Williamspetty0421

Implications of our results on cardiac physiology are also discussed.We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the two alternatives, represented by a variable p∈[0,1]. When an agent i interacts with another agent j with propensity p_j, then i either increases its propensity p_i by h with probability P_ij=ωp_i+(1-ω)p_j, or decreases p_i by h with probability 1-P_ij, where h is a fixed step. Encorafenib chemical structure We assume that the interactions form a complete graph, where each agent can interact with any other agent. We analyze the system by a rate equation approach and contrast the results with Monte Carlo simulations. We find that the dynamics of propensities depends on the weight ω that an agent assigns to its own propensity. When all the weight is assigned to the interacting partner (ω=0), agents' propensities are quickly driven to one of the extreme values p=0 or p=1, until an extremist absorbing consensus is achieved. However, for ω>0 the system first reaches a quasistationary state of symmetric polarization where the distribution of propensities has the shape of an inverted Gaussian with a minimum at the center p=1/2 and two maxima at the extreme values p=0,1, until the symmetry is broken and the system is driven to an extremist consensus. A linear stability analysis shows that the lifetime of the polarized state, estimated by the mean consensus time τ, diverges as τ∼(1-ω)^-2lnN when ω approaches 1, where N is the system size. Finally, a continuous approximation allows us to derive a transport equation whose convection term is compatible with a drift of particles from the center toward the extremes.A numerical procedure based on the Schwarz-Christoffel map suitable for the study of the Laplacian growth of thin two-dimensional protrusions is presented. The protrusions take the form of either straight needles or curved fingers satisfying Loewner's equation, and are represented by slits in the complex plane. Particular use is made of Driscoll's numerical procedure, the SC Toolbox, for computing the Schwarz-Christoffel map from a half plane to a slit half plane. Since the Schwarz-Christoffel map applies only to polygonal regions, the growth of curved fingers is approximated by an increasing number of short straight line segments. The growth rate is given by a fixed power η of the harmonic measure at the finger or needle tips and so includes the possibility of "screening" as the needles of fingers interact with themselves and with boundaries. The method is illustrated with examples of multiple needle and finger growth in half-plane and channel geometries. The effect of η on the trajectories of asymmetric bifurcating fingers is also studied.Most treatments of electron-electron correlations in dense plasmas either ignore them entirely (random phase approximation) or neglect the role of ions (jellium approximation). In this work, we go beyond both these approximations to derive a formula for the electron-electron static structure factor which properly accounts for the contributions of both ionic structure and quantum-mechanical dynamic response in the electrons. The result can be viewed as a natural extension of the quantum Ornstein-Zernike theory of ionic and electronic correlations, and it is suitable for dense plasmas in which the ions are classical and the conduction electrons are quantum-mechanical. The corresponding electron-electron pair distribution functions are compared with the results of path integral Monte Carlo simulations, showing good agreement whenever no strong electron resonance states are present. We construct approximate potentials of mean force which describe the effective screened interaction between electrons. Significant deviations from Debye-Hückel screening are present at temperatures and densities relevant to high-energy density experiments involving warm and hot dense plasmas. The presence of correlations between conduction electrons is likely to influence the electron-electron contribution to the electrical and thermal conductivity. It is expected that excitation processes involving the conduction electrons (e.g., free-free absorption) will also be affected.This paper is the continuation of work done in our previous papers [A. A. Doinikov et al., Phys. Rev. E 100, 033104 (2019)2470-004510.1103/PhysRevE.100.033104; Phys. Rev. E 100, 033105 (2019)].2470-004510.1103/PhysRevE.100.033105 The overall aim of the study is to develop a theory for modeling the velocity field of acoustic microstreaming produced by nonspherical oscillations of an acoustically driven gas bubble. In our previous papers, general equations have been derived to describe the velocity field of acoustic microstreaming produced by modes m and n of bubble oscillations. After solving these general equations for some particular cases of modal interactions (cases 0-n, 1-1, and 1-m), in this paper the general equations are solved analytically for the case that acoustic microstreaming results from the self-interaction of an arbitrary surface mode n≥1. Solutions are expressed in terms of complex mode amplitudes, meaning that the mode amplitudes are assumed to be known and serve as input data for the calculation of the velocity field of acoustic microstreaming. No restrictions are imposed on the ratio of the bubble radius to the viscous penetration depth. The self-interaction results in specific streaming patterns a large-scale cross pattern and small recirculation zones in the vicinity of the bubble interface. Particularly the spatial organization of the recirculation zones is unique for a given surface mode and therefore appears as a signature of the n-n interaction. Experimental streaming patterns related to this interaction are obtained and good agreement is observed with the theoretical model.We study the planar motion of telegraphic processes. We derive the two-dimensional telegrapher's equation for isotropic and uniform motions starting from a random walk model which is the two-dimensional version of the multistate random walk with a continuum number of states representing the spatial directions. We generalize the isotropic model and the telegrapher's equation to include planar fractional motions. Earlier, we worked with the one-dimensional version [Masoliver, Phys. Rev. E 93, 052107 (2016)PREHBM2470-004510.1103/PhysRevE.93.052107] and derived the three-dimensional version [Masoliver, Phys. Rev. E 96, 022101 (2017)PREHBM2470-004510.1103/PhysRevE.96.022101]. An important lesson is that we cannot obtain the two-dimensional version from the three-dimensional or the one-dimensional one from the two-dimensional result. Each dimension must be approached starting from an appropriate random walk model for that dimension.We show that an increasingly strong thermal rectification effect occurs in the thermodynamic limit in a one-dimensional, graded rotor lattice with nearest-neighboring interactions only. The underlying mechanism is related to the transition from normal to abnormal heat conduction behavior observed in the corresponding homogeneous lattices as the temperature decreases. In contrast and in addition to that by invoking long-range interactions, this finding provides a distinct scenario to make the thermal rectification effect robust.We examine the equilibrium fluctuation spectrum of a semiflexible filament segment in a network. The effect of this cross linking is to modify the mechanical boundary conditions at the end of the filament. We consider the effect of both tensile stress in the network and its elastic compliance. Most significantly, the network's compliance introduces a nonlinear term into the filament Hamiltonian even in the small-bending approximation. We analyze the effect of this nonlinearity upon the filament's fluctuation profile. We also find that there are three principal fluctuation regimes dominated by one of the following (i) network tension, (ii) filament bending stiffness, or (iii) network compliance. This work provides the theoretical framework necessary to analyze activity microrheology, which uses the observed filament fluctuations as a noninvasive probe of tension in the network.This work addresses the construction of a reduced-order model based on a multigroup maximum entropy formulation for application to high-enthalpy nonequilibrium flows. The method seeks a piecewise quadratic representation of the internal energy-state populations by lumping internal energy levels into groups and by applying the maximum entropy principle in conjunction with the method of moments. The use of higher-order polynomials allows for an accurate representation of the logarithm of the distribution of the low-lying energy states, while preserving an accurate description of the linear portions of the logarithm of the distribution function that characterize the intermediate- and high-energy states. A comparison of the quadratic and the linear reconstructions clearly demonstrates how the higher-order reconstruction provides a more accurate representation of the internal population distribution function at a modest increase in the computational cost. Numerical simulations carried out under conditions relevant to hypersonic flight reveal that the proposed model is able to capture the dynamics of the nonequilibrium distribution function using as few as three groups, thereby reducing the computational costs for simulations of nonequilibrium flows.The stability criterion for the magnetic separation of rare-earth ions is studied, taking dysprosium Dy(iii) ions as an example. Emphasis is placed on quantifying the factors that limit the desired high enrichment. During magnetic separation, a layer enriched in Dy(iii) ions is generated via the surface evaporation of an aqueous solution which is levitated by the Kelvin force. Later, mass transport triggers instability in the enriched layer. The onset time and position of the instability is studied using an interferometer. The onset time signals that an advective process which significantly accelerates the stratification of enrichment is taking place, although the initial phase is quasi-diffusion-like. The onset position of the flow agrees well with that predicted with a generalized Rayleigh number (Ra^*=0) criterion which includes the Kelvin force term acting antiparallel to gravity. Further three-dimensional analysis of the potential energy, combining magnetic and gravitational terms, shows an energy barrier that has to be overcome to initiate instability. The position of the energy barrier coincides well with the onset position of the instability.The Navier-Stokes transport coefficients of multicomponent granular suspensions at moderate densities are obtained in the context of the (inelastic) Enskog kinetic theory. The suspension is modeled as an ensemble of solid particles where the influence of the interstitial gas on grains is via a viscous drag force plus a stochastic Langevin-like term defined in terms of a background temperature. In the absence of spatial gradients, it is shown first that the system reaches a homogeneous steady state where the energy lost by inelastic collisions and viscous friction is compensated for by the energy injected by the stochastic force. Once the homogeneous steady state is characterized, a normal solution to the set of Enskog equations is obtained by means of the Chapman-Enskog expansion around the local version of the homogeneous state. To first order in spatial gradients, the Chapman-Enskog solution allows us to identify the Navier-Stokes transport coefficients associated with the mass, momentum, and heat fluxes. In addition, the first-order contributions to the partial temperatures and the cooling rate are also calculated.