Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a connection has not been fully established, and the numerical evidence remains incomplete. Here we use Monte Carlo simulations to study the percolation properties of several classes of clusters occurring in the Edwards-Anderson Ising spin-glass model in two dimensions. The Fortuin-Kasteleyn–Coniglio-Klein clusters originally defined for the ferromagnetic problem do percolate at a temperature that remains nonzero in the thermodynamic limit. On the Nishimori line, this location is accurately predicted by an argument due to Yamaguchi. More relevant for the spin-glass transition are clusters defined on the basis of the overlap of several replicas. We show that various such cluster types have percolation thresholds that shift to lower temperatures by increasing the system size, in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is linked to the difference in density of the two largest clusters, thus supporting a picture where the spin-glass transition corresponds to an emergent density difference of the two largest clusters inside the percolating phase.

We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the ${|x-y|}^{-s}$ Riesz potential, causing the overdamped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for $0<s<1$, the standard deviations of both quantities grow as $t^{\frac{s}{2(1+s)}}$. When $s>1$, the interactions are effectively short-ranged, and the universal subdiffusive $t^{\frac{1}{4}}$ growth emerges with only amplitude depending on the exponent $s$. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion.

Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods—also known as colloidal bananas—as a function of their opening angle $\alpha$. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from $0^{\circ }$ (straight rods) to nearly ${360}^{\circ }$(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when $\alpha >{180}^{\circ }$. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.

Mechanically quenching a thin film of smectic-$C$ liquid crystal results in the formation of a dense array of thousands of topological defects in the director field. The subsequent rapid coarsening of the film texture by the mutual annihilation of defects of opposite sign has been captured using high-speed, polarized light video microscopy. The temporal evolution of the texture has been characterized using an object-detection convolutional neural network to determine the defect locations, and a binary classification network customized to evaluate the brush orientation dynamics around the defects in order to determine their topological signs. At early times following the quench, inherent limits on the spatial resolution result in undercounting of the defects and deviations from expected behavior. At intermediate to late times, the observed annihilation dynamics scale in agreement with theoretical predictions and simulations of the $2\mathrm{D} XY$ model.

We study the performance of a stochastic algorithm based on the power method that adaptively learns the large deviation functions characterizing the fluctuations of additive functionals of Markov processes, used in physics to model nonequilibrium systems. This algorithm was introduced in the context of risk-sensitive control of Markov chains and was recently adapted to diffusions evolving continuously in time. Here we provide an in-depth study of the convergence of this algorithm close to dynamical phase transitions, exploring the speed of convergence as a function of the learning rate and the effect of including transfer learning. We use as a test example the mean degree of a random walk on an Erdős-Rényi random graph, which shows a transition between high-degree trajectories of the random walk evolving in the bulk of the graph and low-degree trajectories evolving in dangling edges of the graph. The results show that the adaptive power method is efficient close to dynamical phase transitions, while having many advantages in terms of performance and complexity compared to other algorithms used to compute large deviation functions.

Most cities in the United States and around the world were organized around car traffic. In particular, large structures such as urban freeways or ring roads were built for reducing car traffic congestion. With the evolution of public transportation and working conditions, the future of these structures and the organization of large urban areas is uncertain. Here we analyze empirical data for U.S. urban areas and show that they display two transitions at different thresholds. For the first threshold of order $T_c^{\mathrm{FW}}\sim {10}^4$ commuters, we observe the emergence of a urban freeway. The second threshold is larger and on the order $T_c^{\mathrm{RR}}\sim {10}^5$ commuters above which a ring road emerges. In order to understand these empirical results, we propose a simple model based on a cost-benefit analysis which relies on the balance between construction and maintenance costs of infrastructures and the trip duration decrease (including the effect of congestion). This model indeed predicts such transitions and allows us to compute explicitly the commuter thresholds in terms of critical parameters such as the average value of time, average capacity of roads, and typical construction cost. Furthermore, this analysis allows us to discuss possible scenarios for the future evolution of these structures. In particular, we show that because of the externalities associated with freeways (pollution, health costs, etc.), it might become economically justified to remove urban freeways. This type of information is particularly useful at a time when many cities are confronted with the dilemma of renovating these aging structures or converting them into other uses.

Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on the conformation and diffusion of molecular ring polymers simultaneously are challenging due to their inherently small size. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly linked micron-sized colloids with $n=4–8$ segments. We characterize the conformations of these flexible colloidal rings and find that they are freely jointed up to steric restrictions. We measure their diffusive behavior and compare it to hydrodynamic simulations. Interestingly, flexible colloidal rings have a larger translational and rotational diffusion coefficient compared to colloidal chains. In contrast to chains, their internal deformation mode shows slower fluctuations for $n\lesssim 8$ and saturates for higher values of $n$. We show that constraints stemming from the ring structure cause this decrease in flexibility for small $n$ and infer the expected scaling of the flexibility as function of ring size. Our findings could have implications for the behavior of both synthetic and biological ring polymers, as well as for the dynamic modes of floppy colloidal materials.

A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the presences of high kinetic barriers that hinder transitions between metastable states on typical simulation time scales. Many enhanced sampling methods have been developed to address this sampling problem and more efficiently sample rare event systems. An interesting idea, coming from the field of statistics, was introduced in a recent work [Lu, Lu, and Nolen, Accelerating Langevin sampling with birth-death, arXiv:1905.09863] in the form of a novel sampling algorithm that augments overdamped Langevin dynamics with a birth-death process. In this work, we expand on this idea and show that this birth-death sampling scheme can efficiently sample prototypical rare event energy landscapes, and that the speed of equilibration is independent of the barrier height. We amend a crucial shortcoming of the original algorithm that leads to incorrect sampling of barrier regions by introducing an alternative approximation of the birth-death term. We establish important theoretical properties of the modified algorithm and prove mathematically that the relevant convergence results still hold. We investigate via numerical simulations the effect of various parameters, and we investigate ways to reduce the computational effort of the sampling scheme. We show that the birth-death mechanism can be used to accelerate sampling in the more general case of underdamped Langevin dynamics that is more commonly used in simulating physical systems. Our results show that this birth-death scheme is a promising method for sampling rare event energy landscapes.

The mechanical properties of a thin, planar material, perfused by an embedded flow network, have been suggested to be potentially changeable locally and globally by fluid transport and storage, which can result in both small- and large-scale deformations such as out-of-plane buckling. In these processes, fluid absorption and storage eventually cause the material to locally swell. Different parts can hydrate and swell unevenly, prompting a differential expansion of the surface. In order to computationally study the hydraulically induced differential swelling and buckling of such a membrane, we develop a network model that describes both the membrane shape and fluid movement, coupling mechanics with hydrodynamics. We simulate the time-dependent fluid distribution in the flow network based on a spatially explicit resistor network model with local fluid-storage capacitance. The shape of the surface is modeled by a spring network produced by a tethered mesh discretization, in which local bond rest lengths are adjusted instantaneously according to associated local fluid content in the capacitors in a quasistatic way. We investigate the effects of various designs of the flow network, including overall hydraulic traits (resistance and capacitance) and hierarchical architecture (arrangement of major and minor veins), on the specific dynamics of membrane shape transformation. To quantify these effects, we explore the correlation between local Gaussian curvature and relative stored fluid content in each hierarchy by using linear regression, which reveals that stronger correlations could be induced by less densely connected major veins. This flow-controlled mechanism of shape transformation was inspired by the blooming of flowers through the unfolding of petals. It can potentially offer insights for other reversible motions observed in plants induced by differential turgor and water transport through the xylem vessels, as well as engineering applications.

How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation. From the discrete sequences of critical clusters, we find fractal dimensions of $D_f=1.911943\left(1\right)$ and $D_f=1.707234\left(40\right)$ for the two models, significantly different from $D_f=91/48=1.89583...$ of random percolation. The critical exponents $\nu$, determined through a numerical study of cluster sizes and wrapping probabilities on a torus, are also well below the $\nu =4/3$ of random percolation. While these new models do not appear to belong to a universality class, they demonstrate how the removal of randomness can fundamentally change the critical behavior.

We analyze experimentally and theoretically the winding and unwinding of the $\vec{c}$ director in a chiral $\text{smectic-}{C}^{★}$ film crossed by an ethanol flow. This leads to a target pattern under crossed polarizers when the $+1$ defect imposed by the boundary conditions is pinned on the edge of the film. We show that the target is deformed at the center of the film when it is subjected to a flow of ethanol because of the presence of two recirculation vortices of chemohydrodynamical origin. This deformation and the two vortices disappear during the unwinding of the target when the ethanol flow is stopped. This unambiguously shows that the target deformation is due to the vortices and not to the elastic anisotropy. These two points are confirmed theoretically. An estimate of the two so-called chemomechanical and chemohydrodynamical Leslie coefficients is also derived from this study.

We analyze experimentally and theoretically the flows that develop around the core of a $+1$ disclination placed at the center of a freely suspended ferroelectric $\text{smectic-}{C}^{★}$ film subjected to a flow of ethanol. We show that the $\vec{c}$ director partially winds under the action of the Leslie chemomechanical effect by forming an imperfect target and that this winding is stabilized by flows which are induced by the Leslie chemohydrodynamical stress. We show moreover that there is a discrete set of solutions of this type. These results are explained in the framework of the Leslie theory for chiral materials. This analysis confirms that the Leslie chemomechanical and chemohydrodynamical coefficients are of opposite signs and of the same order of magnitude to within a factor of 2 or 3. A method for measuring the velocity field is also proposed, which does not require seeding the film with particles that can disturb the flows.

Financial markets are usually investigated through time series such as prices and volumes that describe the behavior of the system as a whole. Such observables emerge from microeconomic interactions between market participants. Agent-based models have been utilized to shed light on this process. The model's ability to produce statistics frequently found in empirical data is evidence of some correspondence with real markets. Here, an agent-based market model is proposed. Different trader profiles with short- and long-term motivations are considered, and limitations on the agents' skills to manipulate information are inserted into the model. According to their profile and limitations, agents are rational. A differential equation approximation is employed to find the value to which the price converges and the timescale of this process. The relationship between agents' attributes and the evolution of their wealth is explored in different scenarios. Agent's average wealth was not significantly affected by information processing accuracy, but the standard deviation was. The increased risk is the main consequence of low accuracy. The model yielded price series with multifractal behavior and heavy-tailed return distributions, which are nontrivial statistics frequently observed in empirical series.

A CMOS-based implementation of an autonomous Maxwell's demon was recently proposed [Phys. Rev. Lett. 129, 120602 (2022)] to demonstrate that a Maxwell demon can still work at macroscopic scales, provided that its power supply is scaled appropriately. Here we first provide a full analytical characterization of the nonautonomous version of that model. We then study system-demon information flows within generic autonomous bipartite setups displaying a macroscopic limit. By doing so, we can study the thermodynamic efficiency of both the measurement and the feedback process performed by the demon. We find that the information flow is an intensive quantity and that, as a consequence, any Maxwell's demon is bound to stop working above a finite scale if all parameters but the scale are fixed. However, this can be prevented by appropriately scaling the thermodynamic forces. These general results are applied to the autonomous CMOS-based demon.

We present a numerical formulation for the solution of nonisothermal, compressible Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical method is the use of staggered grid momenta along with a finite volume discretization of the thermodynamic variables to solve the resulting stochastic partial differential equations. The key advantages of the numerical scheme are that it significantly simplifies the discretization of diffusive and stochastic momentum fluxes into a more compact form, and it provides an unambiguous prescription of boundary conditions involving pressure. The staggered grid scheme more accurately reproduces the equilibrium static structure factor of hydrodynamic fluctuations in gas mixtures compared to a collocated scheme described previously by Balakrishnan et al. [Phys. Rev. E 89, 013017 (2014)]. The numerical method is tested for ideal noble gases mixtures under various nonequilibrium conditions, such as applied thermal and concentration gradients, to assess the role of cross-diffusion effects, such as Soret and Dufour, on the long-ranged correlations of hydrodynamic fluctuations, which are also more accurately reproduced compared to the collocated scheme. We numerically study giant nonequilibrium fluctuations driven by concentration gradients and fluctuation-driven Rayleigh-Taylor instability in gas mixtures. Wherever applicable, excellent agreement is observed with theory and measurements from the direct simulation Monte Carlo method.

A fundamental issue in biology is the nature of evolutionary transitions from unicellular to multicellular organisms. Volvocine algae are models for this transition, as they span from the unicellular biflagellate Chlamydomonas to multicellular species of Volvox with up to 50,000 Chlamydomonas-like cells on the surface of a spherical extracellular matrix. The mechanism of phototaxis in these species is of particular interest since they lack a nervous system and intercellular connections; steering is a consequence of the response of individual cells to light. Studies of Volvox and Gonium, a 16-cell organism with a plate-like structure, have shown that the flagellar response to changing illumination of the cellular photosensor is adaptive, with a recovery time tuned to the rotation period of the colony around its primary axis. Here, combining high-resolution studies of the flagellar photoresponse of micropipette-held Chlamydomonas with 3D tracking of freely swimming cells, we show that such tuning also underlies its phototaxis. A mathematical model is developed based on the rotations around an axis perpendicular to the flagellar beat plane that occur through the adaptive response to oscillating light levels as the organism spins. Exploiting a separation of timescales between the flagellar photoresponse and phototurning, we develop an equation of motion that accurately describes the observed photoalignment. In showing that the adaptive timescales in Volvocine algae are tuned to the organisms' rotational periods across three orders of magnitude in cell number, our results suggest a unified picture of phototaxis in green algae in which the asymmetry in torques that produce phototurns arise from the individual flagella of Chlamydomonas, the flagellated edges of Gonium, and the flagellated hemispheres of Volvox.

The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how nonperiodic networks—apparently indistinguishable from a snapshot of a fluid—sustain shear. We present a stress-only theory of emergent elasticity for a nonthermal amorphous assembly of grains in a jammed solid, where each grain is subjected to mechanical constraints of force and torque balance. These grain-level constraints lead to the Gauss's law of an emergent $U\left(1\right)$ tensor electromagnetism, which then accounts for the mechanical response of such solids. This formulation of amorphous elasticity has several immediate consequences. The mechanical response maps exactly to the static, dielectric response of this tensorial electromagnetism with the polarizability of the medium mapping to emergent elastic moduli. External forces act as vector electric charges, whereas the tensorial magnetic fields are sourced by momentum density. The dynamics in the electric and magnetic sectors naturally translate into the dynamics of the rigid jammed network and ballistic particle motion, respectively. The theoretical predictions for both stress-stress correlations and responses are borne out by the results of numerical simulations of frictionless granular packings in the static limit of the theory in both 2D and 3D.

We calculate the effect of particle size, concentration, and interactions on the photon transport mean-free path $l^{*}$ that characterizes the multiple light scattering in diffusing wave spectroscopy (DWS). For scatterers of sufficient size, such that the first peak of the suspension structure factor $S\left(q_{\max }\right)$ remains in the range of accessible scattering vectors, neither repulsive nor attractive interactions between scatterers contribute strongly to $l^{*}$; its values are bounded by those for hard spheres and scatterers without interactions. However, for scatterers smaller than the wavelength of light, crowding induced by attraction or repulsion can lead to nonmonotonic behavior in $l^{*}$ with increasing scatterer concentration. The effect is strongest for repulsive particles.

Sperm cells perform extremely demanding tasks with minimal capabilities. The cells must quickly navigate in a noisy environment to find an egg within a short time window for successful fertilization without any global positioning information. Many research efforts have been dedicated to derive mathematical principles that explain their superb navigation strategy. Here we show that the navigation strategy of sea urchin sperm, also known as helical klinotaxis, is a natural implementation of a well-established adaptive control paradigm known as extremum seeking. This bridge between control theory and the biology of taxis in microorganisms is expected to deepen our understanding of the process. For example, the formulation leads to a coarse-grained model of the signaling pathway that offers new insights on the peculiar switching-like behavior between high- and low-gain steering modes observed in sea urchin sperm. Moreover, it may guide engineers in developing bioinspired miniaturized robots with minimal sensors.

Bipedal walking, the habitual gait for man, is rather unique in nature and poses particular challenges for balance and propulsion. The characteristic double-humped ground reaction force profile has been widely observed but not put into functional context. We propose a mathematical model that captures the dynamics of the human foot in walking including the characteristic motion of the center of pressure. Using this model, we analyze the functional interplay of all essential biomechanical contributors to foot dynamics in walking. Our results demonstrate the intricate interplay of a self-stabilizing mechanism which allows extending a leg's stance phase while simultaneously powering rapid swing by condensing the essentials of foot dynamics into a reductionist, biomechanical model. A theory is presented which identifies the foot to be the key functional element and which explains the global dynamics of human walking. The provided insights will impact gait therapy and rehabilitation, the development of assistive devices, such as leg prostheses and exoskeletons, and provide guidelines for the design and control of versatile humanoid robots.