Percolation of site trimers ($k$-mers with $k=3$) is investigated in a detailed way making use of an analytical model based on renormalization techniques in this problem. Results are compared to those obtained here by means of extensive computer simulations. Five different deposition possibilities for site trimers are included according to shape and orientation of the depositing objects. Analytical results for the percolation threshold $p_c$ are all close to 0.55, while numerical results show a slight dispersion around this value. A comparison with $p_c$ values previously reported for monomers and dimers establishes the tendency of $p_c$ to decrease as $k$ increases. Critical exponent $\nu$ was also obtained both by analytical and numerical methods. Results for the latter give values very close to the expected value 4/3 showing that this percolation case corresponds to the universality class of random percolation.

A body in a free-molecular gas accelerated by a constant external force is considered on the basis of kinetic theory. The body is an infinitely long rectangular hollow column with one face removed, and thus it has a squarish $\mathsf{U}$-shaped cross section. The concave part of the body points toward the direction of motion, and thus the gas molecules may be trapped in the concavity. Gas molecules undergo diffuse reflection on a base part, whereas specular reflection on two lateral parts. It is numerically shown that the velocity of the body approaches a terminal velocity, for which a drag force exerted by the gas counterbalances the external force, in such a way that their difference decreases in proportion to the inverse square of time for a large time. This rate of approach is slower than the known rate proportional to the inverse cube of time in the case of a body without concavity [Aoki et al., Phys. Rev. E 80, 016309 (2009)]. Based on the detailed investigation on the velocity distribution function of gas molecules impinging on the body, it is clarified that the concavity prevents some molecules from escaping to infinity. This trapping enhances the effect of recollision between the body and the gas molecules, which is the cause of the inverse power laws, and thus leads to the slower approach.

By taking full advantage of the dynamic property imposed by the detailed balance condition, we derive a new refined unified fluctuation theorem (FT) for general stochastic thermodynamic systems. This FT involves the joint probability distribution functions of the final phase-space point and a thermodynamic variable. Jarzynski equality, Crooks fluctuation theorem, and the FTs of heat as well as the trajectory entropy production can be regarded as special cases of this refined unified FT, and all of them are generalized to arbitrary initial distributions. We also find that the refined unified FT can easily reproduce the FTs for processes with the feedback control, due to its unconventional structure that separates the thermodynamic variable from the choices of initial distributions. Our result is heuristic for further understanding of the relations and distinctions between all kinds of FTs and might be valuable for studying thermodynamic processes with information exchange.

The equivalence of thermodynamic ensembles is at the heart of statistical mechanics and central to our understanding of equilibrium states of matter. Recently, a formal connection has been established between the dynamics of open quantum systems and statistical mechanics in an extra dimension: an open system dynamics generates a matrix product state (MPS) encoding all possible quantum jump trajectories which allows to construct generating functions akin to partition functions. For dynamics generated by a Lindblad master equation, the corresponding MPS is a so-called continuous MPS which encodes the set of continuous measurement records terminated at some fixed total observation time. Here, we show that if one instead terminates trajectories after a fixed total number of quantum jumps, e.g., emission events into the environment, the associated MPS is discrete. The continuous and discrete MPS correspond to different ensembles of quantum trajectories, one characterized by total time, the other by total number of quantum jumps. Hence, they give rise to quantum versions of different thermodynamic ensembles, akin to “grand canonical” and “isobaric,” but for trajectories. Here, we prove that these trajectory ensembles are equivalent in a suitable limit of long time or large number of jumps. This is in direct analogy to equilibrium statistical mechanics where equivalence between ensembles is only strictly established in the thermodynamic limit. An intrinsic quantum feature is that the equivalence holds only for all observables that commute with the number of quantum jumps.

Differential capacitance (DC) data have been widely used to characterize the structure of electrolyte solutions near charged interfaces and as experimental validation of models for electrolyte structure. Fixing a large class of models of electrolyte free energy that incorporate finite-volume effects, a reduction is identified which permits the identification of all free energies within that class that return identical DC data. The result is an interpretation of DC data through the equivalence classes of nonideality terms, and associated boundary layer structures, that cannot be differentiated by DC data. Specifically, for binary salts, DC data, even if measured over a range of ionic concentrations, are unable to distinguish among models which exhibit charge asymmetry, charge reversal, and even ion crowding. The reduction applies to capacitors which are much wider than the associated Debye length and to finite-volume terms that are algebraic in charge density. However, within these restrictions the free energy is shown to be uniquely identified if the DC data are supplemented with measurements of the excess chemical potential of the system in the bulk state.

Using Monte Carlo computer simulations we explore the self-assembly and ordering behavior of a hybrid, soft magnetic system consisting of small magnetic nanospheres in a liquid-crystalline (LC) matrix. Inspired by recent experiments with colloidal rod matrices, we focus on conditions where the sphere and rod diameters are comparable. Already in the absence of a magnetic field, the nematic ordering of the LC can stabilize the formation of magnetic chains along the nematic or smectic director, yielding a state with local (yet no macroscopic) magnetic order. The chains, in turn, increase the overall nematic order, reflecting the complex interplay of the structure formation of the two components. When increasing the sphere diameter, the spontaneous uniaxial ordering is replaced by biaxial lamellar morphologies characterized by alternating layers of rods and magnetic chains oriented perpendicular to the rod's director. These ordering scenarios at zero field suggest a complex response of the resulting hybrid to external stimuli, such as magnetic fields and shear forces.

Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative detailed fluctuation theorem is derived, expressed solely in terms of forward statistics. It is illustrated for a linear kinetic equation with kangaroo rates.

We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to $M$ consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian. We first show that the Frobenius norm bounds the time scale of relaxation of the operator at high temperatures. We find operators with significantly slower relaxation than the slowest simple “hydrodynamic” mode due to energy diffusion. Then we examine some properties of the nontrivial slow operators. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain; this system is hydrodynamically “trivial,” with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity.

Emulsions consisting of droplets immersed in a fluid are typically unstable since they coarsen over time. One important coarsening process is Ostwald ripening, which is driven by the surface tension of the droplets. Stability of emulsions is relevant not only in complex fluids but also in biological cells, which contain liquidlike compartments, e.g., germ granules, Cajal bodies, and centrosomes. Such cellular systems are driven away from equilibrium, e.g., by chemical reactions, and thus can be called active emulsions. In this paper, we study such active emulsions by developing a coarse-grained description of the droplet dynamics, which we analyze for two different chemical reaction schemes. We first consider the simple case of first-order reactions, which leads to stable, monodisperse emulsions in which Ostwald ripening is suppressed within a range of chemical reaction rates. We then consider autocatalytic droplets, which catalyze the production of their own droplet material. Spontaneous nucleation of autocatalytic droplets is strongly suppressed and their emulsions are typically unstable. We show that autocatalytic droplets can be nucleated reliably and their emulsions stabilized by the help of chemically active cores, which catalyze the production of droplet material. In summary, different reaction schemes and catalytic cores can be used to stabilize emulsions and to control their properties.

Yielding transitions in athermal amorphous materials undergoing steady-state shear flow resemble critical phenomena. Historically, they have been described by the Herschel-Bulkley rheological formula, which implies singular behaviors at yield points. In this paper, I examine this class of phenomena using an elementary version of the thermodynamic shear-transformation-zone (STZ) theory, focusing on the role of the effective disorder temperature, and paying special attention to scaling and dimensional arguments. I find a wide variety of Herschel-Bulkley-like rheologies but, for fundamental reasons not specific to the STZ theory, conclude that the yielding transition is not truly critical. In particular, for realistic many-body models with short-range interactions, there is a correlation length that grows rapidly but ultimately saturates near the yield point.

We numerically demonstrate the transition from the isotropic liquid to the tetratic phase with quasilong-range tetratic alignment order (i.e., with nearly parallel or perpendicular aligned rods), for the cold two-dimensional (2D) short spherocylinder system before crystallization and investigate the thermal assisted heterogeneous rotational and translational micromotions. Comparing with the 2D liquid of isotropic particles, spherocylinders introduce extra rotational degrees of freedom and destroy packing isotropy and the equivalence between rotational and translational motions. It is found that cooling leads to the stronger dynamical heterogeneity with more cooperative hopping and the stronger retardations of rotational hopping than translational hopping. Under topological constraints from nearly parallel and perpendicular rods of the tetratic phase, longitudinal and transverse translational hopping can occur without rotational hopping, but not the reverse. The empty space trailing a neighboring translational hopping patch is needed for triggering the patch rotational hopping with its translational motion into the empty space. It is the origin for the observed increasing separation of hopping time scales and the one-way coupling between rotational and translational hopping. Strips of longitudinally or transversely aligned rods can be ruptured and reconnected with neighboring strips through buckling, kink formation, and patch rotation, under the unbalanced torques or forces from their neighboring rods and thermal kicks.

We have conducted extremely long molecular dynamics simulations of glasses to microsecond times, which close the gap between experimental and atomistic simulation time scales by two to three orders of magnitude. Static, thermal, and structural properties of silica glass are reported for glass cooling rates down to $5\times {10}^9$ K/s and viscoelastic response in silica melts and glasses are studied over nine decades of time. We present results from relaxation of hydrostatic compressive stress in silica and show that time-temperature superposition holds in these systems for temperatures from 3500 to 1000 K.

The transition from stick to slip at a dry frictional interface occurs through the breaking of microjunctions between the two contacting surfaces. Typically, interactions between junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasistatic fronts, via fronts much slower than elastic wave speeds, to fronts faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic two-dimensional spring-block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that material slip speed and rupture front speed are proportional across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even along homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Last, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.

The internal dynamics of active gels both in artificial (in vitro) model systems and inside the cytoskeleton of living cells has been extensively studied with experiments of recent years. These dynamics are probed using tracer particles embedded in the network of biopolymers together with molecular motors, and distinct nonthermal behavior is observed. We present a theoretical model of the dynamics of a trapped active particle, which allows us to quantify the deviations from equilibrium behavior, using both analytic and numerical calculations. We map the different regimes of dynamics in this system and highlight the different manifestations of activity: breakdown of the virial theorem and equipartition, different elasticity-dependent “effective temperatures,” and distinct non-Gaussian distributions. Our results shed light on puzzling observations in active gel experiments and provide physical interpretation of existing observations, as well as predictions for future studies.

We theoretically investigate the membrane fluctuations of red blood cells with focus laid on the role of the cytoskeleton, viewing the system as a membrane coupled to a sparse spring network. This model is exactly solvable and enables us to examine the coupling strength dependence of the membrane undulation. We find that the coupling modifies the fluctuation spectrum at wavelengths longer than the mesh size of the network, while leaving the fluid-like behavior of the membrane intact at shorter wavelengths. The fluctuation spectra can be markedly different, depending on not only the relative amplitude of the bilayer bending energy with respect to the cytoskeleton deformation energy but also the bilayer-cytoskelton coupling strength.

The average economic agent is often used to model the dynamics of simple markets, based on the assumption that the dynamics of a system of many agents can be averaged over in time and space. A popular idea that is based on this seemingly intuitive notion is to dampen electric power fluctuations from fluctuating sources (as, e.g., wind or solar) via a market mechanism, namely by variable power prices that adapt demand to supply. The standard model of an average economic agent predicts that fluctuations are reduced by such an adaptive pricing mechanism. However, the underlying assumption that the actions of all agents average out on the time axis is not always true in a market of many agents. We numerically study an econophysics agent model of an adaptive power market that does not assume averaging a priori. We find that when agents are exposed to source noise via correlated price fluctuations (as adaptive pricing schemes suggest), the market may amplify those fluctuations. In particular, small price changes may translate to large load fluctuations through catastrophic consumer synchronization. As a result, an adaptive power market may cause the opposite effect than intended: Power demand fluctuations are not dampened but amplified instead.

We propose a general nonlinear analytical framework to study the effect of an external stimulus in the internal state of a population of moving particles. This novel scheme allows us to study a broad range of excitation transport phenomena. In particular, considering social systems, it gives insight of the spatial dynamics influence in the competition between propaganda (mass media) and convincement. By extending the framework presented by Terranova et al. [Europhys. Lett. 105, 30007 (2014)], we now allow changes in individual's opinions due to a reflection induced by mass media. The equations of the model could be solved numerically, and, for some special cases, it is possible to derive analytical solutions for the steady states. We implement computational simulations for different social and dynamical systems to check the accuracy of our scheme and to study a broader variety of scenarios. In particular, we compare the numerical outcome with the analytical results for two possible real cases, finding a good agreement. From the results, we observe that mass media dominates the opinion state in slow dynamics communities; whereas, for higher agent active speeds, the rate of interactions increases and the opinion state is determined by a competition between propaganda and persuasion. This difference suggests that kinetics can not be neglected in the study of transport of any excitation over a particle system.

We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling and demonstrate that their multiplicity depends on both the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

The responses of soft-mode turbulence, a kind of spatiotemporal chaos seen in electroconvection of a nematic liquid crystal, to alternating-current magnetic fields is investigated to uncover the dynamical properties of spatiotemporal chaos. The dynamical responses can be measured by an order parameter, $M_p\left(t\right)$, which indicates ordering in the convective roll pattern induced by the magnetic field. Determined by properties of the liquid crystal in a magnetic field, $M_p\left(t\right)$ oscillates in accordance with the square of the magnetic field. The relaxation time of the system was obtained by fitting the frequency dependence of the complex susceptibility for the pattern obtained from the oscillation of $M_p\left(t\right)$ to the Debye-type relaxation spectra. However, for the high-frequency regime, the susceptibility deviates from the spectra because slow and large fluctuations of $M_p\left(t\right)$ contribute to the oscillation. The properties of this type of fluctuation were investigated by introducing a dynamic ordering parameter defined as the period average of $M_p\left(t\right)$.

In this paper, a simple and constructive method is presented to find the generalized perturbation $(n,M)$-fold Darboux transformations (DTs) of the modified nonlinear Schrödinger (MNLS) equation in terms of fractional forms of determinants. In particular, we apply the generalized perturbation $(1,N-1)$-fold DTs to find its explicit multi-rogue-wave solutions. The wave structures of these rogue-wave solutions of the MNLS equation are discussed in detail for different parameters, which display abundant interesting wave structures, including the triangle and pentagon, etc., and may be useful to study the physical mechanism of multirogue waves in optics. The dynamical behaviors of these multi-rogue-wave solutions are illustrated using numerical simulations. The same Darboux matrix can also be used to investigate the Gerjikov-Ivanov equation such that its multi-rogue-wave solutions and their wave structures are also found. The method can also be extended to find multi-rogue-wave solutions of other nonlinear integrable equations.