Search results for "Mathematical analysis"
showing 10 items of 2409 documents
A 3D Meshless Approach for Transient Electromagnetic PDEs
2012
A full wave three dimensional meshless approach for electromagnetic transient simulations is presented. The smoothed particle hydrodynamic (SPH) method is used by considering the particles as interpolation points, arbitrarily placed in the computational domain. Maxwell’s equations in time domain with the assigned boundary and initial conditions are numerically solved by means of the proposed method. The computational tool is assessed and, for the first time, a 3D test problem is simulated in order to validate the proposed approach.
Characteristic structure of the resistive relativistic magnetohydrodynamic equations
2012
We present the analysis of the characteristic structure of the resistive (non-ideal) relativistic magnetohydrodynamics system of equations. This is a necessary step to develop high-resolution shock-capturing schemes that use the full characteristic information (Godunov-type methods), and it is convenient to establish proper boundary conditions.
An Exact Riemann Solver for Multidimensional Special Relativistic Hydrodynamics
2001
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics (Marti and Muller, 1994) for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. This solution has been used to build up an exact Riemann solver implemented in a multidimensional relativistic (Godunov-type) hydro-code.
On the saddle loop bifurcation
1990
It is shown that the set of C∞ (generic) saddle loop bifurcations has a unique modulus of stability γ ≥]0, 1[∪]1, ∞[ for (C0, Cr)-equivalence, with 1≤r≤∞. We mean for an equivalence (x,μ) ↦ (h(x,μ), ϕ(μ)) with h continuous and ϕ of class Cr. The modulus γ is the ratio of hyperbolicity at the saddle point of the connection. Already asking ϕ to be a lipeomorphism forces two saddle loop bifurcations to have the same modulus, while two such bifurcations with the same modulus are (C0,±Identity)-equivalent.
The threshold behaviour of partial wave scattering amplitudes and theN/D-method
1964
It is shown that in partial wave dispersion relations the weight function on the unphysical cut must have a certain number of zeros in order to permit the correct threshold behaviour of the amplitude. Assuming a solution — not necessarily with correct threshold behaviour — of the once-subtractedN/D-equations to exist, the role of the subtraction parameters in repeatedly subtractedN/D equations is studied with particular reference to the threshold behaviour.
Shape Optimization in Contact Problems. 1. Design of an Elastic Body. 2. Design of an Elastic Perfectly Plastic Body
1986
The optimal shape design of a two dimensional body on a rigid foundation is analyzed. The problem is how to find the boundary part of the body where the unilateral boundary conditions are assumed in such a way that a certain energy integral (total potential energy, for example) will be minimized. It is assumed that the material of the body is elastic. Some remarks will be given concerning the design of an elastic perfectly plastic body. Numerical examples will be given.
An extended Ritz formulation for buckling and post-buckling analysis of cracked multilayered plates
2018
Abstract An extended Ritz formulation for the analysis of buckling and post-buckling behaviour of cracked composite multilayered plates is presented. The formulation is based on: (i) the First-order Shear Deformation Theory to model the mechanics of the multilayered plate; (ii) the von Karman’s theory to account for geometric non-linearities ; (iii) the use of an extended set of approximating functions able to model the presence of an embedded or edge crack and to capture the crack opening fields as well as the global behaviour within a single cracked domain. The numerical results of the buckling analyses and the equilibrium paths in the post-buckling regime are compared with the results fr…
The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics
2000
We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution on the tangential velocities is analysed, and the impact of this result on the development of multidimensional relativistic hydrodynamic codes (of Godunov type) is discussed.
Analytical investigation of solitary waves in nonlinear Kerr medium
2004
Abstract We study analytically the solution of nonlinear equation which result from the propagation of electromagnetic waves within a nonlinear Kerr medium. The medium is characterized by a dielectric constant which varies periodically and depends on the local field intensity. As a first step, we detail the resolution of the nonlinear equations with a quadratic nonlinearity. After that, we apply the slowly varying envelope approximation to obtain a Sine–Gordon equation. In this kind of nonlinearity, a gap solitons occurs. Moreover we verify that the solutions of the nonlinear equation for all frequencies within the gap are solitons solutions. After that we study the conditions of apparition…
Non-stationary spectral moments of base excited MDOF systems
1988
The paper deals with the evaluation of non-stationary spectral moments of multi-degree-of-freedom (MDOF) line systems subjected to seismic excitations. The spectral moments of the response are evaluated in incremental form solution by means of an unconditionally stable step-by-step procedure. As an application, the statistics of the largest peak of the response are also evaluated.