 Let me see how many. Yeah, we have 34 people online and hopefully everybody's coming back Yeah, I should you're online. Yes. Yes, we can hear you. We have your slides on and Well, maybe we wait 30 seconds, you know 33 people online Okay, we have 33 people online Maybe 10 people short, but do you want to start? Right Okay, so yeah, okay, let me introduce you Ashwin Gopal you work with Edgar and Stefano Roffa You work in Teresa Cisa, right? Title of talk would be power minimized to shove critical oscillators in an active bath 15 minutes Maybe the alone time for cushions because this kind of topic I sort of feel that there will be more questions on active matter today, okay? Sure, just a correction. I am Just graduated my master's from eyes of Pune in India and I did this work on the prophesied girl and Professor Stefano for my master thesis project So Let me get straight into the model as there has been enough motivation for the active matter Just one thing that I want to add regarding active matter is that When you consider a bath filled with active agents such as bacteria Then these these this bath acts as a non-equilibrium bath And it's it has properties and phenomenology which are not shown by a cordial particle in a thermal bath so we'll be mainly focusing on the motion of this oscillator in an active bath, but I'll also discuss the properties in the thermal bath to get an idea of the problem So we will be using Langevin dynamics for the system where the system is extremely driven by a constant torque F and it's a non-linear potential periodic potential and this model in adding the deterministic limit is called an angular oscillator and in this case We are studying in the presence of a bath the difference between our two baths the active and the thermal bath is in the correlation two point correlation function for the bath statistics and as we see as we know in the thermal bath case the system Has a direct delta correlation whereas in the active one It has been shown experimentally that the system have an exponential correlation with time So there is an extra parameter of tau which is the correlation time Due to the collisions in the of the active agents on the passive particle So one of the key things to identify here is that when tau goes to zero the correlation time goes to zero we recover back the thermal bath limit Direct delta correlations. So the system becomes memory less In effect, whereas when you go to dou tins to infinity limit as you can see the attitude of the noise Goes to zero and it's infinitely correlated. So this this corresponds to a deterministic limit. So this in this model It is important to understand the bifurcation diagram and the goal of this project was to understand the effect of fluctuations on the Thermodynamic quantities near the bifurcation. So this system this non-linear system has a standard node bifurcation where when the external torque strength of the external torque is less than the Strength of the potential k. The system goes to an equilibrium fixed point stable fixed point Whereas when f is greater than k the system just keeps on oscillating as you can see the system is also an example of our dynamics in a washboard potential where When f is less than k the system can Equilibrate to a fixed point. Whereas when f is greater than k it just keeps on rolling So this model has a wide variety of applications This is the simplest model for Brownian motors, which are key for interest or transport and In another biological example, these are models used to study face locking in the hair pundits where the system where the hair cells are used to amplify the incoming signals in the air and From a physical electronic perspective there are circuit elements Controsives and junctions and the constant bias these are the models is to study and Also for the applicants of face lockers Now since we are going to study the thermodynamic quantities Here, we will be using the tools of stochastic thermodynamics so that we will we can get the thermodynamic Quantities at the mesoscopic scale. So these are all these thermodynamic quantities are random variables and depends on the individual So we'll be using the city motors definition given here for defining heat and work First since we are the top inch to zero limit goes to the thermal back limit and discuss the Results that we derived and the features in the thermal bath. So as you can see in the figure We are we derived an exact expression for the average power inputted into the system. So with increasing even though the noise is a caution symmetric noise due to the presence presence of the external thought the system has a constant current and and the constant current increases with increasing temperature or increasing diffusion coefficient as you can see and One we also derived the fact that at the bifurcation point The average power has also a scaling behavior given by the average for our proportion to temperature power now We also looked at the Variance of the work important into the system in the steady state So in the steady state what we see is that for small temperatures we clearly see the signatures of the bifurcation behavior In the variance. So there are these peaks that appear in the variance And these peaks corresponds to the sum of two variances that are governed below and above the bifurcation as as you as you guess the Below bifurcation the system is just diffusing around an equilibrium part So the variance is just governed by the diffusion coefficient. Whereas above the bifurcation the system is oscillating along with the Diffusion so these are governed by all the parameters in the system. So these two different variances account for a peak in the Near the bifurcation for the variance and as you can see the analytical results matched really well with the simulations than due to emissions now Now we want now the main part of the project was to understand what happens in the presence of a non-equilibrium bar Especially in an active one. So So the activity is mainly governed by the parameter the correlation time and as I explained from tau equal to zero it corresponds to the thermal part limit and tau tends to infinity corresponds to the Deterministic limit and as you can see here On the on the average power What you see is Expected and you see that as you increase from zero to infinity you go from the finite of our Curve analytical curve for the thermal bar limit and with increasing tau you effectively go from a thermal to a deterministic bar limit whereas The key point is that it's not just similar to decreasing the strength of the Noise in the thermal bar limit and this is what I discussed and there are different phenomenologies about below and about the bifurcation but sorry What's the D parameter here? D is the strength of the noise or usually it's the bare diffusion coefficient of the colloidal particle in the bottom Okay, you know I'm in the figure that you have shown that the active bath you fix the D. I guess that's right Constantly and we are varying Just the correlation. So it corresponds to the blue curve here The blue curve here in the thermal bar limit And now we are changing the correlation times. So as as we expect the average power should decrease to the deterministic limit Okay, thanks So as as in the previous case where the variance shows significant peaks near the bifurcation point here also the peaks appear but the key thing to understand here is that With the increase in the activity of the path the The peaks also get enhanced. So the variance in the world also get enhanced at the bifurcation point so Next to understand this better There are these quantities for fan of actor, which is the relative uncertainty For a random variable in the system. So the fan of actor for the work Clearly shows his behavior. So the at the bifurcation point the The system shows a peak in the fan of actor. So it's it's always safe to stay away from the bifurcation point for a precise input of power and there are these inequalities the fundamental bounds for Stochastic thermodynamics called the thermodynamic uncertainty relations these quantify how How the dissipation in the system is related Is related to the precision for for an input of a Stainless chip current. So in this case, we derived an exact lower bound for the The fan of actor, which Which in the case of taut ending to zero goes back to the thermal path limit, which is 2 kbt and In the in the case of active path we find that far from equilibrium the The the bound can be lowered. The lower bound can be much lower than the Thermal path bound and also it is a finite. It's a time dependent bound It depends on the ratio of t by top As you can see with increasing tau for fix fix t in the steady state the the lower bound is Much lower than 2 in this case Now I should add a question for you so in in these In the right panel where you have these circles diamonds and squares. These are from numerical simulation in the case of active walk these These curves correspond to the numerical results. Whereas We have I'll explain this that Do you have to do like you have to do multiple like Realizations over many initial conditions to get these uh, nonic to converge these non-equilibrium, you know, okay Yeah, so we reach the we reach the steady state with around 10 power 5 trajectories and then these are the status Okay. All right. Thanks so Now the key result of the key phenomenology and the key results of this project was to identify that Above bifurcation point the system has a the power input in the system can be minimized at a finite correlation time so As expected below the bifurcation point increasing the correlation time means that you go from the thermal bath limit to the deterministic limit. So below the bifurcation point, uh, the Average power is zero. So it it's it's it's effectively increasing the correlation time is effectively effectively like cooling the system Whereas above the bifurcation point, you see that it's just not the Decreasing power behavior. You see that the power decreases and it goes below the value average average power in the deterministic limit and uh, and it is minimum at a finite correlation time and it increases back Sorry, I had another question for you. Just it's a it's a really stupid question. But the Um, what is it correct to say that the the integral of this thing on the right is the free energy? or no So, uh In this case, we are just considering a single oscillator Okay So, uh, you you have to define a non-equilibrium free energy in this case uh, I'm I'm just wondering if there's any connection between that and Okay Thermal bath case, uh, the free energy has contributions from the entropy Okay, so in the case of uh, in the case of Active bath, uh, the power Is not uh, easily So in the thermal bath case, uh, let me explain it better the average power is related to the average average Key dissipated. So in that case you can that relate to the entropy production Okay, whereas in the case of active bath you have non-marcovine effects So the active bath constantly produces uh entropy in itself because it's a non-equilibrium bath Also the motion of the colloidal particles also generates some um entropy So it's uh, so mathematically. It's not easy to Distinguish easy to identify the dissipation term in the Uh entropy production. So My answer is no Ashwin, we are at the minute 12 30. We have less than three minutes overall. Okay. Um, I'll try to wrap up first So this is the key result that uh, we are we are showing and uh, you'll hope for experiments to um Prove this next, uh, so all these earlier results were In numerical results and we wanted to get an idea of whether uh, these decreasing and increasing behavior can be captured by analytic results But the problem is that the exact master equation for this equation has uh, this uh diffusive term This does not which has infinite terms if you expand expand the interval. It does not converge to a single term So one has to go to markovian approximations for this non markovian problem to Get a sense of Average power in an analytical form. So, uh, we studied uh, two of the known approximations for low correlation time approximations fox and ucna And uh, we also derived another approximation at the last star limit where we derived an exact expression for the average So here are the results. So, uh, we found that ucna does not capture the behavior, uh, in this, uh In this problem, whereas fox approximations, uh, works for a particular range of correlation time And I want you to focus in this figure where I have brought it, uh, the analytical curves from the fox for the phase distribution and the numerical, uh results for the Phase distribution as you can see the for low correlation time where the fox approximation works The angular velocity distribution is close to gaussian. Whereas when the angular velocity distribution, uh, is deviated from gaussian The phase distribution predicted by the fox does not work So this this is this is due to the fact that the complete picture for the system is given by the joint distribution of phase and angular velocity So, um Also one can see that our large star approximation, uh, uh clearly captures this increasing behavior in the system Now, uh, just to generalize this, uh, system we tried, uh, numerically with different potentials With a square wave driving triangular wave and also the addler driving and we find that, uh, The phenomenology of power minimization is found in all these three kind of potentials. So, uh, our We think that, uh, uh, the, uh, the recipe for this power of power minimization is, uh, non-linear periodic potential external driving and active method So to conclude, um, we, you know, we find that the statistics of this thermodynamic quantities are sensitive near the bifurcation part And, uh, the power can be optimized to minimize minimum value at a finite correlation time over the bifurcation time Also, the ingredients for such a power minimization are non-linear periodic potential external driving and an active method We hope to collaborate with, uh, uh, experimentalists to study this, uh, field This behavior and I'm open for questions. Thank you Thank you very much, uh, for the very nice talk and we had the questions throughout the talk. Therefore, we proceed with the next, uh, uh, presentation uh, that is on continued modeling of electrophoresis and Zeta potential of air bubbles in pure water by our Baban Tartuifar, again from our institute Uh She is doing jointly with me and, uh, Ali Hassan Ali at ICTP. How are you online? Everything is okay With your presentation Yes, uh, okay