Physical review. E最新文献

Statistics of diffusion, modeled by random walks, such as the mean number of distinct sites visited S(t) at time t, the mean probability P_{0}(t) of being at the origin of the walk, and the mean-squared displacements 〈R^{2}(t)〉 of the random walkers have been studied extensively in the past in both regular lattices and such disordered media as percolation clusters and other fractal structures, and universal power laws for such quantities have been derived. S(t) provides insight into reaction properties of geological formations, while P_{0}(t) is directly linked with the problem of back diffusion in remediation of groundwater aquifers. In all such studies, it was assumed that the conductances of the bonds that connect nearest-neighbor sites of the lattices are equal. Motivated by the problem of transport and reaction in large-scale porous media that are characterized by a broad spatial distribution of hydraulic conductances, we demonstrate, using extensive Monte Carlo simulations, that the statistics of random walks, when the conductances are broadly distributed, depend on the structure of the distribution. Five geologically relevant conductance distributions, namely, normal, log-normal, fractional Brownian motion (FBM), log-FBM, and stable distributions, are considered and random walks in a two-dimensional model with the five distributions are simulated. The first two distributions are uncorrelated, while the last three induce long-range correlations in the values of the conductance. We show that if S(t)∼t^{p} and P_{0}(t)∼t^{-ζ}, the exponents p and ζ may depend on the conductance distribution, in which case they are neither equal to those for homogeneous lattices, nor those for percolation clusters and other fractal structures. For at least three of the conductance distributions, diffusion is anomalous, with 〈R^{2}(t)〉 not growing linearly with the time t, even in the long-time limit. In addition to being of scientific interest, and the fact that transport processes in geomedia are simulated by random walks, the dependence of such statistics on the distribution of the conductances and their deviations from the statistics of random walks in homogeneous systems, and percolation and other types of fractal structures, indicate that diffusion in highly heterogeneous porous media is anomalous, and is described by fractional partial differential equations in which the temporal and spatial fractional orders depend on the details of the conductance distribution.

The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has received limited attention. Here, we adapt and enhance the mean-field approach originally proposed by Stiller and Radons [Phys. Rev. E 58, 1789 (1998)1063-651X10.1103/PhysRevE.58.1789] to study the asynchronous state in the Kuramoto model with a finite number of oscillators and with disordered connectivity. By employing an iterative stochastic mean field approximation, the complex N-oscillator system can effectively be reduced to a one-dimensional dynamics, both for homogeneous and heterogeneous networks. This method allows us to investigate the power spectra of individual oscillators as well as of the multiplicative "network noise" in the Kuramoto model in the asynchronous regime. By taking into account the finite system size and disorder in the connectivity, our findings become relevant for the dynamics of coupled oscillators that appear in the context of biological or technical systems.

Active curling of epithelial tissues, as an indispensable component of developmental morphogenesis, occurs frequently both in vivo and in vitro microenvironments. Deciphering the mechanisms underlying the active curling of epithelial monolayers is crucial for understanding many physiological and pathological processes. Here, a multiscale structure-based cell monolayer model and an active constitutive relation are established to characterize this spontaneous curling of the epithelial tissue. It is shown that the asymmetric distribution of Myosin II along the apicobasal axis generates an active moment that drives spontaneous curling of the suspended epithelial tissue. The time-dependent deflection and rotation angle of the active curling are analytically solved, proving that the curling is driven by the active bending moment directly associated with the apicobasal asymmetric contractile force. Moreover, we demonstrate that the rotation angle is proportional to the apicobasal force ratio and inversely proportional to the thickness of epithelial tissues. In addition, we derive an approximate analytical relation between the out-of-plane curling behavior and in-plane stress, in good agreement with the experimental data and our simulation results. This study provides a pathway to elucidate the mechanical mechanism underlying complex morphological development as well as the physiological and pathological phenomena of epithelial tissues.

We investigate synchronization behaviors of a Kuramoto oscillator network with a two-dimensional square-lattice configuration. We show that the oscillator network can reach a phase-locking vortex synchronized state in the long time limit starting from random initial oscillator phases sampled according to the von Mises distribution characterized by a zero mean and a finite concentration parameter. We further reveal that the stability of the vortex synchronized state is sensitive to the presence of local node defects, in contrast to the usual knowledge that oscillator networks should exhibit robustness against local perturbations. Moreover, we explore the behaviors of the vortex synchronized state in networks with an additional temporal white noise on the oscillator phases or a spatial noise due to randomly distributed oscillator frequencies. Interestingly, we find that the vortex synchronized state can become immune to local node defects when the variance of spatial noise is above a certain threshold, suggesting a beneficial role of usually unwanted spatial noise in protecting vortex-synchronized networks.

This work presents a theoretical analysis of the motion of a tracer colloid driven by a time-dependent force through a viscoelastic fluid. The recoil of the colloid after application of a strong force is determined. It provides insights into the elastic forces stored locally in the fluid and their weakening by plastic processes. We generalize the mode-coupling theory of microrheology to include time-dependent forces. After deriving the equations of motion for the tracer correlator and simplifying to a schematic model, we apply the theory to a switch-off force protocol that features the recoiling of the tracer after cessation of the driving. We also include Langevin dynamics simulations to compare to the results of the theory. A nonmonotonic trend of the recoil amplitude is found in the theory and confirmed in the simulations. The linear-response approximation is also verified in the small-force regime. While the overall agreement between simulation and theory is good, simulation shows that the theory predicts a too strong nonmonotonous dependence of the recoil distance on the applied force.

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response theory. The proposed relativistic theory is able to recover the viscosity of nonrelativistic classical gases, with all its key dependencies on mass, temperature, particle diameter, and Boltzmann constant, in the limit of Lorentz factor γ=1. It also unveils the relativistic enhancement mechanism of viscosity. In the limit of ultrarelativistic fluids, the theory provides an analytical formula which reproduces the cubic increase of viscosity with temperature in agreement with various estimates for hot dense matter and the quark-gluon-plasma-type fluid.

In this paper, we introduce a computational technique for modeling heterogeneous thermoresponsive hydrogels. The model resolves local fluid-solid interactions in hydrogel pores during the deswelling process. The model is a Lagrangian particle-based technique, which benefits from computational grids that represent polymer beads inside hydrogel scaffolds. The results show that the mechanical properties of hydrogels during deswelling, e.g., shrinkage ratio and elastic modulus, have a direct effect on the development of the front of expelled fluid. It is also observed that in certain parameter regimes the hydrogel may generate inertial fluid jets at the early stages of deswelling. Finally, simple heterogeneous designs are developed using Menger sponge-inspired shapes to investigate the effect of design heterogeneity on promoting directional release.

The problem of an optimal mapping between Hilbert spaces IN of |ψ〉 and OUT of |ϕ〉 based on a set of wavefunction measurements (within a phase) ψ_{l}→ϕ_{l}, l=1,⋯,M, is formulated as an optimization problem maximizing the total fidelity ∑_{l=1}^{M}ω^{(l)}|〈ϕ_{l}|U|ψ_{l}〉|^{2} subject to probability preservation constraints on U (partial unitarity). The constructed operator U can be considered as an IN to OUT quantum channel; it is a partially unitary rectangular matrix (an isometry) of dimension dim(OUT)×dim(IN) transforming operators as A^{OUT}=UA^{IN}U^{†}. An iterative algorithm for finding the global maximum of this optimization problem is developed, and its application to a number of problems is demonstrated. A software product implementing the algorithm is available from the authors.

Proton radiography is a central diagnostic technique for measuring electromagnetic (EM) fields in high-energy-density, laser-produced plasmas. In this technique, protons traverse the plasma where they accumulate small EM deflections which lead to variations in the proton fluence pattern on a detector. Path-integrated EM fields can then be extracted from the fluence image through an inversion process. In this work, experiments of laser-driven foils were conducted on the OMEGA laser and magnetic field reconstructions were performed using both "fluence-based" techniques and high-fidelity "mesh-based" methods. We implement nonzero boundary conditions into the inversion and show their importance by comparing against mesh measurements. Good agreement between the methods is found only when nonzero boundary conditions are used. We also introduce an approach to determine the unperturbed proton source profile, which is a required input in fluence reconstruction algorithms. In this approach, a fluence inversion is embedded inside of a mesh region, which provides overconstrained magnetic boundary conditions. A source profile is then iteratively optimized to satisfy the boundary information. This method substantially enhances the accuracy in recovering EM fields. Lastly, we propose a scheme to quantify uncertainty in the final inversion that is introduced through errors in the source retrieval.

A new scaling regime characterized by a z=1 dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations. In these works, this scaling, differing from the well-known KPZ one z=3/2, was found to emerge in the tensionless limit for the interface and in the inviscid limit for the fluid. Based on functional renormalization group, the origin of this scaling has been elucidated. It was shown to be controlled by a yet unpredicted fixed point of the one-dimensional Burgers-KPZ equation, termed inviscid Burgers (IB) fixed point. The associated universal properties, including the scaling function, were calculated. All these findings were restricted to d=1, and it raises the intriguing question of the fate of this new IB fixed point in higher dimensions. In this work, we address this issue and analyze the multidimensional Burgers-KPZ equation using functional renormalization group. We show that the IB fixed point exists in all dimensions d≥0, and that it controls the large momentum behavior of the correlation functions in the inviscid limit. It turns out that it yields in all d the same super-universal value z=1 for the dynamical exponent.