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- Martin Z. Bazant, Kevin T. Chu, B. J. Bayly
- SIAM Journal of Applied Mathematics
- 2005

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)

- Kevin T Chu, Martin Z Bazant
- Physical review. E, Statistical, nonlinear, and…
- 2006

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)

- Kevin T. Chu, Martin Z. Bazant
- SIAM Journal of Applied Mathematics
- 2005

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)

- Kevin T Chu, Martin Z Bazant
- Journal of colloid and interface science
- 2007

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)

- Youngjean Jung, Kevin T. Chu, Salvatore Torquato
- J. Comput. Physics
- 2007

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)

—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)

- THIN FILMS, MARTIN Z. BAZANT, KEVIN T. CHU, B. J. BAYLY
- 2005

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)

- Kevin T. Chu
- J. Comput. Physics
- 2009

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)

- Kevin T. Chu
- Applied Mathematics and Computation
- 2011

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)