共查询到20条相似文献,搜索用时 109 毫秒
1.
Luca Placidi Leopoldo Greco Sara Bucci Emilio Turco Nicola Luigi Rizzi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2016,67(5):114
We present numerical simulations of rectangular woven fabrics made of two, initially orthogonal, families of inextensible fibres. We consider an energy functional which includes both first and second gradients of the displacement. The energy density is expressed in terms of the angles between the fibres directions, using trigonometric functions and their gradients. In particular, we focus on an energy density depending on the squared tangent of the shear angle, which automatically satisfies some natural properties of the energy. The numerical results show that final configurations obtained by the second gradient energies are smoother than the first gradient ones. Moreover, we show that if a second gradient energy is considered, the shear energy is better uniformly distributed. 相似文献
2.
Claire Chainais‐Hillairet Ansgar Jüngel Polina Shpartko 《Numerical Methods for Partial Differential Equations》2016,32(3):819-846
An implicit Euler finite‐volume scheme for a spinorial matrix drift‐diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly coupled equations for the charge and spin‐vector densities, coupled to the Poisson equation for the electric potential. The equations are solved in a bounded domain with mixed Dirichlet–Neumann boundary conditions. The charge and spin‐vector fluxes are approximated by a Scharfetter–Gummel discretization. The main features of the numerical scheme are the preservation of nonnegativity and bounds of the densities and the dissipation of the discrete free energy. The existence of a bounded discrete solution and the monotonicity of the discrete free energy are proved. For undoped semiconductor materials, the numerical scheme is unconditionally stable. The fundamental ideas are reformulations using spin‐up and spin‐down densities and certain projections of the spin‐vector density, free energy estimates, and a discrete Moser iteration. Furthermore, numerical simulations of a simple ferromagnetic‐layer field‐effect transistor in two space dimensions are presented. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 819–846, 2016 相似文献
3.
S. P. Kshevetskii 《Computational Mathematics and Mathematical Physics》2006,46(11):1988-2005
An analysis shows that nonsmooth solutions have to be considered. Weak solutions to the Euler equations describing an incompressible stratified fluid under gravity are defined and studied. The study makes use of a wave energy functional proposed for the nonlinear equations. It is shown that the Euler equations are insufficient for stating a well-posed generalized problem. Additional conditions based on physical considerations are proposed. One condition is energy conservation, and the other is a constraint imposed on the density, which is required for stability. A numerical method is developed that is used to analyze how wave breakdown in a stratified fluid depends on stratification. The numerical results are in satisfactory agreement with experiments. 相似文献
4.
In this article, we derive expressions for conditional expectations in terms of regular expectations without conditioning but involving some weights. For this purpose, we apply two approaches: the conditional density method and the Malliavin method. We use these expressions for the numerical estimation of the price of American options and their deltas in a Lévy and jump-diffusion setting. Several examples of applications to financial and energy markets are given including numerical examples. 相似文献
5.
We present a semi-implicit scheme for a two-dimensional multilayer shallow water system with density stratification, formulated on general staggered meshes. The main result of the present note concerns the control of the mechanical energy at the discrete level, principally based on advective fluxes implying a diffusion term expressed in terms of the gradient pressure. The scheme is also designed to capture the dynamics of low-Froude-number regimes and offers interesting positivity and well-balancing results. A numerical test is proposed to highlight the scheme's efficiency in the one-layer case. 相似文献
6.
Based on the static theory of strain-gradient viscoplasticity proposed by [1], a one-dimensional dynamic analysis is derived for finite element computation of isotropic hardening materials. The kinetic energy is assumed to be composed of the conventional and internal kinetic energy. The internal energy is described phenomenologically in terms of the equivalent plastic strain in order to capture the heterogeneity of plastic flow. Herein, the microscopic density is assumed to be related to the macroscopic one through a microscopic-inertia parameter. The macroscopic- and microscopic-force balances including inertia effects are derived. The performance of the proposed formulation is illustrated through the numerical simulation of a one-dimensional dynamic problem. A parameter study to find the microscopic-inertia parameter is carried out. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
The present contribution is concerned with a numerical analysis of the uncertainties in the structural response of threedimensional structural foams with partially open cells. The effective thermo mechanical material response is determined by means of an energy based homogenization procedure. Stochastic effects in the geometry and topology of the microstructure are treated by means of a repeated analysis of small-scale representative volume elements with prescribed relative density and prescribed cell size distribution. The results are evaluated by stochastic methods. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Many energy flow models have been proposed for high-frequency forced vibration analysis of structures. In this paper, a novel energy flow model is developed to predict the high-frequency vibration response of panels in supersonic airflow and quantify the effects of supersonic airflow on high-frequency forced vibration characteristics. The additional damping due to supersonic airflow is derived from the motion equation of a two-dimensional panel. The relationship between the wavenumber and the group velocity is introduced to describe the energy transmission property considering the effects of supersonic airflow. Then the energy density governing equation (i.e. energy flow model) is established and solved by the energy flow analysis (EFA) and the energy finite element method (EFEM). Finally, comparing the vibration responses obtained by the present energy flow model with the corresponding exact analytical solutions, the developed energy flow model is verified to be effective for high-frequency vibration analysis of panels in supersonic airflow. Furthermore, the numerical simulations indicate that supersonic airflow can affect the equivalent damping of the propagating elastic waves, and thus change the energy density distribution of the panel. 相似文献
10.
We study a phenomenon occurring in various areas of quantum physics, in which an observable density (such as an energy density) which is classically pointwise non-negative may assume arbitrarily negative expectation values after quantization, even though the spatially integrated density remains non-negative. Two prominent examples which have previously been studied are the energy density (in quantum field theory) and the probability flux of rightwards-moving particles (in quantum mechanics). However, in the quantum field context, it has been shown that the magnitude and space-time extension of negative energy densities are not arbitrary, but restricted by relations which have come to be known as quantum inequalities. In the present work, we explore the extent to which such quantum inequalities hold for typical quantum mechanical systems. We derive quantum inequalities of two types. The first are kinematical quantum inequalities where spatially averaged densities are shown to be bounded below. Specifically, we obtain such kinematical quantum inequalities for the current density in one spatial dimension (imposing constraints on the backflow phenomenon) and for the densities arising in Weyl–Wigner quantization. The latter quantum inequalities are direct consequences of sharp Gårding inequalities. The second type are dynamical quantum inequalities where one obtains bounds from below on temporally averaged densities. We derive such quantum inequalities in the case of the energy density in general quantum mechanical systems having suitable decay properties on the negative spectral axis of the total energy.Furthermore, we obtain explicit numerical values for the quantum inequalities on the one-dimensional current density, using various spatial averaging weight functions. We also improve the numerical value of the related backflow constant previously investigated by Bracken and Melloy. In many cases our numerical results are controlled by rigorous error estimates.submitted 27/01/04, accepted 05/05/04 相似文献
11.
A. V. Boiko Yu. M. Nechepurenko M. Sadkane 《Computational Mathematics and Mathematical Physics》2010,50(11):1914-1924
This work is devoted to the numerical analysis of small flow disturbances, i.e. velocity and pressure deviations from the
steady state, in ducts of constant cross sections. The main emphasis is put on the disturbances causing the most kinetic energy
density growth, the so-called optimal disturbances, whose knowledge is important in laminar-turbulent transition and robust
flow control investigations. Numerically, this amounts to computing the maximum amplification of the 2-norm of a matrix exponential
exp{tS} for a square matrix S at t ≥ 0. To speed up the computations, we propose a new algorithm based on low-rank approximations of the matrix exponential
and prove that it computes the desired amplification with a given accuracy. We discuss its implementation and demonstrate
its efficiency by means of numerical experiments with a duct of square cross section. 相似文献
12.
In this paper we derive upper and lower bounds on the homogenized energy density functional corresponding to degenerated p-Poisson equations. Moreover, we give some non-trivial examples where the bounds are tight and thus can be used as good approximations of the homogenized properties. We even present some cases where the bounds coincide and also compare them with some numerical results. 相似文献
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The consistent and correct model of media taking into account scale effects (cohesion and adhesive interactions) is constructed as a special case of the Cosserat's pseudocontinuum model. The variant of the interphase layer theory is elaborated, which includes the following moments: formal mathematical statement, physical constitutive equations, numerical estimations of an interphase layer influence on the stress state and energy density distribution in a composite. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
G. A. Platov 《Numerical Analysis and Applications》2016,9(3):231-245
The results of numerical experiments with a model of coastal trapped waves are presented to identify two important features for regional modeling of the interaction of a shelf zone with open ocean. First, a wave train of this type can be formed by wind action at a considerable distance from the place of impact. The waves propagate along a coastline without significant loss of energy, provided that the coastline and shelf zone topography have no features comparable to the Rossby radius. However, the waves lose energy while passing over capes and submarine canyons and when the shelf width decreases. For regional modeling, remote generation of waves must be thoroughly investigated and taken into account. The other feature is that the propagating waves can use part of energy to form density anomalies on the shelf by raising intermediate waters from the adjacent offshore areas of the open ocean. Thus, coastal trapped waves can carry wind energy from wind action areas to other coastal areas to form density anomalies and other types of motion. 相似文献
16.
T. Blesgen 《Advances in Computational Mathematics》2007,27(2):179-194
The Γ-limit of certain discrete free energy functionals related to the numerical approximation of Ginzburg–Landau models is
analysed when the distance h between neighbouring points tends to zero. The main focus lies on cases where there is competition between surface energy
and elastic energy. Two discrete approximation schemes are compared, one of them shows a surface energy in the Γ-limit. Finally,
numerical solutions for the sharp interface Cahn–Hilliard model with linear elasticity are investigated. It is demonstrated
how the viscosity of the numerical scheme introduces an artificial surface energy that leads to unphysical solutions.
相似文献
17.
The propagation of strong shocks in an atmosphere of variable density at rest is studied. The energy gain of the flow enveloped by the shock is assumed to be time-dependent. Analytical and numerical solutions of the similarity flows behind such shocks are obtained. 相似文献
18.
Rodrigues Ferreira E.; Boulanger Ph.; Destrade M. 《The Quarterly Journal of Mechanics and Applied Mathematics》2008,61(3):353-371
In the context of the finite elasticity theory, we considera model for compressible solids called compressible neo-Hookeanmaterial. We show how finite-amplitude inhomogeneousplane wave solutions and finite-amplitude unattenuated solutionscan combine to form a finite-amplitude Love wave. We take alayer of finite thickness overlying a solid half-space, bothmade of different prestressed compressible neo-Hookean materials.We derive an exact solution of the equations of motion and boundaryconditions and also obtain results for the energy density andthe energy flux of the waves. Finally, we investigate the specialcase when the interface between the layer and the substrateis in a principal plane of the prestrain. A numerical exampleis given. 相似文献
19.
Andrzej F. Nowakowski Shaban A. Jolgam Ahmed R. Ballil Franck C.G.A. Nicolleau 《PAMM》2011,11(1):781-782
The system of extended Euler type hyperbolic equations is considered to describe a two-phase compressible flow. A numerical scheme for computing multi-component flows is then examined. The numerical approach is based on the mathematical model that considers interfaces between fluids as numerically diffused zones. The hyperbolic problem is tackled using a high resolution HLLC scheme on a fixed Eulerian mesh. The global set of conservative equations (mass, momentum and energy) for each phase is closed with a general two parameters equation of state for each constituent. The performance of various variants of a diffuse interface method is carefully verified against a comprehensive suite of numerical benchmark test cases in one and two space dimensions. The studied benchmark cases are divided into two categories: idealized tests for which exact solutions can be generated and tests for which the equivalent numerical results could be obtained using different approaches. The ability to simulate the Richtmyer-Meshkov instabilities, which are generated when a shock wave impacts an interface between two different fluids, is considered as a major challenge for the present numerical techniques. The study presents the effect of density ratio of constituent fluids on the resolution of an interface and the ability to simulate Richtmyer-Meshkov instabilities by various variants of diffuse interface methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献