We study the static Einstein equation coupled with a scalar field with axial symmetry. The zero curvature equation both for the scalar field and a part of the metric in the scalar-Einstein equation enables one to obtain soliton solutions for both the scalar field and the metric. Of the infinite series of solutions for the metric and the scalar field we focus on the solution composed of 4-solito...

Abstract. Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equations. Finite difference schemes for the ap...

We consider a D-dimensional cosmological model describing an evolution of (n+1) Einstein factor spaces (n ≥ 2) in the theory with several dilatonic scalar fields and generalized electro-magnetic forms, admitting an interpretation in terms of intersecting p-branes. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system...

Carbon nanotube field-effect transistors (CNTFETs) have been studied in recent years as a potential alternative to CMOS devices, because of the capability of ballistic transport. In order to account for the ballistic transport we solved the coupled Poisson and Schrödinger equations for the analysis these devices. Conventionally the coupled Schrödinger-Poisson equation is solved iteratively, by ...

Using exact results from the theory of completely integrable systems of the Painlevé/Toda type, we examine the consequences for the theory of polyelectrolytes in the (nonlinear) Poisson-Boltzmann approximation.

A parallel electrostatic Poisson’s equation solver coupled with parallel adaptive mesh refinement (PAMR) is developed in this paper. The three-dimensional Poisson’s equation is discretized using the Galerkin finite element method using a tetrahedral mesh. The resulting matrix equation is then solved through the parallel conjugate gradient method using the non-overlapping subdomain-by-subdomain ...

We revisit the non-linear BPS equation: the Dirac monopole of the Born-Infeld theory in the B-field background. The rotation used in our previous papers to discuss the scalar field by transforming the BPS equation into a linear one is extended to the case of gauge field. We also find that this transformation is a symmetry of the action. Moreover using the Legendre-dual formalism we present a si...

A novel boundary integral equation (BIE) is developed for eddy-current nondestructive evaluation problems with surface crack under a uniform applied magnetic field. Once the field and its normal derivative are obtained for the structure in the absence of cracks, normal derivative of scattered field on the conductor surface can be calculated by solving this equation with the aid of method of mom...

Non-linear field equations such as the KPZ equation for deposition and the Navier-Stokes equation for hydrodynamics are discussed by the derivation of transport equations for the correlation function of the field h (r, t), i.e. 〈h (r, t)h (r′, t ′)〉, where h satisfies a diffusion equation driven by a noise, f , defined as noise with a given spectrum, and containing a non linear term, Mhh, which...

We analyze the electromagnetic scattering of massive particles with and without spin wherein one particle (or both) is electrically neutral. Using the techniques of effective field theory, we isolate the leading long distance effects, both classical and quantum mechanical. For spinless systems results are identical to those obtained earlier via more elaborate dispersive methods. However, we als...