Search results for "equation"
showing 10 items of 4219 documents
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.
Nonlinear magneto-optical resonances atD1excitation ofR85bandR87bfor partially resolved hyperfineFlevels
2009
Experimental signals of nonlinear magneto-optical resonances at ${D}_{1}$ excitation of natural rubidium in a vapor cell have been obtained and described with experimental accuracy by a detailed theoretical model based on the optical Bloch equations. The ${D}_{1}$ transition of rubidium is a challenging system to analyze theoretically because it contains transitions that are only partially resolved under Doppler broadening. The theoretical model took into account all nearby transitions, the coherence properties of the exciting laser radiation, and the mixing of magnetic sublevels in an external magnetic field and also included averaging over the Doppler profile. The experimental signals wer…
A laboratory experiment on inferring Poiseuille's law for undergraduate students
2006
In this paper a laboratory experiment is proposed to infer Poiseuille's law. A simple set-up based on two flasks joined by a detachable tube allows one to measure using tubes of different radii and different lengths. One of the flasks is connected to a vacuum pump to control the pressure differential between the tube extremes. The influence on the flow of different radii, lengths, pressures and viscosities can be studied in a didactic way by measuring the flow rate for each of these variables. The experiment can be performed getting together the students in groups, so that each group concentrates on the effect on the flow of a specific variable, leaving the rest fixed. After putting togethe…
Type D vacuum solutions: a new intrinsic approach
2013
We present a new approach to the intrinsic properties of the type D vacuum solutions based on the invariant symmetries that these spacetimes admit. By using tensorial formalism and without explicitly integrating the field equations, we offer a new proof that the upper bound of covariant derivatives of the Riemann tensor required for a Cartan-Karlhede classification is two. Moreover we show that, except for the Ehlers-Kundt's C-metrics, the Riemann derivatives depend on the first order ones, and for the C-metrics they depend on the first order derivatives and on a second order constant invariant. In our analysis the existence of an invariant complex Killing vector plays a central role. It al…
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.
Numerical study of the stability of the Peregrine solution
2017
International audience; The Peregrine solution to the nonlinear Schrödinger equations is widely discussed as a model for rogue waves in deep water. We present here a detailed fully nonlinear numerical study of high accuracy of perturbations of the Peregrine solution as a solution to the nonlinear Schrödinger (NLS) equations.We study localized and nonlocalized perturbations of the Peregrine solution in the linear and fully nonlinear setting. It is shown that the solution is unstable against all considered perturbations.
Dynamics of a flexible ferromagnetic filament in a rotating magnetic field.
2017
Flexible magnetic filaments have garnered considerable attention as prospective materials for the creation of different microdevices. We describe a theoretical model of a ferromagnetic filament and derive its equations of motion by variational techniques. The numerical algorithm used to solve the filament dynamics in magnetic fields of different configurations is described. It is found that in a rotating field the filament transitions between synchronous and asynchronous regimes with respect to the rotating field, similarly to a rigid magnetic dipole. The mean angular velocity of the filament is well described by a relation valid for a rigid magnetic dipole with quantitative differences att…
Diffusion in active magnetic colloids
2013
Abstract Properties of active colloids of circle swimmers are reviewed. As a particular example of active magnetic colloids the magnetotactic bacteria under the action of a rotating magnetic field is considered. The relation for a diffusion coefficient due to the random switching of the direction of rotation of their rotary motors is derived on the basis of the master equation. The obtained relation is confirmed by the direct numerical simulation of random trajectory of a magnetotactic bacterium under the action of the Poisson type internal noise due to the random switching of rotary motors. The results obtained are in qualitative and quantitative agreement with the available experimental r…
Stochastic models for heterogeneous relaxation: Application to inhomogeneous optical lineshapes
2001
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale. Starting from the most simple Gaussian Markov process we model the exchange between 'slow' and 'fast' environments by treating the fluctuating single-particle variable as a projection from a higher-dimensional Markov process. The moments of the resulting stochastic process are calculated from the corresponding Master equations or Langevin equations, depending on the model. The calculations show the importance of the way to treat exchange processes. The result…
The Crossing Symmetric Bethe-Salpeter Equation
1972
As you may recall from the lectures of Prof. Sand-has [1], in non-relativistic quantum theory,the scattering amplitude satisfies the Lippmann-Schwinger equation, $$T = V + V{G_o}T$$ (1) It can be explicitly shown that if V=V+, T satisfies the elastic unitarity relation, Im T=TT+.