Gallegosfisker9076

The inverse problem of finding the optimal network structure for a specific type of dynamical process stands out as one of the most challenging problems in network science. Focusing on the susceptible-infected-susceptible type of dynamics on annealed networks whose structures are fully characterized by the degree distribution, we develop an analytic framework to solve the inverse problem. We find that, for relatively low or high infection rates, the optimal degree distribution is unique, which consists of no more than two distinct nodal degrees. For intermediate infection rates, the optimal degree distribution is multitudinous and can have a broader support. We also find that, in general, the heterogeneity of the optimal networks decreases with the infection rate. A surprising phenomenon is the existence of a specific value of the infection rate for which any degree distribution would be optimal in generating maximum spreading prevalence. The analytic framework and the findings provide insights into the interplay between network structure and dynamical processes with practical implications.The free-energy lattice Boltzmann (LB) model is one of the major multiphase models in the LB community. The present study is focused on a class of free-energy LB models in which the divergence of thermodynamic pressure tensor or its equivalent form expressed by the chemical potential is incorporated into the LB equation via a forcing term. Although this class of free-energy LB models may be thermodynamically consistent at the continuum level, it suffers from thermodynamic inconsistency at the discrete lattice level owing to numerical errors [Guo et al., Phys. Selleck MS023 Rev. E 83, 036707 (2010)10.1103/PhysRevE.83.036707]. The numerical error term mainly includes two parts one comes from the discrete gradient operator and the other can be identified in a high-order Chapman-Enskog analysis. In this paper, we propose an improved scheme to eliminate the thermodynamic inconsistency of the aforementioned class of free-energy LB models. The improved scheme is constructed by modifying the equation of state of the standard LB equation, through which the discretization of ∇(ρc_s^2) is no longer involved in the force calculation and then the numerical errors can be significantly reduced. Numerical simulations are subsequently performed to validate the proposed scheme. The numerical results show that the improved scheme is capable of eliminating the thermodynamic inconsistency and can significantly reduce the spurious currents in comparison with the standard forcing-based free-energy LB model.A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law, and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). The entropy of mixing, the mixing area, the mixing width, the kinetic and internal energies, and the maximum and minimum temperatures are investigated during the dynamic KHI process. It is found that the mixing degree and fluid flow are similar in the KHI process for cases with various thermal conductivity and initial temperature configurations, while the maximum and minimum temperatures show different trends in cases with or without initial temperature gradients. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI morphological structure.We revisit the question of wave-number selection in pattern-forming systems by studying the one-dimensional stabilized Kuramoto-Sivashinsky equation with additive noise. In earlier work, we found that a particular periodic state is more probable than all others at very long times, establishing the critical role of noise in the selection process. However, the detailed mechanism by which the noise picked out the selected wave number was not understood. Here, we address this issue by analyzing the noise-averaged time evolution of each unstable mode from the spatially homogeneous state, with and without noise. We find drastic differences between the nonlinear dynamics in the two cases. In particular, we find that noise opposes the growth of Eckhaus modes close to the critical wave number and boosts the growth of Eckhaus modes with wave numbers smaller than the critical wave number. We then hypothesize that the main factor responsible for this behavior is the excitation of long-wavelength (q→0) modes by the noise. This hypothesis is confirmed by extensive numerical simulations. We also examine the significance of the magnitude of the noise.Cells of the social amoeba Dictyostelium discoideum migrate to a source of periodic traveling waves of chemoattractant as part of a self-organized aggregation process. An important part of this process is cellular memory, which enables cells to respond to the front of the wave and ignore the downward gradient in the back of the wave. During this aggregation, the background concentration of the chemoattractant gradually rises. In our microfluidic experiments, we exogenously applied periodic waves of chemoattractant with various background levels. We find that increasing background does not make detection of the wave more difficult, as would be naively expected. Instead, we see that the chemotactic efficiency significantly increases for intermediate values of the background concentration but decreases to almost zero for large values in a switch-like manner. These results are consistent with a computational model that contains a bistable memory module, along with a nonadaptive component. Within this model, an intermediate background level helps preserve directed migration by keeping the memory activated, but when the background level is higher, the directional stimulus from the wave is no longer sufficient to activate the bistable memory, suppressing directed migration.