 them in the chat. Yeah, I can do that. Well, yes, I can go ahead and do that now. Thank you very much again for your excellent talk. And we close up today with Nick to factory from MIT on the odd dynamics of living crystals. So are you with us? Yes. Can I share my screen or go ahead? Okay, I think I should wait for John to on share. Oh, I'm sorry. I'm sorry. You can probably overrule it. Yeah, you could have you could have just taken over. Just putting thumbs up next to a couple of questions that came up for you, John. Yeah, I'm thinking about them. Right. Take it away. Okay, well, first of all, thanks to the organizers for invitation to speak. I'm going to continue with the theme of the session on active matter and I will highlight a particular direction in my group that I'm very excited about, namely how non reciprocal interactions or raking the golden rule of non reciprocity can give rise to collective dynamics and work generation in the absence of cyclic protocols. First, I'll give you a broad overview of what my group's interests are. And one of the fundamental questions that we ask in physics is basically discovering the underlying laws in the system. But even more importantly, we are interested in understanding and explaining the new laws that emerge when many individual components interact. And to discover these laws, we do not always keep track of all the electrons and protons. We're always looking for important variables, or key degrees of freedom. And once these variables are identified, we combine them into what is called an order parameter, which is the quantification of the emergent phenomena. And in equilibrium physics, this concept of order parameter has been very powerful. And it plays a crucial role in defining a wide range of phenomena. I think magnetization is a classic example that we are all familiar with. Now, asking for the order parameters of the living state or living systems is a very hard problem. And it's also not a well defined question. Because when equilibrium is given, statistical mechanics frames the behavior and phenomena in terms of minimizing energy, since no energy is added or lost. But when a system is out of equilibrium by necessity, such as what we have in living systems, they can no longer follow an energy optimization principle. So then the question is, can we identify general principles that can guide us in developing a physics of living systems that can reach the same level of predictive power that's the standard in any other area of physics? And this is a challenge that we have been trying to address. And to do so, we develop experimental tools to observe and identify non-equilibrium degrees of freedom. We develop data analysis frameworks to define order parameter fields. And finally, we develop theoretical frameworks which have predictive power. Of course, the concepts that we develop, the hope is that there are system independent. However, to develop these concepts, we need model systems with rich phenomenology and self-organizing principles. And there are many model systems to choose. One in particular that I find very interesting is a multicellular systems. And in particular, the system that my group uses is C-star OSITE. And this is actually one of the oldest known developmental biology model systems. And if you think about it, multicellular development starting from a single OSITE all the way to the full organism, as it has evolved over the past billion years, is truly an accomplishment in the realm of self-organization in formation processing. The processes need to be orchestrated in space and time to give us robust outcomes. So I'm going to show you this slide which highlights my group's approach. This is a journey in space and time to showcase the broken symmetries that we have identified and the emergent phenomena that we have discovered at each spatial temporal scale. Probably the most important broken symmetry, which is the defining feature of non-equilibrium systems, is time reversal. And my group has a broad interest in understanding how we can use tools from stochastic thermodynamics to identify spatial temporal scales of energy dissipation in living systems and in complex systems. Moving up the scale as well as complexity, my group is interested in understanding how biochemical signaling proteins self-organize at cellular scale and how cells use these patterns to perform computational operations. But today I'm going to go even further up the scale and I will tell you a story on the discovery of odd elasticity in a living system. Odd elasticity, as you will see in my talk, is the broken symmetry of the stress tensor or broken symmetry of the response of the system. And it happens in systems with two conditions. One, broken time reversal symmetry as well as non-reciprocal interactions. So before I tell you what actually this odd elasticity is and what's the consequence of having that in a system, I'm going to talk about this paradigmatic system that allowed us to reveal this exotic material property. So to do so, we're going to look at the star of my talk today, which is the fertilized starfish embryo. And when I played this video here, you can see that basically we are starting from a single cell and the fertilization process gets started. And you can see the cells on their go symmetric cell divisions. This process occurs many, many times. You can clearly see that the number of cells is increasing. There is a lot of cell rearrangement and cell migration. And you can also start noticing that there's a group of cells that are at the surface at the periphery of these spheres. And these cells have a very important organ known as celia. And if you must know, celia is this her like protrusion that beats and it's involved in swimming and developmental signaling. Now these embryos are covered with celia. At first, this celia is beating asynchronously and that's why you can see this chaotic motion. At some point, they start beating synchronously and that's where each of these embryos start swimming around. There are two important broken symmetries here. One is time reversal because the development has started, as well as chiral symmetry breaking. And I'm going to emphasize this chiral symmetry breaking. So let me show you a microscopy close up of one of these embryos, so this ellipsoid object. And you can see that the embryo is covered with celia, this her like protrusion. And the ciliary beating pattern is involved in actually induction of left, right asymmetry in many organisms, including us. So if you take a look at this red box here, what you can actually see is that we have a sparse ciliary carpet that's actively beating and it's generating this metachronal waves. And that's why each of these embryos are swimming in a chiral way in the fluid. Now we decided to put a large number of these embryos together and we observed an absolutely remarkable phenomena. So this is the first frame of a video. And note that in this frame, each of these spheres is one of these swimming embryos. And I'm going to start playing the video. And what you see this, it's absolutely beautiful phenomena, which is this spontaneous crystallization of a large assembly of these developing embryos. And over the course of their natural development, thousands of these embryos come together to form what we call a living chiral crystal structure that can persist for many, many hours. And the whole self assembly dynamics and dissolution of the crystals are controlled entirely by the embryos internal developmental program. And I want you to note the scales here. So this is a collective phenomena that happens over days and on the millimeter scale. So you can actually observe this by eye. So to give you a sense of scale, this is a photo of one of these crystals that I've taken on my iPhone camera. And for those of you for experimentalists in the audience, this is actually a six well plate. So it's about a few centimeters across. And you can see that this is truly a phenomena that you're observing. You can observe with your naked eye. Now, first, I'm going to give you a bit of an intuition of why this process happens. So what you see here is a side view of one of these embryos. And what you can see is that the embryo is elongated along an axis of symmetry, which is called anterior posterior or AP axis. And when the embryos swim towards the water interface, they can attain a stable configuration, such that the AP axis aligns perpendicular to the interface. And you can actually in this image see the fluid flow that's generated around the embryo by the ciliary ability. And when a group of these embryos align in this manner, they can spontaneously self organize into two dimensional hexagonal crystals. But then as the embryo develops, what we observe is that the shape, as well as the topology of this self generated fluid flow near the embryo surface changes substantially, which leads to first basically a way of introducing noise in the system, which leads to disassembly and eventually complete the solution of this crystal. Now, if you look at this radial inflow that I described, you can see that we can actually accurately describe this type of flow using a stoke slit. And for those of you are interested in fluid mechanics, the stoke set is a solution to the stokes equation that describes a generic fluid flow near a force exerting object. And you can see here that both the fit to our experimental data as well as theory. Now, this self generated stoke slit does two things. One is that it stabilizes the upright AP axis orientation of the embryos. But importantly, it induces an effective long range hydrodynamic attraction between embryos, which results in facilitating the assembly of long leaf crystals at the water air interface. Now, if you notice something interesting is happening when two of these embryos are coming together again note that they have a handedness to the direction of their rotation. So first of all, we have the traditional reciprocal attractive force between the embryos mediated by the fluid, which affects their potential energy, which is the stored energy that's determined solely by the relative position of these objects in the crystal. But the motion of the fluid is also generating a second transfer force that cannot be ascribed to a potential energy. And this is going to lead to emergence of very interesting material properties that I'm going to describe in a few slides. Now, I want to emphasize that this non reciprocal type of force is actually a result of the non equilibrium nature of this system. And this is again an example of basically the two body interaction and three body interaction. And you can see that the bodies are rotating because of this type of microscopic non reciprocity in the system. Now, very briefly based on the experimental insights, we constrained a minimal model in which each of the upright spinning embryos are rigid discs that interact through hydrodynamic stocks that mediated pervise attraction, a pervise transfer force exchange and pervise chiral torque exchange. And this is the equation that describes their dynamics. I'm not going to go into detail, but happy to answer questions. And we can use the stocks that strength that's determined from our experimental fits and become parameterized the force and torque exchange based on rotation frequency measurements of the bound per and triplets. And then we were able to show that this minimal model is sufficient to quantitatively describe the formation and phenomenology of the crystal over several orders of magnitude in cluster size embryo spinning frequency and cluster rotation frequency. Now, of course, we have a crystal. So one of the first things we wanted to focus on is the properties of the ground state of this system. And of course, one of the striking features that we observed was that this whole process of nucleation growth and dissolution is happening naturally as the development progress. And what you can what we observe is that first the crystalline order increases during the growth space. Whereas the dissolution is preceded by a loss of orientational, translational and dynamic order. So I'm going to focus on one of these orders, which is the orientational order. And to quantify orientational order, we calculate the local bond orientational order parameter or size six. Just to give you an intuition, the magnitude of size six is quantifying the local hexatic order. And the phase angle indicates the local bond orientation. And the videos that you're observing in this slide are experimental measurements of the evolution of this order parameter during the whole lifetime of the crystal. So I'm going to just briefly skip over this slide. So this shows the probability distribution of the phase of the size six, as well as the magnitude of size six and how it evolves with time. And there are of course other types of order to look for the ground state of this system. For instance, we can look at translational order and dynamic order. And each of these again shows that there is a progressive loss of the order, which as the as the embryos develop and you create more and more noise in the system, either because of the fluid flow generation or the particle shape. So this is what the ground state looks like, but actually it turns out that the excitations in this system looks very interesting. And in particular, one of the questions we had was, what is the consequence of breaking parity in this system? Because we have a material that's individual components are spinning. And because of this spinning motion, we have a transverse force and torque in the system. So first of all, I want to remind you that when we were looking at the first video of this crystal that I showed you, there was a global chiral symmetry breaking. So there's a global rotation of the crystal. And this is because of the rotation of individual components of the system. But we observe something more striking. If you look at the co-rotating frame of the cluster, so this is going to the co-rotating frame of the system. And what we saw was the fact that the crystal supports self-sustained chiral waves and shear cycles. And what I want to emphasize is that the time scales that you observe are quite extraordinary. You can see that the wave is actually propagating for as long as an hour. And this is quite surprising because this is an over-damped system. And again, this can only happen when you have a non-equilibrium system at hand. So to better visualize the chiral waves and shear cycles, we can measure the displacement field, both angle and magnitude. And now you can clearly observe the propagation of these self-excited displacement waves, which again in some cases can persist for longer than an hour. And again, I want to remind you that this is a fluid-embedded crystal lattice, which is overdamped. So the existence of such waves should come as a total surprise. So let's kind of like take a step back and try to understand where do we get such interesting behavior in an elastic system that we think of it as an elastic media. So just a quick recap. In standard elasticity, just taking Landau-Lipschitz book, we derive the entries of the stiffness tensor under a variety of assumptions. And of course, energy conservation is an important requirement, which has a very important consequences. And in the case where we have a two-dimensional isotropic media, this constraint results in basically constraining the stiffness tensor to only two independent diagonal entries. The bulk and shear modulite, the modulite that we deal with in everyday materials. Now, there was a beautiful theory work from Wincenzo Vittal's group and others in University of Chicago that came out in 2020, where they show that by waiving the standard requirement of energy conservation in linear elasticity, one can actually unravel unexpected mechanical behavior that has previously been overlooked. And this is because entirely new elastic moduli appear in the stiffness tensor. And these moduli, these components are off diagonal and odd, and hence they term this odd elasticity. Now, one of the consequences of odd elasticity is that the system in, you can excite these type of waves in response to an external compression, or in general a system can display odd behavior, which is basically this oscillatory motion in response to a specific stimuli. And this is exactly where the self-sustained chiral waves come about. And to visualize these oscillation waves, we can determine the displacement gradient tensor and extract the four principal strain components. So it's divergence, curl, shear one and shear two. And the plots on the left is showing you basically climographs or spacetime projections of these waves. And you can see that you have these periods of sustained oscillation in time. Now, what's more interesting is if we take two of these components and construct a two-dimensional face-based trajectory of, for instance, shear one, shear two pair, what we observe is that it traces out a closed ellipse. And this ellipse indicates the emergence of an autonomous self-sustaining elastic engine cycle in which the system converts internal energy into mechanical work to offset the dissipative losses. And again, what I want to emphasize is that this is a system that's once it's been kicked and it just goes into this cycle. So we're not actually performing a cyclic protocol. The system gets excited and it undergoes this, it basically generates work. And the area that's embedded by these curves is the work that's done on the environment. And I find this quite remarkable because we're really linking rigid body mechanics to thermodynamics. And this is similarly true if you look at two additional components, the face-based that's spanned by divergence and curl. Now, there are two pieces of information we can extract from these cycles. Well, first one is that we can quantify lower bounds of the work that's associated with these strain cycles. And to do that, we actually look at the statistical irreversibility of observed cycles using the many tools that is available from stochastic thermodynamics. And we calculate the face-based currents for each of these embryo positions in the crystal. And we can construct a spatial heat map of the local entropy production that arises from the divergence curl coupling and shear one, shear two coupling. And you can see that these maps reveal the spatial temporal variation of the entropy production rate with higher rates appearing when the crystal is excited. But you can also see local heterogeneities, which actually happens mostly in the vicinity of vacancy defects. I'm going to briefly mention something about that in a couple of slides. And the second piece of information we can get from these cycles is the handedness of the cycle. And the handedness of the cycle in the strain space corresponds to basically whether the system is doing work on the environment or absorbing. It's basically the environment is absorbing the work. And to quantify that, we can basically look at the cycles and then try to assign handedness to this. And in this system, we can predominantly see counterclockwise cycles. And basically the components of the odd elastic moduli that we have, what it means is that the system is doing work on their environment. I'm going to briefly mention the fact that everything I talked about has been elasto dynamics, where it shows that we have the existence of this type of odd elasticity. But the question is, can we also extract these odd elastic coefficients? And what we can do is we can actually look at the strain around lattice defects. And in this system, we can have different types of defects. You can have defects with seven-fold coordination, or you can have five-fold coordinated vacancy defects. You can also have defect pairs. And for those of you who are interested in crystallography, in these hexagonal lattices, we can look at the strain field that's associated with a pair of five-seven-fold coordinated defects. And the strain field encodes information about the effective mechanical properties of the system. In the interest of time, I'm going to skip this slide, but happy to talk about it. But in practice, you can extract basically information about these non-banishing odd moduli, which are these off-diagonal components in the system. And of course, in the maybe last couple of minutes, let me just say that this is truly, for us, is just the beginning. Because so far, our experiments have been focused on observations of the intrinsic fluctuations. So we've been doing fluctuation measurements. Of course, the logical next step is to actively perturb the system and to do response measurements, and then try to understand how different symmetry-breaking phenomena influences linear and nonlinear response to this type of external perturbations. So this is an example of one experiment. I call it a crystal in a box. And where in this system, we can actually apply a step compression. And if you choose the correct strain, basically the correct step compression, you can excite the crystal. And again, then the crystal undergoes the cyclic type work generation. And I think this system will allow you to develop a generalized fluctuation dissipation theorem for parity-violating systems in which both chiral symmetry and detailed balance are broken. Now, there are other types of experiments one can do. You can excite the system locally so we can replace one of these objects or embryos with a ferrofluid droplet, which you can externally actuate. And then again, look at the type of response that you get locally in the system. But I think what I'm mostly excited about is that these structures that support self-sustained chiral waves exemplify this idea in active matter that we have upward energy transport from individual microscopic constituents to the macro scale. And again, if you think about this system, even at the single particle level, we have actually a collection of celia that are kind of that are dissipating energy all the way to the whole crystal which can generate work. And I think this is the first time that we have this opportunity to try to look at how we can for signatures of this upward energy cascade in an active matter system. And the last thing I'll mention is that you can also start playing these games, which is instead of looking at crystals with identical particles where you start all of them at the same developmental stage, you can start mixing particles of different developmental stage, which means that you are basically changing or you're tuning the strength of nonreciprocity or non-reciprocal interactions between these particles. And then you can start thinking about the consequence of non-reciprocity and collective behavior of these many body systems, which basically, again, the dynamics is not governed by an optimization principle. And I'll just mention that, and it's not just C star. So C star is only one species in this incredible branch phylogenetic tree, which is the kinoderms. There's other species such as C urchin, which they actually exhibit even more interesting features, namely, they break shape symmetry as well. So they have this triangular shape, which actually results in what we believe some really interesting features such as a piatic liquid crystal. And this is an active area that we are very excited to further explore. So with that, I'm going to leave you with two things. One of the thing is that this kind of, of course, biology has been very successful in this enumeration and characterization of the molecular components of life. But I think what's really interesting about living systems is that there are many features that rises from the interactions of many of these molecular components. And this active matter gives us the tool to bridge these scales from microscopic to macroscopic, which can lead to discovery of new physics and new kinds of ordering in phenomena across scales. And I will advertise for this review article, perspective article that I've written with three of my colleagues, which we highlight. Some of these new frontiers were in active matter in particular, I think stochastic thermodynamics is really kind of one of the frontiers to explore in active matter systems and go beyond just coarse graining and writing down hydrodynamic equation. And with that, I will thank my wonderful group of students, graduate, undergraduate, postdoctoral fellows and my colleagues, and happy to take questions. Okay, thank you very much. Very inspiring talk to finish the day on. So Peter Ryan's hand up. Do we have any, before we go to Peter Ryan, do we have any more junior people who are interested in asking a question? Not to cast aspersions on your age, Peter. Now go ahead, pick things off. All right. Thanks for a beautiful talk. I was wondering, can you control the activity of these cells, the degree to which they are alive, and do you then, what kind of phase transition would you then see, or do you expect them to see a phase transition induced by the activity? That's such a wonderful question. So in fact, we're, as we have started exploring the system, we've been looking into ways of kind of like playing with this, but the energetics of the system, and there are two ways to do that. One is the traditional way of trying to titrate ATP concentration in the system and then see what kind of like basically properties emerges when you kind of the system becomes less active or more active. So that's one thing we have been exploring. But it turns out that there's also ways to modify cilia beating, and like you can use drug perturbations and kind of like change the number of beating cilia. So effectively make the particle less motile. And that I think also is kind of another axis. Again, we reached very, it's the very recent kind of explorations, but one of the most interesting questions, I think to explore in a system like this. So yeah, thanks for that question. Yeah, thanks. Excellent. Beautiful. Thank you. Yeah, so thanks. Very nice talk. So I was just wondering that when you are calculating the entropy production rate of the system, like you map the divergence field on the car and on the current you are getting and they are what was the actual entropy production rate you were calculating from there. Yeah. So let me let me say that it's not actually the it's a bound and it's definitely a lot of not a very tight bound. It's basically, we look at the statistical irreversibility of the cycles. So we have the face based cycles and then from the cycles we calculate kind of like the amount of entropy production in the system. There is another way to do it as well. If you know exactly what the module I are, which is actually the area enclosed by the cycle is the work, but we don't have the actual modular. We have the ratios of the modular. So that's something that we are kind of like using the response measurements. We are trying to get go beyond just the ratio and then get the actual modular and that would be another way to kind of get a maybe better estimations of that. Thanks. Does anybody else have any question before we wrap up? Can I have a very sort of naive question? So at the level of the embryo, why do they, why is it advantageous to form the sort of crystals? You see this across all of the species. I'm just confused. I can, yeah, that's a wonderful question. So let me just show my last slide. It's a slide that I get that question quite a bit. So I think whether, so it's not entirely clear why this collective phenomena is advantageous as you mentioned. I do mention that the starfish or sea urchin in general, they, they're broadcast spawners. So they, they spawn in this intertidal zones, which the water fluctuations, both in terms of levels, pH and temperature varies quite a bit. So one of the kind of my, my hypothesis is that maybe this is a way for the system. I mean, they're generating work. So maybe this is a way for kind of like fighting with this broad range of like temperature fluctuations, for instance, in a system. This is of course a very kind of like, it's certainly a hypothesis, but I think that's the, is a very interesting question. And whether it's an epiphenomenal or a phenomena that has been now evolved to have some kind of useful thing for, I mean, it's a type of flocking. So it's interesting to further explore that. Yes. Yeah. Thanks for the question. Thank you. Okay. If that's everything for today. Thank you to all of the speakers we've had today. Very much appreciated. It's been nice to see a really broad range of topics, including multiple experiments that are making contact with theory. So that's, that's, and vice versa. So that's really good. Thank you everybody. I won't be here tomorrow, but for those of you who are enjoying the last day of the workshop and see you around. Thank you. Thanks. Bye bye.