29 papers · ranked by Valyu relevance
Gabriel Barreiro, Vladimir Pérez-Veloz
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local models. This paper investigates a nonlinear diffusion equation where the…
Thomas Forrest Kieffer, Jakob Cupp, John S. Van Dyke, Paraj Titum + 1 more
We consider nonlinear partial differential equations (PDEs) for advection-diffusion processes which are augmented by an auxiliary parameter δ such that δ = 0 corresponds to linear advection-diffusion. We derive potentially non-perturbative series expansions in δ that provide a process to obtain the solution of the…
Achraf Zinihi, Matthias Ehrhardt, Moulay Rchid Sidi Ammi
We propose and analyze a nonstandard finite difference (NSFD) scheme for nonlinear parabolic equations involving a p-Laplacian-type diffusion operator in one- and two-dimensional spatial domains. Following Mickens' design principles, the proposed discretization employs a nonlinear denominator function phi(.) together…
P. I. Hurtado, G. Cortés-Guillén
We study a bulk-driven nonlinear variant of the Kipnis-Marchioro-Presutti model of stochastic energy diffusion in which local collisions are biased to induce a net energy flow, resembling the effect of an external field. Starting from the microscopic master equation, we derive the hydrodynamic description of the driven…
Silvia Preda, Walter Boscheri, Matteo Semplice, Maurizio Tavelli
In this work, we propose a new semi-Lagrangian (SL) finite difference scheme for nonlinear advection-diffusion problems. To ensure conservation, which is fundamental for achieving physically consistent solutions, the governing equations are integrated over a space-time control volume constructed along the…
Gabriel G. da Rocha, Michely P. Rosseto, Rodrigo J. Jaronski, Derik W. Gryczak + 3 more
in Electrolytic Cells: A Generalized Poisson–Nernst–Planck Model with Memory Effects Authors: Gabriel G. da Rocha, Michely P. Rosseto, Rodrigo J. Jaronski, Derik W. Gryczak, Luiz R. Evangelista, Rafael S. Zola, Ervin K. Lenzi We present an extension of the standard Poisson-Nernst-Planck model by incorporating temporal…
Shuonan Wu, Bing Yu, Yuhai Tu, Lei Zhang
Title: Highlights 1. • We propose a generic and efficient numerical algorithm to systematically construct the complete solution landscape of reaction-diffusion systems. 2. • We demonstrate that Turing instability is not the prerequisite to generate stable spatial patterns, uncovering a generic nonlinear mechanism that…
Horacio S. Wio, Roberto R. Deza, Jorge A. Revelli, Rafael Gallego + 3 more
Interfaces of rather different natures-as, e.g., bacterial colony or forest fire boundaries, or semiconductor layers grown by different methods (MBE, sputtering, etc.)-are self-affine fractals, and feature scaling with universal exponents (depending on the substrate’s dimensionality d and global topology, as well as on…
Klaus Mainzer
The intuitive idea of self-organisation in complex dynamical systems is that global patterns and structures emerge from locally interacting elements like atoms in laser beams, molecules in chemical reactions, proteins in cells, cells in organs, neurons in brains, agents in markets, etc. Hermann Haken introduced a…
Sudeep Sarma, Harrison Truscott, Da Xu, Kendall Reid + 3 more
Diffusion models have emerged as the state-of-the-art method in generative artificial intelligence (AI) and have shown great success in image synthesis, video generation, molecular design, and protein structure prediction. For biophysical problems, such as protein folding and association, a fundamental question in…
Avraham Moriel, Howard A. Stone
Many industrial applications and biological scenarios involve the interdiffusion of two polymeric species. Motivated by biological subcellular source-driven processes, we study polymer-polymer interdiffusion problems in the absence or the presence of a polymeric source, for both unentangled and entangled scenarios.…
Nartallo-Kaluarachchi, Ramón, Lambiotte, Renaud + 2 more
We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains. Using finite-volume approximations, we derive an approximate master equation…
Tejas Bansod, Thomas Hillen
Oncolytic virotherapy is a promising targeted cancer treatment that employs viruses, which selectively infect tumor cells. Although its clinical efficiency has remained limited and it is often used in conjunction with other therapies, advances in genetic engineering have produced stronger and more selective viral…
A. Girelli, G. Giantesio, A. Musesti, R. Penta
This work explores diffusion with scale-dependent coefficients, starting from a general advection-diffusion framework from a theoretical standpoint, and then focusing numerically on a purely diffusive regime. Advection-diffusion processes are central to modeling transport phenomena in natural and engineered systems.…
Hadrien Oliveri, Emilia Cozzolino, Alain Goriely
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), e.g. the spread of an infectious agent between different countries, or the transport and replication of toxic proteins across different brain regions in neurodegenerative diseases. In these…
Nikos I. Kavallaris, Farrukh Javed
We introduce a mechanistic, nonlocal tumour-growth model designed specifically to capture explosive dynamics that are not adequately explained by standard logistic reaction–diffusion descriptions. The motivation is empirical: the universal scaling law reported in [1] provides compelling cross-sectional evidence of…
Liyao Lyu, Huan Lei
We propose a stochastic branching particle-based method for solving nonlinear nonconservative advection–diffusion–reaction equations. The method splits the evolution into an advection–diffusion step, based on a linearized Kolmogorov forward equation and approximated by stochastic particle transport, and a reaction step…
Anže Hubman, Franci Merzel
An efficient variational method is presented for estimating the diffusion coefficients and free-energy profiles along selected collective variables from projected molecular dynamics trajectories under both equilibrium and nonequilibrium conditions. The method is based on the assumption that the short-time transition…
Authors not listed
Atomistic simulations provide essential mechanistic insights into chemical processes, yet many important phenomena in chemistry and materials science occur on timescales that are inaccessible to molecular dynamics. Existing computational approaches force a choice between atomic resolution on relatively short timescales…
Authors not listed
The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
Valentin Anfray, Hong-Yan Shih
Asymmetric self-organization is a hallmark of cell polarity, yet the diversity of observed polarization patterns is frequently attributed to specialized, complex biochemical mechanisms motifs beyond simple positive feedback. Here, we demonstrate that spatial heterogeneity alone fundamentally reshapes polarization…
Authors not listed
Bonkowski and De Souza [Sol. Stat. Ionics 429, 116967 (2025)] provide a guide for performing molecular dynamics simulations of ion transport, including methods for estimating diffusion coefficients and their uncertainties from mean-squared displacement (MSD) data. The discussion of uncertainty in estimated diffusion…
Galal M. Moatimid, Yasmeen M. Mohamed
The nonlinear stability of two horizontal interfaces of three-layered stratified non-Newtonian fluids plays a pivotal role in advanced engineering applications. This phenomenon encompasses temperature management systems, microfluidic devices, and precise coating technologies. In an existing study, a multilayer system…
Authors not listed
Predicting how often molecules collide in dilute solution remains a long-standing challenge often with several orders of magnitude difference between theoretical values and experimental values also among different experimental values. Traditional frameworks from Smoluchowski and Langmuir rely on the formation of stable…
Navid Akbari, Kai Mason, Aaron Gruber, Wilten Nicola
Spiking Neural Networks (SNNs) have the potential to replicate the brain’s computational efficacy by explicitly incorporating action potentials or “spikes”, which is not a feature of most artificial neural networks. However, training SNNs is difficult due to the non-differentiable nature of the most common spiking…
Vyom Raval, Rachel Oaks-Leaf, Qiang Chen, Fred Rieke
Receptive fields provide a concise description of the stimulus selectivity of visual neurons. But this stimulus selectivity is neither static nor linear, and these nonlinear effects are not well captured by standard linear or pseudo-linear receptive field models. At the same time, receptive field models incorporating…
Authors not listed
Metastable states and the conformational transitions in between them are key to understanding dynamical behaviour and function of large-scale molecular systems. By combining basic dimensionality reduction techniques with a state-of-the art approximation of the Koopman operator associated to molecular dynamics…
Authors not listed
Tuning of the intramolecular charge transfer (ICT) in a molecule could lead to red-shifted absorption and emission maxima as well as enhanced nonlinear optical (NLO) response. Optimization of the electronic donor (D) and acceptor (A) strength, pi-conjugation and the medium could result in enhancement of first…
Mankun Sang, Margaret E. Johnson
Binding reactions in effectively one-dimensional systems, such as proteins diffusing along DNA or other filaments, pose a fundamental coarse-graining challenge because stochastic trajectories are recurrent in one dimension and therefore do not admit a unique, separation-independent macroscopic association rate. As a…