We define a stochastic reaction-diffusion process that describes a consensus formation in a nonsedentary population. The process is a diffusive version of the majority-vote model, where the state update follows two stages: In the first stage, spins are allowed to jump to a random neighbor node with probabilities $D_{+}$ and $D_{-}$ for the respective spin orientations, and in the second stage, the spins in the same node can change its values according to the majority-vote update rule. The model presents a consensus formation phase when the concentration is greater than a threshold value and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. Setting unequal diffusion probabilities for the respective spin orientations is the same as applying an external magnetic field. The system undergoes a discontinuous phase transition for concentrations higher than the critical threshold on the external field. The individuals that diffuse more dominate the stationary collective opinion.

We evaluate the mean escape time of overdamped particles over potential barriers in short-correlated quenched Gaussian disorder potentials in one dimension at low temperature. The thermally activated escape is very sensitive to the form of the tail of the potential barrier probability distribution. We evaluate this tail by using the optimal fluctuation method. For monotone decreasing autocovariances, we reproduce the tail obtained by Lopatin and Vinokur (2001). However, for nonmonotonic autocovariances of the disorder potential which exhibit negative autocorrelations, we show that the tail is higher. This leads to an exponential increase of the mean escape time. The transition between the two regimes has the character of a first-order transition.

We find the relation between reliability and entropy production in a realistic model of electronic memory (low-power metal-oxide-semiconductor-based SRAM) where logical values are encoded as metastable nonequilibrium states. We employ large deviation techniques to obtain an analytical expression for the bistable quasipotential describing the nonequilibrium steady state and use it to derive an explicit expression bounding the error rate of the memory. Our results go beyond the dominant contribution given by classical instanton theory and provide accurate estimates of the error rate as confirmed by comparison with stochastic simulations.

Geometric stress focusing, e.g., in a crumpled sheet, creates pointlike vertices that terminate in a characteristic local crescent shape. The observed scaling of the size of this crescent is an open question in the stress focusing of elastic thin sheets. According to experiments and simulations, this size depends on the outer dimension of the sheet, but intuition and rudimentary energy balance indicate it should only depend on the sheet thickness. We address this discrepancy by modeling the observed crescent with a more geometric approach, where we treat the crescent as a curved crease in an isometric sheet. Although curved creases have already been studied extensively, the crescent in a crumpled sheet has its own unique features: the material crescent terminates within the material, and the material extent is indefinitely larger than the extent of the crescent. These features together with the general constraints of isometry lead to constraints linking the surface profile to the crease-line geometry. We construct several examples obeying these constraints, showing finite curved creases are fully realizable. This approach has some particular advantages over previous analyses, as we are able to describe the entire material without having to exclude the region around the sharp crescent. Finally, we deduce testable relations between the crease and the surrounding sheet and discuss some of the implications of our approach with regards to the scaling of the crescent size.

While microstructure in soft materials is usually given by the self-assembly of their constituting building blocks, colloidal assembly can also be obtained via templating a morphology in a disordered suspension of particles by solidification of the melt. This order-templating process is applicable to different soft-matter systems with a variety of characteristic length scales, including particle suspensions in water, liquid-crystal materials, and polymer melts. In this work, we numerically investigate the effect of particle size and solvent size in the process of solidification templating by implementing a coarse-grain model of hard-sphere particles at a moving melt–crystal interface. This approach captures the dependence of crystallization templating on speed of crystal growth, showing the existence of a threshold speed for crystallization templating to occur. Results in this work show that the threshold speed changes following a power form as solvent size and particle size change. Furthermore, this work analyzes and reports the effect of particle–crystal interaction strength in combination with size effects. This scaling study from a numerical perspective sets a starting point for the development of hybrid soft materials via structural templating, allowing solidification-driven particle ordering in different systems with a variety of length scales.

A system of hard rigid rods of length $k$ on hypercubic lattices is known to undergo two phase transitions when chemical potential is increased: from a low density isotropic phase to an intermediate density nematic phase, and on further increase to a high-density phase with no orientational order. In this paper, we argue that, for large $k$, the second phase transition is a first-order transition with a discontinuity in density in all dimensions greater than 1. We show that the chemical potential at the transition is $\approx kln[k/lnk]$ for large $k$, and that the density of uncovered sites drops from a value $\approx (lnk)/k^2$ to a value of order $exp(-ak)$, where $a$ is some constant, across the transition. We conjecture that these results are asymptotically exact, in all dimensions $d\ge 2$. We also present evidence of coexistence of nematic and disordered phases from Monte Carlo simulations for rods of length 9 on the square lattice.

We study a damped kicked top dynamics of a large number of qubits ($N\to \infty$) and focus on an evolution of a reduced single-qubit subsystem. Each subsystem is subjected to the amplitude damping channel controlled by the damping constant $r\in [0,1]$, which plays the role of the single control parameter. In the parameter range for which the classical dynamics is chaotic, while varying $r$ we find the universal period-doubling behavior characteristic to one-dimensional maps: period-2 dynamics starts at $r_1\approx 0.3181$, while the next bifurcation occurs at $r_2\approx 0.5387$. In parallel with period-4 oscillations observed for $r\le r_3\approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx 0.544$, responsible for a small-scale chaotic dynamics inside the attractor. The doubling of the principal bifurcation tree continues until $r\le r_{\infty }\sim 0.578$, which marks the onset of the full scale chaos interrupted by the windows of the oscillatory dynamics corresponding to the Sharkovsky order. Finally, for $r=1$ the model reduces to the standard undamped chaotic kicked top.

We present an electron injection scheme for plasma wakefield acceleration. The method is based on a recently proposed technique of fast electron generation via laser-solid interaction: a femtosecond laser pulse with the energy of tens of mJ hitting a dense plasma target at ${45}^{\circ }$ angle expels a well collimated bunch of electrons and accelerates these close to the specular direction up to several MeVs. We study trapping of these fast electrons by a quasilinear wakefield excited by an external beam driver in a surrounding low density plasma. This configuration can be relevant to the AWAKE experiment at CERN. We vary different injection parameters: the phase and angle of injection, the laser pulse energy. An approximate trapping condition is derived for a linear axisymmetric wake. It is used to optimize the trapped charge and is verified by three-dimensional particle-in-cell simulations. It is shown that a quasilinear plasma wave with the accelerating field $\sim$ 2.5 GV/m can trap electron bunches with $\sim$ 100 pC charge, $\sim 60\mu \mathrm{m}$ transverse normalized emittance and accelerate them to energies of several GeV with the spread $\lesssim$ 1% after 10 m..

We study the statistical distribution of the ergotropy and of the efficiency of a single-qubit battery ad of a single-qubit Otto engine, respectively fueled by random collisions. The single qubit, our working fluid, is assumed to exchange energy with two reservoirs: a nonequilibrium “hot” reservoir and a zero-temperature cold reservoir. The interactions between the qubit and the reservoirs are described in terms of a collision model of open system dynamics. The qubit interacts with the nonequilibrium reservoir (a large ensemble of qudits all prepared in the same pure state) via random unitary collisions and with the cold reservoir (a large ensemble of qubits in their ground state) via a partial swap. Due to the random nature of the interaction with the hot reservoir, fluctuations in ergotropy, heat, and work are present, shrinking with the size of the qudits in the hot reservoir. While the mean, “macroscopic” efficiency of the Otto engine is the same as in the case in which the hot reservoir is a thermal one, the distribution of efficiencies does not support finite moments, so that the mean of efficiencies does not coincide with the macroscopic efficiency.

Achieving the Carnot efficiency at finite power is a challenging problem in heat engines due to the trade-off relation between efficiency and power that holds for general heat engines. It is pointed out that the Carnot efficiency at finite power may be achievable in the vanishing limit of the relaxation times of a system without breaking the trade-off relation. However, any explicit model of heat engines that realizes this scenario for arbitrary temperature difference has not been proposed. Here, we investigate an underdamped Brownian Carnot cycle where the finite-time adiabatic processes connecting the isothermal processes are tactically adopted. We show that in the vanishing limit of the relaxation times in the above cycle, the compatibility of the Carnot efficiency and finite power is achievable for arbitrary temperature difference. This is theoretically explained based on the trade-off relation derived for our cycle, which is also confirmed by numerical simulations.

We study the quantum statistical electronic properties of random networks which inherently lack a fixed spatial dimension. We use tools like the density of states (DOS) and the inverse participation ratio to uncover various phenomena, such as unconventional properties of the energy spectrum and persistent localized states (PLS) at various energies, corresponding to quantum phases with zero-dimensional (0D) and one-dimensional (1D) order. For small ratio of edges over vertices in the network $R$ we find properties resembling graphene(honeycomb) lattices, like a similar DOS containing a linear dispersion relation at the band center at energy $E=0$. In addition, we find PLS at various energies including $E=-1,0,1$, and others, for example, related to the golden ratio. At $E=0$ the PLS lie at vertices that are not directly connected with an edge, due to partial bipartite symmetries of the random networks (0D order). At $E=-1,1$ the PLS lie mostly at pairs of vertices (bonds), while the rest of the PLS at other energies, like the ones related to the golden ratio, lie at lines of vertices of fixed length (1D order), at the spatial boundary of the network, resembling the edge states in confined graphene systems with zigzag edges. As the ratio $R$ is increased the DOS of the network approaches the Wigner semicircle, corresponding to random symmetric matrices(Hamiltonians) and the PLS are reduced and gradually disappear as the connectivity in the network increases. Finally, we calculate the spatial dimension $D$ of the network and its fluctuations. We obtain both integer and noninteger $D$ and a logarithmic dependence on $R$. In addition, we examine the relation of $D$ and its fluctuations to the electronic properties derived. Our results imply that universal physics can manifest in physical systems irrespectively of their spatial dimension. Relations to emergent spacetime in quantum and emergent gravity approaches are also discussed.

Traditional Boltzmann-Gibbs statistical mechanics does not apply to systems with unstable interactions, because for such systems the conventional thermodynamic limit does not exist. In unstable systems the ground state energy does not have an additive lower bound, i.e., no lower bound linearly proportional to the number $N$ of particles or degrees of freedom. In this article unstable systems are studied whose ground state energy is bounded below by a regularly varying function of $N$ with index $\sigma \ge 1$. The index $\sigma \ge 1$ of regular variation introduces a classification with respect to stability. Stable interactions correspond to $\sigma =1$. A simple example for an unstable system with $\sigma =2$ is an ideal gas with a nonvanishing constant two-body potential. The foundations of statistical physics are revisited, and generalized ensembles are introduced for unstable interactions in such a way that the thermodynamic limit exists. The extended ensembles are derived by identifying and postulating three basic properties as extended foundations for statistical mechanics: first, extensivity of thermodynamic systems, second, divisibility of equilibrium states, and third, statistical independence of isolated systems. The traditional Boltzmann-Gibbs postulate, resp. the hypothesis of equal a priori probabilities, is identified as a special case of the extended ensembles. Systems with unstable interactions are found to be thermodynamically normal and extensive. The formalism is applied to ideal gases with constant many-body potentials. The results show that, contrary to claims in the literature, stability of the interaction is not a necessary condition for the existence of a thermodynamic limit. As a second example the formalism is applied to the Curie-Weiss-Ising model with strong coupling. This model has index of stability $\sigma =2$. Its thermodynamic potentials [originally obtained in R. Hilfer, Physica A 320, 429 (2003)] are confirmed up to a trivial energy shift. The strong coupling model shows a thermodynamic phase transition of order 1 representing a novel mean-field universality class. The disordered high temperature phase collapses into the ground state of the system. The metastable extension of the high temperature free energy to low temperatures ends at absolute zero in a phase transition of order 1/2. Between absolute zero and the critical temperature of the first order transition all fluctuations are absent.

The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize it for confined laser-cooled atoms in the semiclassical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semiclassical regime.

Machine learning for phase transition has received intensive research interest in recent years. However, its application in percolation still remains challenging. We propose an auxiliary Ising mapping method for the machine learning study of the standard percolation as well as a variety of statistical mechanical systems in correlated percolation representation. We demonstrate that unsupervised machine learning is able to accurately locate the percolation threshold, independent of the spatial dimension of system or the type of phase transition, which can be first-order or continuous. Moreover, we show that, by neural network machine learning, auxiliary Ising configurations for different universalities can be classified with a high confidence level. Our results indicate that the auxiliary Ising mapping method, despite its simplicity, can advance the application of machine learning in statistical and condensed-matter physics.

We introduce a compartment model with memory for the dynamics of epidemic spreading in a constant population of individuals. Each individual is in one of the states $\mathbf{S}=\text{susceptible}$, $\mathbf{I}=\text{infected}$, or $\mathbf{R}=\text{recovered}$ (SIR model). In state $\mathbf{R}$ an individual is assumed to stay immune within a finite-time interval. In the first part, we introduce a random lifetime or duration of immunity which is drawn from a certain probability density function. Once the time of immunity is elapsed an individual makes an instantaneous transition to the susceptible state. By introducing a random duration of immunity a memory effect is introduced into the process which crucially determines the epidemic dynamics. In the second part, we investigate the influence of the memory effect on the space-time dynamics of the epidemic spreading by implementing this approach into computer simulations and employ a multiple random walker's model. If a susceptible walker meets an infectious one on the same site, then the susceptible one gets infected with a certain probability. The computer experiments allow us to identify relevant parameters for spread or extinction of an epidemic. In both parts, the finite duration of immunity causes persistent oscillations in the number of infected individuals with ongoing epidemic activity preventing the system from relaxation to a steady state solution. Such oscillatory behavior is supported by real-life observations and not captured by the classical standard SIR model.

The analysis of irregularly sampled time series remains a challenging task requiring methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases. The edit distance is an effective metric to quantitatively compare time series segments of unequal length by computing the cost of transforming one segment into the other. We show that transformation costs generally exhibit a nontrivial relationship with local sampling rate. If the sampling resolution undergoes strong variations, this effect impedes unbiased comparison between different time episodes. We study the impact of this effect on recurrence quantification analysis, a framework that is well suited for identifying regime shifts in nonlinear time series. A constrained randomization approach is put forward to correct for the biased recurrence quantification measures. This strategy involves the generation of a type of time series and time axis surrogates which we call sampling-rate-constrained (SRC) surrogates. We demonstrate the effectiveness of the proposed approach with a synthetic example and an irregularly sampled speleothem proxy record from Niue island in the central tropical Pacific. Application of the proposed correction scheme identifies a spurious transition that is solely imposed by an abrupt shift in sampling rate and uncovers periods of reduced seasonal rainfall predictability associated with enhanced El Niño-Southern Oscillation and tropical cyclone activity.

In this paper, we investigate the motion of particle(s) under the action of peristaltic flow. The particle trajectories are simulated by considering sinusoidal peristaltic waves. The fluid flow is governed by a two-dimensional Navier-Stokes equation, whereas for the particle dynamics we use the Basset-Boussinesq-Oseen (BBO) equation. The particle trajectories computed for different characteristic peristaltic flows, that is, trapping flow, augmented flow, and backward flow, show that the net horizontal particle displacement is largest for the augmented flow case. In general, the particle motion depends on its location in the peristaltic channel because of the wall curvature, which directly affects the flow velocities. The reported results for a cluster of particles show that whilst a fraction of particles form a group and propagate along the wave, some particles are left behind that deposit on the channel wall. In many biological processes it is desirable to know the number of particles that accumulate on the channel walls. In the present work, we propose empirical relations which can be used to calculate particle adhesion as a function of time.

Binary mixtures of the mesogen [1″,7″-bis(4-cyanobiphenyl-4′-yl)heptane] and a long chain amphiphile (e.g., 2-octadecoxypropanol) are examined for the structure, stability, and electro-optical behavior of nematic drops dispersed in the isotropic phase, in planar cells. Subjected to tangential boundary conditions, the drops adopt, besides the escaped concentric and untwisted bipolar geometries, the less common bound vortex geometry with a pair of half-strength disclination lines. The concentric drop, as it grows, switches its axis from an in-layer to the layer-normal direction corresponding to the stablest of all geometries. Bipolar drops in equilibrium have their axes parallel to the easy axis of the cell. Obliquely oriented bipolar drops rotate to attain the equilibrium disposition by the shorter of the clockwise and anticlockwise routes, the extent of rotation decreasing exponentially with time. The bipolar structure is marginally less stable than the concentric, and transforms to the latter geometry occasionally. In bound vortex drops, the separation between the lines varies as the drop diameter, the bipolar and concentric geometries appearing as the limiting cases. The complex course of Fréedericksz transition in all the different types of drops terminates in the division of the original large drop into many smaller drops, each with a surface charge 2, in conformity with the Poincaré-Hopf theorem. In low frequency electric fields, concentric drops exhibit flexoelectro-optic rotation in evidence of their escaped character.

Disks of two sizes and weights in alternating sequence are confined to a long and narrow channel. The axis of the channel is horizontal and its plane vertical. The channel is closed off by pistons that freeze jammed microstates out of loose disk configurations subject to moderate pressure, gravity, and random agitations. Disk sizes and channel width are such that under jamming no disk remains loose and all disks touch one wall. We present exact results for the characterization of jammed macrostates including volume and entropy. The rigorous analysis divides the disk sequences of jammed microstates into overlapping tiles from which we construct a small number of species of statistically interacting particles. Jammed macrostates depend on dimensionless control parameters inferred from ratios between measures of expansion work against the pistons, gravitational potential energy, and intensity of random agitations. These control parameters enter the configurational statistics via the activation energies prior to jamming of the particles. The range of disk weights naturally divides into regimes where qualitatively different features come into play. We sketch a path toward generalizations that include random sequences under a modified jamming protocol.