We numerically solve the underdamped Langevin equation to obtain the trajectories of a particle in a sinusoidal potential driven by a temporally sinusoidal force in a medium with coefficient of friction periodic in space as the potential but with a phase difference. With the appropriate choice of system parameters, like the mean friction coefficient and the period of the applied field, only two kinds of periodic trajectories are obtained for all possible initial conditions at low noise strengths: one with a large amplitude and a large phase lag with respect to the applied field and the other with a small amplitude and a small phase lag. Thus, the periodic potential system is effectively mapped dynamically into a bistable system. Though the directional asymmetry, brought about only by the frictional inhomogeneity, is weak we find both the phenomena of stochastic resonance, with ready explanation in terms of the two dynamical states of trajectories, and ratchet effect simultaneously in the same parameter space. We analyze the results in detail attempting to find plausible explanations for each.

We use virial series to study the equilibrium properties of confined soft-spheres fluids interacting through the inverse-power potentials. The confinement is induced by hard walls with planar, spherical, and cylindrical shapes. We evaluate analytically the coefficients of order two in density of the wall-fluid surface tension $\gamma$ and analyze the curvature contributions to the free energy. Emphasis is in bending and Gaussian rigidities, which are found analytically at order two in density. Their contribution to $\gamma \left(R\right)$ and the accuracy of different truncation procedures to the low curvature expansion are discussed. Finally, several universal relations that apply to low-density fluids are analyzed.

Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems.

A fundamental problem in community ecology is understanding how ecological processes such as selection, drift, and immigration give rise to observed patterns in species composition and diversity. Here, we analyze a recently introduced, analytically tractable, presence-absence (PA) model for community assembly, and we use it to ask how ecological traits such as the strength of competition, the amount of diversity, and demographic and environmental stochasticity affect species composition in a community. In the PA model, species are treated as stochastic binary variables that can either be present or absent in a community: species can immigrate into the community from a regional species pool and can go extinct due to competition and stochasticity. Building upon previous work, we show that, despite its simplicity, the PA model reproduces the qualitative features of more complicated models of community assembly. In agreement with recent studies of large, competitive Lotka-Volterra systems, the PA model exhibits distinct ecological behaviors organized around a special (“critical”) point corresponding to Hubbell's neutral theory of biodiversity. These results suggest that the concepts of ecological “phases” and phase diagrams can provide a powerful framework for thinking about community ecology, and that the PA model captures the essential ecological dynamics of community assembly.

Water transport in a leaf is vulnerable to viscosity-induced changes. Recent research has suggested that these changes may be partially due to variation at the molecular scale, e.g., regulations via aquaporins, that induce reductions in leaf hydraulic conductance. What are the quantitative as well as qualitative changes in temperature-dependent viscosity due to the role of aquaporins in tuning activation energy and activation volume? Using the transition-state approach as well as the boundary perturbation method, we investigate temperature-dependent viscosity tuned by activation energy and activation volume. To validate our approach, we compare our numerical results with previous temperature-dependent viscosity measurements. The rather good fit between our calculations and measurements confirms our present approach. We have obtained critical parameters for the temperature-dependent (shear) viscosity of water that might be relevant to the increasing and reducing of leaf hydraulic conductance. These parameters are sensitive to temperature, activation energy, and activation volume. Once the activation energy increases, the (shear) viscosity of water increases. Our results also show that as the activation volume increases (say, ${10}^{-23}{\mathrm{m}}^3$), the (shear) viscosity of water decreases significantly and the latter induces the enhancing of leaf hydraulic conductance. Within the room-temperature regime, a small increase in the activation energy will increase the water viscosity or reduce the leaf hydraulic conductance. Our approach and results can be applied to diverse plant or leaf attributes.

There are various kinds of macromolecules in bacterial cell cytoplasm. The size polydispersity of the macromolecules is so significant that the crystallization and the phase separation could be suppressed, thus stabilizing the liquid state of bacterial cytoplasm. On the other hand, recent experiments suggested that the macromolecules in bacterial cytoplasm should exhibit glassy dynamics, which should be also affected significantly by the size polydispersity of the macromolecules. In this work, we investigate the anomalous and slow dynamics of highly polydisperse colloidal suspensions, of which size distribution is chosen to mimic Escherichia coli cytoplasm. We find from our Langevin dynamics simulations that the diffusion coefficient $\left(D_{\text{tot}}\right)$ and the displacement distribution functions $\left(P(r,t)\right)$ averaged over all colloids of different sizes do not show anomalous and glassy dynamic behaviors until the system volume fraction $\varphi$ is increased up to 0.82. This indicates that the intrinsic polydispersity of bacterial cytoplasm should suppress the glass transition and help maintain the liquid state of the cytoplasm. On the other hand, colloids of each kind show totally different dynamic behaviors depending on their size. The dynamics of colloids of different size becomes non-Gaussian at a different range of $\varphi$, which suggests that a multistep glass transition should occur. The largest colloids undergo the glass transition at $\varphi =0.65$, while the glass transition does not occur for smaller colloids in our simulations even at the highest value of $\varphi$. We also investigate the distribution $\left(P(\theta ,t)\right)$ of the relative angles of displacement for macromolecules and find that macromolecules undergo directionally correlated motions in a sufficiently dense system.

We use computer simulations to analyze the yielding transition during large-amplitude oscillatory shear of a simple model for soft jammed solids. Simultaneous analysis of global mechanical response and particle-scale motion demonstrates that macroscopic yielding, revealed by a smooth crossover in mechanical properties, is accompanied by a sudden change in the particle dynamics, which evolves from nondiffusive motion to irreversible diffusion as the amplitude of the shear is increased. We provide numerical evidence that this sharp change corresponds to a nonequilibrium first-order dynamic phase transition, thus establishing the existence of a well-defined microscopic dynamic signature of the yielding transition in amorphous materials in oscillatory shear.

We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a $1/2$ ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.

We show by direct numerical simulations (DNSs) that in different types of isotropic turbulence, the fourth-order statistical invariants have approximately a linear relation, which can be represented by a straight line in the phase plane, passing two extreme states: the Gaussian state and the restricted Euler state. Also, each DNS case corresponds to an equilibrium region that is roughly Reynolds-dependent. In addition, both the time reversal and the compressibility effect lead to nonequilibrium transition processes in this phase plane. This observation adds a new restriction on the mean-field theory.

The nonlinear phenomena that occur in the electric double layer (EDL) that forms at charged surfaces strongly influence electrokinetic effects, including electro-osmosis and electrophoresis. In particular, saturation effects due to either dielectric decrement or ion crowding effects are of paramount importance. Dielectric decrement significantly influences the ionic concentration in the EDL at high $\zeta$ potential, leading to the formation of a condensed layer near the particle's surface. In this article, we present a model incorporating both steric effects due to the finite size of ions and dielectric decrement to describe the physics in the electric double layer. The model remains valid in both weakly and strongly nonlinear regimes, as long as the electric double layer remains in quasiequilibrium. We apply this model to the study of two archetypal problems in electrokinetics, namely the electrophoresis of particles with fixed surface charges and the electrophoresis of ideally polarizable particles.

We applied the multiparticle collision dynamics (MPC) simulation technique to highly asymmetric electrolytes in solution, i.e., charged nanoparticles and their counterions in a solvent. These systems belong to a domain of solute size which ranges between the electrolyte and the colloidal domains, where most analytical theories are expected to fail, and efficient simulation techniques are still missing. MPC is a mesoscopic simulation method which mimics hydrodynamics properties of a fluid, includes thermal fluctuations, and can be coupled to a molecular dynamics of solutes. We took advantage of the size asymmetry between nanoparticles and counterions to treat the coupling between solutes and the solvent bath within the MPC method. Counterions were coupled to the solvent bath during the collision step and nanoparticles either through a direct interaction force or with stochastic rotation rules which mimic stick boundary conditions. Moreover, we adapted the simulation procedure to address the issue of the strong electrostatic interactions between solutes of opposite charges. We show that the short-ranged repulsion between counterions and nanoparticles can be modeled by stochastic reflection rules. This simulation scheme is very efficient from a computational point of view. We have also computed the transport coefficients for various densities. The diffusion of counterions was found in one case to increase slightly with the volume fraction of nanoparticles. The deviation of the electric conductivity from the ideal behavior (solutes at infinite dilution without any direct interactions) is found to be strong.

In this paper, we explore the possibilities and limitations of recovering sparse signals in an online fashion. Employing a mean field approximation to the Bayes recursion formula yields an online signal recovery algorithm that can be performed with a computational cost that is linearly proportional to the signal length per update. Analysis of the resulting algorithm indicates that the online algorithm asymptotically saturates the optimal performance limit achieved by the offline method in the presence of Gaussian measurement noise, while differences in the allowable computational costs may result in fundamental gaps of the achievable performance in the absence of noise.

A decrease in system size can induce qualitatively different behavior compared to the macroscopic behavior of the corresponding large-size system. The mechanisms of this transition, which is known as the small-size transition, can be attributed to either a relative increase in the noise intensity or to the discreteness of the state space due to the small system size. The former mechanism has been intensively investigated using several toy and realistic models. However, the latter has rarely been analyzed and is sometimes confused with the former, because a toy model that extracts the essence of the discreteness-induced transition mechanism is lacking. In this work, we propose a one- and three-body reaction system as a minimal model of the discreteness-induced transition and derive the conditions under which this transition occurs in more complex systems. This work enriches our understanding of the influence of small system size on system behavior.

We consider the power adiabatic stroke of the Otto optomechanical heat engine introduced in Phys. Rev. Lett. 112, 150602 (2014). We derive the maximum extractable work of both optomechanical normal modes in the minimum time while the system experiences quantum friction effects. We show that the total work done by the system in the power adiabatic stroke is optimized by a bang-bang control. The time duration of the power adiabatic stroke is of the order of the inverse of the effective optomechanical-coupling coefficient. The optimal phase-space trajectory of the Otto cycle for both optomechanical normal modes is also obtained.

Diffusion in liquids is accompanied by nonequilibrium concentration fluctuations spanning all the length scales comprised between the microscopic scale $a$ and the macroscopic size of the system, $L$. Up to now, theoretical and experimental investigations of nonequilibrium fluctuations have focused mostly on determining their mean-square amplitude as a function of the wave vector. In this work, we investigate the local properties of nonequilibrium fluctuations arising during a stationary diffusion process occurring in a binary liquid mixture in the presence of a uniform concentration gradient, $\mathbf{\nabla }{c}_0$. We characterize the fluctuations by evaluating statistical features of the system, including the mean-square amplitude of fluctuations and the corrugation of the isoconcentration surfaces; we show that they depend on a single mesoscopic length scale $l=\sqrt{aL}$ representing the geometric average between the microscopic and macroscopic length scales. We find that the amplitude of the fluctuations is very small in practical cases and vanishes when the macroscopic length scale increases. The isoconcentration surfaces, or fronts of diffusion, have a self-affine structure with corrugation exponent $H=1/2$. Ideally, the local fractal dimension of the fronts of diffusion would be $D_l=d-H$, where $d$ is the dimensionality of the space, while the global fractal dimension would be $D_g=d-1$. The transition between the local and global regimes occurs at a crossover length scale of the order of the microscopic length scale $a$. Therefore, notwithstanding the fact that the fronts of diffusion are corrugated, they appear flat at all the length scales probed by experiments, and they do not exhibit a fractal structure.

We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response theory for nonequilibrium overdamped stochastic systems. To validate these results, we introduce a reweighting procedure that mimics the actual realization of the perturbation and allows extracting the susceptibility of the system from steady-state data. This procedure is closely related to other fluctuation-response relations based on the knowledge of the steady-state probability distribution. As an example, we show that the nonequilibrium heat capacity in general does not correspond to the correlation between the energy of the system and the heat flowing into it. Rather, also nondissipative aspects are relevant in the nonequilibrium fluctuation-response relations.

The zero-temperature, classical $XY$ model on an $L\times L$ square lattice is studied by exploring the distribution ${\mathrm{\Phi }}_L\left(y\right)$ of its centered and normalized magnetization $y$ in the large-$L$ limit. An integral representation of the cumulant generating function, known from earlier works, is used for the numerical evaluation of ${\mathrm{\Phi }}_L\left(y\right)$, and the limit distribution ${\mathrm{\Phi }}_{L\to \infty }\left(y\right)={\mathrm{\Phi }}_0\left(y\right)$ is obtained with high precision. The two leading finite-size corrections ${\mathrm{\Phi }}_L\left(y\right)-{\mathrm{\Phi }}_0\left(y\right)\approx a_1\left(L\right){\mathrm{\Phi }}_1\left(y\right)+a_2\left(L\right){\mathrm{\Phi }}_2\left(y\right)$ are also extracted both from numerics and from analytic calculations. We find that the amplitude $a_1\left(L\right)$ scales as $ln(L/L_0)/L^2$ and the shape correction function ${\mathrm{\Phi }}_1\left(y\right)$ can be expressed through the low-order derivatives of the limit distribution, ${\mathrm{\Phi }}_1\left(y\right)={[y{\mathrm{\Phi }}_0\left(y\right)+{\mathrm{\Phi }}_0^{\prime }\left(y\right)]}^{\prime }$. Thus, ${\mathrm{\Phi }}_1\left(y\right)$ carries the same universal features as the limit distribution and can be used for consistency checks of universality claims based on finite-size systems. The second finite-size correction has an amplitude $a_2\left(L\right)\propto 1/L^2$ and one finds that $a_2{\mathrm{\Phi }}_2\left(y\right)\ll a_1{\mathrm{\Phi }}_1\left(y\right)$ already for small system size ($L>10$). We illustrate the feasibility of observing the calculated finite-size corrections by performing simulations of the $XY$ model at low temperatures, including $T=0$.

A feedback vertex set (FVS) of an undirected graph contains vertices from every cycle of this graph. Constructing a FVS of sufficiently small cardinality is very difficult in the worst cases, but for random graphs this problem can be efficiently solved by converting it into an appropriate spin-glass model [H.-J. Zhou, Eur. Phys. J. B 86, 455 (2013)]. In the present work we study the spin-glass phase transitions and the minimum energy density of the random FVS problem by the first-step replica-symmetry-breaking (1RSB) mean-field theory. For both regular random graphs and Erdös-Rényi graphs, we determine the inverse temperature ${\beta }_l$ at which the replica-symmetric mean-field theory loses its local stability, the inverse temperature ${\beta }_d$ of the dynamical (clustering) phase transition, and the inverse temperature ${\beta }_s$ of the static (condensation) phase transition. These critical inverse temperatures all change with the mean vertex degree in a nonmonotonic way, and ${\beta }_d$ is distinct from ${\beta }_s$ for regular random graphs of vertex degrees $K>60$, while ${\beta }_d$ are identical to ${\beta }_s$ for Erdös-Rényi graphs at least up to mean vertex degree $c=512$. We then derive the zero-temperature limit of the 1RSB theory and use it to compute the minimum FVS cardinality.

We study a nanoscale machine composed of a rack and a pinion with no contact, but intermeshed via the lateral Casimir force. We adopt a simple model for the random velocity of the rack subject to external random forces, namely, a dichotomous noise with zero mean value. We show that the pinion, even when it experiences random thermal torque, can do work against a load. The device thus converts the kinetic energy of the random motions of the rack into useful work.