Free-boundary plasma equilibria with toroidal plasma flows

Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and the scrape-off layer are developed for the 'divertor-type' and 'limiter-type' free boundaries in the tokamak cylindrical coordinator. With a toroidal plasma flow, the flux functions are considerably different under the isentropic and isothermal assumptions. The effects of the toroidal flow on the magnetic axis shift are investigated. In a high beta plasma, the magnetic shift due to the toroidal flow are almost the same for both the isentropic and isothermal cases, and are about 0.04a0 (a0 is the minor radius) for M0=0.2 (the toroidal Alfvѐn Mach number on the magnetic axis). In addition, the X-point is slightly shifted upward by 0.0125 a0. But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M0 is usually less than 0.05 in a real tokamak. The effects of the toroidal flow on the plasma parameters are also investigated. The high toroidal flow shifts the plasma outward due to the centrifugal effect. Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.

Long-time dynamics of an epidemic model with nonlocal diffusion and free boundaries

<abstract><p>In this paper, we consider a reaction-diffusion epidemic model with nonlocal diffusion and free boundaries, which generalises the free-boundary epidemic model by Zhao et al. ^{[<xref ref-type="bibr" rid="b1">1</xref>]} by including spatial mobility of the infective host population. We obtain a rather complete description of the long-time dynamics of the model. For the reproduction number $ R_0 $ arising from the corresponding ODE model, we establish its relationship to the spreading-vanishing dichotomy via an associated eigenvalue problem. If $ R_0 \le 1 $, we prove that the epidemic vanishes eventually. On the other hand, if $ R_0 &gt; 1 $, we show that either spreading or vanishing may occur depending on its initial size. In the case of spreading, we make use of recent general results by Du and Ni ^{[<xref ref-type="bibr" rid="b2">2</xref>]} to show that finite speed or accelerated spreading occurs depending on whether a threshold condition is satisfied by the kernel functions in the nonlocal diffusion operators. In particular, the rate of accelerated spreading is determined for a general class of kernel functions. Our results indicate that, with all other factors fixed, the chance of successful spreading of the disease is increased when the mobility of the infective host is decreased, reaching a maximum when such mobility is 0 (which is the situation considered by Zhao et al. ^{[<xref ref-type="bibr" rid="b1">1</xref>]}).</p></abstract>

A new technique for modelling phonon scattering processes at rough interfaces and free boundaries of solids

Scattering processes at interfaces and free boundaries of solids strongly affect heat transfer in micro- and nanostructures such as integrated circuits, periodic nanostructures, multilayer thin films, and other nanomaterials. Among many influencing factors, surface roughness due to atomic disorder plays a significant role in the rate of thermal transport. Existing approaches have been developed only for the limiting cases of smooth or completely diffuse surfaces. We have developed a new effective and simple method based on a direct consideration of the scattering of elastic waves from a statistically random profile (using a normal Gaussian surface as an example). This approach, first, allows to generalize common methods for determining the thermal properties of a real random rough surface using simple modifications, and, second, provides a tool for calculating the Kapitza conductance and the effective longitudinal thermal conductivity and studying the influence of roughness on heat transfer.

A fast thermoelastic model based on the half-space theory applied to elastohydrodynamic lubrication of line contacts involving free boundaries

This study allows contact models based on semi-analytical methods including the impacts of thermoelastic deformations in contacts of finite dimension bodies. The proposed method controls heat flows crossing free boundaries. A comparison with FEA reveals that the proposed method can reduce the calculation times by more than 98%. The paper introduces the thermoelasticity effects into thermal-elastohydrodynamic lubrication (TEHL) modeling of line contact problems. The analysis reveals that including thermoelastic deformations changes the pressure profile and tends to localize the pressure close to the distribution center. Compared to TEHL simulations, the examined configurations caused an overall increase in the maximum pressure by about 9%, an overall film thickness reduction of about 7%, and an overall temperature increase of about 2 K.

Two-phase problem with a free boundary for systems of parabolic equations with a nonlinear term of convection

Эта статья посвящена задаче со свободной границей для полулинейных параболических уравнений, в которой описывается феномен сегрегации местообитаний в популяционной экологии. Основная цель — показать глобальное существование, единственность решений проблемы. Предлагается двухфазная математическая модель со свободными границами для параболических уравнений типа реакция-диффузия. Установлены априорные оценки щаудеровского типа, на основе которых доказана однозначная разрешимость задачи. Неустойчивость каждого решения полностью определяется с помощью теоремы сравнения. This article is concerned with a free boundary problem for semilinear parabolic equations, wbich describes the habitat segregation phenomenon in population ecology. The main goal is to show global existence, the uniqueness of solutions to the problem. A two-phase mathematical model with free boundaries for parabolic equations of the reaction-diffusion type is proposed. A priori estimates of Schauder type are established, on the basis of which the unique solvability of the problem is proved. The instability of each solution is fully determined using the comparison theorem.

Rayleigh-Benard Convection in Nanofluids Layer saturated in a Rotating Anisotropic Porous Medium with Feedback Control and Internal Heat Source

Control strategy on Rayleigh-Benard convection in rotating nanofluids saturated in anisotropic porous layer heated from below is studied in the presence of uniformly internal heat source for rigid-rigid, free-free, and lower-rigid and upper-free boundaries. Feedback control strategy with an array of sensors situated at the top plate and actuators located at the bottom plate of the nanofluids layer are considered in this study. Linear stability analysis based on normal mode technique has been performed, the eigenvalue problem is obtained numerically by implementing the Galerkin method and computed by using Maple software. Model employed for the nanofluids includes the mechanisms of Brownian motion and thermophoresis. The problem of the onset of convective rolls instabilities in a horizontal porous layer with isothermal boundaries at unequal temperatures known as Horton-Roger-Lapwood model based on the Darcy model for the fluids flow is used. The influences of internal heat source’s strength, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection, meanwhile the mechanical anisotropy parameter, thermal anisotropy parameter, porosity, rotation, and controller effects are to slow down the process of convective instability. No visible observation on the modified particle density increment and rigid-rigid boundaries are the most stable system compared to free-free and rigid-free boundaries.