We consider a stochastic dynamics for a system of diffusing hard-core particles on a periodic chain with asymmetric diffusion rules. A given cluster of particles can diffuse to the right as a whole but the particle located on the left boundary of the cluster is allowed to break off from it and diffuse to the left. Clusters of particles can eventually merge with other clusters. These rules allow for the creation of clusters of different sizes. We discuss the size distribution of the clusters in the long time or steady state limit, as a function of the particle concentration $c$. We consider the general time dependent master equation based on Smoluchowski's theory for local cluster merging or fragmentation and diffusion processes, and study the solutions using the generating function in the large size limit. We found that there exists a critical density $c^{*}=\sqrt{2}-1$ for which the cluster distribution decays like a power law with exponent 5/2.

The steady-state fluctuation theorem (SSFT) gives the relative probability of occurrence of events violating the second law of thermodynamics in a system with a small number of degrees of freedom. Using two-dimensional complex plasma as a working medium, wherein particle level observation of instantaneous velocities and positions has become experimentally possible, we perform “first-principles” molecular-dynamics simulations using the Yukawa potential in the presence of external gravity and an external temperature gradient leading to the onset and formation of Rayleigh-Bénard convection cells. In such a far-from-equilibrium steady state, the SSFT is put to the test. It is demonstrated that the SSFT is satisfied without any additional fit parameter for observation time $\tau$, comparable to or greater than the relevant microscopic timescale associated with the system under observation.

We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns: the gauge symmetry $Z_2$. This symmetry is present in physical problems from topological transitions to quantum chromodynamics, and controls the computational hardness of instances of spin-glasses. Here, we show how to design a neural network, and a dataset, able to learn this symmetry and to find compressed latent representations of the gauge orbits. Our method pays special attention to system-wrapping loops, the so-called Polyakov loops, known to be particularly relevant for computational complexity.

We use a generalized nonlinear Poisson-Boltzmann cell model that includes excluded-volume effects to investigate whether the effective charge ($Z_{\mathrm{eff}}$) of charged thermosensitive hydrogel particles increases or decreases upon the hydrogel thermal collapse. We find the existence of a crossover charge, $Z^{*}$, that separates two regimes. For hydrogel bare charges below $Z^{*}$ the system shows a behavior consistent with theories based on linear approximations, i.e., $Z_{\mathrm{eff}}$ increases in the collapsed state. However, for bare charges above $Z^{*}$, the system enters an anomalous regime, in which $Z_{\mathrm{eff}}$ decreases in the collapsed state. We show that diluted hydrogel suspensions at low ionic strength are more likely to follow the anomalous behavior. Our theory provides a full physical justification for the controversial theoretical and experimental results reported in this regard, and describes how the interplay between electrostatic, excluded-volume and entropic effects affects this crossover.

Transition from bending-dominated to stretching-dominated elastic response in semiflexible fibrous networks plays an important role in the mechanical behavior of cells and tissues. It is induced by changes in network connectivity and relies on the construction of new cross-links. We propose a simple continuum model of this transition with macroscopic strain playing the role of order parameter. An unusual feature of this Landau-type theory is that it is based on a single-well potential. The theory predicts that bending-to-stretching transition should proceed through propagation of the fronts separating domains with affine and nonaffine elastic response.

Quantum dynamical simulations of statistical ensembles pose a significant computational challenge due to the fact that mixed states need to be represented. If the underlying dynamics is fully unitary, for example, in ultrafast coherent control at finite temperatures, then one approach to approximate time-dependent observables is to sample the density operator by solving the Schrödinger equation for a set of wave functions with randomized phases. We show that, on average, random-phase wave functions perform well for ensembles with high mixedness, whereas at higher purities a deterministic sampling of the energetically lowest-lying eigenstates becomes superior. We prove that minimization of the worst-case error for computing arbitrary observables is uniquely attained by eigenstate-based sampling. We show that this error can be used to form a qualitative estimate of the set of ensemble purities for which the sampling performance of the eigenstate-based approach is superior to random-phase wave functions. Furthermore, we present refinements to both schemes which remove redundant information from the sampling procedure to accelerate their convergence. Finally, we point out how the structure of low-rank observables can be exploited to further improve eigenstate-based sampling schemes.

Soluto-inertial (SI) suspension interactions allow colloidal particles to be driven large distances over sustained periods of time. These interactions involve soluto-inertial “beacons” that establish and maintain solute fluxes over long times by slowly absorbing or emitting solutes in response to changes in the surrounding solution. Suspended particles then migrate in response to solute fluxes via diffusiophoresis (DP). Beacon materials must be chosen to maintain these solute fluxes, with range and duration in mind. Here we present a general strategy to facilitate qualitative design and quantitative prediction of SI interactions for a given beacon-solute pair. Specifically, we look at two classes of SI beacons: those that partition solute and those that associate with solute. We identify the design parameters for these systems to construct a parameter space map, calculate characteristic timescales over which SI fluxes persist, and generate approximate analytical expressions for solute concentration profiles. Further, we use these expressions to predict the DP velocity of colloids interacting with beacons, noting qualitative differences between beacon sources that release solute and beacon sinks that absorb solute. Proof-of-principle experiments of beacon sources and sinks, of partitioning, and associating types highlight the basic findings. More broadly, the conceptual approach outlined here can be adapted to treat SI interactions mediated by other materials such as dissolving solids, gases, evaporating liquids, ion-exchange resins, and others.

The inhomogeneous cooling state describing the hydrodynamic behavior of a freely evolving granular gas strongly confined between two parallel plates is studied, using a Boltzmann kinetic equation derived recently. By extending the idea of the homogeneous cooling state, we propose a scaling distribution in which all the time dependence occurs through the granular temperature of the system, while there is a dependence on the distance to the confining walls through the density. It is obtained that the velocity distribution is not isotropic, and it has two different granular temperature parameters associated to the motion perpendicular and parallel to the confining plates, respectively, although their cooling rates are the same. Moreover, when approaching the inhomogeneous cooling state, energy is sometimes transferred from degrees of freedom with lower granular temperature to those with a higher one, contrary to what happens in molecular systems. The cooling rate and the two partial granular temperatures are calculated by means of a Gaussian approximation. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.

Recently, Richtmyer-Meshkov instability (RMI) experiments driven by high explosives and fielded with perturbations on a free surface have been used to study strength at extreme strain rates and near zero pressure. The RMI experiments reported here used impact loading, which is experimentally simpler, more accurate to analyze, and which also allows the exploration of a wider range of conditions. Three experiments were performed on tantalum at shock stresses from 20 to 34 GPa, with six different perturbation sizes at each shock level, making this the most comprehensive set of strength-focused RMI experiments reported to date on any material. The resulting estimated average strengths of 1200–1400 MPa at strain rates of ${10}^7/\mathrm{s}$ exceeded, by 40% or more, a common power law extrapolation from data at strain rates below ${10}^4/\mathrm{s}$. Taken together with other data in the literature that show much higher strength at simultaneous high rates and high pressure, these RMI data isolated effects and indicated that, in the range of conditions examined, the pressure effects are more significant than rate effects.

Motivated by biological membrane-containing organelles in plants and photosynthetic bacteria, we study charge regulation in a model membrane stack. Considering (de)protonation as the simplest mechanism of charge equilibration between the membranes and with the bathing environment, we uncover a symmetry-broken charge state in the stack with a quasiperiodic effective charge sequence. In the case of a monovalent bathing salt solution our model predicts complex, inhomogeneous charge equilibria depending on the strength of the (de)protonation reaction, salt concentration, and membrane size. Our results shed light on the basic reorganization mechanism of thylakoid membrane stacks.

Mobile discrete breathers (MDBs) are here suggested as localized excitations underlying the trapping and transport of charged particles (electron or hole) along a DNA-like molecular wire with anchored ends such as attached to two electrodes. For illustration the Peyrard-Bishop-Dauxois-Holstein (PBDH) model is used. MDBs are excited by imposing appropriate disturbances to velocities or space positions of adjacent nucleotide pairs or lattice units of the wire. They can be directed either towards or away from the wire hence transverse to it. Numerical computer simulations show that a rather stable quasiparticle MDB + electron is possible when just a few of the nucleotide pairs near one of the fixed ends of the wire are excited. For the process to be effective, the charge, e.g., the electron, must be initially placed around the disturbed region of the molecule. Once the MDB + electron quasiparticle is formed it may be transported to quite a long distance up to ca. 60–70 nm in real space. Our findings show that such process does not demand intervention of an externally applied electric field and hence it may be considered as alternative to the polaron transport process.

We investigate the effect of the amount of disorder on the statistics of breaking bursts during the quasistatic fracture of heterogeneous materials. We consider a fiber bundle model where the strength of single fibers is sampled from a power-law distribution over a finite range, so that the amount of materials' disorder can be controlled by varying the power-law exponent and the upper cutoff of fibers' strength. Analytical calculations and computer simulations, performed in the limit of equal load sharing, revealed that depending on the disorder parameters the mechanical response of the bundle is either perfectly brittle where the first fiber breaking triggers a catastrophic avalanche, or it is quasibrittle where macroscopic failure is preceded by a sequence of bursts. In the quasibrittle phase, the statistics of avalanche sizes is found to show a high degree of complexity. In particular, we demonstrate that the functional form of the size distribution of bursts depends on the system size: for large upper cutoffs of fibers' strength, in small systems the sequence of bursts has a high degree of stationarity characterized by a power-law size distribution with a universal exponent. However, for sufficiently large bundles the breaking process accelerates towards the critical point of failure, which gives rise to a crossover between two power laws. The transition between the two regimes occurs at a characteristic system size which depends on the disorder parameters.

We prove the validity of multiparameter universality for the exact critical bulk correlation functions of the anisotropic square-lattice and triangular-lattice Ising models on the basis of the exact scaling structure of the correlation function of the two-dimensional anisotropic scalar ${\phi }^4$ model with four nonuniversal parameters. The correlation functions exhibit a directional nonuniversality due to principal axes whose orientation depends on microscopic details. We determine the exact anisotropy matrices governing the bulk and finite-size critical behavior of the ${\phi }^4$ and Ising models. We also prove the validity of multiparameter universality for an exact critical bulk amplitude relation.

It is known that the probability of decoding error has a phase transition at information rate equal to the channel capacity. The corresponding thermodynamic limit requires infinite coding dimension, hence making the actual decoding practically impossible. In this Rapid Communication we analyze finite-size effects that occur in limited neural populations. We report that the achievable rate approaches the asymptote in a remarkably nonlinear manner with the population size. Qualitatively, our findings do not seem to depend on the details of the model.

Nonintegrability is a necessary condition for the thermalization of a generic Hamiltonian system. In practice, the integrability can be broken in various ways. As illustrating examples, we numerically studied the thermalization behaviors of two types of one-dimensional (1D) diatomic chains in the thermodynamic limit. One chain was the diatomic Toda chain whose nonintegrability was introduced by unequal masses. The other chain was the diatomic Fermi-Pasta-Ulam-Tsingou-$\beta$ chain whose nonintegrability was introduced by quartic nonlinear interaction. We found that these two different methods of destroying the integrability led to qualitatively different routes to thermalization in the near-integrable region, but the thermalization time, $T_{eq}$, followed the same scaling law; $T_{eq}$ was inversely proportional to the square of the perturbation strength. This law also agreed with the existing results of 1D monatomic lattices. All these results imply that there is a universal scaling law of thermalization that is independent of the method of breaking integrability.

The problem of eliminating fast-relaxing variables to obtain an effective diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more unified view is thereby obtained of the effect of environmental inhomogeneity on the motion of a diffusing particle, in particular, whether a drift is induced, covering both passive and active particles. Infinitesimal generators (equivalently, drift-diffusion fields) for the contracted processes are worked out in detail for several models.

The percolation behavior of aligned rigid rods of length $k$ ($k$-mers) on two-dimensional triangular lattices has been studied by numerical simulations and finite-size scaling analysis. The $k$-mers, containing $k$ identical units (each one occupying a lattice site), were irreversibly deposited along one of the directions of the lattice. The connectivity analysis was carried out by following the probability $R_{L,k}\left(p\right)$ that a lattice composed of $L\times L$ sites percolates at a concentration $p$ of sites occupied by particles of size $k$. The results, obtained for $k$ ranging from 2 to 80, showed that the percolation threshold $p_c\left(k\right)$ exhibits a increasing function when it is plotted as a function of the $k$-mer size. The dependence of $p_c\left(k\right)$ was determined, being $p_c\left(k\right)=A+B/(C+\sqrt{k})$, where $A=p_c(k\to \infty )=0.582\left(9\right)$ is the value of the percolation threshold by infinitely long $k$-mers, $B=-0.47\left(0.21\right)$, and $C=5.79\left(2.18\right)$. This behavior is completely different from that observed for square lattices, where the percolation threshold decreases with $k$. In addition, the effect of the anisotropy on the properties of the percolating phase was investigated. The results revealed that, while for finite systems the anisotropy of the deposited layer favors the percolation along the parallel direction to the alignment axis, in the thermodynamic limit, the value of the percolation threshold is the same in both parallel and transversal directions. Finally, an exhaustive study of critical exponents and universality was carried out, showing that the phase transition occurring in the system belongs to the standard random percolation universality class regardless of the value of $k$ considered.

A state-dependent vulnerability of synchronization is shown to exist in a complex network composed of numerically simulated electronic circuits. We demonstrate that disturbances to the local dynamics of network units can produce different outcomes to synchronization depending on the current state of its trajectory. We address such state dependence by systematically perturbing the synchronized system at states equally distributed along its trajectory. We find the states at which the perturbation desynchronizes the network to be complicatedly mixed with the ones that restore synchronization. Additionally, we characterize perturbation sets obtained for consecutive states by defining a safety index between them. Finally, we demonstrate that the observed vulnerability is due to the existence of an unstable chaotic set in the system's state space.

The magnitudes of the terms in periodic orbit semiclassical trace formulas are determined by the orbits' stability exponents. In this paper, we demonstrate a simple asymptotic relationship between those stability exponents and the phase-space positions of particular homoclinic points.

Here we investigate the mechanism for explosive synchronization (ES) of a complex neural network composed of nonidentical neurons and coupled by Newman-Watts small-world matrices. We find a range of nonlocal connection probabilities for which the network displays an abrupt transition to phase synchronization, characterizing ES. The mechanism behind the ES is the following: As the coupling parameter is varied in a network of distinct neurons, ES is likely to occur due to a bistable regime, namely a chaotic nonsynchronized and a regular phase-synchronized state in the phase space. In this case, even small coupling changes make possible a transition between them. The onset of ES occurs via a saddle-node bifurcation of a periodic orbit that leads the network dynamics to display a locally stable phase-synchronized state. The presence of this regime is accompanied by a hysteresis loop on the network dynamics as the coupling parameter is adiabatically increased and decreased. The end of the hysteresis loop is marked by a frontier crisis of the chaotic attractor which also determines the end of the coupling strength interval where ES is possible.