A simple prescription for computing the stress-energy tensor

A non-variational technique for computing the stress-energy tensor is presented. The prescription is used, among other things, to obtain the correct field equations for Prasanna's highly nonlinear electrodynamics.

Gap solitons in superfluid boson-fermion mixtures

Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic optical-lattice (OL) potential, the boson and fermion components being in the states of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer superfluid, respectively. Fundamental GSs are compact states trapped, essentially, in a single cell of the lattice. Full families of such solutions are constructed in the first two band gaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intragap and intergap solitons, with the chemical potentials of the boson and fermion components falling in the same or different band gaps, respectively. Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.

RELATIVISTIC 3-PARTICLE SCATTERING EQUATIONS

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.

SELF-CONSISTENT SOLUTION OF THE SCHWINGER-DYSON EQUATIONS FOR THE NUCLEON AND MESON PROPAGATORS

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.

SUPERSYMMETRY, VARIATIONAL METHOD AND HULTHEN POTENTIAL

The formalism of supersymmetric quantum mechanics provides us with the eigenfunctions to be used in the variational method to obtain the eigenvalues for the Hulthen potential.

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.

A W-matrix methodology for solving sparse network equations on multiprocessor computers

This paper describes a methodology for solving efficiently the sparse network equations on multiprocessor computers. The methodology is based on the matrix inverse factors (W-matrix) approach to the direct solution phase of A(x) = b systems. A partitioning scheme of W-matrix , based on the leaf-nodes of the factorization path tree, is proposed. The methodology allows the performance of all the updating operations on vector b in parallel, within each partition, using a row-oriented processing. The approach takes advantage of the processing power of the individual processors. Performance results are presented and discussed.

DISSIPATIVE BOUSSINESQ SYSTEM OF EQUATIONS IN THE BENARD-MARANGONI PHENOMENON

By using the long-wavelength approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a Benard-Marangoni system is obtained. It includes nonlinearity, dispersion, and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained.

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

Reformulation of variational inequalities on a simplex and compactification of complementarity problems

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple constraints and unconstrained reformulations based on the penalized Fischer-Burmeister function. It is proved that bounded level set results hold for these reformulations under quite general assumptions on the operator. Therefore, it can be guaranteed that minimization algorithms generate bounded sequences and, under monotonicity conditions, these algorithms necessarily nd solutions of the original problem. Some numerical experiments are presented.

Self-consistent equilibrium calculation through a direct variational technique in tokamak plasmas

A self-consistent equilibrium calculation, valid for arbitrary aspect ratio tokamaks, is obtained through a direct variational technique that reduces the equilibrium solution, in general obtained from the 2D Grad-Shafranov equation, to a 1D problem in the radial flux coordinate rho. The plasma current profile is supposed to have contributions of the diamagnetic, Pfirsch-Schluter and the neoclassical ohmic and bootstrap currents. An iterative procedure is introduced into our code until the flux surface averaged toroidal current density (J(T)), converges to within a specified tolerance for a given pressure profile and prescribed boundary conditions. The convergence criterion is applied between the (J(T)) profile used to calculate the equilibrium through the variational procedure and the one that results from the equilibrium and given by the sum of all current components. The ohmic contribution is calculated from the neoclassical conductivity and from the self-consistently determined loop voltage in order to give the prescribed value of the total plasma current. The bootstrap current is estimated through the full matrix Hirshman-Sigmar model with the viscosity coefficients as proposed by Shaing, which are valid in all plasma collisionality regimes and arbitrary aspect ratios. The results of the self-consistent calculation are presented for the low aspect ratio tokamak Experimento Tokamak Esferico. A comparison among different models for the bootstrap current estimate is also performed and their possible Limitations to the self-consistent calculation is analysed.

Supersymmetric variational energies for the confined Coulomb system

The methodology based on the association of the variational method with supersymmetric quantum mechanics is used to evaluate the energy states of the confined hydrogen atom. (C) 2002 Elsevier B.V. B.V. All rights reserved.