Molecular dynamics simulations of binary dusty plasmas have been performed and their behavior with respect to the phase separation process has been analyzed. The simulated system was inspired by experimental research on phase separation in dusty plasmas under microgravity on parabolic flights. Despite vortex formation in the experiment and in the simulations the phase separation could be identified. From the simulations it is found that even the smallest charge disparities lead to phase separation. The separation is due to the force imbalance on the two species and the separation becomes weaker with increasing mean particle size. In comparison, experiments on the phase separation have been performed and analyzed in view of the separation dynamics. It is found that the experimental results are reproduced by the simulation regarding the dependency on the size disparity of the two particle species.

We determine thresholds $p_c$ for random-site percolation on a triangular lattice for all available neighborhoods containing sites from the first to the fifth coordination zones, including their complex combinations. There are 31 distinct neighborhoods. The dependence of the value of the percolation thresholds $p_c$ on the coordination number $z$ are tested against various theoretical predictions. The proposed single scalar index $\xi ={\sum }_i{z}_i{r}_i^2/i$ (depending on the coordination zone number $i$, the neighborhood coordination number $z$, and the square distance $r^2$ to sites in $i\mathrm{th}$ coordination zone from the central site) allows one to differentiate among various neighborhoods and relate $p_c$ to $\xi$. The thresholds roughly follow a power law $p_c\propto {\xi }^{-\gamma }$ with $\gamma \approx 0.710\left(19\right)$.

We report on the experimental investigation of the fluctuation properties in the resonance frequency spectra of a flat resonator simulating a dissipative quantum billiard subject to partial time-reversal-invariance violation (TIV) which is induced by two magnetized ferrites. The cavity has the shape of a quarter bowtie billiard of which the corresponding classical dynamics is chaotic. Due to dissipation it is impossible to identify a complete list of resonance frequencies. Based on a random-matrix theory approach we derive analytical expressions for statistical measures of short- and long-range correlations in such incomplete spectra interpolating between the cases of preserved time-reversal invariance and complete TIV and demonstrate their applicability to the experimental spectra.

We theoretically investigate the optical properties of a one-dimensional non-Hermitian dispersive layered system with saturable gain and loss. We solve the nonhomogeneous Helmholtz equation perturbatively by applying the modified transfer matrix method and we obtain closed-form expressions for the reflection or transmission coefficients for TM incident waves. The nonreciprocity of the scattering process can be directly inferred from the analysis of the obtained expressions. It is shown that by tuning the parameters of the layers we can effectively control the impact of nonlinearity on the scattering characteristics of the non-Hermitian layered structure. In particular, we investigate the asymmetric and nonreciprocal characteristics of the reflectance and transmittance of multilayered parity-time (PT)-symmetric slab. We demonstrate that incident electromagnetic wave may effectively tunnel through the PT-symmetric multilayered structures with zero reflection. The effect of nonlinearity to the scattering matrix eigenvalues is systematically examined.

The competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks. In this model, two different paradigms or interests compete with each other to dominate the network's relations and impose their own values. In this paper, using the mean-field method, we examine the thermal behavior of the competitive balance model. Our results show that under a certain temperature, the symmetry between two competing interests will spontaneously break which leads to a discrete phase transition. So, starting with a heterogeneous signed network, if agents aim to decrease tension stemming from competitive balance theory, evolution ultimately chooses only one of the existing interests and stability arises where one paradigm dominates the system. The critical temperature depends linearly on the number of nodes, which is a linear dependence in the thermal balance theory as well. Finally, the results obtained through the mean-field method are verified by a series of simulations.

Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by complex dynamical systems reproducing spatial movements of molecules and their collisions. Such molecular dynamics systems may implicitly capture intricate phenomena that affect reaction rates but are not accounted for in the macroscopic models. In this work we present a data assimilation procedure for learning nonhomogeneous kinetic parameters from molecular simulations with many simultaneously reacting species. The learned parameters can then be plugged into the deterministic reaction rate equations to predict long time evolution of the macroscopic system. In this way, our procedure discovers an effective differential equation for reaction kinetics. To demonstrate the procedure, we upscale the kinetics of a molecular system that forms a complex covalently bonded network severely interfering with the reaction rates. Incidentally, we report that the kinetic parameters of this system feature peculiar time and temperature dependences, whereas the probability of a network strand to close a cycle follows a universal distribution.

Living systems at the subcellular, cellular, and multicellular levels are often crowded systems that contain active particles. The active motion of these particles can also propel passive particles, which typically results in enhanced effective diffusion of the passive particles. Here we study the diffusion of a passive tracer particle in such a dense system of active crowders using a minimal lattice model incorporating particles pushing each other. We show that the model exhibits several regimes of motility and quantify the enhanced diffusion as a function of density and activity of the active crowders. Moreover, we demonstrate an interplay of tracer diffusion and clustering of active particles, which suppresses the enhanced diffusion. Simulations of mixtures of passive and active crowders show that a rather small fraction of active particles is sufficient for the observation of enhanced diffusion.

We study a Langevin equation describing the stochastic motion of a particle in one dimension with coordinate $x$, which is simultaneously exposed to a space-dependent friction coefficient $\gamma \left(x\right)$, a confining potential $U\left(x\right)$ and nonequilibrium (i.e., active) noise. Specifically, we consider frictions $\gamma \left(x\right)={\gamma }_0+{\gamma }_1{\left|x\right|}^p$ and potentials $U\left(x\right)\propto {\left|x\right|}^n$ with exponents $p=1,2$ and $n=0,1,2$. We provide analytical and numerical results for the particle dynamics for short times and the stationary probability density functions (PDFs) for long times. The short-time behavior displays diffusive and ballistic regimes while the stationary PDFs display unique characteristic features depending on the exponent values $(p,n)$. The PDFs interpolate between Laplacian, Gaussian, and bimodal distributions, whereby a change between these different behaviors can be achieved by a tuning of the friction strengths ratio ${\gamma }_0/{\gamma }_1$. Our model is relevant for molecular motors moving on a one-dimensional track and can also be realized for confined self-propelled colloidal particles.

Because of the large mass differences between electrons and ions, the heat diffusion in electron-ion plasmas exhibits more complex behavior than simple heat diffusion found in typical gas mixtures. In particular, heat is diffused in two distinct, but coupled, channels. Conventional single fluid models neglect the resulting complexity, and can often inaccurately interpret the results of heat pulse experiments. However, by recognizing the sensitivity of the electron temperature evolution to the ion diffusivity, not only can previous experiments be interpreted correctly, but informative simultaneous measurements can be made of both ion and electron heat channels.

This paper is concerned with the reduced-order modeling of the strongly nonlinear wave turbulence system. The motivation for such an attempt comes from the utility of the probabilistic coarse-grained model in facilitating the theoretical and numerical analysis of the true dynamical system model. One typical practice of simplifying the complex physical model is, in the spirit of Brownian motion, to replace the nonlinear interactions by white noise forcing and linear dissipation. For the case of slowly varying longwave, the resulting Markov process is an accurate approximate model. However, this conventional scheme is highly inappropriate for the description of shortwaves because the rapidly varying turbulent signal acquires a significantly non-Markovian character resulting from the poor timescale separation between the relevant mode and the environmental wave field. To resolve the issue, we discuss a simplification technique for which the central concept is the quasi-Markovian property; a non-Markov stochastic process is referred to as quasi-Markovian if it can be represented as a component of Markovian system made by adding a finite number of auxiliary variables. Our contribution in this work is to single out the nontrivial and near resonances from the nonlinear interactions in search of the auxiliary variable. We perform a comparison analysis of the autocorrelation matrices of the true and approximate models, and numerically demonstrate the effectiveness of our Markovian formulation of the inherently non-Markov turbulent signal.

Entropy has recently drawn considerable interest both as a marker to detect the onset of phase transitions and as a reaction coordinate, or collective variable, to span phase transition pathways. We focus here on the behavior of entropy along the vapor-liquid phase coexistence and identify how the difference in entropy between the two coexisting phases vary in ideal and metallic systems along the coexistence curve. Using flat-histogram simulations, we determine the thermodynamic conditions of coexistence, critical parameters, including the critical entropy, and entropies along the binodal. We then apply our analysis to a series of systems that increasingly depart from ideality and adopt a metal-like character, through the gradual onset of the Friedel oscillation in an effective pair potential, and for a series of transition metals modeled with a many-body embedded-atoms force field. Projections of the phase boundary on the entropy-pressure and entropy-temperature planes exhibit two qualitatively different behaviors. While all systems modeled with an effective pair potential lead to an ideal-like behavior, the onset of many-body effects results in a departure from ideality and a markedly greater exponent for the variation of the entropy of vaporization with temperature away from the critical temperature.

In photosynthetic organisms the energy of the illuminating light is absorbed by the antenna complexes and transmitted by the excitons to the reaction centers (RCs). The energy of light is either absorbed by the RCs, leading to their “closing” or is emitted through fluorescence. The dynamics of the light absorption is described by a simple model developed for exciton migration that involves the exciton hopping probability and the exciton lifetime. During continuous illumination the fraction of closed RCs $x$ continuously increases, and at a critical threshold $x_c$, a percolation transition takes place. Performing extensive Monte Carlo simulations, we study the properties of the transition in this correlated percolation model. We measure the spanning probability in the vicinity of $x_c$, as well as the fractal properties of the critical percolating cluster, both in the bulk and at the surface.

Developing the thermodynamics of nanoscale friction is needed in a wide range of tribological applications, where the key objective is to optimally control the energy dissipation. Here we show that modern stochastic thermodynamics allows us to interpret the measurements obtained by friction force microscopy, which is the standard tool for investigating the frictional properties of materials, in terms of basic thermodynamics concepts such as fluctuating work and entropy. We show that this allows the identification of the heat produced during the friction process as an unambiguous measure of thermodynamic irreversibility. We have applied this procedure to quantify the heat produced during the frictional sliding in a broad velocity range, and we observe velocity-dependent scaling behavior, which is useful for interpreting the experimental outcomes.

The theory developed in our previous papers [Phys. Rev. E 99, 030101(R) (2019); Phys. Rev. E 103, 032611 (2021)] is applied in this paper to investigate the dependence of slowing down of dynamics of glass-forming liquids on the attractive and repulsive parts of intermolecular interactions. Through an extensive comparison of the behavior of a Lennard-Jones glass-forming liquid and that of its WCA reduction to a model with truncated pair potential without attractive tail, we demonstrate why the two systems exhibit very different dynamics despite having nearly identical pair correlation functions. In particular, we show that local structures characterized by the number of mobile and immobile particles around a central particle markedly differ in the two systems at densities and temperatures where their dynamics show large difference and nearly identical where dynamics nearly overlap. We also show how the parameter $\psi \left(T\right)$ that measures the role of fluctuations embedded in the system on size of the cooperatively reorganizing cluster (CRC) and the crossover temperature $T_a$ depend on the intermolecular interactions. These parameters stemming from the intermolecular interactions characterize the temperature and density dependence of structural relaxation time ${\tau }_{\alpha }$. The quantitative and qualitative agreements found with simulation results for the two systems suggest that our theory brings out the underlying features that determine the dynamics of glass-forming liquids.

The shape of clouds has proven to be essential for classifying them. Our analysis of images from fair weather cumulus clouds reveals that, in addition to turbulence, they are driven by self-organized criticality. Our observations yield exponents that support the fact the clouds, when projected to two dimensions, exhibit conformal symmetry compatible with $c=-2$ conformal field theory. By using a combination of the Navier-Stokes equation, diffusion equations, and a coupled map lattice, we successfully simulated cloud formation, and obtained the same exponents.

The population decay due to a small opening in an otherwise closed cavity supporting chaotic classical dynamics displays a quantum correction on top of the classical exponential form, a pure manifestation of quantum coherence that acquires a universal form and can be explained by path interference. Being coherent, such enhancement is prone to decoherence effects due to the coupling of the system to an external environment. We study this interplay between incoherent and coherent quantum corrections to decay by evaluating, within a Caldeira-Leggett scenario, off-diagonal contributions to the decoherence functional coming from pairs of correlated classical paths in the time regime where dissipative effects are neglected and decoherence does not affect the classical dynamics, but quantum interference must be accounted for. We find that the competing effects of interference and decoherence lead to a universal nonmonotonic form for the survival probability depending only on the coupling strength and macroscopic parameters of the cavity.

A practical approach to the search for (quasi-) discrete breathers (DBs) in a triangular $\beta$-FPUT lattice (after Fermi, Pasta, Ulam, and Tsingou) is proposed. DBs are obtained by superimposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Zero-dimensional and one-dimensional DBs are obtained. The former ones are localized in both spatial dimensions, and the latter ones are only in one dimension. Among the one-dimensional DBs, two families are considered: the first is based on the DNVMs of a triangular lattice, and the second is based on the DNVMs of a chain. We speculate that our systematic approach on the triangular $\beta$-FPUT lattice reveals all possible types of spatially localized oscillations with frequencies bifurcating from the upper edge of the phonon band as all DNVMs with frequencies above the phonon band are analyzed.

Phase-isostable reduction is an emerging model reduction strategy that can be used to accurately replicate nonlinear behaviors in systems for which standard phase reduction techniques fail. In this work, we derive relationships between the cycle-to-cycle variance of the reduced isostable coordinates for systems subject to both additive white noise and periodic stimulation. Using this information, we propose a data-driven technique for inferring nonlinear terms of the phase-isostable coordinate reduction framework. We apply the proposed model inference strategy to the biologically motivated problem of eliminating cardiac alternans, an arrhythmia that is widely considered to be a precursor to more deadly cardiac arrhythmias. Using this strategy, by simply measuring a series of action potential durations in response to periodic stimulation, we are able to identify energy-optimal, nonfeedback control inputs to stabilize a period-1, alternans-free solution.

In this paper we present the properties of the voltage fluctuations driven by a cluster of ligand-gated channels. First, the second-order moment of the voltage is expressed in form of the integrated resistance and the random force. Then the power spectrum of the voltage noise is obtained analytically, and it is proved to have the $1/{\omega }^4$-form. Its mechanism lies in that the randomness of the voltage fluctuation is weaker than channel (conductance) noise, which can be approximately described by the Ornstein-Ulenbeck process.

A molecular-statistical theory of the orientational elasticity of nematic liquid crystals has been developed employing the orientational deformation tensor which describes the rotation of the director. An explicit expression for the general elasticity tensor of the nematic phase has been obtained and the Frank elastic constants are expressed in terms of the three independent parameters of this tensor. Explicit expressions for the Frank elastic constants have been derived in the molecular field approximation in terms of the orientational order parameters and the corresponding coefficients of expansion of the intermolecular potential in spherical invariants. Frank elastic constants have been calculated numerically for nematic liquid crystals composed of both polar and nonpolar molecules together with the orientational order parameters using the classical Gay-Berne model interaction potential and the two of its popular modifications. The polarity of the uniaxial molecular shape has been directly introduced into the model potential by modifying the distance of closest approach. The elastic constants are presented as functions of temperature for different values of the molecular elongation, the anisotropy of the potential well and the molecular shape polarity. It has been shown that the elastic constants are much more sensitive to the details of the intermolecular interaction potential in comparison with the orientational order parameters. In particular, a relatively weak polarity of the molecular shape may result in an unusual decrease of the splay constant $K_{11}$ which may vanish at some temperature leading to the instability of the homogeneous nematic phase. This may represent a mechanism of the formation of the splay-bend phase.