Search results for "Poisson's equation"

Metric-affine f(R,T) theories of gravity and their applications

2018

We study $f(R,T)$ theories of gravity, where $T$ is the trace of the energy-momentum tensor ${T}_{\ensuremath{\mu}\ensuremath{\nu}}$, with independent metric and affine connection (metric-affine theories). We find that the resulting field equations share a close resemblance with their metric-affine $f(R)$ relatives once an effective energy-momentum tensor is introduced. As a result, the metric field equations are second-order and no new propagating degrees of freedom arise as compared to GR, which contrasts with the metric formulation of these theories, where a dynamical scalar degree of freedom is present. Analogously to its metric counterpart, the field equations impose the nonconservatio…

Serrin-Type Overdetermined Problems: an Alternative Proof

2008

We prove the symmetry of solutions to overdetermined problems for a class of fully nonlinear equations, namely the Hessian equations. In the case of the Poisson equation, our proof is alternative to the proofs proposed by Serrin (moving planes) and by Weinberger. Moreover, our proof makes no direct use of the maximum principle while it sheds light on a relation between the Serrin problem and the isoperimetric inequality.

Diffusion and Migration

2003

The sections in this article are Introduction Fundamental Concepts Diffusion–migration Flux Equations Poisson Equation and the LEN Assumption Continuity Equation Ohm's Law and Migrational Transport Numbers Diffusion-conduction Flux Equation Diffusion Boundary Layer Faraday's Law and Integral Transport Numbers Nernst Equation and Concentration Overpotential Steady State Current–voltage Curves of Systems with One Active Species Integration of the Transport Equations Solutions of Homovalent Ions, |zi | =z Binary Electrolyte Solutions Ternary Electrolyte Solutions. The Supporting Electrolyte Weak Binary Electrolyte Steady State Current–overpotential Curves in the Presence of Supporting Electrol…

Silica masks for improved surface poling of lithium niobate

2005

Surface periodic poling of congruent lithium niobate was performed with the aid of photolithographically defined silica masks. The latter helped improving the control of duty cycle in the periodic domain poling, with 50:50 mark-to-space ratios. The role of silica was ascertained by numerically solving the Poisson equation.

Efficient and accurate computation of Green's function for the Poisson equation in rectangular waveguides

2009

[1] In this paper, a new algorithm for the fast and precise computation of Green's function for the 2-D Poisson equation in rectangular waveguides is presented. For this purpose, Green's function is written in terms of Jacobian elliptic functions involving complex arguments. A new algorithm for the fast and accurate evaluation of such Green's function is detailed. The main benefit of this algorithm is successfully shown within the frame of the Boundary Integral Resonant Mode Expansion method, where a substantial reduction of the computational effort related to the evaluation of the cited Green's function is obtained.

Multiplicative cases from additive cases: Extension of Kolmogorov–Feller equation to parametric Poisson white noise processes

2007

Abstract In this paper the response of nonlinear systems driven by parametric Poissonian white noise is examined. As is well known, the response sample function or the response statistics of a system driven by external white noise processes is completely defined. Starting from the system driven by external white noise processes, when an invertible nonlinear transformation is applied, the transformed system in the new state variable is driven by a parametric type excitation. So this latter artificial system may be used as a tool to find out the proper solution to solve systems driven by parametric white noises. In fact, solving this new system, being the nonlinear transformation invertible, …

A fast solver for nonlocal electrostatic theory in biomolecular science and engineering

2011

Biological molecules perform their functions surrounded by water and mobile ions, which strongly influence molecular structure and behavior. The electrostatic interactions between a molecule and solvent are particularly difficult to model theoretically, due to the forces' long range and the collective response of many thousands of solvent molecules. The dominant modeling approaches represent the two extremes of the trade-off between molecular realism and computational efficiency: all-atom molecular dynamics in explicit solvent, and macroscopic continuum theory (the Poisson or Poisson--Boltzmann equation). We present the first fast-solver implementation of an advanced nonlocal continuum theo…

Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle

2000

We prove that a discrete maximum principle holds for continuous piecewise linear finite element approximations for the Poisson equation with the Dirichlet boundary condition also under a condition of the existence of some obtuse internal angles between faces of terahedra of triangulations of a given space domain. This result represents a weakened form of the acute type condition for the three-dimensional case.

The Homogeneous Poisson Point Process

2008

On finite element approximation of the gradient for solution of Poisson equation

1981

A nonconforming mixed finite element method is presented for approximation of ?w with Δw=f,w| r =0. Convergence of the order $$\left\| {\nabla w - u_h } \right\|_{0,\Omega } = \mathcal{O}(h^2 )$$ is proved, when linear finite elements are used. Only the standard regularity assumption on triangulations is needed.