Search results for "Equations"
showing 10 items of 955 documents
Soil ionization in earth electrodes by a finite difference time domain scheme
2004
This paper proposes a finite difference time domain numerical scheme devoted to analyze the transient behavior of earth electrodes during the soil breakdown that can take place when a surge current has to be drained. To this aim, Maxwell's equations together with a space-time variable resistivity function are used. The model has been validated by comparing the computed results with data available in the technical literature. Simulation results related to complex earth electrodes of limited extension are reported. Electrodes of larger extension can be easily simulated but requiring more computational resources.
Waves on a vortex filament: exact solutions of dynamical equations
2014
In this paper we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated…
CONDENSATE FRACTION IN THE DYNAMIC STRUCTURE FUNCTION OF BOSE FLUIDS
2007
We present results on the behavior of the dynamic structure function in the short wave length limit using the equation of motion method. The one-body continuity equation defines the self-energy, which becomes a functional of the fluctuating two-body correlation function. We evaluate the self-energy in this limit and show that sum rules up to the second moment, which requires the self-energy in the short wave length limit and zero frequency to be proportional to the kinetic energy per particle, are exactly satisfied. We compare our results with the impulse approximation and calculate the condensate fraction. An analytic expression for the momentum distribution is also derived.
Kohn–Sham energy decomposition for molecules in a magnetic field
2018
We study the total molecular electronic energy and its Kohn–Sham components within the framework of magnetic-field density-functional theory (BDFT), an alternative to current-dependent density-functional theory (CDFT) for molecules in the presence of magnetic fields. For a selection of closed-shell dia- and paramagnetic molecules, we investigate the dependence of the total electronic energy and its Kohn–Sham components on the magnetic field. Results obtained from commonly used density-functional approximations are compared with those obtained from Lieb optimizations based on magnetic-field dependent relaxed coupled-cluster singles-and-doubles (CCSD) and second-order Moller–Plesset (MP2) den…
Spinorial formulation of the GW-BSE equations and spin properties of excitons in two-dimensional transition metal dichalcogenides
2021
In many paradigmatic materials, such as transition metal dichalcogenides, the role played by the spin degrees of freedom is as important as the one played by the electron-electron interaction. Thus an accurate treatment of the two effects and of their interaction is necessary for an accurate and predictive study of the optical and electronic properties of these materials. Despite the fact that the GW-BSE approach correctly accounts for electronic correlations, the spin-orbit coupling effect is often neglected or treated perturbatively. Recently, spinorial formulations of GW-BSE have become available in different flavors in material-science codes. However, an accurate validation and comparis…
Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation
2004
In this paper we, to our knowledge, for the first time obtain the rate equations for Zeeman coherences in the broad line approximation and steady-state balance equations directly from optical Bloch equations without the use of the perturbation theory. The broad line approximation allows us to use the adiabatic elimination procedure in order to eliminate the optical coherences from the optical Bloch equations, but the steady-state condition allows us to derive the balance equations straightforward. We compare our approach with the perturbation theory approach as given previously and show that our approach is more flexible in analyzing various experiments. Meanwhile we also show the validity …
Electric field induced hyperfine level-crossings in (nD)Cs at two-step laser excitation: experiment and theory
2005
The pure electric field level-crossing of m_F Zeeman sublevels of hyperfine F levels at two-step laser excitation was described theoretically and studied experimentally for the nD_3/2 states in Cs with n = 7,9, and 10, by applying a diode laser in the first 6S_1/2 to 6P_3/2 step and a diode or dye laser for the second 6P_3/2 to nD_3/2 step. Level-crossing resonance signals were observed in the nD_3/2 to 6P_1/2 fluorescence. A theoretical model was developed to describe quantitatively the resonance signals by correlation analysis of the optical Bloch equations in the case when an atom simultaneously interacts with two laser fields in the presence of an external dc electric field. The simulat…
Relativistic transport equations with generalized mass shell constraints
1999
We reexamine the derivation of relativistic transport equations for fermions when conserving the most general spinor structure of the interaction and Green function. Such an extension of the formalism is needed when dealing with {\it e.g.} spin-polarized nuclear matter or non-parity conserving interactions. It is shown that some earlier derivations can lead to an incomplete description of the evolution of the system even in the case of parity-conserving, spin-saturated systems. The concepts of kinetic equation and mass shell condition have to be extended, in particular both of them acquire a non trivial spinor structure which describe a rich polarization dynamics.
Catastrophic process of coherence degradation
2018
We predict a catastrophic process of coherence degradation characterized by a virtually unlimited spectral broadening of the waves. This effect is described by self-similar solutions of the kinetic equations inherent to the wave turbulence theory.
A posteriori estimates for a coupled piezoelectric model
2017
Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)