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...

Boltzmann Transport Equation [1-2] has been modelled in close conjunction with Maxwell’s equation, investigations for 2D and 3D transport carriers have been proposed. Exact solution of Boltzmann Equation still remains the core field of research. We have worked towards evaluation of 2D and 3D solutions of BTE. Application of our work can be extended to study the electromagnetic wave transport in...

Based on the coupling between the spin of a particle and gravitoelectromagnetic field, the equation of motion of a spinning test particle in gravitational field is deduced. From this equation of motion, it is found that the motion of a spinning particle deviates from the geodesic trajectory, and this deviation originates from the coupling between the spin of the particle and gravitoelectromagne...

We study the stationary Kac equation in the presence of an external force field and a Gaussian thermostat, and investigate the behavior of a solution to this equation for varying field strength. We prove that for a weak field, the stationary density is continuous, but for a strong field the density has a singularity. Monte Carlo simulations illustrating the same are also presented.