Gyro-kinetic simulation of charge separation and velocity shear at a plasma edge

Two numerical codes have been developed to study the existence and evolution of a charge separation at a plasma edge. In the first code, the finite gyro-radius guiding center approximation, which also includes the polarisation drift, is used to describe the ions, and a gyro-kinetic equation is used for the electrons. In the second code, both ions and electrons are treated with gyro-kinetic equations. The effect of a small dissipation term on the solution is studied.     

The self-consistent response of the electron density of a crystal copper film to an external electrostatic field

The response of the electrons of an fcc copper (001) film to an external electrostatic field is calculated. In order to determine the distribution of the screening charge, the equations of the electron density-functional theory are solved self-consistently by an original method. The position of the “image plane,” which is involved in a correct asymptotic expression for the exchange-correlation potential in the vacuum region, is first determined when performing a quantum-mechanical calculation for an anisotropic crystal film. The nonlinear electron response is characterized by the evolution of the “center of gravity” of the induced charge, which is also investigated. The calculations take into account the crystal structure of the film, and the results differ essentially from the predictions of the “jelly” model.     

On the physical interpretation of asymptotically flat gravitational fields

A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum, i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the form of a conservation law is found. Third Award in the 2008 Essay Competition of the Gravity Research Foundation.     

Kicked quantum circuits with charge discreteness: Resonance condition

In this work we study a quantum electrical circuit with charge discreteness perturbed by periodic external kicks. Time evolution equations, for energy and electrical current, are solved analytically. Time evolution fluctuations are also studied and they become bounded. Resonances are well characterized including arbitrary (generic) quantum circuits with charge discreteness.     

Sources of gravitational waves in asymptotically flat Einstein-Maxwell spacetime

In this work, the dynamic of isolated systems in general relativity is described when gravitational radiation and electromagnetic fields are present. In this construction, the asymptotic fields received at null infinity together with the regularized null cone cuts equation, and the center of mass of an asymptotically flat Einstein-Maxwell spacetime are used. A set of equations are derived in the low speed regime, linking their time evolution to the emitted gravitational radiation and to the Maxwell fields received at infinity. These equations should be useful when describing the dynamic of compact sources, such as the final moments of binary coalescence and the evolution of the final black hole. Additionally, we compare our equations with those coming from a similar approach given by Newman, finding some differences in the motion of the center of mass and spin of the gravitational system.     

Direct numerical simulation of electrohydrodynamic plumes generated by a hyperbolic blade electrode

This paper presents a numerical study of two-dimensional EHD flow occurring between a hyperbolic blade and a plate electrode. The whole set of coupled equations is solved: Navier–Stokes equations, Poisson equation and charge conservation equation. A finite volume approach designed for non-orthogonal structured grid is used to discretize all governing equations. An efficient numerical procedure based on total variation diminishing (TVD) scheme is implemented to compute the distribution of charge density. Two different injection laws are considered: a simple autonomous one and a non autonomous which relates the charge injected by the blade and the local electric field. The flow structure which results in an EHD plume analogous to a thermal plume, has also been successfully characterized numerically by the temporal evolution of the charge density distribution. Preliminary results indicate that the flow is characterized by two different regimes according the value of the applied voltage. The critical Reynolds number for which the transition between the steady and unsteady regimes occurs has been determined to be within the range Re = [1000, 1100].     

Cosmological solutions with charged black holes

We consider the problem of constructing cosmological solutions of the Einstein–Maxwell equations that contain multiple charged black holes. By considering the field equations as a set of constraint and evolution equations, we construct exact initial data for N charged black holes on a hypersphere. This corresponds to the maximum of expansion of a cosmological solution, and provides sufficient information for a unique evolution. We then consider the specific example of a universe that contains eight charged black holes, and show that the existence of non-zero electric charge reduces the scale of the cosmological region of the space. These solutions generalize the Majumdar–Papapetrou solutions away from the extremal limit of charged black holes, and provide what we believe to be some of the first relativistic calculations of the effects of electric charge on cosmological backreaction.     

Charge and spin dynamics of interacting fermions in a one-dimensional harmonic trap

We study an atomic Fermi gas interacting through repulsive contact forces in a one-dimensional harmonic trap. Bethe-ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation, the edges cause a giant increase of the separation between these modes.     

Charge in cosmological models

The balanced field equations due to Penney are used to find solutions for cosmological models in the presence of charge. Herein, it is found that the introduction of charge adds additional terms to the Einstein conservation equation and distribution expressions. The curvature parameter is affected and it is concluded that whereas matter affects it positively, the charge does so negatively. There then arises also the possibility of an evolution of local systems against the background of a global expansion.     

Hamiltonian model of a free electron laser including high-density effects

Both the Compton and the Raman regimes of a free electron laser are described by a relativistic Hamiltonian which originates the evolution equations for 2N+2 canonically conjugate electron and field variables, with the space coordinate as the independent variable. Space charge and field contribution to electron transverse velocity are included.     

Structure scalars for charged cylindrically symmetric relativistic fluids

We investigate some structure scalars developed through Riemann tensor for self-gravitating cylindrically symmetric charged dissipative anisotropic fluid. We show that these scalars are directly related to the fundamental properties of the fluid. We formulate dynamical-transport equation as well as the mass function by including charge which are then expressed in terms of structure scalars. The effects of electric charge are investigated in the structure and evolution of compact objects. Finally, we show that all possible solutions of the field equations can be written in terms of these scalars.     

Evolution of Spiral Waves in Excitable Systems

Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.     

On the interaction between a charged drop and an external acoustic field

An interaction between capillary oscillations of a charged drop and an external acoustic field is investigated under conditions in which nonlinear components of the acoustic pressure on the drop surface may be neglected. It is shown that equations describing the temporal evolution of modes of the capillary waves in this case may be either the Mathieu-Hill equations or ordinary inhomogeneous equations of the second order describing forced oscillations. In both cases, the drop instability (of a parametric or resonance type) may result in its disintegration due to deformation caused by the acoustic field at its own drop charge, subcritical in the sense of the Rayleigh criterion.     

Exact partial solutions for the surface dynamics of a dielectric liquid with a charged surface in the gravitational field

We study the evolution of instability in the boundary of a perfect dielectric liquid with a free surface charge in an external electric field. Conformal variables are used to find exact partial solutions to the equations of motion for the case when the charge completely shields the field above the liquid, the electrostatic and gravitational forces being taken into account. The solutions describe the development of instability of the initially planar boundary until sharp dimples are formed on it.     

金属/掺杂聚合物/金属结构中载流子的注入与输运

基于紧束缚的Su-Schrieffer-Heeger模型,利用非绝热的动力学方法,研究了金属/聚合物/金属三明治结构中载流子注入与输运的动力学过程,其中,聚合物中含有一个掺杂离子. 电子波函数随时间的演化满足含时Schrdinger方程,晶格运动满足经典的牛顿运动方程. 研究发现,掺杂离子对注入到聚合物中的载流子的作用类似一个控制阀门,阀门的状态与电场的强度和偏压的大小密切相关. 关键词： 载流子输运 波包 非绝热动力学     

The Functional Callan-Symanzik Equation for the Coulomb Gas

A non-perturbative scheme, based on the functional generalization of the Callan-Symanzik equation is developed to treat the Coulomb interaction in an electron gas. The one-particle irreducible vertex functions are shown to satisfy an evolution equation whose initial condition is given by means of the classical action and the final point corresponds to the physical system. This equation is truncated by expanding it in momenta and excitation energies, leaving the electric charge as an arbitrary, not necessarily small parameter. Exact coupled partial differential equations up to first order in the frequencies and excitation energies are derived. The numerical integration of these equations is left to a later stage. Nevertheless, in order to demonstrate the relation with the perturbation expansion the one-loop Lindhard function and screening are reproduced in the independent mode approximation of the evolution equation.     

Formation of singularities on the charged surface of a liquid-helium layer with a finite depth

The dynamics of the development of an instability of a charged surface of a liquid-helium layer with a finite depth is investigated. The equations describing the evolution of the free surface are derived with the use of conformal variables for the case in which the charge completely screens the electric field above the liquid. A model of the evolution of a spatially localized perturbation of a liquid-helium surface is proposed for the strong-field limit where the dynamics of the liquid is predominantly determined by the effect of electrostatic forces. This model describes the development of an instability of the initially planar boundary to the point of the formation of cuspidal dimples. The limit of an infinitely deep liquid is considered. The stability of the previously revealed liquid flow regime described by the Laplacian growth equations is proved without significant constraints on the surface geometry.     

Boson Nebulae Charge

We use the first-order approximate solutions to the nonlinear system of Klein-Gordon-Maxwell-Einstein equations describing the minimally coupled charged spin-less field to a spherically symmetric spacetime to analyze a becoming boson star. In the far future and long-range approximation, we derive an analytical time-dependent charge which allows us to point out several significant moments in the evolution of the boson nebula.     

Numerical Simulation of Plasma Edge Turbulence Due to E×B Flow Velocity Shear

A numerical code is used to study the nonlinear evolution of the Kelvin-Helmholtz instability, and the existence and time evolution of a charge separation with the self-consistent electric field at a plasma edge. Both ions and electrons are described by gyrokinetic equations that include the ions finite Larmor radius correction and the polarization drift. We present results for the case where the plasma layer is two-dimensional, and the magnetic field makes an angle very close to the normal to the plane of the plasma. At = 88.5°, the nonlinear evolution of the Kelvin-Helmholtz instability shows a spectrum which is turbulent and is dominated by higher harmonics, saturates at low level and has little effect on the electrons and ions initial equilibrium density profiles. At an angle of the magnetic field closer to 90°, when the component of the motion of the electrons along the magnetic field decreases, the behavior is in accordance with some basic physics associated with the set of equations describing the behavior of a guiding center plasma in a strong magnetic field, namely the energy condensing in the lowest k modes (inverse cascades). The results show the sensitivity of the turbulent spectrum to the motion of the electrons along magnetic field lines. In particular, we study the effect of different algorithms to compute this sensitive electrons motion, and their effect on the turbulent spectrum. We show that Eulerian Vlasov codes associated with cubic spline interpolations perform favorably when compared to other methods.