Bounds on size-dependent behaviour of composites

Computational homogenisation is a powerful strategy to predict the effective behaviour of heterogeneous materials. While computational homogenisation cannot exactly compute the effective parameters, it can provide bounds on the overall material response. Thus, central to computational homogenisation is the existence of bounds. Classical first-order computational homogenisation cannot capture size effects. Recently, it has been shown that size effects can be retrieved via accounting for elastic coherent interfaces in the microstructure. The primary objective of this contribution is to present a systematic study to attain computational bounds on the size-dependent response of composites. We show rigorously that interface-enhanced computational homogenisation introduces two relative length scales into the problem and investigate the interplay between them. To enforce the equivalence of the virtual power between the scales, a generalised version of the Hill–Mandel condition is employed, and accordingly, suitable boundary conditions are derived. Macroscopic quantities are related to their microscopic counterparts via extended average theorems. Periodic boundary conditions provide an effective behaviour bounded by traction and displacement boundary conditions. Apart from the bounds due to boundary conditions for a given size, the size-dependent response of a composite is bounded, too. The lower bound coincides with that of a composite with no interface. Surprisingly, there also exists an upper bound on the size-dependent response beyond which the expected ‘smaller is stronger’ trend is no longer observed. Finally, we show an excellent agreement between our numerical results and the corresponding analytical solution for linear isotropic materials which highlights the accuracy and broad applicability of the presented scheme.     

Electron theory of fast and ultrafast dissipative magnetization dynamics

For metallic magnets we review the experimental and electron-theoretical investigations of fast magnetization dynamics (on a timescale of ns to 100 ps) and of laser-pulse-induced ultrafast dynamics (few hundred fs). It is argued that for both situations the dominant contributions to the dissipative part of the dynamics arise from the excitation of electron-hole pairs and from the subsequent relaxation of these pairs by spin-dependent scattering processes, which transfer angular momentum to the lattice. By effective field theories (generalized breathing and bubbling Fermi-surface models) it is shown that the Gilbert equation of motion, which is often used to describe the fast dissipative magnetization dynamics, must be extended in several aspects. The basic assumptions of the Elliott-Yafet theory, which is often used to describe the ultrafast spin relaxation after laser-pulse irradiation, are discussed very critically. However, it is shown that for Ni this theory probably yields a value for the spin-relaxation time T(1) in good agreement with the experimental value. A relation between the quantity α characterizing the damping of the fast dynamics in simple situations and the time T(1) is derived.     

Accurate Solutions of the Navier-Stokes Equations Despite Unknown Outflow Boundary Data

A very common procedure when constructing boundary conditions for the time-dependent Navier-Stokes equations at artificial boundaries is to extrapolate the solution from grid points near the boundary to the boundary itself. For supersonic outflow, where all the characteristic variables leave the computational domain, this leads to accurate results. In the case of subsonic outflow, where one characteristic variable enters the computational domain, one cannot in general expect accurate solutions by this procedure. The problem with outflow boundary operators of extrapolation type at artificial boundaries with errors in the boundary data of order one will be investigated. Both the problem when the artificial outflow boundary is located in essentially uniform flow and the situation when the artificial outflow boundary is located in a flow field with large gradients are discussed. It will be shown, that in the special case when there are large gradients tangential to the boundary, extrapolation methods can be used even in the subsonic case.     

Interaction of surface electromagnetic waves with an electron beam moving along the interface between metamaterials

Excitation of surface polaritons by an infinitely narrow electron beam propagating in the vacuum gap between a metal-like medium and an artificial dielectric with a negative permeability is studied theoretically. A dispersion relation is derived for the waves excited by the beam for an arbitrary thickness of the gap. The possibility of the emergence of absolute instability is demonstrated for an infinitely narrow vacuum gap, and the corresponding increments are calculated with allowance for small dissipative losses.     

Dissipative Instability of Shock Waves

A new condition is obtained for the linear instability of a plane front of an intense shock wave in an arbitrary medium, which is determined by the finiteness of the viscosity. It is shown that the shock front instability occurs due to dissipative instability of the flow behind the front, which is analogous to the flow instability in the boundary layer. It is found that in the low-viscosity limit, one-dimensional longitudinal perturbations increase much faster than two-dimensional (corrugation) perturbations. The results are compared with the available data of experimental observation and numerical simulation of instability of shock waves. The comparison shows a better agreement between the new absolute shock instability as compared to the condition of such instability in the classical D’yakov theory disregarding viscosity.     

标模外形化学非平衡流场数值模拟

利用三维并行计算代码求解Navier-Stokes方程,数值模拟标模(ELECTRE)化学非平衡绕流,研究真实气体效应对标模气动热特性的影响,反应模型为Dunn和Kang的7组元7反应化学动力学模型.利用典型弹道点的飞行试验数据验证化学非平衡流计算程序的可靠性.在此基础上,研究不同壁面催化条件下攻角和高度变化对热流的影响.计算表明:真实气体效应主要发生在物面附近很薄的激波层内,并使激波脱体距离减小;完全催化壁驻点热流值高于非催化壁热流值;随着攻角增大,热流分布差异明显,而且攻角越大时,物面电子数密度越小;飞行高度越高,O₂和N₂离解程度越低,驻点热流越低.     

耗散紧致格式的频谱特性研究与应用

采用Fourier分析方法,给出线性耗散紧致格式和基于m级Runge-Kutta时间积分方法的全离散格式的频谱特性,并应用五阶耗散紧致格式模拟典型高频波传播和超声速平面Couette流动的特征值问题及其稳定性边值问题,展示耗散紧致差分格式良好的频谱特性.     

The Thouless formula: From disordered to chaotic spectra

A new expression of the dissipative dc conductance is presented in terms of the scattering phase shift by a time dependent Aharonov-Bohm flux line. It is then related to the Thouless conductance defined as the curvature of the energy levels under a change of the boundary conditions. The relation between these two conductances is found to be universal for all systems obeying Wigner-Dyson statistics. This provides a new characterization of quantum chaotic systems.     

主喷管叶片中热壁面对分流管道流场特性的影响

连续波化学激光器运转时,位于主喷管叶片内的副气流的分流管道壁面将被主喷管叶片加热而形成热壁面。通过3维的数值模拟,分析了单端、双端不同供气方式下,热壁面对分流管道流场特性的影响。热壁面将使总管气流总温沿着气流的流动方向逐渐升高,由此引起的支管入口总温的升高会降低支管的流量。无论是单端供气,还是双端供气,热壁面引起的管道流量波动幅度都要远大于绝热壁面的情况,最大波动幅度达2.16%。对进入总管的气流预热,适当增加供气总温,或将冷却管道与供气管道分开设计,气流总温变化引起的流量波动将会得到一定地抑制。     

Breakup of an invariant curve in a dissipative standard mapping

A critical value for the existence of an invariant curve in a dissipative standard mapping is calculated by a new method in relation to Arnold's tongue. It is shown that the golden mean invariant curve is not the last curve for the strongly dissipative parameter region.     

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.     

Hexagonal structures of current in a “semiconductor-gas-discharge gap” system

The results of experimental investigation of the stability boundary for a spatially homogeneous state of a discharge in the planar gap of a “semiconductor-gas-discharge” cryogenic system filled with nitrogen are considered. The semiconductor cathode was prepared from single-crystalline silicon doped with a deep-lying impurity. Quantitative data are obtained for the conditions of formation of a hexagonal dissipative structure in the current distribution for two values of the discharge gap length upon a change in the gas pressure and in the conductivity of the cathode. It is found that for a fixed gap length, the formation of the critical state can be described approximately by a universal function of the electrode conductivity and gas pressure.     

Generation of magnetic field during shearing motion of a conducting viscous medium

Magnetic field generation in shear flows of an incompressible viscous conducting medium across the flux lines of the initial field created in them is considered in the framework of the plane 1D problem of magnetohydrodynamics. The conditions of free slip and “sticking” are stipulated at the boundary between the flows. The variations of the magnetic field and velocity of shear flow occurring in the moving medium correspond to an Alfven wave “spreading” during its propagation due to dissipative processes in the medium associated with its viscosity and electrical resistance. It is shown that a high-rate shear of metals under explosive or impact loading may lead to generation of megagauss magnetic fields.     

Two-dimensional random walk description of fluid flow in the presence of a wall: The origin of stick versus slip boundary conditions in the continuum limit

It is shown how a fairly simple random walk on a lattice provides insight into the nature of hydrodynamic boundary conditions. In a flow parallel to the boundary, collisions of up and downward moving particles induce lateral bulk diffusion. At the wall the model accounts essentially for 1) specular reflection, 2) diffuse reflection and 3) trapping at the surface. The steady state is solved exactly. In the continuum limit the case of stick versus slip boundary conditions is explained in its relation to the interplay of bulk and boundary processes.     

Amplification of short-wave radiation based on the resistive instability of a relativistic electron beam (Quasi-optical theory)

The quasi-optical approach has been used to study the linear and nonlinear stages of instability of an electron beam propagating near a flat boundary of an absorbing medium with dissipative characteristics that can be described by the Leontovich impedance boundary conditions. It has been shown that resistive instability can be used to amplify radiation in the short-wave ranges, including the terahertz range. The instability increments and the efficiency of energy transfer have been determined.     

Cellular automaton model within the fundamental-diagram approach reproducing some findings of the three-phase theory

We propose a simple cellular automaton for traffic flow within the fundamental diagram, which could reproduce aspects of the three-phase theory. This so-called average space gap model (ASGM) is based on the Nagel–Schreckenberg model with additional slow-to-start and anticipation rules. The anticipation rule takes into account the average space gap of multiple leading vehicles and conveys to the model its three-phase property. Due to the anticipation rule, ASGM can show the transition from free flow to synchronized flow. Due to the slow-to-start rule, ASGM can show the spontaneous wide moving jam emerges in the synchronized flow. Simulations are carried out for periodic and open boundary conditions. Under periodic boundary condition, the fundamental diagram, and the properties of synchronized flow are studied. Under open boundary condition, different congested patterns induced by an on-ramp are analyzed. We found that the ASGM produces the same spatiotemporal dynamics as many of the more complex three-phase models. Due to its simplicity and its close relation to conventional slow-to-start models, this model can shed light on the relation between ‘two-phase’ and three-phase models.     

Tunable-slip boundaries for coarse-grained simulations of fluid flow

On the micro- and nanoscale, classical hydrodynamic boundary conditions such as the no-slip condition no longer apply. Instead, the flow profiles exhibit "slip" at the surface, which is characterized by a finite slip length (partial slip). We present a new, systematic way of implementing partial-slip boundary conditions with arbitrary slip length in coarse-grained computer simulations. The main idea is to represent the complex microscopic interface structure by a spatially varying effective viscous force. An analytical equation for the resulting slip length can be derived for planar and for curved surfaces. The comparison with computer simulations of a DPD (dissipative particle dynamics) fluid shows that this expression is valid from full slip to no slip.     

耗散粒子动力学处理复杂固体壁面的一种有效方法

耗散粒子动力学(dissipative particle dynamics,DPD)作为一种介观尺度拉格朗日型粒子方法,已经成功地应用于微纳米流动和生化科技的研究中.复杂固体壁面的处理和壁面边界条件的实施一直是DPD方法发展及应用的一个障碍.提出了处理复杂固体壁面的一种新的方法.复杂固体区域通过冻结随机分布并且达到平衡状态的DPD粒子代表;所冻结的DPD粒子位于临近流动区域的一个截距内;在靠近固体壁面的流动区域中设置流动反弹层,当流动DPD粒子进入此流动层后反弹回流动区域.应用这种固体壁面处理方法对简单流动区域的Poiseuille流动和复杂多孔介质内的流动进行了分析.研究表明,这种新的固体壁面处理方法能够有效模拟复杂固体区域,准确实施壁面边界条件.     

微尺度后台阶流动的Monte Carlo直接模拟

对DSMC方法中压力边界条件的实现给出了一种改进的方法,并分区模拟了微尺度后台阶气体流动,得到了其流动的一般典型结构.计算结果表明经典后台阶流动中的回流区在一定参数范围内仍然存在,但上壁面的分离区消失.讨论了流动参数对流动结构的影响,并给出了再附长度与流动参数的关系.