? So basically filament length control is determined by the ratio of the perpendicular heat diffusivity and to the parallel heat diffusivity. Obviously in a magnetized plasma, the parallel diffusivity along the field is much higher than the perpendicular. Just in classical processes where we have just say electron ion collisions or some collisional transport is dominant. So basically the length of the filament, you can control it mainly by adjusting these perpendicular and parallel transport coefficients, those collisional ones. And so if you just sort of go into any standard textbook description of transport in a magnetized plasma with just collisions, electron ion collisions dominantly, you see how they scale, how these parallel and perpendicular transport coefficients scale. So if you just go down to the bottom here, the parallel thermal diffusivity scales roughly like temperature to the five halves power. However, the perpendicular component because you have electrons are magnetized, they scale like the inverse of the magnetic field squared and the electron temperature square root. So based on these scalings, you can then organize the ratio of this kappa parallel over kappa perp. And then that's how you can then work out what the length of the filament will be, right? By just adjusting the magnetic field and electron temperatures, that's how we actually get the length. That's why the length is 10 meters in the way we designed the parameters for those five electron volts, for example, case. So that's really, this works very, very well. We could predict very accurately from classical theory at least the length of a filament. And so here's kind of, and then that's just a simple heat equation, but if you couple it to the continuity equation, so equation for density and momentum equation, and if you include the heat source here, and so these are called so-called Brighinsky equations, and if you sort of solve those equations, you can actually predict the length based on the properties of your heat source. So for example, early time and then late time, this is your steady state filament. So in this case, this is an eight meter long filament, which goes along with those sort of predictions back to the envelope. Okay, now that's the classical picture. Now the wave picture, you have basically fluctuations that develop from the steep plasma, the temperature gradients. And so here's a kind of early work that characterize this transport from classical when the filament is getting set up, and then when the gradients are sufficiently steep. So here's a plot of like the electron temperature, right? Here's the filament, and if you take the profile, the radial yet, as with the average profile, you see here, it's got a very steep gradient here, and that drives fluctuations, like really large, and these are on the order of 20, 30, 40 kilohertz type fluctuations, and they start, of course, diffusing, they contribute to the perpendicular, so anomalous thermal diffusivity. And so here's kind of now point measurements. So there's actually several modes that are very important here. So this, if you actually are sitting just at the region where the gradient is maximum, you get these M equal one type modes, that's this red here, and these frequencies are on order of 30 kilohertz or so. And then actually at the very center of the filament, you get these lower frequency oscillations, which are about five to eight kilohertz.  So basically you have sound waves, which are basically trapped in this thermal filament, and then this creates this low frequency oscillation, which actually we're still trying to understand. We don't have a full picture of how that works, but we, yeah, it's easily observed in experiments. And then outside the filament, you get these spikes, which are actually sort of Lorentzian pulses, which Walter had talked a bit at the end toward the end of his talk. And so that shows that these are kind of far field effects, because we're kind of now as you move out, you can actually see some of these pulses. And so when we put multiple filaments, like film is near each other, then these interaction of Lorentzian pulses is kind of what we're trying to understand. So just a kind of quick physical picture of this electron temperature instability. So essentially when you have a temperature gradient, so here's one filament with a thermal gradient, and here's a magnetic field. So what happens is that you have a perturbation. So this is the shaded part is hot, and this is cold. And so you get basically electric potential fluctuation, which is in phase with the electron temperature fluctuation. And so you get this kind of electron diamagnetic drift effect. But then if the phase relation between potential and temperature is not, if it's finite, then from coupling to the parallel dynamics, you can actually get this perturbation to amplify. This will grow and this will decrease here. So you get basically kind of like an interchange-like type of mode, and then this is the origin of this drift-alphaene fluctuation. So parallel dynamics couples to this perpendicular dynamics.  So Peckley numbers for the kind of plasmas, which is the rate of advection to heat diffusion. So if you kind of use the E cross B motion, that's how the plasma really moves in a perpendicular direction to the magnetic field. This Peckley number scales something like the collisionality times the fluctuation. And so typically these are around three to 30. So we're at a greater than one Peckley number, where advection kind of dominates. So I'll just kind of go to, yeah. So basically we've been able to successfully model these temperature gradient instabilities. And I'll just kind of go to sort of the simulations. These are basically simulations based on the so-called gyro-kinetic equations, which gyro-kinetic description of plasma is like an E cross B, each charged particle is sort of E cross B drifting. And we solve this kinetically with millions of particles. And here's a cross section of the electric potential which develops in time. And we see the m equal one mode pattern consistent with what we see in the experiments. But we also see smaller scales, features, and that's connected with convective cells, which are purely, these are essentially k parallel equals zero, or actually average sort of modes that are present. So they relax the temperature profiler simulation showing the relaxation of the temperature from these temperature gradient driven modes. So I'll just go now to the multiple film and experiments that'll be, this is my ending here. So basically what we're now trying to do is do experiments where we have multiple filaments like, and we started with three. And our goal is to study sort of nonlinear convective transport and presence of fluctuating magnetic fields. If they're close enough, the field lines can become stochastic and nonlinear E cross B convection. So what we do is, now we introduce into the plasma not just one heat source, but we introduce three. So we put these crystals on a probe drive, on three probe drives, and here we can make them arbitrary close from this close to arbitrary separation. And each crystal is on a separate electronics. So basically we can bias each crystal independently and so we can say, for example, have one bias to say 15 volts and then these would be biased to say four volts, for example. So this is the view down the machine when you put the crystals on these probe drives and then we can just move them spatially in close together or far apart. And so here's, yeah, that's just a single heat source. But here if we have the three, so we started off with a far separation. So again, this is the electron temperature essentially. Each of the three crystals, they're biased the same amount in this case. So we get the five electron volt peak temperatures here and then we see that there's actually convective tail. So these surprisingly, even though these are very far apart, there are many gyro-radi or skin depth apart, we still get actually interaction between the filaments. So a single filament, if we turn these two off, a single filament would just have a nice sort of Gaussian type shape, whereas now we sort of get interaction. And so here's the fluctuations in the saturation curve essentially, fluctuation in temperature. And we see modes that develop like mode one, M equal one, M equal two modes that develop around each of these filaments. And so there's a symmetry breaking, these offer symmetry breaking perturbations. So now the mode structure around here is not the same as that structure there. And so what we see is that we put the filaments very close together, we form a very complex structure, but then there's an outer gradient that forms because the inside is relaxed very quickly and we build up an outer gradient. And so here's just, we've been modeling this with again, Bruginski transport equations and trying to study the nonlinear convective transport. So just in summary, we've made isolated magnetized electron temperature filaments, various sizes, using crystals from a few millimeters to, and then with masks on larger cathode, we can make a centimeter scale or even larger. And the close-case-case patterns, we tend to get very sort of chaotic cross-field transport enhanced E-Crosby flows and convective tails. And so what we're trying to actually do is characterize these structures as the so-called Lagrangian-coherent structures. And it's kind of interesting because the turbulent mixing, the logo is actually a Lagrangian-coherent structure where you actually see large convective tails. In this case, they're using four filaments and we're using three in a triangular pattern, if you will. So we can try to make sort of fluid analogs in these magnetized plasmas. So thanks very much for listening.


This review aims to collate and analyze studies evaluating digital health education for medical students to inform the development of future courses and identify areas where curricula may need to be strengthened. The results show that most of the reported digital health courses were elective, integrated into the existing curriculum and focused on medical informatics. Most of the courses targeted medical students from the first to third year, and the duration of the courses ranged from one hour to three academic years. Most of the studies evaluated courses mostly by using an uncontrolled before and after design, and generally reported improvements in students' learning outcomes. However, there is a need for high quality studies that evaluate digital health education. This article was authored by Lorraine Tudorkar, Bone Minkyo, Rishi S. Nananpande and others.


Am I right?  What? Well, eventually if you keep going, you'll end up on the left.  I'm Rick. And you follow us on Twitter, Twitter. Juicy content. Juicy content. Juicy. Juicy. Juicy. Juicy. Juicy. Juicy. How do they do it every day, twice a day? Today we are reacting to a little clip from Coffee with Karam. Oh. Hopefully it does get blocked.  It's true. Come on, Karam. Give us a break. There's, I think, a Ranbir and Karina and an Amir Khan on Patreon. Is that? It's true, sorry. But this is a little clip. This is Amir Khan talks about Shah Rukh Khan. Oh, cool. Somebody wanted us to see that and what he says. I don't know what their history is. I don't know if they love each other, if they hate each other, if they're friends. I don't know anything. It's two of the three Khans and they've been together for all of their careers. So, here we go. The three of you started on the same time.  65. Yes, and all of you a few months apart. I mean, that is a really strange coincidence.  You, of course, were senior in terms of you released your film in 88, Salman in 89, Shah Rukh in 91. But if Salman had one released before... Yeah, yeah, yeah. B.B. Hothwas. Yeah, yeah. But I mean, technically his first burst of stardom happened with many parents, right? And Diwana Shah Rukh in 91. And there's always so much conjecture and talk about all three of you as being this, you know, the ruling of the Khandam. Do you feel at all that there is much more talk than required or the fact that really it's quite great that you three are still doing such solid work? You know, when I came into the industry, I had no idea where I would reach and I had not even given a thought. It is remarkable that there are three actors. It happens to be the three of us, but it is remarkable that there are three actors who've got such a long span. Right. All three, Kuli is successful and all three exactly at the same time. It's not very common. Not at all. I remember there was Raj Raji and Dilip Kumar and Devanand who were... Yes, who were the other troublemakers. The other troublemakers. Yeah. I think they were called... So like this is the modern age strip movie. Yeah, but it's not very often that that happens, you know. So it is remarkable that it's happening. What is your genuine vibe with Shah Rukh? Is there just a civilness between the two of you? I think that there is a genuine regard and respect for each other's work and for each other's space. And if I have to be honest, there is also a certain amount of guardedness. There is a certain amount of... There's certainly a warmth. I wouldn't say that there is no warmth. There is certainly warmth. When you eat each other. Between Shah Rukh and me. But there have also been moments when there have been a fair bit of stress in the relationship. If I put it very honestly. Yeah. Have you tried to work at that or you just keep to each his own and what should kind of do? Have you reached out? I mean, we don't meet that often, you know. But you're not telling me to reach out. Our life don't converge so much that we really need to. I think he's doing very well for himself. Right. And I think he's got a great family. He's got a great bunch of people around him. And so I don't think he really needs me or has space in his life for me. Right. And I wish him well, you know. I really genuinely wish him well. I like to see his work. I like to see his films. And I, as an audience, enjoy his work as well. Right. I appreciate that. I want to know their history. Yeah. Like, have they done a film together? That's what I was wanting to know if they have or all three of them have. And what's their, because you could tell that he was thinking of some history they've had. And also normally people will not reveal that much of if there is a rift, there's no. Because that's not good PR. No. Unless it's a really big rift and then you can milk that. Yeah. But, well, yeah, their careers, first of all, they're going to see each other at the awards shows all the time. They'll cross paths in various places and various things. And I'm sure there's been times where something's been said falsely. For example, there's probably some story about SRK that was false and it was really hurtful. And so Amir reached out to him and said, hey, just wanted you to know I'm sorry what's going on. Things like that, because they can have a commiserate connection. But at the same time, I wonder, do one or the other view the other person? Cause they have films that can be released on the same weekend. So you're vying for the box office together.  The condom is. Yeah. That's what I was saying before I said it. So I don't know, but yeah, they're clearly there's apparently they've worked together on a song but they've actually never done a film together. I don't believe, which is crazy for as long as they've both been around. They sound and Saif and they, I think they've all done films together. Sarkaj Amir. It's very interesting. I would like to know. The degrees of separation between them and the rest of the industry is like zero. Yeah. And it's true. So that's interesting. But it was, it was interesting especially I'm sure for people that know what their history is. Yeah. Cause clearly there's something that he says there's been tension, which I guess makes sense. Yeah. The thing, the one thing he said about, I feel, and I didn't think there was animosity in it. I think he's just being honest when he said, I don't think he has room in his life for me. And incredibly huge, incredibly busy, busy, very busy guys. And it just very well, maybe that there may have been opportunities where they had an opportunity to reach out and he couldn't follow up and they're just, it didn't happen.  So yeah, I appreciated his honesty about that. I'd love to hear what SRK would say in that regard. Yeah. And I'd love to see them in something together. Yeah. Have they? I don't, I think that's what I looked over on the end of this is they haven't really worked together outside of a song. Well, it's, it's, it's funny. That's that way here in Hollywood too. Like, once upon a time in Hollywood was the first time Leo and Brad worked together after how many years together in the industry? Yeah. They've both been in the industry for 30 something years but this was the first time, and you know they've seen each other constantly at the Oscars and the globes and they're talking and they have had dinners and people scheduled. So there's constantly people, massive stars that never worked together. Yeah.  But it is strange that they have never actually done a film together. Yeah. Because SRK and Saif have done a film together. SRK and I believe Salman have done a film together. I believe Salman and Amir have done a film together. And there's definitely history. Yeah. There's definitely an answer. There's definitely some history there. And I don't know what the history is and I don't think it's, because like he was saying, he's like, I appreciate his work and I like watching him. But it is interesting. And I'm wondering if you can probably tell us their whole, like they're like, well, in 1997. Yeah. He tweeted that. So I don't know what it is. It was interesting to watch though. And I think that Amir is actually a really intellectual interviewer. He's everything we've seen when he talks. Seems like he's always thinking. He seems to be comparatively of the two because we've seen both of them in those situations. Amir seems to be more of the stoic. You know, a bit more of the intellectual, a bit more of the stoic, whereas SRK is definitively intelligent and articulate. I get the sense that he's a bit more jokey, silly, goofy and then Amir. Which is funny, because I think Amir has played more, more goofy, silly characters than Shahrukh has played. Yeah, but it's interesting. That was very interesting. I did appreciate that he seemed to be answering honestly. You can tell when people don't answer a question for whatever reason, you're like, oh, okay. They don't want us to go there. But he seemed to genuinely want to answer it and be honest and he was thoughtful about it. And there's definitely history. Yeah. I wonder how many, if it's similar to here in Hollywood, I'm sure it is that publicists will come and be like, you can't ask him about this. You can't ask him about this. I guarantee it. You can't ask him about that. I guarantee it. Don't bring up this. Because in Hollywood, that's a huge thing. Huge thing. There's been actors who are asked things and publicists have told them beforehand, don't ask, and they walk out of an interview because they were told, don't ask him about that. Don't ask her about that.  You shouldn't ask him. Exactly. That's one of the agreements for you being on the show. Exactly. Somebody came on the show and they were like, don't talk about, whoa, not that we are trying to get a scoop on anybody. No, but even something like, Adam Driver recently walked out of an interview because they played the clip of him singing in Marriage Story. But at face value, people would think, wow, how rude. Adam Driver has a legit phobia about hearing himself sing. It's a phobia. When he hears himself sing, it freaks him out. He can't, he doesn't want to hear it. And my guess is either they didn't know, and oops, if they didn't know, that's really bad. We've done that to him on an interview like that. Yeah. Well, that was awesome. Let us know more interviews and stuff like that that we can all, I'm hoping this could be on the channel. If not, Tell us the truth. We like knowing the truth about stuff.  So just please tell us the real deal if you know it. And if you don't, then just don't tell us anything.


Hi, I'm Zor. Welcome to a new Zor education Many times I was talking that the most important part of any course of mathematics is to solve problems Well, let's solve problems today The problems will be about derivatives and everything we know by by now about derivatives just six yet six problems Where different aspects of whatever we have learned should be applied Now this lecture is part of the advanced course of mathematics presented on unizor.com. I Suggested to watch this lecture from this website Because the lecture every lecture actually has very detailed notes, which can serve as a textbook basically and also the assigned in students can Participate in an educational process which involves enrollment and for this you need your supervisor or a parent And you can take exams as many times as you want just to gauge your Success in learning the material and the site is free by the way. All right, so a few problems The problem number one is Let's consider this function So my statement is about behavior of this function When x goes to infinity and basically I'm saying that e to the power of minus x and you know The graph is something like this goes to zero much faster than X to the power of n which graphs like this approximately so this goes to infinity and this goes to to zero and Obviously just looking at it is it's not obvious where their product actually would go But here is what I suggest. Let's rewrite it as and Use the L'Hopital's rule now the L'Hopital's rule states that if you have This ratio of two functions it behaves when x goes to some limit including infinity Exactly the same way as the ratio of their derivatives now Let's think about derivatives Well, the derivative of this would be what there's no equal sign derivative of numerator would be n x to the power of n and e to the power of x right This is sorry minus one This is derivative of this and e to the power of x is derivative of e to the power of x as we know, right? so The limit of this as x goes to infinity is equal to the limit of this as x goes to infinity But now we still have some kind of Indeterminate limit because this is infinity and this is infinity as x goes to infinity, right? Well, okay, but let's use the L'Hopital's rule again. The next would be n times n minus one x to the power of n minus two That's the derivative of numerator and Here we will still we will still have the same Okay, is it better? Well, not much. It's still infinity, right? But now let's do this process and times and what do we have in this case? Well after n times we will have n factorial obviously, right? n times n minus two minus n minus two times n minus three, etc and x would be basically to the power of zero which is one and in the Denominator we still have e to the power of x because this is the n's derivative of this, right? and Now this n is a constant, right? Now this we know for sure goes to zero so after Implementing this after using this L'Hopital's rule and times we basically have Reduced our problem of determining this limit to this from this to this and from this to this and this is easy and Result is zero so that actually signifies that a to the power of minus x Goes much faster to zero than x to any numeric power. I'm talking about obviously Natural number n otherwise. We would not have nice Constant one at the very end. All right, so that's my first so x to the power of n grows slower than e to the power of minus x Diminishing Now let's consider a different combination of function Okay, so x to the power of n We know is growing not as fast as e to the power of x or e to the power of minus x goes to zero Faster than x to the power of n. Now. How about logarithm? well, the logarithm is going to Infinity slower than x to any power and How can we prove it again? Let's use the Lopital's rule. So the limit of this as x goes to infinity is equal to Ratio of their derivatives derivative of logarithm x is 1x derivative of this is n power n x to the power n minus 1 and Now it's obvious that it if x goes to infinity Then this goes to zero which proves that x to the power of n is is growing faster than logarithm x or if you wish x to the power of minus n goes to zero faster than logarithm n goes to infinity So that's my second problem So as far as speed of growing logarithm is slower than power Function and powers slower than exponential function okay next is about Approximity calculation Using differential instead of increment of the function. Let's just think about this Now given that natural logarithm of ten is equal to two point three zero two five eight five Somebody gave me this number. All right, but I do want to calculate really is logarithm of ten point one So remember how we will be dealing with this f of x plus delta x Now this is ten and this is zero point one and F obviously is logarithm, right? Now remember this this is Delta f of x now Approximately if Delta x is really small Remember we were talking about that this is approximately Or Delta x doesn't really matter So this is something which we were talking about when we were discussing differential. So this is increment of the function and We were talking that since if this is if we divided by Delta x and Delta x goes to zero We will get a derivative right remember this f of x plus Delta x minus f of x divided by Delta x if Delta x Goes to zero it's equal to derivative at point x right so if x is relatively Delta x is it is relatively small Then we can say that Forget about this limit then This is approximately plus some kind of infinitesimal variable, right now we go multiply by Delta x and we will get this and to be exact this is plus Epsilon Delta x Right from this but epsilon is infinitesimal and Delta x is infinitesimal While this is not an infinitesimal. So this is an infinitesimal of a higher order than this and that's why we can do this Approximation instead of equal we can put approximately and Get rid of this now obviously this needs to be Somehow some kind of justified because Delta x can go to zero but question is how close to zero which is etc So it all depends obviously However, what I'm asking in this problem problem is well forget about all these nuances Just consider that point one is as small enough and if it's a small enough how to use this formula for Differential of the function. This is differential of the function. This is increment of the function. So replace increment of the function So how much this grows relatively to this? replace it with Differential of the function now Why is it better? Well, it's significantly better because this is very easy to find out What is the derivative of logarithm? It's 1 over x So I know that this is 1 over x where x is equal to 10 now this is 0.1 So I can actually very easy calculate my value as Function of x which is given plus this piece 2.30 2585 plus This is one tenth Right one over x at x is equal to ten times another zero point one. So it's zero point zero one and the result is two point three one two five eight five Okay So that's approximate value of this That's what our calculations show Now how good is it? Well, let me give you an exact number which I got from the calculator So this is approximation now exact value would be two point three one two five three five so we have this fifth digit after the decimal point Wrong, which is not bad. So up to four digits after decimal. We are okay. All right well now you can ask why should actually do all these Mathematical manipulations if I can just go to a calculator and and get and get this number Well, it has educational purposes. All right, just to show that you can use differential as an approximation To increment of the function. So the problem is not practical problem is educational. All right, so let's just settle on that next problem Also educational I Would like to make this more precise and For this I would like to use the Taylor series. Do you remember the Taylor series? We can actually represent So this is Taylor series So if you don't remember it just go to the corresponding lecture Where I explained what actually this is all about and how to Drive this basically So my point is the following now. This is a series which means it's converging Which means we can cut some kind of a tail and we will get an approximate value of this thing Right, so what I'm asking you the next problem is cut this tail So leave only up to second derivative and Do exactly the same problem calculate? Approximately what exactly the result would be if I'm using this where x 0 is obviously 10 and X is obviously 10.1 x minus x 0 is obviously 0.1 and Now you can calculate it now the first derivative now this is Lagerism of 10 which is given right so it's 2.3 0 2 5 8 5 Now this is exactly what we had the first time right the derivative, which is 0.1 Because it's 1 over 10 One over x is derivative of logarithm and x is equal to 10 right so it's one-tenths and this is also Difference between these two so it's also one-tenth so it's times Plus one one hundredth right so zero point zero one Okay, second derivative. It's from one over x. It's minus one over x square right So minus one over x square x is equal to ten so it's minus zero point zero one times This is also one-tenths square one hundredth Divided by Two so it's zero point zero zero five right So we subtract Sorry we yes, I have to sorry. I have to multiply Sorry multiplication This is from the derivative and this is from this member right and if I multiply it will be minus 2.0 0 0 0 5 right to Zero and then I have to move it to the right by two positions. So that's what would be All right, so it's minus zero point one two three four five Okay, let's see what happens Well, it's two point three zero two Now it's three one two if I add this five eight five minus zero point zero zero Zero zero five zero So it's five three five two one three point two And this is by the way equals to whatever I got on calculator. So up to Six positions after the decimal point my calculations just based on two Members of the tail or series is already Corresponds to the calculator Right, so one position gives me four digits after decimal point correctly Two members of the Taylor series give me six, right? Now without this one, that's the previous problem basically and With the second Derivative that gives me even more precision All right, that was my Other problem, let's go so we had the problem related to Lopitas rule we had the problem related to differential and Taylor series and Now we will talk about Differential along the curve So my I have two problems about this my first Curve is a circle and let's imagine that we have a particle which moves On this circle of radius R So it moves on this circle and this is how it moves I basically give the angle as a function of time So as the time goes whatever this function is Well, it's obviously in in regions. That's how it goes. All right That's if it's increasing well, it might actually increase it might decrease. It's a function, right? So a function can go anywhere it wants it has its own mind on its own, right? So and the particle along this Circle goes along goes according to this particular function. My question is What is its Absolute speed as it goes along this curve and what are the components of this speed? which are projections of the vector of Velocity of this particular Particle on x and y axis Okay, so First of all, we have to find out what are the coordinates of our Curve and that gives us the movement as the function of time, right? So X coordinate of the point is equal to R times cosine Of the angle and angle is a function of time So angle is changing it's a function of time and that's why my x coordinate is and y coordinate It's obviously sine of this now If we are talking about the speed remember what speed actually is well, you have to take a Small piece of the curve of the length of the curve differential along the Along this curve and divide by the time Now obviously this is function of t, right? And you remember that actually it's equal to this It's a very easy thing to To derive this formula It was derived basically when I was talking about Differential along the curve. So this is the absolute speed of Our particle as it moves along the Along this circle Okay, so let's find it out equals to This is equal to R square Now the derivative of the x is r minus sine of phi of t Sine of phi of t and derivative of the t and I didn't put the minus sign because I'm still Raising it to the power of 2 so it's square. So it doesn't matter minus or plus here, right? now similarly here R square cosine square of 5 t times derivative of the phi Square and This is all under the square root and Obviously it is equal to r square and rail and and derivative of the phi square can be Factored out. I will have sine square plus cosine square, which is 1 and the square root would be r and absolute value of derivative of the phi So that's my absolute speed of this particle. So if I have the function Angle as a function of time then absolute speed as it goes along the circle Any direction any way that would be My absolute speed now whenever we are talking about Velocity we are talking about a vector which has certain direction and this length and Direction and lengths obviously are very much related to individual components the projection of this vector of velocity on the x-axis and the V-axis and the y-axis and These projections are obviously here so x Derivative of x of t that would be my Component Along the x-axis Which is equal to minus r sine 5g phi of t and the Y component of my velocity is derivative of the y coordinate and It's our cosine So these are my two components Now is there anything else which I'm missing aha. Yeah So again This would be equal to r and absolute value of the derivative This absolute value of the derivative of the phi of the angle. It's called angular speed by the way so if you have a function Which represents angle as a function of the time derivative of this Angle as a function of the time is angular speed it's exactly similar to if you have a function which is distance as a Function of time then derivative of the distance is the speed Now obviously It's different at different moments in time as the t goes phi is changing and The speed which is derivative of the phi at point t also might not be exactly the same however, if If my angle is proportional to time, which means my movement Actually is is going without changing of the speed Then the derivative would be equal to see right always regardless of the time. It would be constant Angular speed. So that's when we're talking about the movement of the particle Without Changing of the angular speed So that's it, right so that's my Basically the problem where I wanted to talk about the differential along the along the curve ds of t and The next problem also related to curve and differential along this curve Okay, now we are talking about a projectile which we are launching at certain angle to horizon It has certain velocity Which has absolute value and angle, all right, so what's given is an angle and initial Absolute value of the speed we are launching our projector and we basically have to do exactly the same in the previous problem find out vertical and horizontal components and Absolute speed at any moment t Well, let's first Restrict our movement up to the Top point when our projectile is is rising now it's rising obviously But the gravity pulls it down Now we know that there is a constant g Which is equal to 9.8 meters per second square Which is by how much per second my speed would be Decreasing if we go up or increasing if we go down, right my initial speed The has both horizontal and vertical components, right? So we can always represent this velocity as sum of two vectors V is equal to Vx plus Vy Right, that's the rule of parallelogram now it's much easier to approach this Problem from this perspective because we know for sure that Vx the x component doesn't really change with the time because there is no force which is Horizontal the acting but we obviously assume there is no air resistance or something like this However, vertical component is affected by the gravity. So if my initial Value of the vertical component is V times Sine Phi These are constant and phi is a constant. These are initial value So that's my initial value of the Vx. So it's a Vy. Sorry. It's Vy at moment zero Now as the time goes by Every unit of time we are changing my we are changing our speed by g We are reducing speed by g because the gravity pulls it down so it's slowing down and How much time actually? It will it will do it will do up until the point when my speed vertical speed will reach zero, right? That's the total time. That's the time of rising but any time Any time this the speed Would be equal to initial speed minus Constant g times t because every unit of time we are reducing by g so t unit of time we're reducing by g times t so that will be my Law of motion if you wish or dependency of the vertical component of the time so we have actually determined the vertical component and Horizontal component now as you see My horizontal component does not change. It's the same always because there are no forces which are Help or restrict its movement it just goes with this Horizontal speed from the moment zero to any moment time and it's equal to whatever it was initially Which is V times cosine of angle five, right? so that's actually our two components of The speed at any time up to the moment when it reaches the top So what by the way is the time when it reaches the top? That's when these two are equal to each other and the V y is equal to zero so the time to the top is equal to V sine phi divided by g g V sine phi divided by g g right To make it equal to zero So that's the time To the top now up until this time This is the law my horizontal my vertical speed is changing and this is the law my horizontal speed is changing and What's my absolute speed is well again the absolute speed? square root of V x square plus V Y square and It's equal to Okay, it would be square root of V square cosine square phi plus V sine Phi minus g t square under the Square root So this is a function which describes my absolute speed now these are two functions which describe Components of the velocity of the vector which is here now just out of some kind of I always Like to be sure that the formula is correct correct or something like this There is some checking which I would like actually to implement here Let's think about it at the very Moment when it reaches the top again my horizontal speed is still the same right as it was before which is V cosine phi Now my vertical speed is zero which means my total absolute speed should be the same as horizontal speed So if I will substitute this moment t Into this formula for absolute speed. I must have the result equal to be cosine phi, right? Well, let's just check it out Always try to analyze if you have reasonable result alright, so Let's substitute instead of t we will substitute this particular oh my my fault by by t here if this is equal then t is resolved as V sine phi the light divided by g alright, so what do I have I have v square cosine square phi plus v square sine square phi minus 2 v sine phi gt Plus gt square square and this is square Now if instead of t I substitute this I will get here v square sine square phi divided by g square right now instead of this v sine phi divided by g right So obviously g and g g square g square This is v Square and sine square and this is v square and sine square. This is minus 2. This is 1 and This is together would be v square cosine Square phi plus v square sine square phi minus 2 v square sine square phi plus v square sine square phi and this is all under the root and This is Canceling out and as a result I have v cosine As we should So at the top point my formula gives exactly what it would be expected to give all right, so This is just a second problem about The movement along the curve differential the speed and stuff like this Okay, I do suggest you to read all the notes for this lecture on unizor.com Other than that, that's it. Thank you very much and good luck


Hi, my name is Dianni and welcome to Esoteric Moments. This video is going to be super short, but I just wanted to do a quick wrap up of 2016 Booktubeathon. This was my first time participating in Booktubeathon as more than just a viewer. I had grand aspirations of creating all the videos, doing all the Instagram, and reading seven books while going to my normal day job. Needless to say, that didn't quite happen. However, I did get one video challenge done. I also completed four or five of the Instagram photo challenges, so I feel pretty good about that one. And most importantly, I did really well on reading challenges. I finished five books for which were ones that I anticipated reading. I finished Echo by Francesca Lea Block, which was great. It wasn't quite as intriguing to me as I was a Teenage Fairy or Weezy Bad, but it was interesting and followed many of the themes that my favorite author usually does—love, teenage, angst, and kind of self-discovery. I also finished Children of the Sea, which is a graphic novel, and was so cool. I am looking for the next few volumes in the series, and I'm really interested to see what happens to the characters and whether they discover, how people are disappearing, and what meteorites have to do with it all. I also finished The Elfstones of Shinara, which was drastically different than the MTV interpretation of that, and it also counted as a book that was older than I am. It's pretty good. I do think Terry Brooks has books and series that are better than writing, but it's a fantasy novel that's really fun and the characters are interesting. I also listened to the audiobook Fan Girl, which is about two twins that go off to college, one of who is a big fan fiction writer, and she falls in love, and what that all means to her in her first year of college. I especially enjoyed this book, and I could see why so many people on YouTube recommended it. If you haven't checked it out, I really think it's a great read. The audiobook was decent, but not anything to write home about, so take your pick on reading format. I also read Mom, which is a kind of collection of different graphic novels and different artists thrown together. It was interesting, but not my cup of tea, frankly. That's what I accomplished in this past week, and I think I did a pretty good job at my first book, Chewbethon. I think maybe I'd give myself, like, C plus, B minus, maybe, if I was feeling generous. Participation. That's what counts, right? I'm looking forward to doing it again next year, and I think I'll just set aside more time so that I can let the creativity flourish. I'm still reading lots, and I also have more videos that are about my personal druid practice and different things that I'm working on project-wise, so stay tuned. I promise it's not all books all the time. Comments below, I'd love to hear how many books you read last week, and whether you participated in Book Chewbethon with me. Thanks for watching, and as always, may you find peace in the sacred grove.


The second curse that is predominant is called a cast curse.  The scripture says curses without a cause don't stick meaning if somebody curses you if somebody hires a witch to pronounce a spell on you but you did no harm to that person those curses they will never stick but if the curses are pronounced on you and you caused somebody pain those curses will stick if you're not a follower of Jesus and there is no protection on your life of the blood of Jesus then those curses stick. It's important to understand that cast curses affect people who are casting them as well as those directed to. Cast curses don't just work for those who receive them it's also for those who send them.