Search results for "Mathematical analysis"

A marching-on in time meshless kernel based solver for full-wave electromagnetic simulation

2012

A meshless particle method based on an unconditionally stable time domain numerical scheme, oriented to electromagnetic transient simulations, is presented. The proposed scheme improves the smoothed particle electromagnetics method, already developed by the authors. The time stepping is approached by using the alternating directions implicit finite difference scheme, in a leapfrog way. The proposed formulation is used in order to efficiently overcome the stability relation constraint of explicit schemes. In fact, due to this constraint, large time steps cannot be used with small space steps and vice-versa. The same stability relation holds when the meshless formulation is applied together w…

Fourier integral operators and inhomogeneous Gevrey classes

1988

Fourier integral operators with inhomogeneous amplitude and phase junction are studied in the frame of Gevrey classes. Applications are given to propagation of singularities for a pseudodifferential equation.

Zero Viscosity Limit for Analytic Solutions of the Primitive Equations

2016

The aim of this paper is to prove that the solutions of the primitive equations converge, in the zero viscosity limit, to the solutions of the hydrostatic Euler equations. We construct the solution of the primitive equations through a matched asymptotic expansion involving the solution of the hydrostatic Euler equation and boundary layer correctors as the first order term, and an error that we show to be \({O(\sqrt{\nu})}\). The main assumption is spatial analyticity of the initial datum.

Analytische Geometrie nach Prof. Dr. F. Schur

1892

Physical model, theoretical aspects and applications of the flight of a ball in the atmosphere. Part III: Theory in the case of vertical angular freq…

1995

If a ball is viewed as a rigid body, its flight in the atmosphere can be described by six ordinary differential equations, which has been derived in the first part of this paper. In this following third part, some further theoretical aspects in the case of vertical angular frequency will be pointed out using an unknown transformation of the original independent variable, i.e. the time, as indicated in Part II. Last, but not least, the general case of angular frequency is to be treated. A rough qualitative discussion of the solutions is given as well as—if the equations are viewed as a three-dimensional dynamical system—the unique stable equilibrium, which depends on the spin. This equilibri…

Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media

2009

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…

A second strain gradient elasticity theory with second velocity gradient inertia – Part II: Dynamic behavior

2013

Abstract This paper is the sequel of a companion Part I paper devoted to the constitutive equations and to the quasi-static behavior of a second strain gradient material model with second velocity gradient inertia. In the present Part II paper, a multi-cell homogenization procedure (developed in the Part I paper) is applied to a nonhomogeneous body modelled as a simple material cell system, in conjunction with the principle of virtual work (PVW) for inertial actions (i.e. momenta and inertia forces), which at the macro-scale level takes on the typical format as for a second velocity gradient inertia material model. The latter (macro-scale) PVW is used to determine the equilibrium equations …

A gradient elasticity theory for second-grade materials and higher order inertia

2012

Abstract Second-grade elastic materials featured by a free energy depending on the strain and the strain gradient, and a kinetic energy depending on the velocity and the velocity gradient, are addressed. An inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics. The state variables include the body momentum and the surface momentum, related to the velocity in a nonstandard way, as well as the concomitant mass-accelerations and inertial forces, which do intervene into the motion equations and into the force boundary conditions. The boundary traction is the …

Diffusion Acceleration in Randomly Switching Sawtooth Potential

2005

We investigate an overdamped Brownian motion in symmetric sawtooth periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ each other by a translation of half of period. The calculation of the effective diffusion coefficient is reduced to the mean first‐passage time problem, and we obtain the exact expression valid for arbitrary mean rate of switchings and arbitrary intensity of white Gaussian noise. We find the area at parameters plane where acceleration of diffusion in comparison with the free diffusion case takes place.

Wulff shape characterizations in overdetermined anisotropic elliptic problems

2017

We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.