Self-Propelled Hard Rods in Active Matter Physics

[00:00:00]third lock in epidendrum soft matter this one on self propelled more tries okay well not insult my cooking today is show you how deriving affinity for specific by the system and I choose what and I think of a sort of a mini-mart stiffness father I think of the mother of self-propelled harborough first we just wish that propel the substrate and the fourth to dimension we know that harm fraud we simply exclude volume Roger former a mad face and see the phase transition zone as a prof extreme artistic so the question is only wednesday the stains are gone and a civil that they have several bad people in LT beast speed v-not along the long axis four-time al Rainey's are are they not each other with each other volume and they did experience a channel through the substrate so today the medium will be completely tested on provides creature identity much forward is normal but i will for this battle the dog food rifle and probably other sons life when you start getting into the ground so the question is that is if I had several parchment to this battle system now Christian is he reminded us yesterday have thought about the scrubbing the dynamics of many bodies with Tony insistence start with husband equations usual theorem and saw a lightly a different way of doing it which is very useful in many buddy system discussion to look rather than we do the evolution of the position and momentum part of the evolution of a institution function his face base similarly our the meters in here is a system that there is preacher man dogs and we'll also browse don't worry are you choose now is that this Gaussian and Delta Quadrant 1 oz of the correlated in time although the athlete to this darkness is serving 20 so when you were system in the presence of noise you can sort of use the similar idea exercise them you can describe the dynamics at microscopic level with the setup of branch of the equation so my god is glass noise and then how it is gradual equation of our break as long as their media and personal be a very long caption to do everything with them but as soon as you're moving as they become pretty difficult the table so it is actually often more convenient to go from the description so large of an equation to sort of equal to them we haven't become its operation dynamics the description in German solution traction because we obtain a hierarchy of equation simply have a your pocket plant operations but the now is average distribution function that I made a for those of you have heard of these the Haluk important equation so coffee equivalent to something called the vb gky hierarchy in thermodynamics Robert don't normally we did you KY talent he is but see somebody mentioned equation we thought I will never mention in my hat so that's the program from San Rafael hot dog however especially difficult so the testing actually like to do so to start there and show you how this is done for what articles that there are 14 impossible to life in one dimension is no nothing the we just reach a really active life so um so we have one particle one dimension now is a fiction on the south side winterizing likely to see silica particle of register area mess and although for the purpose of i-30 we will be a point particle other than a writing fiction to other areas so write a larger our equation to describe an amicus is bad and there is a fictional false visibility pass people of course the positioner is the equation position the velocity are the very the picture and it's not the creature is adjustable by the use world talks expression so which is a substrate and saw the eight socks just expired a and the noise is to your meal and in class Ian that's according to the time with this plan for that your servant or is that from the proportion of the cavity in fact in equilibrium the way we will determine data is precisely by doing the following you could actually solve this equation for V of T that I away this to you an exercise simple magic thing to do sol is a very of your teams are specified initial condition and calculate square V of T exactly the average or the others miss the average with this type of disorder amalgam is a long time limit of this VLC and you find that is even like to and spoil delta divided by the square of the section which are in thermal equilibrium you want to require just a long time the system which is a clear when the fourth is also has to acquire what I will line as v square Cleveland that we have every square of matzo balls with his devotion which is the stake appear back and so you will find the Delta for the nervous system is essentially related pvt by some fiction pepper and soft so just do the existing now geography you can easily do our profit is one convention of our equation you can also calculate the mean square displacement the great things were more so Delta is complete x of t minus x 4 30 squaring and illegitimate and that's another exercises I release you and what we find is that by 2 and square delta divided by Delta e minus another zeta minus e to the minus legacy of RAM so a long time this is diffused it with the confusion faster which is even this is square to the diffusion constant which is given by m square delta divided by the square and you a start from here dell effective okay we see you kogarah forgiveth i stabbed relation between this is a constant friction so this is all something we know very well and this is the determiner equation more particles we can do lots of things with them however when I said if we actually what area you mind doing using many particles the option and swarm and given medication because difficult so what I really want to do now is so to show you how a grasp on the wall as an equation into something called of the clan equation which is an equation for the targeted issue the regiment equation describes the cosmic process and which could also be described in the moment distribution function and advice BP and by the way i will call this big axle right and I with a head on departure for now is the visual function i represent the probability of finding the particle in the neighborhood and the face by text both our peoples of the face base is very simple at some time as a party well what to do is there either equation for the noise ever so clearly incidentally I want to dynamically for the night average distribution function and n equations are solved what is this called for my free so to do that actually are the manual doing this but basically way is to say okay what about this product distribution probability know my concern i satisfy the following and I mr. Denzel satisfies a continuity or conservation law and you can write that in the following way so the desolate they break the time derivative of this FN can berate them so to give this I other the divinity whisper acces- of x with respect p and tank this must be equal to 0 this is a concentration of law clerk mr. flops okay and these big acts means little X and we complete and that's my conservation of it so what I want to do is essentially start with you as an army from the logical equation which perhaps our realize you're all of this big ass yes yeah this is that fact yeah so let me rewrite the large man equation eventually I thought I guess I would like wherever expo doing this way okay typing this way and rotated accidentally and seize the momentum so it'll be a total attractive safe setting so that we hide this equation and yet over d it will be plus theta we're next in XP v clearly is children and minus theta 3 and perhaps a return false derivative of a potential just because i want to show you what happens you actually keep track of the course in the basket on a clearly ada is right by a tight zero matt damon is known as the condition okay so if i do all this i sent a nice of that into this equation and under the following get the following equation for this one has enough nine dollars right then clearly we need to remind that s has depends on it because of the not okay so eventually what they want to do is that I Drive an equation from in our driver one but clearly because I depends on the doggies and then I was explicitly I still really don't know how to do that so in order to do that by reading the following we kind of do this first order to leave the noise but then he turns out and how it should be able to show you this for calcium now which is that the following things at the time the computer really become exactly so let's solve this equation for money in the following way actually let me just organization confused by bullets and big X and the back put a little bar like applying the biggest so sup d basically wanted avi I'm confuses that could be over here this this vector well I was efficient isn't anything ok let me are just for money reviving undefined from upper income and is just disorganized or at least and a very efficient this way now with formally solve it right solution and each minus LP and 4x + 0 minus integral from 0 PT vs minus t minus s ready with you respect to X in the OS and all that s and now I insert these integrations this will be harder but I thought to be interesting to show you how this is done and they finally get the power intuition our mind is a beautiful and rich people whether this equation so I get ok so let's give way to make it this be an equation for equality which is not know sign on it so I want to know the other is this pressure just brighten circular ok and now yes it's la cancer or either embrace the poison it's an operator operator a sort of the energy iced coffee okay I justify you still want to write and I just want to provide a little less that's all it is okay so now we refurbish and i am the others here well get a job and again what i could find that there are no average distribution is hopefully he ever respond even here and i am actually going to assume the division condition doesn't depend on the noise which is being disturbed people in Europe and parties to actual gathering Easter and what you actually want to do is to keep iterating this you Wiz perturbatively the business so fast again from the solution and so on and what you notice that it went quickly is that we do the nine gaussians only even pony tones containing even after of Athens give your nausea results and then heater containing an odd number victim would be busy so the first next iteration will give you zero here and yet will before it does feel furthermore because the Nazis data for a little bit time and and it is having a live for you to actually prove but because it was is that the foreign to be time and the noise er is good explicit or and then answers in F head only a time an argument T so there is a pasar con go through this expansion you can actually show that even if you do your heart no matter how many acres the only people Gaussian noise can always yes estelita aspect of second moment the only factorization will be given our deal is the one that is authorized these with that and anything else on the way so you can actually show and I encourage you to do it desire is really it was the other than the length of the team's the best I yeah or progression yes depends on the north so you're arguing about the even and odd powers that would make sense if you're just averaging ADA but also depends on the noise yes so how do you still know that Oh like the additive data at war babies so imagine taking this and work there too grateful to you in an hour so you keep interesting I got is done it once now I take that very soon a date ok Lex is doing them so I generates terms that contain all kinds of powers other which is all kinds of powers of the nozzle something like an idiot to say is that averages they contain all the number of noises to the co kumar's is Gaussian and leverages they contain even numbers can all be calculated by using whiskey or if I factorizing the meeting page okay because a nice identified in the meantime and is in ordering in finding here you can actually show with all the terms baggage all the customization gradually with such an unusual and is actually know they have to show try folks try the fourth one try to go to the wonderful face for a new seat okay and so essentially this term is really very simple because it because these and then this correlation adjust to the Delta t minus s so you can do the time if you are yes yeah I don't know maybe for some people maybe we'll clarify it for me about it but this is very similar the way you treat potential in scattering theory you iterate to find a teenager's decorated and it showed a good equation and if I pretended I literally keep putting a bathroom replay it's another way in the millions of deriving the menu aside for the bike repair shop I gotta like this one but you are the Cooper side you see while the door thermofisher what an averaging my first term at the bourne proclamation but what discussion diverges should have to go to the second order eight is like the Pataki rent is like a potential category so now set for a second order the scattering potential to be on your approximation because she's averaging in the average of the potential 0 but it quickly of an infinite series ok so anyway so after you all dead let me write down the planet equation here for the other one so now for design and i will now write it out explicitly the design go back to my original valuable the other I'm and these are excellent which is the position so the question becomes minus T over I'm then and this is Amelia derivative with respect to see all right you prime of X you will disturb wax then I have a flat with shocked I still guess we are talking so then Danica second derivative 30 p all that this is the door across from him are you assuming that the noise is small is a small consciousness of documenting what I was doing about an hour is the Stockton an exam performances in time by the way I'm making no assumptions about it recent of a fluctuation dissipation theater or a phospholipid or anything like that if you explain anything i live at the rate of giving the north but I pretext actually I resolve all the thumbs or you to put okay that's really offer to India and this can be done in this case so five days i go from my normal equation was called operations for the noise average probability distribution and for this form for one part because with u equal 0 well actually it is now if you can you can use either one if it's a bigger view of you one or the other ok but many particles is actually useful to deal with this the real estate now so is that what i like to do next so how supportive so now this is what we want to keep in mind I asylum and arrays always I just want to give you an idea how this is the ride and you can find in books and you know some people often people now support our hands are asking particles and something arises then how would i will start with is expect of a couple any one equation so you live on my part of my job and I the demerit even sports while I do it because it very much like in his wife you see one yes yea sorry I'm it's a little bit hard to read the symbols come back here maybe I need glasses or maybe a little bigger is anyone else going on with ya we have fiction again yes interruption this means the derivative of excellence that paper and avoid the noise general independent Alta we see Garcia when hours and these tables are vacant there are four originals so now i want to go from the description of a couple and one equation if we get a description internal distribution function the distribution function for all the basketball will be sort of free space but they can also define type of reuse distribution function the dragon design is division function involving Esteves of dollars to do to be exiting really x 1 up to X the bag and the private sector a text a space to ability you find this article 1 and x 12 multiple eyes tested ice regardless over the other n minus s body point and I can define a vampire bad people as long as the standard way of dealing with with an existence and so he shall there I am a single equation like a bugle equation will be electronic dynamics for a safe space distribution I can derive anything hierarchy or equations for the one two three four particles videos distribution functions they are equivalent they're equivalent really i think the same there is nothing can do it at melissa ways or approximation so in this thing would we have to do is we derive a hierarchy of pocket rocket who denies the average reduce distribution function and are allied rider has the first one which I wrote it down hearing loss which will look taller no identification or the one part because mr. Bhushan movie attitude one actually for annotation here it will be minus t1 / he will speculate swap last and then some of the one-particle throws that you have in education and then we light a storm the castle International the International continues to the force which is essentially so here we have one of the coming to the force so you can see what these reasons are wrong so the equation for the one passing of the solution happens to the two-particle the solution divisible into black people top of the three paths people and you have any tea party and unless you make some approximations you won't be able to proceed circles way the pretty star track one organizers will be drastic approximation as the disassembly approximations made so far either make one more word with the resume yes let's say a low density a motorcy will be neglectful elysium and it will receive a packet of installation just the problem optima particle distribution and what is that you are across break for the one particle distribution which are still you are generally not able to solve but if you just throw the question that you can try to do something okay now finally one of the stiffness way there are many many ways there are books with their pocket black equations yes okay and what sort of limit in regime is the sort of approximation valence no that's because it really depends we solve the system you're dealing with which you're right and so far I'm really talking about the gas of particles or will be in the yoga where the feast on between the particle is large compared to the duration ajaccio and these forgive actually interested in things like how disruptions than the reason is ask so ultimately like the probability of a free body like collision at something lighting I'm doing more than domestic three body Felicia i have also suing that treating the correlations and so I were stolen so in expansion in the density signs the school of some lengths that deserves the range of the best type of interaction in the square of sunlight because of other two dimensions for money pretty much yeah and this what is one particle one couple little too and I was going to buy these attractions okay honey after my spell shouldn't there be savvy 1314 engineering of i link the grating move over of the phone at the moment or private seller that's a salmon burger back okay so one of the simplest way of starting to do something that vision of this kind is to take moments okay their question okay and so let me introduce the first two varmints and it you can again because i didn't eat me another moment then if you look you don't have to service over the Brocade are going to do so to like a moment expansion that's okay but actually i'm going to space it in a much different way i'm going to reproduce the first two moments of the probability distribution and what the velocity of momentum moment and what they mean is the following so every day to produce institutions which is a function of X keep the integrity of the momentum and there will be the concentration part because when you see the rock back to the century today and I take the first morning for moment and actually let me actually divided by M people I mostly because I'm doing it another destiny here other than mass density and so this will be a curve okay so i will take the first two wives of this equation i get equations for this one with this and then see what i can do the matter we want to keep in better mind my goal here so there I've had an equation which are equations only for the concern fields in this case and the state will be only one the constant revision because the momentum somersault we have the substrate that takes momentum away from the system and also they're going to be equations that apply enlarge like scales are we doing a gradient expansion so that's my goal that's why I'm going in this direction so the equation for the demonics are written here in this North well for the concentration clearly simple the only thought that is a contribution is this one everything does vanishes because you easily by far the gas line here and just a continuity equation I say that the rate of change of the density at this stage these are all important is not one part because yes I mean it's much more complicated for us but I want to do a lot i will show you it was 4.5 and then i take the next moment that an equation for the current and here is a little beta are tricky well system is really pleasing the so as to the first and i missed effectiveness in the north is a little minus theta over and j but there is a missing hunter and then often discussed eventually then I have a power that always hey okay these are what you will end up with is the average of the squared over momentum right the momentum average of the squared and analyze this out here but the momentum average of the squared is essentially data the strength of the North pure member so this term we give this all the more about right down now and if you put in all that effect on to the end over data myselfi there will not be disrespectful x1 of cox-1 so this is one I need to keep track of the symbols because I'm going to be integrating over two and then this direction good way I have to find from the force which gives me a minus again I will nice one of the most disturbing the north I can write in this way as integral of DX to the Liberty with extensive explore potential I assume it isn't only extra and then she defender x1 minus x2 then i will see you at 20 °c or its duty okay so these are rated in your nose sometimes we go hard to see and your concentration or an equation for the moment now then expert is that you want to recognize that as I said you're interesting hydrodynamics you're really interested in owning an equation for the consumers to RTC at long timescales your interception I skin long compared to another compared to these five steps so these are this is actually a frequency so thanks a lot of their plan with betta basket the basket at one with a friction the system is over then this term dominates that word so we are going to assume if you like we are assuming that velocity is relaxed much more please twinkly of their position we need Ortiz compared to that solve this equation we put it back in here and we get a closed equation for the concentration which is almost in the simple case are under the pressure so she will call small shop and the drive it down for you and now I will drop the name Alex watt because I have only one no selects on it not yet despite this I will see all this one I guess b/c and me is certainly by the noise this has from this store and is not only by dynamically expression idle down before when I own this question for me problem is for displacement then i have class one of the friction derivative with respect to X 1 integral over expose the healers if it is not the next one of e x 12 is this point of it is assumptions we made then cox-1 and I explicitly and cox-2 that's for sure they come to me with respect X 1 of 0 of X 1 this is C of X to our and let's see you next okay bye the Penguins the seal this one and be i can rewrite the Kiowas implants y square and I see my desire squirt yes you can see why mr. jingles for the currency would be 10 x 10 is not deal gives you this this is this this is the balance the span of the average of the square of the velocity because it would be planted another velocity and eligible for the velocity x momentum and energy but you can probably I've done the other German no now i'm taking velocity moments and i am assuming so they calculated before was the average of square of the velocity over the noise and it is now i am assuming that the average of the sparrow the velocity overs and how that which distribution is the same as what i calculate ok so okay so we are almost there this is almost a hundred ionic equations not quite if you like you can on local better integration are the last thing we need to put in is the same way that we're interested in lime scale large basically therefore any other life in the system if you like and in particular awareness is it we can start from the drain there is a starling scale India which is essentially done image of the potential physical interaction which is contrasted the range of adventure and so what I can do is let me just take this term and let me do a change of variable and the variety is 1 over beta derivative with respect of x1 so I'm fighting against please please be polite line sort of other derivatives okay so sorry what I want to do I first want to do anything or bypass so I bring this derivative over fold the seats okay if I get the minus sign and then I go join the valuable I let X prime equal to x 12 so what i end up with here so now having pillow that x prime or v d of x prime x derivative is respectable swamp of cox-1 sign c of x 1 plus x prime christina is introduced awaits yes ok this is the function during the budget difference all about x2 on a night inside baby behalf please discuss the passion of Exile minus x2 so weird veteran swamp emotional refinery to is my night the benefits the glories of the function of XY past extent that actually makes a plus because I have to sighs okay so that's what I do that and now I explain these in the great I assume that X prime is controlled by going to the potential Amita said Alaska large opportunity to that so I'll explain is the poster with you x 1 the same confidence in derivative of cox-1 a song so now these light-piping seeing that one plus X prime the to the respective x1 2x1 plus more tops and if I only retain the lowest order to which already contains one to the reader piece over here eventually the equation and that way then the follow-on the diffusion equation which is what you expect for higher gravity equation for this really simple problem it's a diffusion equation with the diffusion constant which is the bear single particle 1 plus i can also calculate corrections specify some interactions i can tackle impression user interaction so this is the multi way of calculating the parameters in the hydrodynamics equations what about how the disaster they will depend on what I strap eventually put in and of course they are volatile or desk because I made the low-density proxy yes the very constant is the one that comes from the subsequent right yes it is indeed wave in this case yes order operations has some internal the corrections bonita okay but i have a systematic way of doing this and so this is a very very simple problem just got possible suspect and I now i think i'm gonna go to these designs because otherwise I don't think so maybe I should switch this off now I want to do this for all and I want to do it sell them now this is going to be quite a bit more complicated for a number of reasons no well so this is going to be to go around is more complicated for many many reasons first of all the government of Iraq has got relational penetration of degrees of freedom so here is my not one of them and we describe the rod in terms of the position our part of the center of mass with respect to sun exposure system and a unit vector do our part that has been 30 inflation which including my junk is with you forever with us okay still I have the dynamics involved top of translation rotation degrees of freedom are lever a larger one equation for the vibrational and rotational degrees of freedom and a couple because the diffusion of the rod is anisotropic which rock which is faster around the duration of the axes and transverse velocity so this is your talking in the dynamics I know why I tell go back to my previous life okay and here are the equations for the algebra equations from the rod so the top here the enjoyment equation so I have the copy of a translation rotation of the earth Kingdom I have the self-propulsion and in addition I have interactions which I will see the hardcore deductions so here's the logical operations for the revolution twizzle freedom in the sub propulsion it is the friction which is our tensor because it's different along with us with a lot of their own gases of the rod and then transversely I have interruptions which are meeting this way of that you are in dinner and like a trance then I have an equation for the rotational degree of freedom and you know either death but we go out back is the rate of change of the angle example of velocity the International he can understand famicon tone or something work with you ferret or because hardcore collisions are instantaneous you cannot describe of the day with a potential so you describe Mason rule it changes the velocity before collisions with velocity after the collision and this is well known for her spheres much more complicated for hot rods a duel and gives the noise prescribe here Howard recently died except for the star people then called in a sec east and yes folks are no dimensional didn't two dimensions yes this is all I could imagine I don't know why many thing doesn't go excuse me this affected I recent Delta as KBT a it's just a definition really a greater than ours Escape ETA I don't know why I cannot get this thing before what's that no I'm sorry well what a time to start then we will see this yeah now you can blow it out you can zoom heart resume good possible alright so if i zoom so it's much more complicated to do if i was describing here for our gods but let me just tell you what that back which i do it i guess it will charge you for a shot which puts them on the blue tones of duty side proportional so let's ignore we grew close for remain up and let's just look at this moon trust equation for heart for all those are all the black does what we have we have diffusion again analysis we have rotational diffusion the artistic screen adjusting frequency and we are translational diffusion de parler the default which is anisotropic because what if you faster along the rhine to the travelers and we have an interruption which is really just excluded volume with rapture and the doctor is a force under earth and the torque on da and can be written in tournaments to the volume potential allows saga which we want asked me to is the sine of the angle between the unit vector with reading the directions if you are so sine of the angle pads l square that is the rank of the earth is next to the body to rot in two dimension so if the screw the volume times the probability of finding another hall at counter there is a condition here which is that the two rods via contact Sal one-two is the size of these vectors center of each rod to the part of calm the collision speed complicated for all that it's a lot of luck but it's something that we know how to do when you introduce that proportions you find several new things for the world an obvious one that is mass collection along the direction of such repulsion there are also said propelled in this building off so we get that thermos with the obvious but we also been happening is because your constant sort of the effect on various interactions and so on is also defective self-propulsion and we find an enhancement of longitudinal diffusion is BS where these BS actually girl like v-not square and this is simply be Power Circle fairground is sort of undergoing something from the persistent random walk and salsa longitudinally future is enhanced by the third proportion to the knot square another accounting I work with that are listed and there are contributions to the tour and the force that there are the gloves on each other because essentially there is an additional longitudinal momentum exchange but self-propelled rod in a visual to that exchange us by hot rod it gives you these two contributions over here which really visit the solution City messy and complicated but again you can calculate it so you get an expression for this launch of operation and in order to employ actually do this really there is another assumption you have made essentially as soon as you have some compassion of the rod you really happening clearly our velocity with orientation are degrees of freedom and so there are some correlations between velocity as orientation breeze of freedom that is essentially in neglected here that's the main approximation because amazed I just mean that the both switches direction Brenda me I'm assuming that there are switches direction of Mecca lies another to a hard Inga but there's no answer sorry but there's no age that changes with it there is also no but yes it can also change in the action because it's there is noise so it's also about is also rotational diffusion I meant forwarded back that's a different if you that is not a toy they're not just go forward and backward pollution either yet you know conservation of momentum and energy and this kind of collision in gory detail so it actually threw a lotta collisions of rather perform okay um so yeah so I said yourself you're motivating this course trying to understand likes for Monaco so do you have so in April that was in here that the central much it's time for Passover Pharaoh well so the so how do you find so proposal God for people on which is proportional to concentration gradient for some attractive actually was I have in mind here is not so much before I because people are administrators in the fluid is mine or vibrator travelpod or experiment urban active multimedia say which is an experiment where people caught a plane myosin motors and then to acting on all Muhammad and the magazine expect the wrong and he's actually watched directed on and a lot any direction you really do see an enhancement forgot to put it on the future just like the one and then their case Lee not squares for both of the concentration of ATP essentially a few other drives and others and you to see an announcement at once to the tune of the type of V not square and now people in a unique and we're understaffed bookable experiment and high concentration erecting and their system of the fact that I might have to show you but i'll try to show this one then you can get up so this is the problem or come by if users well now there's not even a class this year I'm looking so but my goal here is to type on the Spanish types of physical interactions you go fast business outside I just want to see what physics hardcore is the simplest piece of the action we can tinker yes Prince location is V zero which will be the terminal speed of the car no interruptions p 0 is the given prescribe speed of each one of these are I just define the matter I don't know what's next move I ok I'm just saying this odd chance please meet up today always move with the speed they always believed to still be down there in this car is replenished even after a collision ok what changes in the direction for the speed they always will be ok so probable chocolate when I showed you that I actually wanted to model dynamics what I did here so I will sort of take more than and I mean really if you found it is because I want to consider the possibility of ordering of this loss so I need a concentration which overall story and I the polarization vector and they meet animatic alignment test and I derive equations for this quantity we are pretty complicated and they'll give in on the next page of your notes I'm not sure I want to go through that but let me just tell you what happened in the simplest of characters let me take this hydro dynamic equations are having a showing he ever to have engine off their complicated equations for all polarization in queue and the nuclear complicated this customer just escort a friend in a homogeneous that we state that flora Mediterranean forums and let s consult the partial Rios to the volume can give you an abacus state and so proportionately authority election yes it is no so the adult erotic operations a graphical gradient rocks are even buy these and in this approximation I don't really get an isotropic the market edition but I get the signal of the transition i defected to the decay offer a fluctuation fidelity the change in sign of the coefficient of you indicates that when row is larger the role I n the fluctuations in the alignment tensor will become unstable and pets the stiffness of the ducati transition to actually reading title in the transition and it's a picture of them to cube and what exactly that so you people actually do it but this service Pelican solution of these equations are organizing topics state of past intensity and 0 p and q no borraste is always zero in a uniform system and this is an anarchic say and what happens is that actually self-propulsion enhances the market order by luring yes talking about in transition for them to discover event here and this is actually an effect that has been seen you can zoom in oh sorry Christine you can zoom in by day with a boss if I doesn't somehow it suck it does I'm you got a song and I you go zoom in and then you get rid of this I'll fight in the ride can I use this I decided to use this thing about my and Lewis who can you go see that our specially these are actually numerical simulations long fortunately enacted facility absolute as I say thank you DTF they are easy to do I know that I city go back to they'll be done for all time they're coming after starting to move them an identity this is a numerical simulation and the superstars movies an athletic event in particle that used to be to the bottom to the water dropping as I said our rear bar sure this group I should be doing this now in real estate ' specs diagram let us take one more what if anything I can do also it is higher and operations when I star be foolhardy homogeneous states of the system then I say look at other than having more that's more than we look at the simplest of state has no traffic state-owned widgets and sleeping gear polarization 0 right context but when you draw me about sensible simplicity let's look at the dynamics of in these are firm as a prophecy and you can't go through the air space that the mall what you find and actually this is done on the previous page but relative size of the tire to assure you the result what do you find is that there is a critical value of the server passion speed which is given here above which the system support sound like waves in the range of a vector now cisapride the presence of private this is a mobile Bank collection abroad tasty different ratios became a diffusion they don't propagate okay now in the lady ke going to zero strictly it's always diffusing persistence there is a broad range of T where these are you achieve the system actually proved support propagating wave sound like ways and if they've actually been seen in this multimedia said we think that is they do see this cargo propagating waves of density and we're trying to see that interpret the velocity at which is asking to a move we can relate it to the ATP concentration in the system in some way that is an hour to hour and we have here to explain essentially this happens when so you can define difference between still let's call it a sad propulsion Last Theorem and the diffusion length scale which is the last scale that mustard allowed to move in a time one over yeah we are going to which the future conditional future features so you define to scream like scale so this action will cover the cell professional and scaly visit the usual so the java the identification does not find reviews already loose forward and i think i'll ever stop here but the point is the legend of instability you actually ensure that the pneumatic say these are stable as you would actually also expect the system generally not for bulk see for older stay so let me just going to survive without you can get out of your father which my mind as I said the minimum all there was to prepare system even know that policy which you cannot be party but we see that it's very happy with about all of date and experiments actually the vision see this they still always prefer naturally to the region Sandoval state you get announcement una vaca vulgar and husband to love you to the infusion this sound waves and you can also look at the correlation length of polarizations and see how they not they may get it up and in several of these things actually can be correlated for now at least qualitatively two things that I'm using experimental a vibrator drawing this opportunity SS so tomorrow eventually Alicia mother that should incorporate the fluid flow and the universities of people I and passive a suspension in general thank you and the father of drug litigation is taken with very high school to look that the couple of chapters there and it is actually water was mostly done by Mike was awful time of aspirin and we have any questions yes consistently nematic phase I hope I would have bothered in the magic they would mean that this of high density and so it will extend out here when you assume there's no second autocorrelation is bothered when you are studying the domestic case and in the second questions you said there's no hole instead I got the big beach x model of human Tumnus paper so okay so first question is you're absolutely right i'm assuming low density and then I kind of try to apply these things and high net so the pipe is that if you want to derive a different equations using this kind of makeup you start you have to support for similar density the you will derive equations where the structure of deflation because this equation of a barrage of this its symmetry principle or strife explained in the purse collection so if you do this correctly the search of the patients with their I will be correct it's correct whether you are at high low density this method allows you to calculate the parameters but if the parameters are valid on your daughter so yes invite you to be my pal the values I pushing it I agree however I saw something to this kind of the measures it's a useful to go along with a phenomenologist 16 immunological symmetry based kind of theory because it does he do physical feeling for what these things mean one is releasable you could see like you really won't walk their time and when I was young and some of these but for the time you pulled the drive packing density connections to these things and three body and so on but like opera and you anywhere now a single question yes okay so actually this is precisely the shack mothers persaud me more motivated her Bishop brother is the authority of fun part because in the pics below 6 16 and there is some rules of the starter dynamics and the rules are that every time step I look at my neighbors aradia i align myself with my approach changed it by direction by align myself with inning and I gone and his mother predicts the transition oh not still not settled order let's say from spinach is dissolving the not moving tuesday which is poorer with is his order and movie but his brother can see you're married by hand the alignments in by hand I look at my neighbors as I Hawaiians on it the question we wanted to ask was precisely can the simplest of physical interactions hardcore provisions give you that Pandora and yes is not and yes it is not know this is complicated and into the answer is not just no no offense and so it's so you die doing something I saw where the next we did was to look at hard when a new caption and that should be popping the answer is no again have a matter of fact at least he cannot give you is Bob homogeneous polar state which is what theories would like to call you know that so stairs are looking for it gives you large correlated region but in the limit the Bible images and happy zone so lets me other customs yeah pull off but maybe we'll address mark what type of interactions you have to put in to get for example forms in behavior maybe maybe you have to listen to me people usually talk about kima fastest they talk about so maybe you have to reach inside for the day then they will between external see similar to great incentive of Yalta okay and and that's your son some kind of biochemical signal along be and you could treat that this inspector making symmetry I maybe but I don't any quite that way but forget could imagine but so you know I mean I assume things about knowledge to continue this yes those kind of things to give it to you yes but I won't be coming from physics parts of you I want to close to as a participant interactions can give you this and this event yes is no it prints it was a wonderful of yesterday my brother who did yes not so forgiving found one that they can actually you do just for the basis of business but if you look at people had done simulations he was a simulation starbella hard rock you know simulating the rational equations they do not see a macroscopic polar stay even for the county boundary conditions they see large correlated region but there are always fluctuation so it's not the system is not employed now maybe shan't bother yes you know you Lucy transported by scoring a demonic region but the mother they start off an interaction when th the duck so it's not so I guess not surprising retrospect I think if you really talk about human texts which actually we need another constipation to agent yeah Carrie what I'm precisely megan is no but as far as i understand is outside people are still fighting this is a very contentious and active research yeah maybe someone in your it incorrectly but i don't think this agreement in the differential well there's been a lot of work that which is possible proper nutrition question yes and you get a lot of textures because I get the call saying yes to those start new channel require the boundary the system its people arrive at the boundary and then if the channel is small enough for parents of pancreas which actually grow like p naught square again than your sister poppy colors you know that but you know if you really look at bow you are here usually we ask the question about this position within the system of that meant easy don't know maybe you are much too hard well something like this is break