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The dc response of an electrochemical thin film, such as the separator in a micro-battery, is analyzed by solving the Poisson-Nernst-Planck equations, subject to boundary conditions appropriate for an electrolytic/galvanic cell. The model system consists of a binary electrolyte between parallel-plate electrodes, each possessing a compact Stern layer, which… (More)

We study a model electrochemical thin film at DC currents exceeding the classical diffusion-limited value. The mathematical problem involves the steady Poisson–Nernst–Planck equations for a binary electrolyte with nonlinear boundary conditions for reaction kinetics and Stern-layer capacitance, as well as an integral constraint on the number of anions. At… (More)

We analyze the simplest problem of electrochemical relaxation in more than one dimension-the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck… (More)

In this paper, we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions (phases) that the surface separates. Using a variational level set method formulation, we present a theoretical characterization of and a numerical algorithm for computing these surfaces. We use our theoretical and… (More)

In studies of interfaces with dynamic chemical composition, bulk and interfacial quantities are often coupled via surface conservation laws of excess surface quantities. While this approach is easily justified for microscopically sharp interfaces, its applicability in the context of microscopically diffuse interfaces is less theoretically well-established.… (More)

In this pedagogical article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. The method is based on a formulation of the discretized equations in vector form using only matrix-vector products and component-wise… (More)

In this article, we present a simple technique for boosting the order of accuracy of finite difference schemes for time dependent partial differential equations by optimally selecting the time step used to advance the numerical solution and adding defect correction terms in a non-iterative manner. The power of the technique is its ability to extract as much… (More)

—We extend the technique of optimal time step (OTS) selection for finite difference (FD) schemes of time dependent PDEs to PDEs where the leading-order spatial derivative term has a spatially varying coefficient. The basic approach involves identifying a transformation of the domain that eliminates the spatial dependence of the coefficient for the… (More)

- KEVIN T. CHU
- 2007

In this article, we present a simple direct matrix method for analytically computing the Jacobian of nonlinear algebraic equations that arise from the discretization of nonlinear integro-differential equations. This method is based on a formulation of the discretized equations in vector form using only matrix-vector products and component-wise operations.… (More)