Related papers: The uniform spreading speed in cooperative systems…
In this two-part paper, we consider multicomponent systems in which each component can iteratively exchange information with other components in its neighborhood in order to compute, in a distributed fashion, the average of the components'…
Diffusion models have demonstrated remarkable performance in generating unimodal data across various tasks, including image, video, and text generation. On the contrary, the joint generation of multimodal data through diffusion models is…
We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…
This paper studies the fundamental communication properties of urban vehicle networks by exploiting the self-similarity and hierarchical organization of modern cities. We use an innovative model called "hyperfractal" that captures the…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
This paper investigates the large time behaviour of a three species reaction-diffusion system, modelling the spatial invasion of two predators feeding on a single prey species. In addition to the competition for food, the two predators…
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
Inspired by recent studies associating shifting temperature conditions with changes in the efficiency of predator species in converting their prey to offspring, we propose a predator-prey model of reaction-diffusion type to analyze the…
Redundant storage maintains the performance of distributed systems under various forms of uncertainty. This paper considers the uncertainty in node access and download service. We consider two access models under two download service…
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds…
A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain…
We apply diffusion strategies to develop a fully-distributed cooperative reinforcement learning algorithm in which agents in a network communicate only with their immediate neighbors to improve predictions about their environment. The…
In this paper, we investigate spreading properties of the solutions of the Kolmogorov-Petrovsky-Piskunov-type, (to be simple,KPP-type) lattice system \begin{equation}\label{firstequation}\overset{.}u_{i}(t)…
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both…
Droplet impacts are common in many applications such as coating, spraying, or printing; understanding how droplets spread after impact is thus of utmost importance. Such impacts may occur with different velocities on a variety of…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
This paper is concerned with the speeds of propagation for the monostable Lotka-Volterra competition-diffusion system in general unbounded domains of $\mathbb{R}^N$. We first establish various definitions of spreading speeds at large time…
Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated…
In an incompressible flow, fluid density remains invariant along fluid element trajectories. This implies that the spatial distribution of non-interacting noninertial particles in such flows cannot develop density inhomogeneities beyond…
Exploring the internal mechanism of information spreading is critical for understanding and controlling the process. Traditional spreading models often assume individuals play the same role in the spreading process. In reality, however,…