8 papers
Linear Reduction and Homotopy Control for Steady Drift-Diffusion Systems in Narrow Convex Domains
Joseph W. Jerome
This article develops and applies results, originally introduced in earlier work, for the existence of homotopy curves, terminating at a desired solution. We describe the principal…
The Multidimensional Damped Wave Equation: Maximal Weak Solutions for Nonlinear Forcing via Semigroups and Approximation
Joseph W Jerome
The damped nonlinear wave equation, also known as the nonlinear telegraph equation, is studied within the framework of semigroups and eigenfunction approximation. The linear semigr…
A Tight Nonlinear Approximation Theory for Time Dependent Closed Quantum Systems
Joseph W. Jerome
The approximation of fixed points by numerical fixed points was presented in the elegant monograph of Krasnosel'skii et al. (1972). The theory, both in its formulation and implemen…
Consistency of the Local Density Approximation and Generalized Quantum Corrections for Time Dependent Closed Quantum Systems
Joseph W. Jerome
Time dependent quantum systems are the subject of intense inquiry, in mathematics, science, and engineering, particularly at the atomic and molecular levels. In 1984, Runge and Gro…
Convergent Iteration in Sobolev Space for Time Dependent Closed Quantum Systems
Joseph W. Jerome
Time dependent quantum systems have become indispensable in science and its applications, particularly at the atomic and molecular levels. Here, we discuss the approximation of clo…
Three-Dimensional Simulation of Biological Ion Channels Under Mechanical, Thermal and Fluid Forces
Riccardo Sacco, Paolo Airoldi, Aurelio G. Mauri +1
In this article we address the three-dimensional modeling and simulation of biological ion channels using a continuum-based approach. Our multi-physics formulation self-consistentl…
Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels
Riccardo Sacco, Fabio Manganini, Joseph W. Jerome
In this article we address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is…
Discretization of Time-Dependent Quantum Systems: Real-Time Propagation of The Evolution Operator
Joseph W. Jerome, Eric Polizzi
We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent densi…