相关论文: Hierarchical Electrochemical Modeling and Simulati…

In the context of high penetration of renewables, the need to build dynamic models of power system components based on accessible measurement data has become urgent. To address this challenge, firstly, a neural ordinary differential…

Species transport models typically combine partial differential equations (PDEs) with relations from hindered transport theory to quantify electromigrative, convective, and diffusive transport through complex nanoporous systems; however,…

We investigate micro-to-macroscopic derivations in two models of living cells, in presence to cell-cell adhesive interactions. We rigorously address two PDE-based models, one featuring non-local terms and another purely local, as a a result…

Many physical systems are governed by ordinary or partial differential equations (see, for example, Chapter ''Differential equations'', ''System of Differential Equations''). Typically the solution of such systems are functions of time or…

We represent an algorithm reducing a big class of systems of ($M+1$)-dimensional nonlinear partial differential equations (PDEs) to the systems of $M$-dimensional first order PDEs. Thus, we integrate the original system with respect to only…

Electrohydrodynamics is crucial in many nanofluidic and biotechnological applications. In such small scales, the complexity due to the coupling of fluid dynamics with the dynamics of ions is increased by the relevance of thermal…

Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…

Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work, we develop conservative, positivity-preserving, energy…

In this paper we consider multi-dimensional partial differential equations of parabolic type involving divergence form operators that possess a discontinuous coefficient matrix along some smooth interface. The solution of the equation is…

The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a…

We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over…

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

Efficient modeling of High Temperature Superconductors (HTSs) is crucial for real-time quench monitoring; however, full-order electromagnetic simulations remain prohibitively costly due to the strong nonlinearities. Conventional…

A kinetic model of the electron transfer at the electrode / electrolyte solution interface is developed, implemented in a Monte Carlo framework, and applied to simulate this process in idealised systems consisting of the primitive model of…

Biochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a…

We present BioNetFlux, an open-source Python framework for the numerical simulation of coupled systems of partial differential equations (PDEs) on one-dimensional multi-arc networks by the Hybridized Discontinuous Galerkin method. Its…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…

Cellular electrophysiology is often modeled using the cable equations. The cable model can only be used when ionic concentration effects and three dimensional geometry effects are negligible. The Poisson model, in which the electrostatic…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…