The Richtmyer-Meshkov (RM) instability of a nominally flat interface (${\mathrm{N}}_2/{\mathrm{SF}}_6$) subjected to a rippled shock, as the counterpart of a corrugated interface interacting with a planar shock, is studied experimentally in a vertical shock tube using both schlieren photography and fog visualization diagnostics. The nonplanar incident shock wave is produced by a planar shock diffracting around a rigid cylinder, and the flat interface is created by a membraneless technique. Three different distances $\eta$ (the ratio of spacing from cylinder to interface over cylinder diameter) are considered. Schlieren images indicate that the nonplanar incident shock can be divided into three different segments separated by two triple points. Fog visualization pictures show the formation of overall “$\mathrm{\Lambda }$” shaped interface structures and a ${\mathrm{N}}_2$ cavity at the center and two interface steps at both sides. With the increase of the dimensionless time, the dimensionless interface amplitude increases as well as the penetration depth of the cavity, and both curves exhibit reasonable collapse for different $\eta$ numbers. Through equating the preinterface perturbation of the rippled shock with a preshock perturbation of a corrugated interface, the growth rate of this instability is found to be noticeably smaller than that of the standard RM instability.

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements, which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a nonvanishing resistance toward shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

Ising spin-glass models with bimodal, Gaussian, uniform, and Laplacian interaction distributions in dimension five are studied through detailed numerical simulations. The data are analyzed in both the finite-size scaling regime and the thermodynamic limit regime. It is shown that the values of critical exponents and of dimensionless observables at criticality are model dependent. Models in a single universality class have identical values for each of these critical parameters, so Ising spin-glass models in dimension five with different interaction distributions each lie in different universality classes. This result confirms conclusions drawn from measurements in dimension four and dimension two.

The escape rate of a Brownian particle over a potential barrier is accurately described by the Kramers theory. A quantitative theory explicitly taking the activity of Brownian particles into account has been lacking due to the inherently out-of-equilibrium nature of these particles. Using an effective equilibrium approach [Farage et al., Phys. Rev. E 91, 042310 (2015)] we study the escape rate of active particles over a potential barrier and compare our analytical results with data from direct numerical simulation of the colored noise Langevin equation. The effective equilibrium approach generates an effective potential that, when used as input to Kramers rate theory, provides results in excellent agreement with the simulation data.

Directed transport of self-propelled particles is numerically investigated in a three-dimensional asymmetric potential. Beside the steric repulsive forces, hydrodynamic interactions between particles have been taken into account in an approximate way. From numerical simulations, we find that hydrodynamic interactions can strongly affect the rectified transport of self-propelled particles. Hydrodynamic interactions enhance the performance of the rectified transport when particles can easily pass across the barrier of the potential, and reduce the rectified transport when particles are mainly trapped in the potential well.

Range expansion of species is driven by the interactions among individual- and population-level processes and the spatial pattern of habitats. In this work we study how cooperatively growing populations spread on networks representing the skeleton of complex landscapes. By separating the slow and fast variables of the expansion process, we are able to give analytical predictions for the critical conditions that divide the dynamic behaviors into different phases (extinction, localized survival, and global expansion). We observe a resonance phenomenon in how the critical condition depends on the expansion rate, indicating the existence of an optimal strategy for global expansion. We derive the conditions for such optimal migration in locally treelike graphs and numerically study other structured networks. Our results highlight the importance of both the underlying interaction pattern and migration rate of the expanding populations for range expansion. We also discuss potential applications of the results to biological control and conservation.

We investigate the $q$-voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to $q$, some discrepancies originate. It is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamics with noise. Up till now, the analytical results have been obtained only for a complete graph. We show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network.

We investigate the dynamical role of inhibitory and highly connected nodes (hub) in synchronization and input processing of leaky-integrate-and-fire neural networks with short term synaptic plasticity. We take advantage of a heterogeneous mean-field approximation to encode the role of network structure and we tune the fraction of inhibitory neurons $f_I$ and their connectivity level to investigate the cooperation between hub features and inhibition. We show that, depending on $f_I$, highly connected inhibitory nodes strongly drive the synchronization properties of the overall network through dynamical transitions from synchronous to asynchronous regimes. Furthermore, a metastable regime with long memory of external inputs emerges for a specific fraction of hub inhibitory neurons, underlining the role of inhibition and connectivity also for input processing in neural networks.

The interactions between T-cell receptor (TCR) and peptide-major-histocompatibility complex (pMHC), which enable T-cell development and initiate adaptive immune responses, have been intensively studied. However, a central issue of how lipid rafts affect the TCR-pMHC interactions remains unclear. Here, by using a statistical-mechanical membrane model, we show that the binding affinity of TCR and pMHC anchored on two apposing cell membranes is significantly enhanced because of the lipid raft-induced signaling protein aggregation. This finding may provide an alternative insight into the mechanism of T-cell activation triggered by very low densities of pMHC. In the case of cell-substrate adhesion, our results indicate that the loss of lateral mobility of the proteins on the solid substrate leads to the inhibitory effect of lipid rafts on TCR-pMHC interactions. Our findings help to understand why different experimental methods for measuring the impact of lipid rafts on the receptor-ligand interactions have led to contradictory conclusions.

We have performed Monte Carlo (MC) simulations on two-dimensional systems of quadrupole particles confined to a triangular lattice in order to determine the conditions that permit the formation of a limit-periodic phase. We have found that limit-periodic structures form only when the rotations of the particles are confined to a set of six orientations aligned with the lattice directions. Related structures including striped and unidirectional rattler phases form when $\pi /\phantom{\pi 6}6$ rotations or continuous rotations are allowed. Order parameters signaling the formation of the limit-periodic structure and related structures are measured as a function of temperature. Our findings on the formation of the limit-periodic structure elucidate features relevant to the experimental creation of such a structure, which is expected to have interesting vibrational and electromagnetic modes.

We use numerical simulations to study the effect of particle friction on suspension flows of non-Brownian hard particles. By systematically varying the microscopic friction coefficient ${\mu }_p$ and the viscous number $J$, we build a phase diagram that identifies three regimes of flow: frictionless, frictional sliding, and rolling. Using energy balance in flow, we predict relations between kinetic observables, confirmed by numerical simulations. For realistic friction coefficients and small viscous numbers (below $J\sim {10}^{-3}$), we show that the dominating dissipative mechanism is sliding of frictional contacts, and we characterize asymptotic behaviors as jamming is approached. Outside this regime, our observations support the idea that flow belongs to the universality class of frictionless particles. We discuss recent experiments in the context of our phase diagram.

The influence of line tension on the thermostability of a droplet nucleated from an oversaturated vapor at the interface of the vapor and another immiscible liquid is investigated. Along with the condition of mechanical equilibrium, the notion of extremization of the reversible work of formation is considered to obtain the critical parameters related to heterogeneous nucleation. From the energetic formulation, the critical reversible work of formation is found to be greater than that of homogeneous nucleation for high value of the positive line tension. On the other hand, for high value of the negative line tension, the critical reversible work of formation becomes negative. Therefore, these thermodynamic instabilities under certain substrate wettability situations necessitate a free-energetics-based stability of the nucleated droplet, because the system energy is not minimized under these conditions. This thermostability is analogous to the transition-based stability proposed by Widom [B. Widom, J. Phys. Chem. 99, 2803 (1995)] in the case of partial wetting phenomena along with the positive line tension. The thermostability analysis limits the domain of the solution space of the present critical-value problem as the thermodynamic transformation in connection with homogeneous and workless nucleation is considered. Within the stability range of the geometry-based wetting parameters, three limiting modes of nucleation, i.e., total-dewetting-related homogeneous nucleation, and total-wetting-associated and total-submergence-associated workless nucleation scenarios, are identified. Either of the two related limiting wetting scenarios of workless nucleation, namely, total wetting and total submergence, is found to be favorable depending on the geometry-based wetting conditions. The line-tension-associated nucleation on a liquid surface can be differentiated from that on a rigid substrate, as in the former, the stability based on mechanical equilibrium and a typical case of workless nucleation with complete submergence are observed.

Periodical patterns (bands) developing at the interface of two immiscible fluids under vibration parallel to interface are observed under zero-gravity conditions. Fluids are slightly below their liquid-vapor critical point where they behave in a scaled, universal manner. In addition, liquid and vapor densities are close and surface tension is very low. Linear stability analyses and direct numerical simulation show that this instability, although comparable to the frozen wave instability observed in a gravity field, is nonetheless noticeably different when gravity becomes zero. In particular, the neutral curve minimum corresponds to the long-wave perturbations with $k=0$ and zero dimensionless vibrational parameter, corresponding to no instability threshold. The pattern wavelength thus corresponds to the wavelength of the perturbations with maximal growth rate. This wavelength differs substantially from the neutral perturbations wavelength at the same vibrational parameter value. The role of viscosity is highlighted in the pattern formation, with a critical wavelength dependence on vibration parameters that strongly depends on viscosity. These results compare well with experimental observations performed in the liquid-vapor phases near the critical point of $\mathrm{C}{\mathrm{O}}_2$ (in weightlessness) and ${\mathrm{H}}_2$ (under magnetic levitation).

We present findings from an experimental study of the impact of liquid marbles onto solid surfaces. Using dual-view high-speed imaging, we reveal details of the impact dynamics previously not reported. During the spreading stage it is observed that particles at the surface flow rapidly to the periphery of the drop, i.e., the lamella. We characterize the spreading with the maximum spread diameter, comparing to impacts of pure liquid droplets. The principal result is a power-law scaling for the normalized maximum spread in terms of the impact Weber number, $D_{max}/D_0\sim {\text{We}}^{\alpha }$, with $\alpha \approx 1/3$. However, the best description of the spreading is obtained by considering a total energy balance, in a similar fashion to Pasandideh-Fard et al. [Phys. Fluids 8, 650 (1996)]. By using hydrophilic target surfaces, the marble integrity is lost even for moderate impact speeds as the particles at the surface separate and allow liquid-solid contact to occur. Remarkably, however, we observe no significant difference in the maximum spread between hydrophobic and hydrophilic targets, which is rationalized by the presence of the particles. Finally, for the finest particles used, we observe the formation of nonspherical arrested shapes after retraction and rebound from hydrophobic surfaces, which is quantified by a circularity measurement of the side profiles.

We identify the temperature being measured by a thermometer in a nonequilibrium scenario by studying heat conduction in a three-dimensional Lennard-Jones (LJ) system whose two ends are kept at different temperatures. It is accomplished by modeling the thermometer particles also with the LJ potential but with added tethers to prevent their rigid body motion. These models of the system and the thermometer mimic a real scenario in which a mechanical thermometer is “inserted” into a system and kept there long enough for the temperature to reach a steady value. The system is divided into five strips, and for each strip the temperature is measured using an embedded thermometer. Unlike previous works, these thermometers are small enough not to alter the steady state of the nonequilibrium system. After showing initial transients, the thermometers eventually show steady-state conditions with the subregions of the system and provide values of the different temperature definitions—kinetic, configurational, dynamical, and higher-order configurational. It is found that their kinetic and the configurational temperatures are close to the system's kinetic temperature except in the two thermostatted regions. In the thermostatted regions, where the system's kinetic and the configurational temperatures are significantly different, the thermometers register a temperature substantially different from either of these two values. With a decrease in the system density and size, these differences between the kinetic and the configurational temperatures of the thermometer become more pronounced.

The spanning cluster properties of a percolation model with nucleation and preferential growth exhibit first-order transitions depending on the values of the growth parameter $g_0$ and the initial seed concentration $\rho$. Except for the preferential growth of smaller clusters with a size-dependent growth probability of amplitude $g_0$, the model preserves all other criteria of the original percolation model. As $\rho$ decreases starting from the percolation threshold $p_c$ of the original percolation, a line of continuous transition encounters a coexistence region of percolative and nonpercolative large clusters. At sufficiently small values of $\rho$ ($\le 0.05$), the value of $g_0$ exceeds $p_c$ and generates compact spanning clusters leading to first-order discontinuous transitions.

The ground state of a two-level system (associated with probabilities $p$ and $1-p$, respectively) defined by a general Hamiltonian $\widehat{H}={\widehat{H}}_0+\lambda \widehat{V}$ is studied. The simple case characterized by $\lambda =0$, whose Hamiltonian ${\widehat{H}}_0$ is represented by a diagonal matrix, is well established and solvable within Boltzmann-Gibbs statistical mechanics; in particular, it follows the third law of thermodynamics, presenting zero entropy ($S_{\mathrm{BG}}=0$) at zero temperature ($T=0$). Herein it is shown that the introduction of a perturbation $\lambda \widehat{V}$ ($\lambda >0$) in the Hamiltonian may lead to a nontrivial ground state, characterized by an entropy $S\left[p\right]$ (with $S\left[p\right]\ne S_{\mathrm{BG}}\left[p\right]$), if the Hermitian operator $\widehat{V}$ is represented by a $2\times 2$ matrix, defined by nonzero off-diagonal elements $V_{12}=V_{21}=-z$, where $z$ is a real positive number. Hence, this new term in the Hamiltonian, presenting $V_{12}\ne 0$, may produce physically significant changes in the ground state, and especially, it allows for the introduction of an effective temperature $\theta$ ($\theta \propto \lambda z$), which is shown to be a parameter conjugated to the entropy $S$. Based on this, one introduces an infinitesimal heatlike quantity, $\delta Q=\theta dS$, leading to a consistent thermodynamic framework, and by proposing an infinitesimal form for the first law, a Carnot cycle and thermodynamic potentials are obtained. All results found are very similar to those of usual thermodynamics, through the identification $T\leftrightarrow \theta$, and particularly the form for the efficiency of the proposed Carnot Cycle. Moreover, $S$ also follows a behavior typical of a third law, i.e., $S\to 0$, when $\theta \to 0$.

We study the totally asymmetric exclusion process (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or defects. We allow weak particle nonconservation via Langmuir kinetics (LK), which are parametrized by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state—the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between the above phases are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are spatially uniform low- and high-density phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

First-passage-time problems are ubiquitous across many fields of study, including transport processes in semiconductors and biological synapses, evolutionary game theory and percolation. Despite their prominence, first-passage-time calculations have proven to be particularly challenging. Analytical results to date have often been obtained under strong conditions, leaving most of the exploration of first-passage-time problems to direct numerical computations. Here we present an analytical approach that allows the derivation of first-passage-time distributions for the wide class of nondifferentiable Gaussian processes. We demonstrate that the concept of sign changes naturally generalizes the common practice of counting crossings to determine first-passage events. Our method works across a wide range of time-dependent boundaries and noise strengths, thus alleviating common hurdles in first-passage-time calculations.

We investigate the detectability thresholds of various modular structures in the stochastic block model. Our analysis reveals how the detectability threshold is related to the details of the modular pattern, including the hierarchy of the clusters. We show that certain planted structures are impossible to infer regardless of their fuzziness.