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A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
The original binary-encounter Bethe model of Kim and Eugene Rudd (1994 Phys. Rev. A 50 3954-67) has proven to be an accurate analytical representation of total impact ionisation cross sections of electrons colliding with atoms and…
In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The DEs are typically nonlinear and difficult to analyze,…
Layered semiconductors show promise as channel materials for field-effect transistors (FETs). Usually, such devices incorporate solid back or top gate dielectrics. Here, we explore de-ionized (DI) water as a solution top gate for…
Bethe-Salpeter equation (BSE) in the self-consistent Hartree-Fock (HF) basis is often used for describing complex many-body effects in material science applications. Its exact solution on the real-frequency axis at finite temperature for…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phenomena are prevalent in fluid dynamics and materials science,…
We study the response of single nanosized spherical colloids in electrolyte solution to an alternating electric field (AC field) by computer simulations. We use a coarse-grained mesoscopic simulation approach that accounts in full for…
This work builds on our earlier work on designing demodulators for diffusion-based molecular communications using a Markovian approach. The demodulation filters take the form of an ordinary differential equation (ODE) which computes the…
Bipolar nanoporous membranes and bipolar nanochannels are used in water desalination and energy-harvesting systems that provide clean water and green energy, respectively. The growing need for both requires continuous improvement of their…
Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…
The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electron excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present…
A nanoscale device consisting of a metal nanowire, a dielectric, and a gate is proposed. A combination of quantum and thermal stochastic effects enable the device to have multiple functionalities, serving alternately as a transistor, a…
Nonlinear partial differential equations (PDEs) are pivotal in modeling complex physical systems, yet traditional Physics-Informed Neural Networks (PINNs) often struggle with unresolved residuals in critical spatiotemporal regions and…
This paper is concerned with diffusion-reaction equations where the classical diffusion term, such as the Laplacian operator, is replaced with a singular integral term, such as the fractional Laplacian operator. As far as the reaction term…
We consider a discrete particle system of two species coupled through nonlocal interactions driven by the one-dimensional Newtonian potential, with repulsive self-interaction and attractive cross-interaction. After providing a suitable…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
The temperature dependence of the nuclear free induction decay in the presence of a magnetic-field gradient was found to exhibit motional narrowing in gases upon heating, a behavior that is opposite to that observed in liquids. This has led…
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have…