Related papers: Deterministic Partial Differential Equation Model …
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
The electrostatic potential in the neighborhood of a biomolecule can be computed thanks to the non-linear divergence-form elliptic Poisson-Boltzmann PDE. Dedicated Monte-Carlo methods have been developed to solve its linearized version (see…
Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy,…
We present a novel numerical method for solving the elliptic partial differential equation problem for the electrostatic potential with piecewise constant conductivity. We employ an integral equation approach for which we derive a system of…
In this paper, an approach to estimating a nonlinear deterministic model is presented. We introduce a stochastic model with extremely small variances so that the deterministic and stochastic models are essentially indistinguishable from…
A number of visions for a new generation of dose-efficient electron microscopes have been advanced. These proposals, while inspired by quantum principles, make little contact with the broader field of quantum metrology. We discuss a…
We propose an analytical model based on diffusion-reaction equation approach for electrochemical electron transfer reaction, where the rate is limited by the electron transfer process. The electron transfer from an ion in solution to the…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics.…
We investigate the evolution of tumor growth relying on a nonlinear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application.…
Although there is an extensive statistical literature showing the disadvantages of discretizing continuous variables, categorization is a common practice in clinical research which results in substantial loss of information. A large…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the…
Computing numerical solutions of the thermal radiative transfer equations on a finely resolved grid can be costly due to high computational and memory requirements. A numerical reduced order method that has recently been applied to a wide…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
Rapid technological advances in radiation therapy have significantly improved dose delivery and tumor control for head and neck cancers. However, treatment-related toxicities caused by high-dose exposure to critical structures remain a…
Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the…
We develop a self-consistent first-principle method based on the density functional theory. Physical quantities, such as the density of states, Fermi energy and electron density are obtained using a time-dependent random state method…
Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those…
A key challenge in sequential decision making is optimizing systems safely under partial information. While much of the literature has focused on the cases of either partially known states or partially known dynamics, it is further…