Thermodynamics of strange quark matter with the density-dependent bag constant

The thermodynamics of strange quark matter with density dependent bag constant are studied self-consistently in the framework of the general ensemble theory and the MIT bag model.In our treatment,an additional term is found in the expression of pressure.With the additional term,the zero pressure locates exactly at the lowest energy state,indicating that our treatment is a self-consistently thermodynamic treatment.The self-consistent equations of state of strange quark matter in both the normal and color-fla...     

The covariant form of the Klein-Kramers equation and the associated moment equations

We provide a covariant, coordinate-free formulation of the many-dimensional Klein-Kramers equation for the phase space distribution of a Brownian particle. We construct a complete set of eigenfunctions of the collision operator adapted to the coordinate system, which involve covariant tensorial Hermite polynomials. The Klein-Kramers equation can then be reformulated as a system of coupled equations for the expansion coefficients with respect to this system. Truncation of this system of moment equations and application of a subsidiary condition yields a covariant generalization of Grad's thirteen-moment equations. As an application we give the explicit form of these equations for spherically symmetric, stationary solutions in spherical coordinates. We briefly comment on possible extensions of our treatment to slightly more complicated cases.     

The immersed boundary method for advection–electrodiffusion with implicit timestepping and local mesh refinement

We describe an immersed boundary method for problems of fluid–solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection–electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties.     

INTEGRABILITY OF LIE SYSTEMS THROUGH RICCATI EQUATIONS

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyze a geometric method to construct integrability conditions for Riccati equations following these approaches. Our procedure provides us with a unified geometrical viewpoint that allows us to analyze some previous works on the topic and explain new properties. Moreover, this new approach can be straightforwardly generalized to describe integrability conditions for any Lie system. Finally we show the usefulness of our treatment in order to study the problem of the linearizability of Riccati equations.     

A finite difference scheme for fractional sub-diffusion equations on an unbounded domain using artificial boundary conditions

One-dimensional fractional anomalous sub-diffusion equations on an unbounded domain are considered in our work. Beginning with the derivation of the exact artificial boundary conditions, the original problem on an unbounded domain is converted into mainly solving an initial-boundary value problem on a finite computational domain. The main contribution of our work, as compared with the previous work, lies in the reduction of fractional differential equations on an unbounded domain by using artificial boundary conditions and construction of the corresponding finite difference scheme with the help of method of order reduction. The difficulty is the treatment of Neumann condition on the artificial boundary, which involves the time-fractional derivative operator. The stability and convergence of the scheme are proven using the discrete energy method. Two numerical examples clarify the effectiveness and accuracy of the proposed method.     

The dipolar plasmon modes of a small metallic sphere

We consider here a treatment of the dipolar plasmon of a small metallic sphere, for which the radial extension of the surface profile is small compared with the radius of the sphere. We obtain the eigenvalues and damping by solving the classical equations for a non-uniform system. The theory is applicable also to the driven response. We compare our results with those recently reported by Apell and Ljungbert.     

Relation between the projection operator formalism and the Faddeev theory

In an earlier paper it was shown by means of the Faddeev equations that the reduction of the three-body problem to formal two-body equations with energy-dependent complex potentials — a procedure which was already well known for separable potentials — can be generalized rigorously to arbitrary potentials. In the present paper we show that the projection operator approach of Feshbach appears as a special, and in a certain sense singular case of our general treatment. Optical potentials for rearrangement scattering are given explicitly and questions of how to calculate them are discussed, showing that the Faddeev approach is better suited in these respects.     

Mode-coupling theory for the lattice dynamics of anharmonic crystals: self-consistent damping and the 1d Lennard-Jones chain

We present a self-consistent theory for the dynamical one-phonon structure factor in anharmonic crystals. The theory is the phonon analogue of the mode-coupling theory of liquid dynamics of Götze and his coworkers. Starting point is the lattice dynamics treatment based on the Mori- Zwanzig technique as formulated by Götze and Michel. We apply the theory to the one-dimensional (1d) Lennard-Jones chain and show that the nonlinear mode-coupling equations can be readily solved in the time domain. The vertices entering the equations as input are calculated exactly by a Monte Carlo technique. We compare our findings with molecular dynamics (MD) simulations and the results of other theoretical approaches.     

Diffusive and dynamical radiating stars with realistic equations of state

We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.     

Some charged polytropic models

The Einstein–Maxwell equations with anisotropic pressures and electromagnetic field are studied with a polytropic equation of state. New exact solutions to the field equations are generated in terms of elementary functions. Special cases of the uncharged solutions of Feroze and Siddiqui (Gen Relativ Gravit 43:1025, 2011) and Maharaj and Mafa Takisa (Gen Relativ Gravit 44:1419, 2012) are recovered. We also obtain exact solutions for a neutral anisotropic gravitating body for a polytrope from our general treatment. Graphical plots indicate that the energy density, tangential pressure and anisotropy profiles are consistent with earlier treatments which suggest relevance in describing relativistic compact stars.     

A self-consistent master equation and a new kind of cumulants

Generalized master equations correspond to different kinds of cumulants. Here, we discuss the recently introduced non-crossing cumulants from a physical point of view and propose the corresponding integro-differential master equation as a new type of equation for a self-consistent treatment of memory effects. We prove the cluster property of the non-crossing cumulants, and show that the Gaussian approximation of our equation is given by a random matrix process. As an instructive example for our expansion formula we treat the random frequency-modulated oscillator.     

A dynamics-controlled truncation scheme for the hierarchy of density matrices in semiconductor optics

We discuss the interaction of coherent electromagnetic fields with the semiconductor band edge in a dynamic density matrix model. Due to the influence of the Coulomb-interaction then-point density matrices are coupled in an infinite hierarchy of equations of motion. We show how this hierarchy is related to an expansion of the density matrices in terms of powers of the exciting field. We make use of the above results to set up a closed set of equations of motion involving two-, four-and six-point correlation functions, from which all third order contributions to the polarization can be calculated exactly. Comparison of our treatment of the hierarchy with the widely used RPA decoupling on the two-point level, gives interesting insight into the validity of the RPA. In particular we find, that a RPA-like factorization for two of the relevant density-matrices yields a solution of their respective equations of motion to lowest order in the electric field.     

Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients

In this paper, we propose a variational integrator for nonlinear Schrdinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrdinger equations with variable coefficients, cubic nonlinear Schrdinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.     

Matrix Computations for the Dynamics of Fermionic Systems

In a series of recent papers we have shown how the dynamical behavior of certain classical systems can be analyzed using operators evolving according to Heisenberg-like equations of motions. In particular, we have shown that raising and lowering operators play a relevant role in this analysis. The technical problem of our approach stands in the difficulty of solving the equations of motion, which are, first of all, operator-valued and, secondly, quite often nonlinear. In this paper we construct a general procedure which significantly simplifies the treatment for those systems which can be described in terms of fermionic operators. The proposed procedure allows to get an analytic solution, both for quadratic and for more general hamiltonians.     

A new calculation method for a thin electric dipole

We consider a new approach to the analysis of a thin electric dipole. The approach, which is unconventional in antenna theory, is based directly on the Maxwell equations written in the cylindrical coordinate system. This allows one to reduce the problem to an integral equation instead of an integro-differential equation. Another feature of our treatment is the use of the theory of singular integral equations (SIEs) developed previously for SHF and EHF slotted-strip structures. The problem is reduced to solving the SIE for the derivative of the surface-current density on the dipole with respect to the longitudinal coordinate. The results of numerical analysis demonstrate fast convergence of the method and simplicity of calculations. Volga State Academy of Telecommunications and Information Sciences, Samara, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 4, pp. 335–344, September, 2000     

Numerical solutions of the orbital equations for diatomic molecules

A basis of Hermite splines is used in conjunction with the collocation method to solve the orbital equations for diatomic molecules. Accurate solutions of the Hartree-Fock equations are obtained using iterative methods over most regions of space, while solving the equations by Gaussian elimination near the nuclear centres. In order to improve the speed and accuracy of our iterative scheme, a new self-adjoint form of the Hartree-Fock equation is derived. Using this new equation, our iterative subroutines solve the Hartree-Fock equations to one part in 10⁶. The Gaussian elimination routines are accurate to better than one part in 10⁸.     

On geometric approach to Lie symmetries of differential-difference equations

Based upon Cartan's geometric formulation of differential equations, Harrison and Estabrook proposed a geometric approach for the symmetries of differential equations. In this Letter, we extend Harrison and Estabrook's approach to analyze the symmetries of differential-difference equations. The discrete exterior differential technique is applied in our approach. The Lie symmetry of (2+1)-dimensional Toda equation is investigated by means of our approach.     

深层地下不稳定流温度场的数值模拟

本文给出一个深层地下不稳定流温度场的数学模型,它把三维空间中的两个耦合的传导(对流)问題,归化为一个传导对流型的积微分方程。为节约数值求解时的计算量和存贮量,文中还特别讨论了后者在时间方向上的离散格式,并给出了数值例子。     

A finite element method for the numerical solution of the coupled Cahn–Hilliard and Navier–Stokes system for moving contact line problems

In this paper, a semi-implicit finite element method is presented for the coupled Cahn–Hilliard and Navier–Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn–Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier–Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples.