We theoretically study bright and dark solitons in an experimentally relevant hybrid system characterized by strong light-matter coupling. We find that the corresponding two-component model supports a variety of coexisting moving solitons including bright solitons on zero and nonzero background and dark-gray and gray-gray solitons. The solutions are found in the analytical form by reducing the two-component problem to a single stationary equation with cubic-quintic nonlinearity. All found solutions coexist under the same set of the model parameters, but, in a properly defined linear limit, approach different branches of the polariton dispersion relation for linear waves. Bright solitons with zero background feature an oscillatory-instability threshold which can be associated with a resonance between the edges of the continuous spectrum branches. “Half-topological” dark-gray and nontopological gray-gray solitons are stable in wide parametric ranges below the modulational instability threshold, while bright solitons on the constant-amplitude pedestal are unstable.

A dynamical system approaching the first-order transition can exhibit a specific type of critical behavior known as self-organized bistability (SOB). It lies in the fact that the system can permanently switch between the coexisting states under the self-tuning of a control parameter. Many of these systems have a network organization that should be taken into account to understand the underlying processes in detail. In the present paper, we theoretically explore an extension of the SOB concept on the scale-free network under coupling constraints. As provided by the numerical simulations and mean-field approximation in the thermodynamic limit, SOB on scale-free networks originates from facilitated criticality reflected on both macro- and mesoscopic network scales. We establish that the appearance of switches is rooted in spatial self-organization and temporal self-similarity of the network's critical dynamics and replicates extreme properties of epileptic seizure recurrences. Our results, thus, indicate that the proposed conceptual model is suitable to deepen the understanding of emergent collective behavior behind neurological diseases.

We present experimental results of pedestrian evacuations through a narrow door under a prescribed safety distancing of either 1.5 or 2 meters. In this situation, flow rate augments with pedestrian velocity due to a complete absence of flow interruptions or clogs. Accordingly, the evacuation improves when the prescribed physical distance is reduced, as this implies shortening the time lapses between the exit of consecutive pedestrians. In addition, the analysis of pedestrian trajectories reveals that the distance to the first neighbor in the evacuation process is rather similar to the one obtained when pedestrians were just roaming within the arena, hence suggesting that this magnitude depends more on the crowd state (desired speed, prescribed safety distance, etc.) than on the geometry where the pedestrian flow takes place. Also, an important difference in pedestrian behavior is observed when people are asked to walk at different speeds: whereas slow pedestrians evidence a clear preference for stop-and-go motion, fast walkers display detouring and stop-and-go behavior roughly in the same proportion.

Weak complementary interactions between proteins and nucleic acids are the main driving forces of intracellular liquid-liquid phase separation. The sticker-spacer model has emerged as a unifying principle for understanding the phase behavior of these multivalent molecules. It remains elusive how specific interactions mediated by stickers contribute to the rheological properties of the liquid condensates. Previous studies have revealed that for strong binding strength ${\varepsilon }_b$, the bulk diffusivity $D$ depends on the effective bond lifetime $\tau$, viz., $D\propto {\tau }^{-1}$. Consequently, equal concentrations of the complementary stickers induce a slow down in the dynamics of the condensates $D\propto e^{-1.5{\varepsilon }_b}$. However, for weak-binding strength, it is expected that the resulting condensates are dynamic, loose network liquids rather than kinetically arrested, compact clusters. We develop a mean-field theory using the thermodynamics of the associative polymers and perform molecular-dynamics simulations based on the sticker-spacer model to study the controlling factors in the structure and dynamics of such condensates in the weak-binding regime. Through scaling analysis, we delineate how the free sticker fraction $W_f$ and the bulk diffusivity $D$ decrease with increasing binding energy and find that the internal dynamics of such network liquids are controlled by the free sticker fraction $D\propto W_f\propto e^{-0.5{\varepsilon }_b}$ rather than the effective bond lifetime. Referred to as the free-sticker-dominated diffusivity, the microscopic slowdown due to a gradual loss of the free stickers affects the viscosity of the condensates as well, with the scaling of the zero-shear viscosity $\eta \propto e^{0.5{\varepsilon }_b}$. Therefore, the way of controlling the structure, diffusivity, and viscosity of the condensates through the binding energy can be tested experimentally.

Many previous studies of sliding locomotion have assumed that body inertia is negligible. Here we optimize the kinematics of a three-link body for efficient locomotion and include among the kinematic parameters the temporal period of locomotion, or equivalently, the body inertia. The optimal inertia is nonnegligible when the coefficient of friction for sliding transverse to the body axis is small. Inertia is also significant in a few cases with relatively large coefficients of friction for transverse and backward sliding, and here the optimal motions are less sensitive to the inertia parameter. The optimal motions seem to converge as the number of frequencies used is increased from one to four. For some of the optimal motions with significant inertia we find dramatic reductions in efficiency when the inertia parameter is decreased to zero. For the motions that are optimal with zero inertia, the efficiency decreases more gradually when we raise the inertia to moderate and large values.

The equilibrium configuration of a gas and brine in a porous medium, and the timescales to reach equilibrium, are investigated analytically. If the gas is continuous in the pore space, we have the traditional gravity-capillary transition zone: $P_c\left(S_w\right)=\mathrm{\Delta }\rho gz$ where $P_c$ is the capillary pressure (pressure difference between the gas and aqueous phases), $S_w$ is the aqueous phase (brine) saturation, $\mathrm{\Delta }\rho ={\rho }_w-{\rho }_g$ is the density difference between the phases, $g$ is the gravitational acceleration, and $z$ is a vertical distance coordinate increasing upwards, where $z=0$ indicates the level where $P_c=0$. However, if the gas is disconnected, as may occur during water influx in carbon dioxide and hydrogen storage, then the nature of equilibrium is different where diffusion through the aqueous phase (Ostwald ripening) maintains a capillary pressure gradient consistent with the thermodynamically-determined brine density as a function of depth: $P_c=P^{*}[e^{(V_g{\rho }_w-m_g)gz/RT}-1]+{\rho }_{w}gz$, where $P^{*}$ is the aqueous phase pressure at $z=0, V_g$ is the specific molar volume of the gas dissolved in the aqueous phase, $m_g$ is the molecular mass of the gas, $R$ is the universal gas constant, and $T$ is the absolute temperature. The capillary pressure decreases with depth. This means that a deep column of trapped gas cannot be sustained indefinitely. Instead a transition zone forms in equilibrium with connected gas near the top of the formation: its thickness is typically less than 1 m for carbon dioxide, hydrogen, methane or nitrogen in a permeable reservoir. The timescales to reach equilibrium are, however, estimated to be millions of years, and hence do not significantly affect long-term storage over millennia. At the scale of laboratory experiments, in contrast, Ostwald ripening leads to local capillary equilibrium in a few weeks to a year, dependent on the gas considered.

We examine methods for calculating the effective mobilities of molecules driven through periodic geometries in the context of particle-based simulation. The standard formulation of the mobility, based on the long-time limit of the mean drift velocity, is compared to a formulation based on the mean first-passage time of molecules crossing a single period of the system geometry. The equivalence of the two definitions is derived under weaker assumptions than similar conclusions obtained previously, requiring only that the state of the system at subsequent period crossings satisfy the Markov property. Approximate theoretical analyses of the computational costs of estimating these two mobility formulations via particle simulations suggest that the definition based on first-passage times may be substantially better suited to exploiting parallel computation hardware. This claim is investigated numerically on an example system modeling the passage of nanoparticles through the slit-well device. In this case, the traditional mobility formulation is found to perform best when the Péclet number is small, whereas the mean first-passage time formulation is found to converge much more quickly when the Péclet number is moderate or large. The results suggest that, given relatively modest access to modern GPU hardware, this alternative mobility formulation may be an order of magnitude faster than the standard technique for computing effective mobilities of biomolecules through periodic geometries.

We report the results of a two-dimensional reference model for the formation of facets on the left and right side of a silicon monograin that is solidified by pulling a thin sample in a constant temperature gradient. Anisotropy functions of both the surface energy and the kinetic attachment coefficient are adapted from a recent model for free growth of silicon micrometer-sized grains [Boukellal et al., J. Cryst. Growth 522, 37 (2019).]. More precise estimates of the physical parameters entering these functions are obtained by reanalyzing available experimental results. We show that the reference model leads to a differential equation for the shape of the solid-liquid interface. The numerical solutions of this equation give a reference law $\mathrm{\Lambda }\left(V_f\right)$ relating the facet length $\mathrm{\Lambda }$ to the facet normal velocity $V_f$. In parallel, phase-field simulations of the reference model are performed for two growth orientations, [001] and [011]. Facet lengths $\mathrm{\Lambda }$ obtained from simulations at different facet velocities are first extrapolated to the limit of vanishing interface width. This extrapolation is made possible by constructing a master curve common to the whole range of $V_f$ values considered. The extrapolated $\mathrm{\Lambda }$ values are then compared with the ones predicted by the $\mathrm{\Lambda }\left(V_f\right)$ reference law. Both sets give comparable values, with an accuracy of a few percent, which confirms that the phase-field model can give quantitative results for faceted solidification of silicon.

Microwave (MW) sustained discharges have distinct advantages over other existing types of discharges in terms of the specific understanding they can provide regarding discharge phenomena and mechanisms. First, only electrons can pick up energy from the discharge $\mathbf{E}$-field since ions cannot respond to rapid oscillations above ≈100 MHz. A second remarkable feature of MW discharges is that their plasma sheath is stationary, unlike in radiofrequency (rf) discharges. Furthermore, the sheath voltage is low, so that the electron energy expended to sustain them can be ignored as a first approximation. These characteristics favored the development of the concept of power per electron, which involves determining the respective roles of the power absorbed per electron ${\theta }_A$ and the power lost on a per-electron basis ${\theta }_L$ in the equilibrium relationship between them. This led to establishing the following: (i) In the equilibrium relation of the power per electron (${\theta }_A={\theta }_L$), the power lost has precedence over the power absorbed, the latter simply adjusting to compensate for the losses. (ii) The value of the power absorbed ${\theta }_A$, when conforming to compensate for the losses, determines the intensity of the high-frequency $\mathbf{E}$-field in the discharge, the maintenance field, construing it as an internal parameter (as opposed to an operator-set). (iii) Ensuring a smaller volume within which power is absorbed (resulting from $\mathbf{E}$-field confinement) compared to the loss volume (plasma) is a way to achieve higher maintenance $\mathbf{E}$-field intensity, thus higher atomic (molecular) excitation and ionization rates, as is the case, for example, with microdischarges. (iv) In pulsed-operated discharges, the $\mathbf{E}$-field intensity is maximum at the very beginning of the pulse and then decreases, eventually reaching stationarity as the pulse time elapses. (v) A significant and more comprehensive similarity law is procured than for direct-current (dc) discharges. (vi) The power per electron concept is valid for all MW discharges. In the case of dc and rf discharges, where ions are also accelerated in the $\mathbf{E}$-field, ${\theta }_A$ is no longer proportional to the $\mathbf{E}$-field intensity: ${\theta }_A$ is then the power necessary to maintain an electron-ion pair in the discharge. It can be used, taking into account the operating conditions (field frequency, gas nature and pressure, and discharge vessel properties), to optimize the power consumed for a given plasma-driven process.

The detailed fluctuation theorem (DFT) is a statement about the asymmetry in the statistics of the entropy production. Consequences of the DFT are the second law of thermodynamics and the thermodynamics uncertainty relation, which translate into lower bounds for the mean and variance of currents, respectively. However, far from equilibrium, mean and variance are not enough to characterize the underlying distribution of the entropy production. The fluctuations are not necessarily Gaussian (nor symmetric), which means their skewness could be nonzero. We prove that the DFT imposes a negative tight lower bound for the skewness of the entropy production as a function of the mean. As application, we check the bound in the heat exchange problem between two thermal reservoirs mediated by a qubit swap engine.

The various regimes observed in the one-dimensional complex Ginzburg-Landau equation result from the interaction of a very small number of elementary patterns such as pulses, fronts, shocks, holes, and sinks. Here we provide three exact such patterns observed in numerical calculations but never found analytically. One is a quintic case localized homoclinic defect, observed by Popp et al. [S. Popp et al., Phys. Rev. Lett. 70, 3880 (1993)], and the two others are bound states of two quintic dark solitons, observed by Afanasyev et al. [V. V. Afanasyev et al., Phys. Rev. E 57, 1088 (1998)].

In the derivation of the thermodynamics of overdamped systems, one ignores the kinetic energy contribution since the velocity is a fast variable. In this paper, we show that the kinetic energy needs to be present in the calculation of the heat distribution to have a correct correspondence between the underdamped and overdamped cases, meaning that the velocity can not be fully ignored in the thermodynamics of these systems. We do this by investigating in detail the effect of the kinetic energy for three different systems: the harmonic potential, the logarithm potential, and an arbitrary non-isothermal process.

We examine a Hamiltonian system which represents an active particle that can move against an opposing external force by drawing energy from an internal depot while immersed in a noisy and dissipative environment. The Hamiltonian consists of two subsystems, one representing the active particle's motion and the other its depot of “fuel.” We show that although the active particle loses some of its energy to dissipation from the environment, dissipation can also help to stabilize the dynamical process that makes the particle active. This raises the possibility that the internal mechanisms of active particles may not only be able to operate in noisy and dissipative environments, but may actually rely on the environment for their control.

We develop methods for investigating protein drift-diffusion dynamics in heterogeneous cell membranes and the roles played by geometry, diffusion, chemical kinetics, and phase separation. Our hybrid stochastic numerical methods combine discrete particle descriptions with continuum-level models for tracking the individual protein drift-diffusion dynamics when coupled to continuum fields. We show how our approaches can be used to investigate phenomena motivated by protein kinetics within dendritic spines. The spine geometry is hypothesized to play an important biological role regulating synaptic strength, protein kinetics, and self-assembly of clusters. We perform simulation studies for model spine geometries varying the neck size to investigate how phase-separation and protein organization is influenced by different shapes. We also show how our methods can be used to study the roles of geometry in reaction-diffusion systems including Turing instabilities. Our methods provide general approaches for investigating protein kinetics and drift-diffusion dynamics within curved membrane structures.

Population annealing is a powerful sequential Monte Carlo algorithm designed to study the equilibrium behavior of general systems in statistical physics through massive parallelism. In addition to the remarkable scaling capabilities of the method, it allows for measurements to be enhanced by weighted averaging [J. Machta, Phys. Rev. E 82, 026704 (2010)], admitting to reduce both systematic and statistical errors based on independently repeated simulations. We give a self-contained introduction to population annealing with weighted averaging, generalize the method to a wide range of observables such as the specific heat and magnetic susceptibility and rigorously prove that the resulting estimators for finite systems are asymptotically unbiased for essentially arbitrary target distributions. Numerical results based on more than ${10}^7$ independent population annealing runs of the two-dimensional Ising ferromagnet and the Edwards-Anderson Ising spin glass are presented in depth. In the latter case, we also discuss efficient ways of measuring spin overlaps in population annealing simulations.

After a sudden quench from the disordered high-temperature $T_0\to \infty$ phase to a final temperature well below the critical point $T_{\mathrm{F}}\ll T_c$, the nonconserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time $t_{{\mathrm{p}}_1}>0$) and stabilization (at time $t_{\mathrm{p}}>t_{{\mathrm{p}}_1}$) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, to study their role on each time regime after the quench ($T_{\mathrm{F}}=0$), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability $p$. We show that observables such as the cluster size heterogeneity $H(t,p)$ and the typical domain size $\ell (t,p)$ have no dependence on $p$ in the first time regime up to $t_{{\mathrm{p}}_1}$. Furthermore, when energy-decreasing flips are forbidden while allowing constant-energy flips, the kinetics is essentially frozen after the quench and there is no percolation event whatsoever. Taken together, these results indicate that the emergence of the first percolating cluster at $t_{{\mathrm{p}}_1}$ is completely driven by energy decreasing flips. However, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: $t_{\mathrm{p}}\left(p\right)\sim p^{-1}$ for $p\ll 1$ (at $p=0$, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, $t_{{\mathrm{p}}_1}$ and $t_{\mathrm{p}}$ in such systems.

We estimate the maximal Lyapunov exponent at different resolutions and Reynolds numbers in large eddy simulations (LES) and direct numerical simulations of sinusoidally driven Navier-Stokes equations in three dimensions. Independent of the Reynolds number when nondimensionalized by Kolmogorov units, the LES Lyapunov exponent diverges as an inverse power of the effective grid spacing showing that the fine scale structures exhibit much faster error growth rates than the larger ones. Effectively, i.e., ignoring the cutoff of this phenomenon at the Kolmogorov scale, this behavior introduces an upper bound to the prediction horizon that can be achieved by improving the precision of initial conditions through refining of the measurement grid.

Mechanical properties of materials are highly dependent on microstructure. One characteristic example is tensile stresses at the grain boundaries, which is one of the most critical factors in crack nucleation. Although experimental techniques have significantly evolved during the past decades with respect to obtaining high-resolution snapshots of the microstructure with methods such as scanning electron microscopy, the quantitative estimation of continuum quantities, such as localized stresses, still remains a very challenging task. The molecular dynamics simulation method has been proven to be a quite effective simulation tool for providing insights in such challenges due to its high spatial and temporal resolution. In this study, molecular dynamics simulations have been performed to obtain a spatial resolution of the residual stresses in solidified aluminum. A best-effort realistic microstructure was obtained by starting from a pure aluminum block which was initially melted and subsequently quenched under various cooling rates, and finally relaxed. The obtained results suggest that residual stresses are higher in absolute terms at the vicinity of grain boundaries than at the grain interiors, and higher crystallinity has been found to be correlated to lower residual stresses. Moreover, it has been shown both qualitatively and quantitatively that grain boundaries undergo tensile loading, in contrast to the grain interiors which are compressed; this result comes to support the conclusions of quite recent experimental investigations, showing that the residual stress is tensile at the grain boundaries and gradually transits into compressive in the grain interiors, and highlights the potential of molecular dynamics simulation to capture nanoscale physical phenomena.

A dynamical model of a highly efficient heat engine is proposed, where an applied temperature difference maintains the motion of particles around the circuit consisting of two asymmetric narrow channels, in one of which the current flows against the applied thermodynamic forces. Numerical simulations and linear-response analysis suggest that, in the absence of frictional losses, the Carnot efficiency can be achieved in the thermodynamic limit.

The Lotka-Volterra predator-prey model still represents the paradigm for the description of the competition in population dynamics. Despite its extreme simplicity, it does not admit an analytical solution, and for this reason, numerical integration methods are usually adopted to apply it to various fields of science. The aim of the present work is to investigate the existence of new predator-prey models sharing the broad features of the standard Lotka-Volterra model and, at the same time, offer the advantage of possessing exact analytical solutions. To this purpose, a general Hamiltonian formalism, which is suitable for treating a large class of predator-prey models in population dynamics within the same framework, has been developed as a first step. The only existing model having the property of admitting a simple exact analytical solution, is identified within the above class of models. The solution of this special predator-prey model is obtained explicitly, in terms of known elementary functions, and its main properties are studied. Finally, the generalization of this model, based on the concept of power-law competition, as well as its extension to the case of $N$-component competition systems, are considered.