This work presents numerical evidence that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance autocorrelation are observed for different systems, namely, exponential decays for the quadratic map, logarithmic for the Hénon map, and power-law for the conservative standard map. In all these cases the decay exponent is close to the positive Lyapunov exponent. For hyperchaotic conservative systems the power-law decay of the distance autocorrelation is not directly related to any Lyapunov exponent.

Intracellular transport in eukaryotic cells consists of phases of passive, diffusion-based transport and active, motor-driven transport along filaments that make up the cell's cytoskeleton. The interplay between superdiffusive transport along cytoskeletal filaments and the anomalous nature of subdiffusion in the bulk can lead to novel effects in transport behavior at the cellular scale. Here we develop a computational model of the process with cargo being ballistically transported along explicitly modeled cytoskeletal filament networks and passively transported in the cytoplasm by a subdiffusive continuous-time random walk (CTRW). We show that, over a physiologically relevant range of filament lengths and numbers, the network introduces a filament-length sensitive superdiffusive phase at early times which crosses over to a phase where the CTRW is dominant and produces subdiffusion at late times. We apply our approach to the problem of insulin secretion from cells and show that the superdiffusive phase introduced by the filament network manifests as a peak in the secretion at early times followed by an extended sustained release phase that is dominated by the CTRW process at late times. Our results are consistent with in vivo observations of insulin transport in healthy cells and shed light on the potential for the cell to tune functionally important transport phases by altering its cytoskeletal network.

While statistical mechanics provides a comprehensive framework for the understanding of equilibrium phase behavior, predicting the kinetics of phase transformations remains a challenge. Classical nucleation theory (CNT) provides a thermodynamic framework to relate the nucleation rate to thermodynamic quantities such as pressure difference and interfacial tension through the nucleation work necessary to spawn critical nuclei. However, it remains unclear whether such an approach can be extended to the crystallization of driven melts that are subjected to mechanical stresses and flows. Here, we demonstrate numerically for hard spheres that the impact of simple shear on the crystallization rate can be rationalized within the CNT framework by an additional elastic work proportional to the droplet volume. We extract the local stress and strain inside solid droplets, which yield size-dependent values for the shear modulus that are about half of the bulk value. Finally, we show that for a complete description one also has to take into account the change of interfacial work between the strained droplet and the sheared liquid. From scaling reasons, we expect this extra contribution to dominate the work formation of small nuclei but become negligible compared to the elastic work for droplets composed of a few hundreds of particles.

We consider the problem of building a continuous stochastic model, i.e., a Langevin or Fokker-Planck equation, through a well-controlled coarse-graining procedure. Such a method usually involves the elimination of the fast degrees of freedom of the “bath” to which the particle is coupled. Specifically, we look into the general case where the bath may be at negative temperatures, as found, for instance, in models and experiments with bounded effective kinetic energy. Here, we generalize previous studies by considering the case in which the coarse graining leads to (i) a renormalization of the potential felt by the particle, and (ii) spatially dependent viscosity and diffusivity. In addition, a particular relevant example is provided, where the bath is a spin system and a sort of phase transition takes place when going from positive to negative temperatures. A Chapman-Enskog-like expansion allows us to rigorously derive the Fokker-Planck equation from the microscopic dynamics. Our theoretical predictions show excellent agreement with numerical simulations.

We report the emergence of a giant Mpemba effect in the uniformly heated gas of inelastic rough hard spheres: The initially hotter sample may cool sooner than the colder one, even when the initial temperatures differ by more than one order of magnitude. In order to understand this behavior, it suffices to consider the simplest Maxwellian approximation for the velocity distribution in a kinetic approach. The largeness of the effect stems from the fact that the rotational and translational temperatures, which obey two coupled evolution equations, are comparable. Our theoretical predictions agree very well with molecular dynamics and direct simulation Monte Carlo data.

The parametron, a resonator-based logic device, is a promising physical platform for emerging computational paradigms. When the parametron is subject to both parametric pumping and external driving, complex phenomena arise that can be harvested for applications. In this paper, we experimentally demonstrate deterministic phase switching of a parametron by applying frequency tuning pulses. To our surprise, we find different regimes of phase switching due to the interplay between a parametric pump and an external drive. We provide full modeling of our device with numerical simulations and find excellent agreement between model and measurements. Our result opens up new possibilities for fast and robust logic operations within large-scale parametron architectures.

Understanding the mechanisms underlying the diversity of tumor invasion dynamics, including single-cell migration, multicellular streaming, and the emergence of various collective migration patterns, is a long-standing problem in cancer research. Here we have designed and fabricated a series of microchips containing high-throughput microscale tracks using protein repelling coating technology, which were then covered with a thin Matrigel layer. By varying the geometrical confinement (track width) and microenvironment factors (Matrigel concentration), we have reproduced a diversity of collective migration patterns in the chips, which were also observed in vivo. We have further classified the collective patterns and quantified the emergence probability of each class of patterns as a function of microtrack width and Matrigel concentration to devise a quantitive “collective pattern diagram.” To elucidate the mechanisms behind the emergence of various collective patterns, we employed cellular automaton simulations, incorporating the effects of both direct cell-cell interactions and microenvironment factors (e.g., chemical gradient and extracellular matrix degradation). Our simulations suggest that tumor cell phenotype heterogeneity, and the associated dynamic selection of a favorable phenotype via cell-microenivronment interactions, are key to the emergence of the observed collective patterns in vitro.

Due to the combined effect of anisotropic interactions and activity, Janus swimmers are capable to self-assemble in a wide variety of structures, many more than their equilibrium counterpart. This might lead to the development of novel active materials capable of performing tasks without any central control. Their potential application in designing such materials endows trying to understand the fundamental mechanism in which these swimmers self-assemble. In the present work, we study a quasi-two-dimensional semidilute suspensions of two classes of amphiphilic spherical swimmers whose direction of motion can be tuned: either swimmers propelling in the direction of the hydrophobic patch or swimmers propelling in the opposite direction (toward the hydrophilic side). In both systems we have systematically tuned swimmers' hydrophobic strength and signature and observed that the anisotropic interactions, characterized by the angular attractive potential and its interaction range, in competition with the active stress, pointing toward or against the attractive patch gives rise to a rich aggregation phenomenology.

A granular chain of elastic spheres via Hertzian contact incorporates a classical nonlinear force model describing dynamical elastic solitary wave propagation. In this paper, the multiple solitary waves and their dynamic behaviors and stability in such a system are considered. An approximate KdV equation with the standard form is derived under the long-wavelength approximation and small deformation. The closed-form analytical single- and multiple-soliton solutions are obtained. The construction of the multiple-soliton solutions is analyzed by using the functional analysis. It is found that the multiple-soliton solution can be excited by the single-soliton solutions. This result is confirmed by the numerical analysis. Based on the soliton solutions of the KdV equation, the analytic solutions of multiple dark solitary waves are obtained from the original dynamic equation of the granular chain in the long-wavelength approximation. The stability of the single and multiple dark solitary wave solutions are numerically analyzed by using both split-step Fourier transform method and Runge-Kutta method. The results show that the single dark solitary wave solution is stable, and the multiple dark solitary waves are unstable.

We present a deep reinforcement learning framework where a machine agent is trained to search for a policy to generate a ground state for the square ice model by exploring the physical environment. After training, the agent is capable of proposing a sequence of local moves to achieve the goal. Analysis of the trained policy and the state value function indicates that the ice rule and loop-closing condition are learned without prior knowledge. We test the trained policy as a sampler in the Markov chain Monte Carlo and benchmark against the baseline loop algorithm. This framework can be generalized to other models with topological constraints where generation of constraint-preserving states is difficult.

We introduce an alternative method to identify phase boundaries in physical systems. It is based on training a predictive model such as a neural network to infer a physical system's parameters from its state. The deviation of the inferred parameters from the underlying correct parameters will be most susceptible and diverge maximally in the vicinity of phase boundaries. Therefore, peaks in the vector field divergence of the model's predictions are used as indication of phase transitions. Our method is applicable for phase diagrams of arbitrary parameter dimension and without prior information about the phases. Application to both the two-dimensional Ising model and the dissipative Kuramoto-Hopf model show promising results.

We study the motion of a Brownian particle in a medium with inhomogeneous temperature. In the overdamped regime of low Reynolds numbers, the probability distribution function (PDF) of the particle is obtained from the van Kampen diffusion equation [J. Phys. Chem. Solids 49, 673 (1988)]. The thermophoretic behavior is commonly described by the Soret coefficient, a parameter that can be calculated from the steady-state PDF. Motivated by recent advances in experimental methods for observing and analyzing single nanoparticle trajectories, we here consider the time-dependent van Kampen equation from which the temporal evolution of the PDF of individual particles can be derived. We analytically calculate the PDF describing dynamics driven by a generalized thermophoretic force. Single-particle statistics are characterized by measures such as the mean displacement (drift) and the probability difference between moving along and against the temperature gradient (bias). We demonstrate that these quantities do not necessarily have the same sign as the Soret coefficient, which causes ambiguity in the distinction between thermophilic and thermophobic response (i.e., migration in and against the direction of the temperature gradient). The different factors determining the thermophoretic response and their influence on each measure are discussed.

A lacunarity analysis of the zero crossings derived from Gaussian stochastic processes with oscillatory autocorrelation functions is evaluated and reveals distinct multiscaling signatures depending on the smoothness and degree of anticorrelation of the process. These bear qualitative similarities and quantitative distinctions from an oscillatory deterministic signal and a Poisson random process both possessing the same mean interval size between crossings. At very small and large scales compared with the correlation length of the random processes, the lacunarity is similar to the Poisson but exhibits significant departures from Poisson behavior if there is a zero-frequency component to the process's power spectrum. A comparison of exact results with the gliding box technique that is frequently used to determine lacunarity demonstrates its inherent bias.

Simulations of a turbulent multicomponent fluid mixture undergoing isotropic deformations are carried out to investigate the sudden viscous dissipation. This dissipative mechanism was originally demonstrated using simulations of an incompressible single-component fluid [S. Davidovits and N. J. Fisch, Phys. Rev. Lett. 116, 105004 (2016)]. By accounting for the convective and diffusive transfer of various species, the current work aims to increase the physical fidelity of previous simulations and their relevance to inertial confinement fusion applications. Direct numerical simulations of the compressed fluid show that the sudden viscous dissipation of turbulent kinetic energy is unchanged from the single-component scenario. More importantly, the simulations demonstrate that the mass fraction variance and covariance for the various species also exhibit a sudden viscous decay. Reynolds-averaged Navier-Stokes simulations were carried out using the $k-l$ model to assess its ability to reproduce the sudden viscous dissipation. Results show that the standard $k-l$ formulation does not capture the sudden decay of turbulent kinetic energy, mass-fraction variance, and mass-fraction covariance for simulations with various compression and expansion rates, or different exponents for the power-law model of viscosity. A new formulation of the $k-l$ model that is based on previous improvements to the $k-\epsilon$ family of models is proposed, which leads to consistently good agreement with the direct numerical simulations for all the isotropic deformations under consideration.

In a recent study [Phys. Rev. E 94, 022103 (2016)] it has been shown that, for a fluid film subject to critical adsorption, the resulting critical Casimir force (CCF) may significantly depend on the thermodynamic ensemble. Here we extend that study by considering fluid films within the so-called ordinary surface universality class. We focus on mean-field theory, within which the order parameter (OP) profile satisfies Dirichlet boundary conditions and produces a nontrivial CCF in the presence of external bulk fields or, respectively, a nonzero total order parameter within the film. Additionally, we study the influence of fluctuations by means of Monte Carlo simulations of the three-dimensional Ising model. We show that, in the canonical ensemble, i.e., when fixing the so-called total mass within the film, the CCF is repulsive for large absolute values of the total OP, instead of attractive as in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we furthermore obtain analytic expressions for the order parameter profiles and analyze the relation between the total mass in the film and the external bulk field.

Fictitious stochastic reservoirs incorporate scattering and dephasing mechanisms into the system in contact with these reservoirs. The reservoir-system coupling is described by the related self-energy in terms of the nonequilibrium Green's function formalism or equivalently the quantum Langevin equation formalism. In this study, we investigate thermal transport in a finite segment of an infinitely extended quantum harmonic chain with an equal self-energy at each site by using the self-consistent reservoir approach. In this setup, the entire system is lattice translation invariant so that mismatched boundaries are excluded from the model. Solving the Landauer-Büttiker equations under the self-consistent adiabatic condition, we quantitatively elucidate a thermally induced crossover of ballistic-to-diffusive transport and its scaling relation prescribed by a temperature-dependent mean free path. It is also shown that normal transport emerges in the diffusive limit for a linear self-energy, while nonlinear higher-order ones generically lead to anomalous transport. Physical implications of these observations are discussed in terms of the persistence of a massless Goldstone mode as well as the conservation of total linear momentum.

We study the connection between heat transport properties of systems coupled to different thermal baths in two separate regions and their underlying nonequilibrium dynamics. We consider classical systems of interacting particles that may exhibit a certain degree of delocalization and whose effective dimensionality can be modified through the controlled variation of a global trapping potential. We focus on Coulomb crystals of trapped ions, which offer a versatile playground to shed light on the role that spatial constraints play on heat transport. We use a three-dimensional model to simulate the trapped ion system and show in a numerically rigorous manner to what extent heat transport properties could be feasibly tuned across the structural phase transitions among the linear, planar zigzag, and helical configurations. By solving the classical Langevin equations of motion, we analyze the steady state spatial distributions of the particles, the temperature profiles, and total heat flux through the various structural phase transitions that the system may experience. The results evidence a clear correlation between the degree of delocalization of the internal ions and the emergence of a nonzero gradient in the temperature profiles. The signatures of the phase transitions in the total heat flux as well as the optimal spatial configuration for heat transport are shown.

We study the voltage drop along three-terminal disordered wires in all transport regimes, from the ballistic to the localized regime. This is performed by measuring the voltage drop on one side of a one-dimensional disordered wire in a three-terminal setup as a function of disorder. Two models of disorder in the wire are considered: (i) the one-dimensional Anderson model with diagonal disorder and (ii) finite-width bulk-disordered waveguides. Based on the known $\beta$ dependence of the voltage drop distribution of the three-terminal chaotic case, $\beta$ being the Dyson symmetry index ($\beta =1$, 2, and 4 for orthogonal, unitary, and symplectic symmetries, respectively), the analysis is extended to a continuous parameter $\beta >0$ and uses the corresponding expression as a phenomenological one to reach the disordered phase. We show that our proposal encompasses all the transport regimes with $\beta$ depending linearly on the disorder strength.

Phase reduction theory has been applied to many systems with limit cycles; however, it has limited applications in incompressible fluid systems. This is because the calculation of the phase sensitivity function, one of the fundamental functions in phase reduction theory, has a high computational cost for systems with a large degree of freedom. Furthermore, incompressible fluid systems have an implicit expression of the Jacobian. To address these issues, we propose a new algorithm to numerically calculate the phase sensitivity function. This algorithm does not require the explicit form of the Jacobian along the limit cycle, and the computational time is significantly reduced, compared with known methods. Along with the description of the method and characteristics, two applications of the method are demonstrated. One application is the traveling pulse in the FitzHugh Nagumo equation in a periodic domain and the other is the Kármán's vortex street. The response to the perturbation added to the Kármán's vortex street is discussed in terms of both phase reduction theory and fluid mechanics.

Statistical equilibration of energies in a slow-fast system is a fundamental open problem in physics. In a recent paper, it was shown that the equilibration rate in a springy billiard can remain strictly positive in the limit of vanishing mass ratio (of the particle and billiard wall) when the frozen billiard has more than one ergodic component [Proc. Natl. Acad. Sci. USA 114, E10514 (2017)]. In this paper, using the model of a springy Sinai billiard, it is shown that this can happen even in the case where the frozen billiard has a single ergodic component, but when the time of ergodization in the frozen system is much longer than the time of equilibration. It is also shown that as the size of the disk in the Sinai billiard is increased from zero, thereby leading to a decrease in the time required for ergodization in the frozen system, the system undergoes a smooth phase transition in the equilibration rate dependence on mass ratio.