Search results for "partial differential equation"
showing 10 items of 326 documents
Computer simulations of hydrogen spectral line shapes in dense plasmas
2002
A new formalism has been elaborated for calculations of hydrogen line profiles emitted by dense plasmas. The main equation of this formalism has a similar form to a set of close-coupled, time-dependent partial differential equations. Calculated line shapes are broadened, shifted and asymmetrical. The formalism yields both shifts and widths of a line calculated within the same theoretical approach. A new basis of the appropriate subspace of the Hilbert space has been built. This basis gives an accurate description of the quadratic Stark effect, and the interaction of the emitter with field gradients. The computer simulation has been used to determine the emitter perturbations by electrons an…
Evolution of the electron distribution function in intense laser-plasma interactions
1994
We report a numerical investigation of the time evolution of the electron distribution function (EDF) in a laser-embedded, fully ionized plasma. A distinctive feature of the calculations is removal of the frequently adopted assumption of small anisotropy of the EDF in velocity space. This requires solving a two-dimensional partial differential equation for the EDF. Within the adopted range of parameters, the EDF undergoes significant changes. An initially isotropic EDF transforms rapidly into an anisotropic one characterized by a longitudinal velocity scale larger than the perpendicular one. This longitudinal stretching persists for several cycles of the radiation field, implying the establ…
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.
Stochastic Kinetics with Wave Nature
2003
We consider stochastic second-order partial differential equations. We indroduce a noisy non-linear wave equation and discuss its connections, in particular via the Lorentz transformation, with known stochastic models.
Non-classical Velocity Statistics in Counterflow Quantum Turbulence
2014
In this work we analyse the statistical distribution of turbulent superfluid velocity components in a He II counterflow channel, via two-dimensional numerical simulations pre- sented in past studies. The Probability Density Functions (PDFs) of the superfluid velocity components are investigated at lengthscales smaller than the average intervortex spacing, for varying vortex densities and different wall-normal distances. The results obtained con- firm the non-classical signature of quantum turbulence already observed in past numerical studies.
A posteriori estimates for a coupled piezoelectric model
2017
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
Dynamics of mean-field spin models from basic results in abstract differential equations
1992
The infinite-volume limit of the dynamics of (generalized) mean-field spin models is obtained through a direct analysis of the equations of motion, in a large class of representations of the spin algebra. The resulting dynamics fits into a general framework for systems with long-range interaction: variables at infinity appear in the time evolution of local variables and spontaneous symmetry breaking with an energy gap follows from this mechanism. The independence of the construction of the approximation scheme in finite volume is proven. © 1992 Plenum Publishing Corporation.
Analysis of equations arising in gyrotron theory
2012
The gyrotron is a microwave source whose operation is based on the stimulated cyclotron radiation of electrons oscillating in a static magnetic field. Powerful gyrotrons can be used to heat nuclear fusion plasma. In addition, they have found a wide utility in plasma diagnostics, plasma chemistry, radars, extra-high-resolution spectroscopy, high-temperature processing of materials, medicine, etc. However, the main application of gyrotrons is in electron cyclotron resonance heating in tokamaks and stellarators. Equations describing gyrotron operation are ordinary differential equations and Schrödinger type partial differential equations. The present paper provides a survey of the analytical a…
Electrokinetic Phenomena Revisited: A Lattice—Boltzmann Approach
2003
The Lattice-Boltzmann method (LBM) is an efficient tool to solve the Navier-Stokes equations. Based on this method we have developed a scheme to investigate electrokinetic phenomena in charged colloidal suspensions. The equations of motion that are solved are the so-called electrokinetic equations, i.e. a set of partial differential equations that couple the gradient of the electrostatic potential to the hydrodynamic flow by means of a mean field theory. These equations have been extensively used to study electroviscous phenomena for the limit of a weakly charged sphere in an unbounded electrolyte. We demonstrate that our method can be applied beyond these limit. As an example we discuss th…
Coupled Multi-Field Continuum Methods for Porous Media Fracture
2015
The focus of the present contribution is on the numerical modelling of hydraulic fracture in fluid-saturated heterogeneous materials, which can be carried out on a macroscopic scale using extended continuum porous media theories. This accounts for the crack nucleation and propagation, deformation of the solid matrix and change in the flow of the interstitial fluid. In particular, fluid-saturated porous materials basically represent volumetrically interacting solid-fluid aggregates, which are modelled using the Theory of Porous Media. The hydraulic- or tension-induced fracture occurs in the solid matrix and is simulated using a diffusive phase-field modelling approach. This way of fracture t…