Itamar Procaccia, WIS
Title: Anomalous Elasticity and Emergent Dipole Screening in Amorphous Solids: Kosterlitz-Thouless-like transition.
Abstract: In recent work, we developed a screening theory for describing the effect of plastic events in amorphous solids on its emergent mechanics. The suggested theory uncovered an anomalous mechanical response of amorphous solids where plastic events collectively induce distributed dipoles that are analogous to dislocations in crystalline solids. The theory was tested against various models of amorphous solids in two and three-dimensions, including frictional and friction-less granular media and numerical models of amorphous glass. We conclude by interpreting the mechanical response as the formation of non-topological distributed dipoles that have no analogue in the crystalline defects literature. Having in mind that the onset of dipole screening is reminiscent of Kosterlitz-Thouless and Hexatic transitions, the finding of dipole screening in both two and three-dimensions is particularly novel.
Eytan Katzav, HUJI
Title: Analytical results for the distribution of first-passage times of random walks on random regular graphs
Abstract: We present analytical results for the distribution of first-passage (FP) times of random walks (RWs) on random regular graphs that consist of nodes of degree . Starting from a random initial node at time , at each time step an RW hops into a random neighbor of its previous node. We calculate the distribution of first-passage times, , from a random initial node to a random target node . A key observation is the distinction between FP trajectories whose backbone follows the shortest path (SPATH) from the initial node to the target node and FP trajectories whose backbone does not follow the shortest path (¬SPATH). The SPATH scenario is probable when the length of the shortest path between and is small and hence its typical time scale is , while the ¬SPATH scenario corresponds to much larger trajectories which are typically of order .
Implications of these results for other properties of RWs are also explored.
I. Tishby, O. Biham and E. Katzav, J. Stat. Mech. 113403 (2022).
Michael Assaf, HUJI
Title: Phase Transition in a Non-Markovian Animal Exploration Model with Preferential Returns
Abstract: We study a non-Markovian model of animal mobility incorporating both exploration and memory in the form of preferential returns. Exact results for the probability of visiting a given number of sites are derived and a practical WKB approximation to treat the nonstationary problem is developed. We show that our generalized model adequately describes empirical movement data of Egyptian fruit bats when accounting for inter-individual variation in the population. We also study the probability of visiting any site a given number of times and derive a mean-field equation. Our analysis yields a remarkable phase transition occurring at preferential returns which scale linearly with past visits. Following empirical evidence, we suggest that this phase transition reflects a trade-off between extensive and intensive foraging modes.
Naftali Smith, BGU
Title: Nonequilibrium steady state for harmonically-confined active particles
Abstract: Active particles consume energy from their environment and turn it into directed motion, leading to remarkable non-equilibrium effects.
I will focus on the run-and-tumble particle (RTP) model, a useful theoretical model which mimics the behavior of many active systems.
I will present recent results for the nonequilibrium steady state that a single RTP reaches when confined by an external harmonic potential.
First I will present the exact position distribution for an overdamped RTP in two dimensions.
Next, I will go beyond the overdamped regime, and focus on the limit in which the RTP switches its orientation very fast.
While typical fluctuations of its position obey a Boltzmann distribution, I will show that large deviations do not, and are instead dominated by a single, most likely trajectory in a coarse-grained dynamical description of the system.
Eli Barkai, BIU
Title: Packets of diffusing particles exhibit universal exponential tails
Abstract: Brownian motion is a Gaussian process described by the central limit theorem. However, exponential decays of the positional probability density function P(X; t) of packets of spreading random walkers, were observed in numerous situations that include glasses, live cells, and bacteria suspensions. We show that such exponential behavior is generally valid in a large class of problems of transport in random media. By extending the large deviations approach for a continuous time random walk, we uncover a general universal behavior for the decay of the density [1, 2]. It is found that fluctuations in the number of steps of the random walker, performed at finite time, lead to an exponential decay (with logarithmic corrections) of P(X; t). This universal behavior also holds for short times, a fact that makes experimental observations readily achievable. Time permitting we then formulate the hitchhiker model where interacting molecules form aggregates, that lead to fluctuations in the diffusion field, and a many body mechanism for the exponential tails [3].
References
[1] EB and Stas Burov Packets of diffusing particles exhibit universal exponential tails Physical Review Letters 124, 060603 (2020).
[2] S. Burov, W. Wang, E. Barkai Exponential Tails and Asymmetry Relations for the Spread of Biased Random Walks cond-mat arXiv:2209.03410 (2022).
[3] M. Hidalgo-Soria, and E. Barkai, The Hitchhiker model for Laplace diffusion processes in the cell environment Physical Review E 102, 012109 (2020).
Guy Bunin, Technion
Title: Local and extensive dynamics in many-variable disordered systems
Abstract: Many-variable dynamical systems with disordered interactions (such as neural networks, ecological communities, and sheared glasses) can exhibit a transition from a fixed-point phase to chaotic dynamics, involving fluctuations of many or all the variables. In similar settings there seem to also exist dynamics that principally involve only a few of the variables, which are often modeled by ignoring the rest of the system. I will discuss, through a dynamical model from ecology, when and how each of these two phenomena may be relevant in one and the same system.
Oded Farago, BGU
Title: Brownian dynamics across discontinuities – algorithms and applications
Abstract: The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of model systems is to match the solutions of the time-dependent diffusion equation in each layer, such that the boundary conditions at the interfaces between them are satisfied. We developed a new computational approach to multi-layer diffusion problems [1]. In this approach, the probability distribution function (PDF) is computed from a large ensemble of independent stochastic trajectories. These are generated using the accurate GJF (Gronbech-Jensen & Farago) Langevin integrator [2], which is supplemented with algorithms for the transitions between the layers. We consider the most general Kedem-Katchalsky interfacial condition that incorporates: (i) a discontinuity in the diffusion coefficient, (ii) a semi-permeable membrane, and (iii) a step-function chemical potential. Examples for the application of the method include: (1) A simple two-layer model of drug diffusion in a cardiovascular stent [3], and (2) the escape problem of particle from a non-confining square potential well [4].
[1] O. Farago, J. Comput. Phys. 423, 109802 (2020).
[2] N. Gronbech-Jensen and O. Farago, Mol. Phys. 111, 983 (2013).
[3] O. Farago and G. Pontrelli, Comput. Biol. Med. 124, 103932 (2020).
[4] O. Farago, Phys. Rev. E 104, 014105 (2021).
Yair Shokef, TAU
Title: Emergent Disorder and Mechanical Memory in Periodic Metamaterials
Abstract: Ordered mechanical systems typically have one or only a few stable rest configurations, and hence are not considered useful for encoding memory. Multistable and history-dependent responses usually emerge from quenched disorder, for example in amorphous solids or crumpled sheets. In contrast, due to geometric frustration, periodic magnetic systems can espouse an extensive manifold of quasi-degenerate configurations. Inspired by the topological structure of frustrated artificial spin ices, we introduce an approach to design ordered, periodic mechanical metamaterials that exhibit an extensive set of spatially disordered states. Our mechanical systems encompass continuous degrees of freedom, and are hence richer than their magnetic counterparts. We show how such systems exhibit history-dependent and non-Abelain responses, as their state may depend on the order in which external manipulations were applied. Thus, multistability and potential to store complex memory emerge from geometric frustration in ordered mechanical lattices that create their own disorder.
Alexandra Tayar, WIS
Title: Active stresses control the phase behavior of liquid phase separation.
Abstract: Liquid-Liquid phase separation (LLPS) has been of fundamental importance in the assembly of thermally driven materials and has recently emerged as an organizational principle for living systems. Biological phase separation is driven out of equilibrium through complex enzyme composition, chemical reactions, and mechanical activity, which reveals a gap in our understanding of this fundamental phenomenon. Here we study the impact of mechanical activity on LLPS. We design a DNA-based LLPS system coupled to flows through molecular motors and a cytoskeleton network. Active stress at an interface of a liquid droplet suppressed phase separation and stabilized a single-phase regime well beyond the equilibrium binodal curve. The phase diagram out of equilibrium revealed a 3-dimensional phase space that depends on temperature and local molecular activity. Similar dynamics and structures are observed in simulations, suggesting that suppression of liquid phase separation by active stress is a generic feature of liquid phase separation.
Avraham Be'er, BGU
Title: Biophysical aspects underlying the swarm to biofilm transition.
Abstract: Bacteria organize in a variety of collective states, from swarming, rapid surface exploration, to biofilms, highly dense immobile communities attributed to stress resistance. It has been suggested that biofilm and swarming are oppositely controlled, making this transition particularly interesting for understanding the ability of bacterial colonies to adapt to challenging environments. Here, the swarm to biofilm transition is studied in Bacillus subtilis by analyzing the bacterial dynamics both on the individual and collective scales. We show that both biological and physical processes facilitate the transition. A few individual cells that initiate the biofilm program cause nucleation of large, approximately scale-free, stationary aggregates of trapped swarm cells. Around aggregates, cells continue swarming almost unobstructed, while inside, trapped cells are added to the biofilm. While our experimental findings rule out previously suggested purely physical effects as a trigger for biofilm formation, they show how physical processes, such as clustering and jamming, accelerate biofilm formation.
Omer Granek, Technion
Title: Flocking in the Active Ising Model
Abstract: The Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at a finite temperature in dimensions two or less in equilibrium systems with short-range interactions. Far from equilibrium, this restriction need not hold, as revealed by the spontaneous flocking of self-propelled particles with polar alignment in two dimensions as in, e.g. the Vicsek model. Most flock phenomenology can be captured by a simpler, discrete-symmetry model known as the Active Ising Model — an active analog to the equilibrium Ising Model. In this talk, I will present numerical and analytical results which show that the dynamics of the active Ising flock are far richer than previously thought.
Kinneret Keren, Technion
Title: Physics of Hydra Morphogenesis.
