We discuss the hydrodynamic collective effects due to active protein molecules that are immersed in lipid bilayer membranes and modeled as stochastic force dipoles. We specifically take into account the presence of the bulk solvent that surrounds the two-dimensional fluid membrane. Two membrane geometries are considered: the free membrane case and the confined membrane case. Using the generalized membrane mobility tensors, we estimate the active diffusion coefficient and the drift velocity as a function of the size of a diffusing object. The hydrodynamic screening lengths distinguish the two asymptotic regimes of these quantities. Furthermore, the competition between the thermal and nonthermal contributions in the total diffusion coefficient is characterized by two length scales corresponding to the two membrane geometries. These characteristic lengths describe the crossover between different asymptotic behaviors when they are larger than the hydrodynamic screening lengths.

The existing theory of incompatible elastic sheets uses the deviation of the surface metric from a reference metric to define the strain tensor [Efrati et al., J. Mech. Phys. Solids 57, 762 (2009)]. For a class of simple axisymmetric problems we examine an alternative formulation, defining the strain based on deviations of distances (rather than distances squared) from their rest values. While the two formulations converge in the limit of small slopes and in the limit of an incompressible sheet, for other cases they are found not to be equivalent. The alternative formulation offers several features which are absent in the existing theory. (a) In the case of planar deformations of flat incompatible sheets, it yields linear, exactly solvable, equations of equilibrium. (b) When reduced to uniaxial (one-dimensional) deformations, it coincides with the theory of extensible elastica; in particular, for a uniaxially bent sheet it yields an unstrained cylindrical configuration. (c) It gives a simple criterion determining whether an isometric immersion of an incompatible sheet is at mechanical equilibrium with respect to normal forces. For a reference metric of constant positive Gaussian curvature, a spherical cap is found to satisfy this criterion except in an arbitrarily narrow boundary layer.

We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.

It has been broadly accepted that the behavior of glass-forming liquids, where their relaxation dynamics exhibit a pronounced slowdown as they are cooled toward the glass transition temperature, is caused by the increase in one or more correlation lengths. However, the role of length scales in the dynamics of glass-forming liquids is not clearly established, and past simulation work that suggests a surprising nonmonotonic temperature evolution of spatial dynamical correlations near the mode-coupling crossover temperature has been both questioned and supported by subsequent work. Here, using molecular dynamics simulation, we also show a striking maximum in the dynamic length scale ${\xi }_{\mathrm{c}}^{\mathrm{dyn}}$ at a given temperature, but the temperature of this maximum is found to shift as the size of the confined system increases. Furthermore, we find that such a maximum disappears for all geometry sizes considered when a rough wall is replaced with a smooth, hard wall, suggesting that the nature of the nonmonotonic temperature dependence of ${\xi }_{\mathrm{c}}^{\mathrm{dyn}}$ does not reflect an intrinsic property of bulk liquids, but originates from wall effects. Our results provide new insights into the dynamics of glass-forming liquids, particularly for quasi-two-dimensional systems.

A model called “colored percolation” has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability $p$ and are then colored by one of the $n$ distinct colors using uniform probability $q=1/n$. Denoting different colors by the letters of the Roman alphabet, we have studied different versions of the model like $AB,ABC,ABCD,ABCDE,...$ etc. Here, only those lattice bonds having two different colored atoms at the ends are defined as connected. The percolation threshold $p_c\left(n\right)$ asymptotically converges to its limiting value of $p_c$ as $1/n$. The model has been generalized by introducing a preference towards a subset of colors when $m$ out of $n$ colors are selected with probability $q/m$ each and the rest of the colors are selected with probability $(1-q)/(n-m)$. It has been observed that $p_c(q,m)$ depends nontrivially on $q$ and has a minimum at $q_{min}=m/n$. In another generalization the fractions of bonds between similarly and dissimilarly colored atoms have been treated as independent parameters. Phase diagrams in this parameter space have been drawn exhibiting percolating and nonpercolating phases.

The work distribution is a fundamental quantity in nonequilibrium thermodynamics mainly due to its connection with fluctuation theorems. Here, we develop a semiclassical approximation to the work distribution for a quench process in chaotic systems that provides a link between the quantum and classical work distributions. The approach is based on the dephasing representation of the quantum Loschmidt echo and on the quantum ergodic conjecture, which states that the Wigner function of a typical eigenstate of a classically chaotic Hamiltonian is equidistributed on the energy shell. Using numerical simulations, we show that our semiclassical approximation accurately describes the quantum distribution as the temperature is increased.

It is known that unconfined dust explosions typically start off with a relatively weak primary flame followed by a severe secondary explosion. We show that clustering of dust particles in a temperature stratified turbulent flow ahead of the primary flame may give rise to a significant increase in the radiation penetration length. These particle clusters, even far ahead of the flame, are sufficiently exposed and heated by the radiation from the flame to become ignition kernels capable to ignite a large volume of fuel-air mixtures. This efficiently increases the total flame surface area and the effective combustion speed, defined as the rate of reactant consumption of a given volume. We show that this mechanism explains the high rate of combustion and overpressures required to account for the observed level of damage in unconfined dust explosions, e.g., at the 2005 Buncefield vapor-cloud explosion. The effect of the strong increase of radiation transparency due to turbulent clustering of particles goes beyond the state of the art of the application to dust explosions and has many implications in atmospheric physics and astrophysics.

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

The coexistence line of a fluid separates liquid and gaseous states at subcritical pressures, ending at the critical point. Only recently, it became clear that the supercritical state space can likewise be divided into regions with liquidlike and gaslike properties, separated by an extension to the coexistence line. This crossover line is commonly referred to as the Widom line, and is characterized by large changes in density or enthalpy, manifesting as maxima in the thermodynamic response functions. Thus, a reliable representation of the coexistence line and the Widom line is important for sub- and supercritical applications that depend on an accurate prediction of fluid properties. While it is known for subcritical pressures that nondimensionalization with the respective species critical pressures $p_{\mathrm{cr}}$ and temperatures $T_{\mathrm{cr}}$ only collapses coexistence line data for simple fluids, this approach is used for Widom lines of all fluids. However, we show here that the Widom line does not adhere to the corresponding states principle, but instead to the extended corresponding states principle. We resolve this problem in two steps. First, we propose a Widom line functional based on the Clapeyron equation and derive an analytical, species specific expression for the only parameter from the Soave-Redlich-Kwong equation of state. This parameter is a function of the acentric factor $\omega$ and compares well with experimental data. Second, we introduce the scaled reduced pressure $p_{\mathrm{r}}^{*}$ to replace the previously used reduced pressure $p_{\mathrm{r}}=p/p_{\mathrm{cr}}$. We show that $p_{\mathrm{r}}^{*}$ is a function of the acentric factor only and can thus be readily determined from fluid property tables. It collapses both subcritical coexistence line and supercritical Widom line data over a wide range of species with acentric factors ranging from $-0.38$ (helium) to 0.34 (water), including alkanes up to n-hexane. By using $p_{\mathrm{r}}^{*}$, the extended corresponding states principle can be applied within corresponding states principle formalism. Furthermore, $p_{\mathrm{r}}^{*}$ provides a theoretical foundation to compare Widom lines of different fluids.

In kinetic theory, a system is usually described by its one-particle distribution function $f(\mathit{r},\mathit{v},t)$, such that $f(\mathit{r},\mathit{v},t)d\mathit{r}d\mathit{v}$ is the fraction of particles with positions and velocities in the intervals $(\mathit{r},\mathit{r}+d\mathit{r})$ and $(\mathit{v},\mathit{v}+d\mathit{v})$, respectively. Therein, global stability and the possible existence of an associated Lyapunov function or $H$ theorem are open problems when nonconservative interactions are present, as in granular fluids. Here, we address this issue in the framework of a lattice model for granularlike velocity fields. For a quite general driving mechanism, including both boundary and bulk driving, we show that the steady state reached by the system in the long-time limit is globally stable. This is done by proving analytically that a certain $H$ functional is nonincreasing in the long-time limit. Moreover, for a quite general energy injection mechanism, we are able to demonstrate that the proposed $H$ functional is nonincreasing for all times. Also, we put forward a proof that clearly illustrates why the “classical” Boltzmann functional $H_B\left[f\right]=\int d\mathit{r}d\mathit{v}f(\mathit{r},\mathit{v},t)lnf(\mathit{r},\mathit{v},t)$ is inadequate for systems with nonconservative interactions. This is done not only for the simplified kinetic description that holds in the lattice models analyzed here but also for a general kinetic equation, like Boltzmann's or Enskog's.

We have examined the conditions under which the breakdown of the Stokes-Einstein (SE) relation occurs in pure Lennard-Jones (LJ) fluids over a wide range of temperatures and packing fractions beyond the critical point. To this end, the temperature and packing-fraction dependence of the self-diffusion coefficient, $D$, and the shear viscosity, ${\eta }_{\mathrm{sv}}$, were evaluated for Xe using molecular dynamics calculations with the Green-Kubo formula. The results showed good agreement with the experimental values. The breakdown was determined in light of the SE equation which we have recently derived for pure LJ liquids: $D{\eta }_{\mathrm{sv}}=(k_{B}T/2\pi ){(N/V)}^{1/3}$, where $k_B$ is the Boltzmann constant, $T$ is the temperature, and $N$ is the particle number included in the system volume $V$. We have found that the breakdown occurs in the lower range of the packing fraction, $\eta <0.2$, and derived the SE relation in its broken form as $D{\eta }_{\mathrm{sv}}=0.007{(1-\eta )}^{-5}{\eta }^{-4/3}{(k_{B}T/\epsilon )}^n{k}_{B}T{(N/V)}^{1/3}$, where $n$ increases from 0 up to 1 with the decreasing $\eta$. The equation clearly shows that the breakdown mainly occurs because the packing-fraction dependence does not cancel out between $D$ and ${\eta }_{\mathrm{sv}}$ in this region, which is attributed to the gaseous behavior in the packing-fraction dependence of the shear viscosity under a constant number density. In addition, the gaseous behavior in the temperature dependence of the shear viscosity also partially causes the breakdown.

Miniaturized heat engines constitute a fascinating field of current research. Many theoretical and experimental studies are being conducted that involve colloidal particles in harmonic traps as well as bacterial baths acting like thermal baths. These systems are micron-sized and are subjected to large thermal fluctuations. Hence, for these systems average thermodynamic quantities, such as work done, heat exchanged, and efficiency, lose meaning unless otherwise supported by their full probability distributions. Earlier studies on microengines are concerned with applying Carnot or Stirling engine protocols to miniaturized systems, where system undergoes typical two isothermal and two adiabatic changes. Unlike these models we study a prototype system of two classical Ising spins driven by time-dependent, phase-different, external magnetic fields. These spins are simultaneously in contact with two heat reservoirs at different temperatures for the full duration of the driving protocol. Performance of the model as an engine or a refrigerator depends only on a single parameter, namely the phase between two external drivings. We study this system in terms of fluctuations in efficiency and coefficient of performance (COP). We find full distributions of these quantities numerically and study the tails of these distributions. We also study reliability of the engine. We find the fluctuations dominate mean values of efficiency and COP, and their probability distributions are broad with power law tails.

We investigate numerically the behavior of a two-component reaction-diffusion system of Fitzhugh-Nagumo type before the onset of subcritical Turing bifurcation in response to local rigid perturbation. In a large region of parameters, the initial perturbation evolves into a localized structure. In a part of that region, closer to the bifurcation line, this structure turns out to be unstable and covers all the available space over the course of time in a process of self-completion. Depending on the parameter values in two-dimensional (2D) space, this process happens either through generation and evolution of new peaks on oscillatory tails of the initial pattern, or through the elongation, deformation, and rupture of initial structure, leading to space-filling nonbranching snakelike patterns. Transient regimes are also possible. Comparison of these results with 1D simulations shows that the prebifurcation region of parameters where the self-completion process is observed is much larger in the 2D case.

We propose an approximation for the probability of tipping when the speed of parameter change and additive white noise interact to cause tipping. Our approximation is valid for small to moderate drift speeds and helps to estimate the probability of false positives and false negatives in early-warning indicators in the case of rate- and noise-induced tipping. We illustrate our approximation on a prototypical model for rate-induced tipping with additive noise using Monte Carlo simulations. The formula can be extended to close encounters of rate-induced tipping and is otherwise applicable to other forms of tipping. We also provide an asymptotic formula for the critical ramp speed of the parameter in the absence of noise for a general class of systems undergoing rate-induced tipping.

Flexible superparamagnetic filaments are studied under the influence of fast precessing magnetic fields using simulations and a continuum approximation analysis. We find that individual filaments can be made to exert controllable tensile forces along the precession axis. These forces are exploited for microscopic actuation. In bulk, the filaments can be rapidly assembled into different configurations whose material properties depend on the field parameters. The precession frequency affects filament aggregation and conformation by changing the net torques on the filament ends. Using a time-dependent precession angle allows considerable freedom in choosing properties for filament aggregates. As an example, we design a field that twists chains together to dynamically assemble a self-healing gel.

We have developed a tunable colloidal system and a corresponding theoretical model for studying the phase behavior of particles assembling under the influence of long-range magnetic interactions. A monolayer of paramagnetic particles is subjected to a spatially uniform magnetic field with a static perpendicular component and a rapidly rotating in-plane component. The sign and strength of the interactions vary with the tilt angle $\theta$ of the rotating magnetic field. For a purely in-plane field, $\theta ={90}^{\circ }$, interactions are attractive and the experimental results agree well with both equilibrium and out-of-equilibrium predictions based on a two-body interaction model. For tilt angles ${50}^{\circ }\lesssim \theta \lesssim {55}^{\circ }$, the two-body interaction gives a short-range attractive and long-range repulsive interaction, which predicts the formation of equilibrium microphases. In experiments, however, a different type of assembly is observed. Inclusion of three-body (and higher-order) terms in the model does not resolve the discrepancy. We further characterize the anomalous regime by measuring the time-dependent cluster size distribution.

The spreading of a cap-shaped spherical droplet on a completely wettable spherical substrate is studied. The nonequilibrium thermodynamic formulation is used to derive the thermodynamic driving force of spreading including the line-tension effect. Then the energy balance approach is adopted to derive the evolution equation of the spreading droplet. The time evolution of the contact angle $\theta$ of a droplet obeys a power law $\theta \sim t^{-\alpha }$ with the exponent $\alpha$, which is different from that derived from Tanner's law on a flat substrate. Furthermore, the line tension must be positive to promote complete wetting on a spherical substrate, while it must be negative on a flat substrate.

The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. If the system is instead integrable, additional quantities conserved by the dynamics intervene in the description of the stationary state. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. Here we argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions of natural observables, quantities which are accessible in experiments.

We perform a numerical study of the $F$ model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multicluster algorithm to study equilibrium properties of this model for systems of moderate size, up to $L=512$. We compare the energy to its exactly known large-$L$ asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyze local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Syljuåsen and Zvonarev and recently studied by Lyberg et al. We point out “(anti)ferroelectric” oscillations close to the corresponding frozen regions as well as “higher-order” oscillations forming an intricate pattern with saddle-point-like features.

Conventional master equation approaches approximate the diffusion of molecules in continuum space by the process of particles hopping on a spatial lattice. The hopping probability from one voxel (spatial lattice point) to its neighbor is usually considered to be constant throughout space. Such an assumption is only consistent with pointlike molecules and thus neglects volume-exclusion effects due to finite particle size. A few studies have attempted to introduce volume-exclusion effects by choosing the hopping probability from one voxel to a neighboring one to be a linear function of the number density. Here, we formulate an alternative master equation in which the hopping probability is equal to the fraction of available space in the neighboring voxel as estimated using scaled particle theory. This leads to the hopping probability being a nonlinear function of the number density. A mean-field approximation (mfa) leads to a partial differential equation of the advection-diffusion type. We show that the time evolution of the particle number density sampled using the stochastic simulation algorithm associated with the new master equation and the number density obtained by numerical integration of the mfa are in good agreement with each other. They are also distinctly different than the time evolution predicted by the conventional master equation and those with hopping probabilities which are linear functions of the number density. The results from the new lattice description are also shown to be in very good agreement with the lattice-free method of Brownian dynamics, even for highly crowded scenarios.