A microscopic theory of molecular motion in classical monatomic liquids, proposed by Glass and Rice [Phys. Rev. 176, 239 (1968)], is revisited and extended to incorporate the dynamic friction in the Brownian description of the atomic diffusion in a mean-time-dependent harmonic force field. A modified, non-Markovian Langevin equation is utilized to derive an equation of motion for the velocity autocorrelation function with time-dependent friction coefficient. Numerical solution of the equation gives an excellent account of the velocity autocorrelation function in Lennard-Jones liquids, liquid alkali, and transition metals over a broad range of density and temperature. Derivation of the equation of motion leads to a self-consistent expression for the time dependence of friction coefficient. Our results demonstrate that the nature of time dependence of the friction coefficient changes dramatically with the liquid density. At low and moderate densities, the dynamic friction decays exponentially whereas it increases exponentially at high liquid densities. Our findings provide an opportunity for a different outlook of the Brownian description of atomic dynamics in liquids.

The observed distributions of stellar parameters, in particular, rotational and radial velocities, often depart from the Maxwellian (Gaussian) distribution. In the absence of a consistent statistical framework, these distributions are, in general, accounted for phenomenologically by employing power-law distributions, such as Tsallis or Kaniadakis distributions. Here we argue that the observed distributions correspond to locally Gaussian distributions, whose characteristic width is regarded as a statistical variable, in accordance with common knowledge that this parameter is mass dependent. The distributions arising within this picture correspond to superstatistics—a formalism emerging naturally in the context of self-gravitating media. We discuss in detail the distributions arising within this formalism and confront them with observational data of open clusters. We compute their moments and show that the Chandrasekhar-Münch relation remains invariant in this scenario. We also address the effect of these distributions on the thermalization of a massive body, e.g., a supermassive black hole, immersed in a stellar gas. We further discuss how the superstatistical picture clarifies certain ambiguities while offering a whole family of distributions (of which asymptotic power laws represent a special case), opening possibilities for fitting observational data.

In recent decades, computer experiments have led to an accurate and fundamental understanding of atomic and molecular mechanisms in fluids, such as different kinds of relaxation processes toward steady physical states. In this paper, we investigate how exactly the configuration of initial states in a molecular-dynamics simulation can affect the rates of decay toward equilibrium for the widely known Langevin canonical ensemble. For this purpose, we derive an original expression relating the system relaxation time ${\tau }_{\mathrm{sys}}$ and the radial distribution function $g\left(r\right)$ in the near-zero and high-density limit. We found that, for an initial state which is slightly marginally inhomogeneous in the number density of atoms, the system relaxation time ${\tau }_{\mathrm{sys}}$ is much longer than that for the homogeneous case and an increasing function of the Langevin coupling constant, $\gamma$. We also found, during structural equilibration, $g\left(r\right)$ at large distances approaches 1 from above for the inhomogeneous case and from below for the macroscopically homogeneous one.

Delocalized nonlinear vibrational modes (DNVMs) supported in crystal lattices are exact solutions to the equations of motion of particles that are determined by the symmetry of the lattices. DNVMs exist for any vibration amplitudes and for any interparticle potentials. It is important to know how the properties of DNVMs depend on the parameters of interparticle potentials. In this work, we analyze the effect of the Morse potential stiffness on the properties of one-component DNVMs in a face-centered cubic (fcc) lattice. In particular, the frequencies, kinetic and potential energy, mechanical stress, and elastic constants of DNVMs in a large range of vibration amplitudes are considered. Frequency-amplitude dependency obtained for the Morse crystal is compared with that obtained earlier for copper by using the potentials of the many-body embedded atom method. The properties of DNVMs are mainly dictated by their symmetry and are less influenced by the interparticle potentials. It is revealed that at low and high stiffness of interparticle bonds, different sets of DNVMs have frequencies above the phonon band. This is important to predict the possible types of discrete breathers supported by the fcc lattice. The results obtained in the work enrich the understanding of the influence of interparticle potentials on the properties of the studied family of exact dynamic solutions.

Traffic congestion is one of the major challenges faced by the transportation industry. While this problem carries a high economic and environmental cost, the need for an efficient design of optimal paths for passengers in multilayer network infrastructures is imperative. We consider an approach based on optimal transport theory to route passengers preferably along layers that are more carbon-efficient than the road, e.g., rails. By analyzing the impact of this choice on performance, we find that this approach reduces carbon emissions considerably compared to shortest-path minimization. Similarly, we find that this approach distributes traffic more homogeneously, thus alleviating the risk of traffic congestion. Our results shed light on the impact of distributing traffic flexibly across layers guided by optimal transport theory.

Dynamic instability—the growth, catastrophe, and shrinkage of quasi-one-dimensional filaments—has been observed in multiple biopolymers. Scientists have long understood the catastrophic cessation of growth and subsequent depolymerization as arising from the interplay of hydrolysis and polymerization at the tip of the polymer. Here we show that for a broad class of catastrophe models, the expected catastrophe time distribution is exponential. We show that the distribution shape is insensitive to noise, but that depletion of monomers from a finite pool can dramatically change the distribution shape by reducing the polymerization rate. We derive a form for this finite-pool catastrophe time distribution and show that finite-pool effects can be important even when the depletion of monomers does not greatly alter the polymerization rate.

Cylindrical interfaces occur in sheared or deformed emulsions and as biological or technological lipid monolayer or bilayer tubules. Like the corresponding spherical droplets and vesicles, these cylinderlike surfaces may host orientational order with $n$-fold rotational symmetry, for example in the positions of lipid molecules or of spherical nanoparticles. We examine how that order interacts with and induces shape modulations of cylindrical interfaces. While on spherical droplets $2n$ topological defects necessarily exist and can induce icosahedral droplet shapes, the cylindrical topology is compatible with a defect-free patterning. Nevertheless, once a modulation is introduced by a mechanism such as spontaneous curvature, nontrivial patterns of order, including ones with excess defects, emerge and have nonlinear effects on the shape of the tube. By examining the equilibrium energetics of the system analytically and with a lattice-based Markov chain Monte Carlo simulation, we predict low-temperature morphologies of modulated cylindrical interfaces hosting orientational order. A shape modulation induces a banded pattern of alternatingly isotropic and ordered interfacial material. Furthermore, cylindrical systems can be divided into type I, without defects, and type II, which go through a spectrum of defect states with up to $4n$ excess defects. The character of the curvature-induced shape transition from unmodulated to modulated cylinders is continuous or discontinuous accordingly.

Even if the trajectory in a viscous flow system stays within a low dimensional subspace in the state space, reinforcement learning (RL) requires many observables in the active control problem. This is because the observables are assumed to follow a policy-independent Markov decision process in the usual RL framework and full observation of the system is required to satisfy this assumption. Although RL with a partially observable condition is generally a difficult task, we construct a consistent algorithm with the condition using the low dimensional property of viscous flow. Using typical examples of active flow control, we show that our algorithm is more stable and efficient than the existing RL algorithms, even under a small number of observables.

Gas-kinetic simulations of rarefied and compressible mixing layers are performed to characterize continuum breakdown and the effect on the Kelvin-Helmholtz instability. The unified gas-kinetic scheme (UGKS) is used to perform the simulations at different Mach and Knudsen numbers. The UGKS stress tensor and heat-flux vector fields are compared against those given by the Navier-Stokes-Fourier constitutive equations. The most significant difference is seen in the shear stress and transverse heat flux. The study demonstrates the existence of two distinct continuum breakdown regimes, one at low and the other at high convective Mach numbers. Overall, at low convective Mach numbers, the deviation from continuum stress and heat flux appears to scale exclusively with the micro-macro length scale ratio given by the Knudsen number. On the other hand, at high convective Mach numbers, the deviation depends on the global micro-macro timescale ratio given by the product of Mach and Knudsen numbers. We further demonstrate that, unlike shear stresses and transverse heat flux, the deviations in normal stresses and the streamwise heat flux depend separately on Knudsen and Mach numbers. A local parameter called the gradient Knudsen number is proposed to characterize the rarefaction effects on the local momentum and thermal transport. Noncontinuum aspects of gas-kinetic stress-tensor and heat-flux behavior that Grad's 13-moment equation model reasonably captures are identified.

We investigate properties of oscillatory dissipative solitons (DSs) in a cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. As a main result we find a transition to dissipative solitons with spatiotemporal disorder as a function of the diffusion coefficient. This transition proceeds via quasiperiodicity and shows incommensurate satellites next to the fundamental frequency and its harmonics indicating a possible route to localized spatiotemporal chaos. The transition back to oscillatory DSs follows a similar scenario.

We report on three-dimensional direct numerical simulation of wave turbulence on the free surface of a magnetic fluid subjected to an external horizontal magnetic field. A transition from capillary-wave turbulence to anisotropic magneto-capillary wave turbulence is observed for an increasing field. At high enough field, wave turbulence becomes highly anisotropic, cascading mainly perpendicularly to the field direction, in good agreement with the prediction of a phenomenological model, and with anisotropic Alfvén wave turbulence. Although surface waves on a magnetic fluid are different from Alfvén waves in plasma, a strong analogy is found with similar wave spectrum scalings and similar magnetic-field dependent dispersionless wave velocities.

Motivated by recent experiments, we investigate the scattering properties of percolation clusters generated by numerical simulations on a three-dimensional cubic lattice. Individual clusters of given size are shown to present a fractal structure up to a scale of order of their extent, even far away from the percolation threshold $p_c$. The influence of intercluster correlations on the structure factor of assemblies of clusters selected by an invasion phenomenon is studied in detail. For invasion from bulk germs, we show that the scattering properties are determined by three length scales, the correlation length $\xi$, the average distance between germs $d_g$, and the spatial scale probed by scattering, set by the inverse of the scattering wave vector $Q$. At small scales, we find that the fractal structure of individual clusters is retained, the structure factor decaying as $Q^{-d_f}$. At large scales, the structure factor tends to a limit, set by the smaller of $\xi$ and $d_g$, both below and above $p_c$. We propose approximate expressions reproducing the simulated structure factor for arbitrary $\xi$, $d_g$, and $Q$, and illustrate how they can be used to avoid to resort to costly numerical simulations. For invasion from surfaces, we find that, at $p_c$, the structure factor behaves as $Q^{-d_f}$ at all $Q$, i.e., the fractal structure is retained at arbitrarily large scales. Results away from $p_c$ are compared to the case of bulk germs. Our results can be applied to discuss light or neutrons scattering experiments on percolating systems. This is illustrated in the context of evaporation from porous materials.

The lateral diffusion and trapping of neurotransmitter receptors within the postsynaptic membrane of a neuron play a key role in determining synaptic strength and plasticity. Trapping is mediated by the reversible binding of receptors to scaffolding proteins (slots) within a synapse. In this paper we introduce a method for analyzing the transient dynamics of proximal axodendritic synapses in a diffusion-trapping model of receptor trafficking. Given a population of spatially distributed synapses, each of which has a fixed number of slots, we calculate the rate of relaxation to the steady-state distribution of bound slots (synaptic weights) in terms of a set of local accumulation times. Assuming that the rates of exocytosis and endocytosis are sufficiently slow, we show that the steady-state synaptic weights are independent of each other (purely local). On the other hand, the local accumulation time of a given synapse depends on the number of slots and the spatial location of all the synapses, indicating a form of transient heterosynaptic plasticity. This suggests that local accumulation time measurements could provide useful information regarding the distribution of synaptic weights within a dendrite.

We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the lattice in one and two dimensions and derive exact results in the continuum limit. Next, we compute the large deviation free-energy function in both one and two dimensions, which we use to compute the moments and the cumulants of the displacements exactly at late times. Our exact results demonstrate that the cross-correlations between the motion in the $x$ and $y$ directions in two dimensions persist in the large deviation function. We also demonstrate that the large deviation function of an active particle with diffusion displays two regimes, with differing diffusive behaviors. We verify our analytic results with kinetic Monte Carlo simulations of an active lattice walker in one and two dimensions.

We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that $n_1,n_2,n_3,...$ distinct sites are visited at times $t_1,t_2,t_3,...$. From this multiple-time distribution, we show that the visitation statistics of one-dimensional random walks are temporally correlated, and we quantify the non-Markovian nature of the process. We exploit these ideas to derive unexpected results for the two-time trapping problem and to determine the visitation statistics of two important stochastic processes, the run-and-tumble particle and the biased random walk.

Understanding the statistical properties of a collection of individuals subject to random displacements and birth-and-death events is key to several applications in physics and life sciences, encompassing the diagnostic of nuclear reactors and the analysis of epidemic patterns. Previous investigations of the critical regime, where births and deaths balance on average, have shown that highly non-Poissonian fluctuations might occur in the population, leading to spontaneous spatial clustering, and eventually to a “critical catastrophe,” where fluctuations can result in the extinction of the population. A milder behavior is observed when the population size is kept constant: the fluctuations asymptotically level off and the critical catastrophe is averted. In this paper, we extend these results by considering the broader class of models with prompt and delayed birth-and-death events, which mimic the presence of precursors in nuclear reactor physics or incubation in epidemics. We consider models with and without population control mechanisms. Analytical or semi-analytical results for the density, the two-point correlation function, and the mean-squared pair distance will be derived and compared with Monte Carlo simulations, which will be used as a reference.

Noise-activated transitions between coexisting attractors are investigated in a chaotic spiking network. At low noise level, attractor hopping consists of discrete bifurcation events that conserve the memory of initial conditions. When the escape probability becomes comparable to the intrabasin hopping probability, the lifetime of attractors is given by a detailed balance where the less coherent attractors act as a sink for the more coherent ones. In this regime, the escape probability follows an activation law allowing us to assign pseudoactivation energies to limit cycle attractors. These pseudoenergies introduce a useful metric for evaluating the resilience of biological rhythms to perturbations.

Establishing sharp and correctly positioned boundaries in spatial gene expression patterns is a central task in both developmental and synthetic biology. We consider situations where a global morphogen gradient provides positional information to cells but is insufficient to ensure the required boundary precision, due to different types of noise in the system. In a conceptual model, we quantitatively compare three mechanisms, which combine the global signal with local signaling between neighboring cells, to enhance the boundary formation process. These mechanisms differ with respect to the way in which they combine the signals by following either an AND, an OR, or a SUM rule. Within our model, we analyze the dynamics of the boundary formation process, and the fuzziness of the resulting boundary. Furthermore, we consider the tunability of the boundary position and its scaling with system size. We find that all three mechanisms produce less fuzzy boundaries than the purely gradient-based reference mechanism, even in the regime of high noise in the local signals relative to the noise in the global signal. Among the three mechanisms, the SUM rule produces the most accurate boundary. However, in contrast to the other two mechanisms, it requires noise to exit metastable states and rapidly reach the stable boundary pattern.

Cell polarization underlies many cellular processes, such as differentiation, migration, and budding. Many living cells, such as budding yeast and fission yeast, use cytoskeletal structures to actively transport proteins to one location on the membrane and create a high-density spot of membrane-bound proteins. Yet, the thermodynamic constraints on filament-based cell polarization remain unknown. We show by mathematical modeling that cell polarization requires detailed balance to be broken, and we quantify the free-energy cost of maintaining a polarized state of the cell. Our study reveals that detailed balance cannot only be broken via the active transport of proteins along filaments but also via a chemical modification cycle, allowing detailed balance to be broken by the shuttling of proteins between the filament, membrane, and cytosol. Our model thus shows that cell polarization can be established via two distinct driving mechanisms, one based on active transport and one based on nonequilibrium binding. Furthermore, the model predicts that the driven binding process dissipates orders of magnitude less free energy than the transport-based process to create the same membrane spot. Active transport along filaments may be sufficient to create a polarized distribution of membrane-bound proteins, but an additional chemical modification cycle of the proteins themselves is more efficient and less sensitive to the physical exclusion of proteins on the transporting filaments, providing insight in the design principles of the Pom1/Tea1/Tea4 system in fission yeast and the Cdc42 system in budding yeast.

We show from experiments and simulations on vibration-activated granular matter that self-propelled polar rods in an elastic medium on a substrate turn and move towards each other. We account for this effective attraction through a coarse-grained theory of a motile particle as a moving point-force density that creates elastic strains in the medium that reorient other particles. Our measurements confirm qualitatively the predicted features of the distortions created by the rods, including the ${\left|x\right|}^{-1/2}$ tail of the trailing displacement field and nonreciprocal sensing and pursuit. A discrepancy between the magnitudes of displacements along and transverse to the direction of motion remains. Our theory should be of relevance to the interaction of motile cells in the extracellular matrix or in a supported layer of gel or tissue.