We propose a reaction-diffusion system that converts topological information of an active nematic into chemical signals. We show that a curvature-activated reaction dipole is sufficient for creating a system that dynamically senses topology by producing a concentration field possessing local extrema coinciding with $\pm \frac{1}{2}$ defects. The enabling term is analogous to polarization charge density seen in dielectric materials. We demonstrate the ability of this system to identify defects in both passive and active nematics. Our results illustrate that a relatively simple feedback scheme, expressed as a system of partial differential equations, is capable of producing chemical signals in response to inherently nonlocal structures in anisotropic media. We posit that such coarse-grained systems can help generate testable hypotheses for regulated processes in biological systems, such as morphogenesis, and motivate the creation of bio-inspired materials that utilize dynamic coupling between nematic structure and biochemistry.

We analyze gravitaxis of a Brownian circle swimmer by deriving and analytically characterizing the experimentally measurable intermediate scattering function (ISF). To solve the associated Fokker-Planck equation, we use a spectral-theory approach, finding formal expressions in terms of eigenfunctions and eigenvalues of the overdamped-noisy-driven pendulum problem. We further perform a Taylor series of the ISF in the wavevector to extract the cumulants up to the fourth order. We focus on the skewness and kurtosis analyzed for four observation directions in the 2D plane. Validating our findings involves conducting Langevin-dynamics simulations and interpreting the results using a harmonic approximation. The skewness and kurtosis are amplified as the orienting torque approaches the intrinsic angular drift of the circle swimmer from above, highlighting deviations from Gaussian behavior. Transforming the ISF to the comoving frame, a measurable quantity, reveals gravitactic effects and diverse behaviors spanning from diffusive motion at low wavenumbers to circular motion at intermediate wavenumbers and directed motion at higher wavenumbers.

The hydrodynamic and thermal interactions between neighboring vapor bubbles on hot surfaces play a crucial role in heat transport and flow characteristics. To investigate these interactions, we conducted numerical simulations of saturated vapor bubbles in a two-dimensional square enclosure filled with liquid water. The water was heated at the bottom and cooled at the top to replicate boiling at $100{}^{\circ }\mathrm{C}$ and normal atmospheric pressure. In our simulations, we varied the Jakob number ($\mathrm{Ja}$), which measures sensible heat to latent heat, and the separation distance ($d$) between the bubbles. We observed that the flow zone between the bubble seeds is thermally active and stable for $d$ less than half the height of the enclosure, and becomes oscillatory for $d$ greater than half the height. The stable state leads to a dipole mode, while the oscillatory state triggers a tripole mode. When $\mathrm{Ja}$ exceeds a critical value (approximately 2.8), hydrodynamic instabilities are induced in both the core bulk region and the boundary layers. At high $\mathrm{Ja}$ values, bubbles frequently move away from the wall, leading to intense hydrodynamic fluctuations and a monopole mode. Our findings indicate that at low $\mathrm{Ja}$, the phase-change-related heat transport dominates, while at high $\mathrm{Ja}$, the convective terms predominate. Furthermore, we observed that overall heat transport in bubbly convection is consistently greater than in classical thermal convection.

We use advances in the formalism of boost agnostic passive fluids to constrain transport in polar active fluids, which are subsequently described by the Toner-Tu equations. Acknowledging that the system fundamentally breaks boost symmetry, we compel what were previously entirely phenomenological parameters in the Toner-Tu model to satisfy precise relationships among themselves. Consequently, we propose a thermodynamic argument to determine the scalings of the transport coefficients under dynamical renormalization group flow given that the scaling of the noise correlator is exact, as has been supported numerically. These scalings perfectly agree with the results of recent state-of-the-art numerical simulation and experiments.

We investigate the dynamical phases and phase transitions arising in a classical two-dimensional anisotropic $XY$ model under the influence of a periodically driven temporal external magnetic field in the form of a symmetric square wave. We use a combination of finite temperature classical Monte Carlo simulation, implemented within a $\text{CPU}+\text{GPU}$ paradigm, utilizing local dynamics provided by the Glauber algorithm and a phenomenological equation-of-motion approach based on relaxational dynamics governed by the time-dependent free energy within a mean-field approximation to study the model. We investigate several parameter regimes of the variables (magnetic field, anisotropy, and the external drive frequency) that influence the anisotropic $XY$ system. We identify four possible dynamical phases: Ising-SBO, Ising-SRO, $XY$-SBO, and $XY$-SRO. Both techniques indicate that only three of them (Ising-SRO, Ising-SBO, and $XY$-SRO) are stable dynamical phases in the thermodynamic sense. Within the Monte Carlo framework, a finite-size scaling analysis, shows that $XY$-SBO does not survive in the thermodynamic limit giving way to either an Ising-SBO or a $XY$-SRO regime. The finite-size scaling analysis further shows that the transitions between the three remaining dynamical phases either belong to the two-dimensional Ising universality class or are first-order in nature. Within the mean-field calculations yield three stable dynamical phases, i.e., Ising-SRO, Ising-SBO and $XY$-SRO, where the final steady state is independent of the initial condition chosen to evolve the equations of motion, as well as a region of bistability where the system flows to either Ising-SBO or $XY$-SRO (Ising-SRO) depending on the initial condition. Unlike the stable dynamical phases, the $XY$-SBO represents a transient feature that is eventually lost to either Ising-SBO or $XY$-SRO. Our mean-field analysis highlights the importance of the competition between switching of the stationary point(s) of the free energy after each half cycle of the external field and the two-dimensional nature of the phase space for the equations of motion.

We investigate random searches under stochastic position resetting at rate $r$, in a bounded 1D environment with space-dependent diffusivity $D\left(x\right)$. For arbitrary shapes of $D\left(x\right)$ and prescriptions of the associated multiplicative stochastic process, we obtain analytical expressions for the average time $T$ for reaching the target (mean first-passage time), given the initial and reset positions, in good agreement with stochastic simulations. For arbitrary $D\left(x\right)$, we obtain an exact closed-form expression for $T$, within a Stratonovich scenario, while for other prescriptions, like Itô and anti-Itô, we derive asymptotic approximations for small and large rates $r$. Exact results are also obtained for particular forms of $D\left(x\right)$, such as the linear one, with arbitrary prescriptions, allowing to outline and discuss the main effects introduced by diffusive heterogeneity on a random search with resetting. We explore how the effectiveness of resetting varies with different types of heterogeneity.

Motivated by the need to understand the factors driving gentrification, we introduce and analyze two simple dynamical systems that model the interplay between three potential drivers of the phenomenon. The constructed systems are based on the assumption that three canonical drivers exist: a subpopulation that increases the desirability of a neighborhood, the desirability of a neighborhood, and the average price of real estate in a neighborhood. The second model modifies the first and implements a simple rent control scheme. For both models, we investigate the linear stability of equilibria and numerically determine the characteristics of oscillatory solutions as a function of system parameters. Introducing a rent control scheme stabilizes the system, in the sense that the parameter regime under which solutions approach equilibrium is expanded. However, oscillatory time series generated by the rent control model are generally more disorganized than those generated by the nonrent control model; in fact, long-lived transient chaos was observed under certain conditions in the rent control case. Our results illustrate that even simple models of urban gentrification can lead to complex temporal behavior.

From cytoskeletal networks to tissues, many biological systems behave as active materials. Their composition and stress generation is affected by chemical reaction networks. In such systems, the coupling between mechanics and chemistry enables self-organization, for example, into waves. Recently, contractile mechanochemical systems have been shown to be able to spontaneously develop localized spatial patterns. Here, we show that these localized patterns can present intrinsic spatiotemporal dynamics, including oscillations and chaotic-like dynamics. We discuss their physical origin and bifurcation structure.

Motivated by the limitations of conventional coarse-grained molecular dynamics for simulation of large systems of nanoparticles and the challenges in efficiently representing general pair potentials for rigid bodies, we present a method for approximating general rigid body pair potentials based on a specialized type of deep neural network that maintains essential properties, such as conservation of energy and invariance to the chosen origins of the particles. The network uses a specialized geometric abstraction layer to convert the relative coordinates of the rigid bodies to input more suitable to a conventional artificial neural network, which is trained together with the specialized layer. This results in geometric representations of the particles optimized for the specific potential. The network can be trained directly on scalar values to fit a model without explicit gradient and then used to efficiently evaluate the force and torque on the particles resulting from the potential. The concept is demonstrated with an atomistic interaction model for carbon nanotubes and the resulting model is compared with a common type of coarse-grained model optimized for the same potential, with even very small networks comparing favourably and larger networks achieving up to two orders of magnitude lower cost. The sensitivity to noise in the training data is investigated and the model is found to strongly reject noise up to $12.5\%$ given a dataset of ${10}^7$ samples. The performance of a proof-of-concept implementation is demonstrated on a variety of hardware, showing the models viability for large-scale simulations. Furthermore, generalization to soft bodies and potentials for polydisperse systems are discussed.

We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring is dynamically influenced by a pacemaker-driven wave originating from the internal domain, leading to the emergence of three distinct dynamical states based on the varying strengths of coupling. The range of dynamics observed includes phase patterning, the propagation of phase waves, and interactions between traveling and phase waves. A simplified linear model effectively explains the mechanisms behind the variety of phase patterns observed, providing insights into the complex interplay between a cell's internal and external environments.

Network systems can exhibit memory effects in which the interactions between different pairs of nodes adapt in time, leading to the emergence of preferred connections, patterns, and subnetworks. To a first approximation, this memory can be modeled through a “plastic” Hebbian or homophily mechanism, in which edges get reinforced proportionally to the amount of information flowing through them. However, recent studies on glia-neuron networks have highlighted how memory can evolve due to more complex dynamics, including multilevel network structures and “metaplastic” effects that modulate reinforcement. Inspired by those systems, here we develop a simple and general model for the dynamics of an adaptive network with an additional metaplastic mechanism that varies the rate of Hebbian strengthening of its edge connections. The metaplastic term acts on a second network level in which edges are grouped together, simulating local, longer timescale effects. Specifically, we consider a biased random walk on a cyclic feed-forward network. The random walk chooses its steps according to the weights of the network edges. The weights evolve through a Hebbian mechanism modulated by a metaplastic reinforcement, biasing the walker to prefer edges that have been already explored. We study the dynamical emergence (memorization) of preferred paths and their retrieval and identify three regimes: one dominated by the Hebbian term, one in which the metareinforcement drives memory formation, and a balanced one. We show that, in the latter two regimes, metareinforcement allows the retrieval of a previously stored path even after the weights have been reset to zero to erase Hebbian memory.

Collagen, the most abundant protein in the human body, must withstand high mechanical loads due to its structural role in tendons, skin, bones, and other connective tissue. It was recently found that tensed collagen creates mechanoradicals by homolytic bond scission. We here employ scale-bridging simulations to determine the influence of collagen's mesoscale fibril structure on molecular breakages, combining atomistic molecular dynamics simulations with a newly developed mesoscopic ultra-coarse-grained description of a collagen fibril. Our simulations identify a conserved structural feature, a length difference of the two helices between pairs of crosslinks, to play a critical role. The release of the extra hidden length enables collagen to buffer mechanical stress. At the same time, this topology funnels ruptures such that the potentially harmful mechanoradicals are readily stabilized, buffering the arising oxidative stress. Our results suggest collagen's hidden length to exploit a sweet spot in the trade-off between breakage specificity and strength.

Diffusion-dominated mix in inertial confinement fusion (ICF) is characterized where the majority of the mix occurs in the immediate fuel-shell interface while hydrodynamic-dominated mix pulls shell material from farther away into the central fuel. A thin (150 nm) separated reactants ICF mix platform is highly sensitive to the amount of mix from the first micron of shell-fuel interface. This fine-spatial resolution platform has revealed that material mix in moderate convergence ($\mathrm{CR}\sim 12$) ICF implosions is dominated by a diffusion mechanism. This technique has now been expanded across a set of OMEGA ICF implosions, observing an increase in mix width and mix amount for cooler, slower, and more compressive implosions. Hydrodynamic simulations require a buoyancy-drag mix model to capture the increasing mix width, suggesting a transition between these two mix mechanisms.

Heider's balance theory emphasizes cognitive consistency in assessing others, as expressed by the phrase “The enemy of my enemy is my friend.” At the same time, the theory of indirect reciprocity provides us with a dynamical framework to study how to assess others based on their actions as well as how to act toward them based on the assessments. Well known are the “leading eight” from L1 to L8, the eight norms for assessment and action to foster cooperation in social dilemmas while resisting the invasion of mutant norms prescribing alternative actions. In this work, we begin by showing that balance is equivalent to stationarity of dynamics only for L4 and L6 (stern judging) among the leading eight. Stern judging reflects an intuitive idea that good merits reward, whereas evil warrants punishment. By analyzing the dynamics of stern judging in complete graphs, we prove that this norm almost always segregates the graph into two mutually hostile groups as the graph size grows. We then compare L4 with stern judging: The only difference of L4 is that a good player's cooperative action toward a bad one is regarded as good. This subtle difference transforms large populations governed by L4 to a “paradise” where cooperation prevails and positive assessments abound. Our study thus helps us understand the relationship between individual norms and their emergent consequences at a population level, shedding light on the nuanced interplay between cognitive consistency and segregation dynamics.

The thermodynamic relations for a Brownian particle moving in a discrete ratchet potential coupled with quadratically decreasing temperature are explored as a function of time. We show that this thermal arrangement leads to a higher velocity (lower efficiency) compared to a Brownian particle operating between hot and cold baths, and a heat bath where the temperature linearly decreases along with the reaction coordinate. The results obtained in this study indicate that if the goal is to design a fast-moving motor, the quadratic thermal arrangement is more advantageous than the other two thermal arrangements. In contrast, the entropy, entropy production rate, and entropy extraction rate are significantly larger in the case of a quadratically decreasing temperature compared to the linearly decreasing temperature case and piecewise constant temperature case. Furthermore, the thermodynamic features of a system consisting of several Brownian ratchets arranged in a complex network are explored. The theoretical findings exhibit that as the network size increases, the entropy, entropy production, and entropy extraction of the system also increase, showing that these thermodynamic quantities exhibit extensive property. As a result, as the number of lattice sizes increases, thermodynamic relations such as entropy, entropy production, and entropy extraction also step up, confirming that these complex networks cannot be reduced to a corresponding one-dimensional lattice. However, in the long time limit, thermodynamic relations such as velocity, entropy production rate, and entropy extraction rate become independent of the network size. These results are also confirmed via a continuum Fokker-Planck model for the overdamped case.

The exact homogenized probability density function, for a photon making a step of length $s$ has been analytically derived for a binary (isotropic-Poisson) statistical mixture with unmatched refractive indexes. The companions, exact, homogenized probability density functions for a photon to change direction (“scatter”), with polar $\vartheta$ and azimuthal $\phi$ angles, and the homogenized albedo, have also been obtained analytically. These functions also apply to negative refractive indexes and can reduce the number of Monte Carlo simulations needed for photon propagation in complex binary (isotropic-Poisson) statistical mixtures from hundreds to just one, for an equivalent homogeneous medium. Note, that this is not an approximate approach, but a mathematically equivalent and exact result. Additionally, some tutorial examples of homogenized Monte Carlo simulations are also given.

The motivation behind the proposed study stems from multilane traffic systems with finite availability of particles. Our investigation revolves around a totally asymmetric simple exclusion process incorporating a finite reservoir and the occurrence of lane-switching phenomena. The study delves into the system's characteristics, including phase diagrams, density profiles, phase transitions, finite-size effects, and shock positions. These analyses concern the number of particles within the system and various weak-coupling rates. The outcomes obtained from the generalized mean-field theory are cross-validated against the results derived from Monte Carlo simulations. In scrutinizing the system's dynamics, we observe several noteworthy observations. Notably, we identified critical mixed profiles featuring instances of double shocks. The system, intriguingly, demonstrates a transition known as reentrance transition. The study also reports a rare phenomenon, namely, the jumping effect within the shock profile, adding a layer of complexity to the system's behavior and proving the significance of limited resources.

Statistics of diffusion, modeled by random walks, such as the mean number of distinct sites visited $S\left(t\right)$ at time $t$, the mean probability $P_0\left(t\right)$ of being at the origin of the walk, and the mean-squared displacements $\langle R^2\left(t\right)\rangle$ of the random walkers have been studied extensively in the past in both regular lattices and such disordered media as percolation clusters and other fractal structures, and universal power laws for such quantities have been derived. $S\left(t\right)$ provides insight into reaction properties of geological formations, while $P_0\left(t\right)$ is directly linked with the problem of back diffusion in remediation of groundwater aquifers. In all such studies, it was assumed that the conductances of the bonds that connect nearest-neighbor sites of the lattices are equal. Motivated by the problem of transport and reaction in large-scale porous media that are characterized by a broad spatial distribution of hydraulic conductances, we demonstrate, using extensive Monte Carlo simulations, that the statistics of random walks, when the conductances are broadly distributed, depend on the structure of the distribution. Five geologically relevant conductance distributions, namely, normal, log-normal, fractional Brownian motion (FBM), log-FBM, and stable distributions, are considered and random walks in a two-dimensional model with the five distributions are simulated. The first two distributions are uncorrelated, while the last three induce long-range correlations in the values of the conductance. We show that if $S\left(t\right)\sim t^p$ and $P_0\left(t\right)\sim t^{-\zeta }$, the exponents $p$ and $\zeta$ may depend on the conductance distribution, in which case they are neither equal to those for homogeneous lattices, nor those for percolation clusters and other fractal structures. For at least three of the conductance distributions, diffusion is anomalous, with $\langle R^2\left(t\right)\rangle$ not growing linearly with the time $t$, even in the long-time limit. In addition to being of scientific interest, and the fact that transport processes in geomedia are simulated by random walks, the dependence of such statistics on the distribution of the conductances and their deviations from the statistics of random walks in homogeneous systems, and percolation and other types of fractal structures, indicate that diffusion in highly heterogeneous porous media is anomalous, and is described by fractional partial differential equations in which the temporal and spatial fractional orders depend on the details of the conductance distribution.