08:04:45 So for today though we have four interesting presentations.
08:04:51 And our first speaker is Yusuke Kosuga from Kyushu University.
08:04:58 Yusuke did his PhD at UCSD and was a postdoc at the, the theory Institute in day job in Korea.
08:05:31 And then joined Hugh shoe University he's known for work on a number of topics, and he's won several awards. Now unit for a young investigator type awards in Japan.
08:05:28 And today he's going to tell us about a topic that he's done work on that he's known for heat flux jams and how heat flux jams trigger layering and magnetized plasmas.
08:05:41 So, go ahead.
08:05:54 All right, so, um, thank you for having me here today.
08:06:00 I'm escape from Kenosha University, and actually it's 1am now I'm really excited to give a talk in this midnight.
08:06:09 So, the topic that I want to discuss today is about this layering the magnetized plasmas, and how this layering could be turned on by the heat flux avalanche John's, as shown here.
08:06:24 So this is an outline of my talk. In the first part, I'll talk about the layering in magnetised plasmas. And here I'll introduce some of the observations of the layout structures.
08:06:37 And they also talk about some realization of the staircases in the numerical simulations.
08:06:44 And in this part also talk about the connection to the avalanches, which is reported already from the game, I guess.
08:06:53 And then the second part of my talk, I'll talk about the heat flux avalanche jump models to challenge the formation of the staircases with the effect of the other lunches.
08:07:05 And in this part I'll talk about some model extensions based on the analogy to the traffic type traffic jam dynamics, shown here.
08:07:16 And then, after talking about this simplified models, I'll talk about some analysis based on these models.
08:07:26 And in this part in this card part, I'll talk about the formation of the staircases from the germ of the heat, what's Avalon T is done in this part I'll talk about a little analysis as well as some numerical results that we have developed quite recently.
08:07:44 And then the final part is conclusion and discussions.
08:07:48 So, here let me start by describing some observation of the staircases in magnetized plasmas.
08:07:58 As you might have already heard from Arash in the last week, this is one observation of the staircase is on the 3d tokamak our total device that combines plasmas.
08:08:11 And what you're seeing here is the temperature profiles on a one regions you have some plot like regions, and in a different regions, you have a steeper gradient as shown here.
08:08:27 And these patterns repeats in space so it starts looking like a staircase like structures.
08:08:32 This is another observations quite recent observations from HL to talk about from China, what is shown here is basically the temperature gradient.
08:08:45 And in some regions you have very steep grad and regions.
08:08:50 And in other regions you have less.
08:08:53 What they got the list steeper gradient.
08:08:56 And these patterns repeat in space as shown here so if you write some profiles read the state grad and here, and then we have some floppy disk profiles, and we have against deep grad and so they have also some staircase like structures in this age to
08:09:25 marks the staircase like structures are also example in numerical simulations. this is the results from the simulations.
08:09:26 And what he's doing he is again the temperature profiles. Well, I'm sorry this is gradient.
08:09:30 And in some regions. You get very steep graduate, and it's repeated in space.
08:09:39 And together, this very steep ground and we have a local edge of loans, as shown here.
08:09:46 And what is interesting about the staircase is that in between these strong rod into regions.
08:10:01 We can have avalanches dominating the transport in these regions.
08:10:00 So, the topic or the mechanism that I want to talk, or another light in this talk is how we can understand the interaction between avalanches and the congregation's and she'll flow formations.
08:10:17 Using a simplified models. Let me just close this deal.
08:10:22 Okay, it's fine.
08:10:24 So, here let me start by talking about the models to describe the other large dynamics in the magnetized plasmas.
08:10:34 And here we are interested in the evolution of the deviation, the temperature profiles from the marginal profiles here this dashed line represent the marginal profiles and the total profile may deviate from this marginalized, and we have some local access
08:10:49 and deficit of the heat in these regions.
08:10:53 So we are interested in the dynamics of the deviation.
08:10:56 In this case.
08:10:58 So this division, they always the heat balance equations are shown here, to describe its dynamics. We need a closed form for the equations and for that we need some models for the flocks and to describe the avalanche like behaviors, with these models.
08:11:20 One way to construct flux is to use symmetry argument.
08:11:25 And this one is based on the joint to reflection on symmetry, and this process is quite nicely, explained in these papers.
08:11:34 The basic idea is we are looking at the excess blobs.
08:11:49 And this has to go out from the systems, or if we have some deficit in the temperatures, they have to propagate inward.
08:11:46 These are required to have the net heat flux to be down the gradient.
08:11:53 And in order to have this type of behaviors, the flux needs to be invariant under these transformations so if we click the direction of the propagation, the clarity of these deviations needs to change simultaneously, and under the these transformations.
08:12:11 Flux needs to be invariant.
08:12:14 And we can construct a very general form for this flux and the simplest form of the flux that satisfy this this symmetry argument is given by this new using this flux, the avalanche dynamics is basically described by this burgers type equations.
08:12:36 And one challenge for, to understand the formation of the staircase volunteers to explain the margins of the particular skills embedded in this staircase patterns.
08:12:50 I hope you can see the picture here, somehow, the video overlaps with the pictures here.
08:12:57 So, To kind this problems.
08:13:01 We worked on an extension of Babylon models to effect to include the effect of the jobs in these papers.
08:13:10 What we have done here is basically we have allowed the instantaneous heat flux can deviate from the main flux.
08:13:18 And this means lots of course constructed, based on the symmetry argument to describe the avalanche behaviors.
08:13:26 And we allow this instantaneous heat flux can deviate from the means and we allow the plasma to push the hill floods toward this mean values in a finite time tall.
08:13:38 I gave you this extension kind of out of blue here but this is based on an analogy to the traffic data traffic jam dynamics models.
08:13:48 Here.
08:13:49 So in this traffic jam dynamics we're looking at the evolution of the car density, which involves due to the flux of cars.
08:13:58 And these clocks, or the speed of the cars.
08:14:04 Each individual cause they need to adjust their speed toward some equilibrium flows.
08:14:11 This call is less once time of the drivers drivers has to digest their speed to the surrounding topics, and if the drivers can respond very quick.
08:14:23 Then the bill Steve because some equilibrium values, then there's no jam happening in this cases we have some uniform flow, the car what topics.
08:14:33 But the drivers takes quite long time to adjust the surroundings. We start having the formation of the jumps. So, here what is floated his car density, the correlation become densities.
08:14:48 The gym is happening everywhere idea here is to introduce this correlation behaviors. To understand the correlation of the temperature profiles observed in these numerical simulations, or staircase formations.
08:15:05 So here I have kind of introduced this time delay in a heuristic burner based on the physical or the analogy to the traffic dynamics models.
08:15:15 But we can do a bit more rigorous derivations to get this generalized heat flux flux granted relations.
08:15:26 We can start from some kinetic equations, we can look at the two point evolutions and by taking Bill C integrals, we can recover the similar structures.
08:15:37 As I introduce based on this topic models here.
08:15:42 And by just going through this algebra class we can identify this response time in the order of the nonlinear mixing time did the equals b connections in melanocytes plasmas.
08:15:57 And while by having this generalize flux on the ground in relations.
08:16:03 Now we can extend the models to describe the avalanche dynamics with the effect of the jobs.
08:16:09 And now the dynamics of the deviation, this temperature deviation stay described by this nonlinear telegraph equations, other than the burgers equations for the avalanche models.
08:16:25 And, here let me talk about some highlights from the JAMA analysis. What kind of behaviors we can get by using this telegraph equations, an important piece of this telegraph equations is that there are two specific speed or Kara characteristics speeds
08:16:44 embedded in their systems one speed is of course the speed of the pulse, which is already included in the bogus type of analysis.
08:16:54 But on top of that by including this time delay effect, we can have a way we feature into the dynamics, and these two Tom's defines a two new speed, which is defined by the ratio between the severity and the response time tall.
08:17:14 So since we have those two different speeds, depending on which one is fast we can have a rather different behaviors.
08:17:21 So the regime we are interested in is the regime where the response time is long plasma is taking so long time to adjust its heat flux, that's where we expect jumped it happens.
08:17:35 And what happens in these cases that since we have a long response time this heat flux waves becomes slower. So the pulse starts overtaking, so the jam can start from indeed systems.
08:17:49 If you want at some different picture on this term formations, you can go to the pulse moving flame.
08:17:56 And in this frame that the severity becomes negative for the long response time so we can have the information through the negative discuss the type phenomena.
08:18:09 And by going through some calculations, we can look for a preferred skills what typical scalars for these jobs.
08:18:19 And by putting some numbers, we find these skills, actually agree quite well with these typical skills of the avalanches are reported from the numerical simulations.
08:18:36 So, so far so good. We have analyzed the initial stage of the jam formations.
08:18:42 But I thought it's better to have better understanding, especially about the job, or the nonlinear stage of project formations.
08:18:51 And also, I thought it's important to look at the relevant feedbacks for these jam growth to saturate.
08:19:01 Also we went to studying how the saturated space of john pattern emerges.
08:19:07 And for that, we kind of have a nice picture based on the analogy to the traffic jam formations.
08:19:14 But I thought it's important to demonstrate how is heat flux dumps happens.
08:19:22 So we've decided to develop some numerical calls to look at the nonlinear behavior of this jams and using these calls.
08:19:37 Well basically we, what we have done is what we solve this nonlinear demographic equations by initiating some initial post, and we saw whether they grow or propagate in a stable manner, or jam happens in what parameter regimes.
08:19:51 We studied that type of behaviors, so fast, we have just looked at the stable case this is just the propagation of the blogs and boys.
08:20:03 For some stable parameters we can recover as Rob's propagating outward, and in some cases this is avoid the call the past localized in the edge and they propagates inward.
08:20:17 So for the stable regimes we can recover the propagation of the blogs and voice, and we can have the solutions that satisfy the join to reflection symmetries.
08:20:32 And, of course, what we're interested in here is the formation of the jobs here, and to get the right parameters to get the jump formations.
08:20:42 One guiding principle is to look for the overtaking conditions.
08:20:47 We can have this overtaking by having a very past pulse was slower.
08:20:53 Second, sound.
08:20:57 And this is a case where we have passed up Paul's larger initial amplitude, in this case yes we do have the formation of the jumps, which looks like a cross selling instabilities in the moving frame of these jobs.
08:21:13 This is different conditions, this is the case where we have a slower heat flux waves.
08:21:21 In this case, palace can overtake again.
08:21:24 And in this case, is we can have the jump formations, again, by going to the moving frame of these pulses.
08:21:34 It looks like the jam happening as a class ending instabilities.
08:21:39 So we have done some parameters holidays to get the condition for the jam formations.
08:21:47 We looked at the parameters for use of power, strength, which is indicative of the how fast it passes and also we have changed the value of the diffuse severity, which is, indeed, which is important for the second heat flux speed.
08:22:03 And what we get here is like, if we plot this word soccer is basically when we get the john formations.
08:22:13 This block means we do not have any germs. This is just a blobs propagating Staveley, and this in the white case, we get the formation of the chance.
08:22:26 If you look at this tendencies we can get these jumps for the faster house or slower, second wave. Yeah. second sound. So that's kind of the overtaking conditions, and to be more quantitative, we can look at the threshold for to get this done formations.
08:22:48 And just by leading of some numbers. This is what we get.
08:22:53 We need a prosperous, to overcome the heat flux waves. So this is a better version of estimate the pulse speed, but just by having this again by having this overtaking conditions, we can have the formation of the John's in this numerical simulations.
08:23:17 So, um.
08:23:21 So, this is just a single john phones and we did not put any feedback, either. There's no feedback from the hyper viscosity there's no feedback from the sharing the inbox.
08:23:32 So what happens with this Job's is they keep growing this keeps a sharpening until the call diverges.
08:23:39 So, we have done some parameters are ways to see how we can stabilize this jam growth.
08:23:49 And one effect we introduced when the sharing feed about by having the correlations we could have a very strong car flows to reduce the formation the jumps, and this is what we have.
08:24:01 The initial stage.
08:24:04 These jump starts growing but as the jam grows a sharing feedback becomes larger and larger to standardize the john.
08:24:14 We also looked at the effect of the hyper divisions. And in this case, these hyper divisions, they slow down the gym growth, and they kind of prevent these sharpening happening.
08:24:28 So both of these shelling feed about and also hypothesis course it is.
08:24:33 They do a good job in terms of regulating job growth as shown here.
08:24:41 So here, let me talk about the four most of the multiple jobs.
08:24:46 So far we have only looked at the formation of the jam, and also the saturation the growth of the jumps.
08:25:01 For the single calls, so we wanted to have the multiple jams happening in the systems to have the staircase like structures.
08:25:05 And to get the multiple John's, again we draw some analogy from traffic jam dynamics to get the multiple jumps. What we need is we need a continuous injection of the cars.
08:25:18 Otherwise, only single one jump on somebody keeps propagating.
08:25:22 So what we have done is we tried this initial conditions we forced the boundaries and see what happens with this
08:25:35 part of patients.
08:25:37 So let me show you some movies.
08:25:39 This is the initial stage we have the formation of the single jumps, and it keeps propagating, and we keeps injecting the heat, and the boundaries.
08:25:53 And after this initial post propagating, we have the secondary jumps forming in these regions.
08:26:01 And those entire pattern keeps propagating upward.
08:26:06 And then at some point, we had the formation of the third jams so we can have the information on the multiple jobs, shown here.
08:26:17 So, let me describe this sequence of the jump formations.
08:26:25 So by starting from this from, like initial conditions. Of course, if we do the stable case we just have the front propagation, nothing happens, these fronts just propagate by choosing right parameters for the instabilities, we can get the jump formations
08:26:43 and in this case we also put the feedback from the sharing as well as Hi Bob is called cities.
08:26:50 And by having these parameters we can have the formation of the multiple jobs, as shown here.
08:26:58 And in this case, let me emphasize that this jumps up here successively, rather than having the generation that Jim was anti patterns.
08:27:08 We can have the multiple jobs, and these jumps from successively, the fast jumps forms and then secondary jumps forms, later on.
08:27:20 And, here let me also talk about some foot crunch from the recent observations. We have this multiple congregations but the similar patterns of the temperature congregations is also observed in case the experiment on case are talking about from the, from
08:27:39 Korea. And in this experiment, they also observe the interaction between these multiple congregations and avalanches on the shelf loads.
08:27:47 So we think these avalanches and the jams is a quite nice way to think about the formation of the staircases at least for the magnetites plasmas.
08:27:59 So maybe I'm running out of my time this is almost the last night. We have also looked at this structure the staircase is, this is the entire patterns on top of these deviations, we put some mean values to get the staircase like structures.
08:28:19 This is a total gradient.
08:28:21 And this is a skill we were interested in from the gym analysis.
08:28:34 So Jama analysis predict these spacing is sensitive to the forcing strength, so we looked at how this jump spacing respond against this strength.
08:28:47 This is what we got.
08:28:50 By changing the strengths of the part of Asians.
08:28:54 These spacing changes according to this jam predictions so I think this jam calculations doing quite well.
08:29:03 So, let me conclude my talk.
08:29:06 In this talk, I have talked about heat flux avalanche john models, and I talked about. It's the extension of governance models based on the traffic model dynamics.
08:29:20 And I also talked about the jam formation as a result on the cross selling is abilities, and we can reproduce the same role correlations or layers from this heat flux avalanche Jones.
08:29:32 And of course, this is just a toy models, and we can walk on the server or extensions.
08:29:38 But in this box of. I was kind of wondering, is there any relevance of this type of stories in the gym, the context and especially relevance of avalanches plumes and things like that for the formation on the staircase is in a different context.
08:29:59 I was kind of wondering, would it be useful to get something like a guy, great on this generalized flux grad into relations for the rotating slots by the rules and things like that.
08:30:12 So, thank you for your attention. And that's it for me.
08:30:17 All right, thank you. You see, okay.
08:30:20 Very nice presentation.
08:30:24 Questions, ladies and gentlemen.
08:30:26 Hello.
08:30:30 Hello. Go ahead.
08:30:33 Okay. My question is, basically in a magnetic confinement plasma equals be a staircase is relevant is relevant because micro barriers. So I think, yeah, micro barriers Yes, y de parte de facto of Avalon say on all Avalon say party de facto equal was equal
08:30:59 to be staircase on the Avalon, it will be decreased or increased.
08:31:03 Well, I mean, those are two different entities you get the average and equals beef laws. They fight with each other. If we have a strong equals b flows, they tend to reduce the avalanches.
08:31:16 But if we have a very strong avalanches.
08:31:20 They drive a strong transport to smear out the congregation so they kind of reduce the strength of the equals beef last year so they kind of fight with each other.
08:31:31 That's what I.
08:31:34 That's my basic understanding.
08:31:38 Right. If you have a question, thank you have questions, please raise your hand in the reaction box I didn't think it was necessary to say that DMA you look What are you, you want to ask.
08:31:54 Okay, everyone else please raise the hand that helps, but go ahead.
08:32:01 Well, I don't have a hand on my on my one, you, you should in reactions.
08:32:09 I don't find it. Sorry for that.
08:32:12 Well thanks you to give up for the talk, you have a relationship between the speed of the pulse, and the diversity in order to get your clustering and stability.
08:32:25 As you will know the this pattern lives close to marginal stability. So the diffusion is not that large, which puts really big constraint on the speed of the balls.
08:32:39 So how do you try to put in numbers and the match with the magnetic or whatever, speed you want to would expect for the avalanches.
08:33:07 Right, um, we haven't tried that seriously about the numbers but
08:32:59 we have basically his is it's a rather large deviations, as you mentioned, and if you know why the strength of the pause this pause starts propagating very slowly, and if you want to look at this in fact maybe we have to run the cord longer.
08:33:18 What we have done is like we have only solved, 20 current tablets correlation time so maybe it's important to look at a longer time behaviors.
08:33:32 Maybe it's important to look at longer time behaviors. I think that's important.
08:33:39 Okay, in the absence.
08:33:41 Did you have anything more again, just may have a follow up since I don't see anyone, raising my hand is up to. So, go ahead. So, well you should that the injection is important.
08:33:56 While you're headed towards source and boundary condition to be important in that thing. Obviously your outer boundary condition is going to the role to rest.
08:34:08 The thing is sleeping. So, have you any ideas, how you would actually with the injection
08:34:20 into the system.
08:34:22 With the end up with the stable state. And then, well that's why it's kind of toy. Again, I mean, I think it's more serious issues like we kind of post in steady manner.
08:34:35 But the way the avalanche is false, is I think it's more stochastic sometimes is excited, and sometimes it's not so more relevant boundary, or forcing condition with the, we need to put some stochastic pausing, and I think that type of analysis we might
08:34:53 need some noisy telegraph equations.
08:34:56 But for that.
08:34:59 That was beyond our ability to develop some color for the stochastic dynamic so we haven't done that much yet.
08:35:08 Regarding the different types of boundary conditions, we tried several boundary conditions like, you know, open and close neighbors to the closed boundary conditions these policies start flipping back and forth in the systems and until they explored.
08:35:26 That's what we got.
08:35:31 Okay, you know what I'm going to ask this whole house of cards from the beginning and doesn't seem to have changed rests on the time delay, right, and what physics.
08:35:49 I mean, is there a time delay is it that simple which one could debate and then of course the scaling of the time delay in particular its behavior. For example in near marginal regimes, which I think could help you because it could become very long, which
08:36:07 is what you need.
08:36:09 Can you comment at all.
08:36:12 Yeah, I mean that's kind of very simplified response time it's just a constant parameter here, but the reality it's just a function of.
08:36:24 I don't know the distance from the marginality and things like that. And then this response time can be a function of tablets intensity or the scales, as you mentioned, you know, very unstable scales or scales calls to the marginals that type of behaviors
08:36:44 that should be implemented, and we haven't done that much, but I heard you're working on that with your students, I guess.
08:36:51 Well, yeah it's it's a complicated problem, right, to put it mildly, but it under the whole story. All right, I think it's important to.
08:37:04 All right, we better move on now actually we're, we're already behind for the day but that's because we started late so let's thank you Yusuke for a very nice talk again.
08:37:17 And remark remarkable for what is it one in the morning.