Related papers: A PDE-ODE Coupled Spatio-Temporal Mathematical Mod…
We report a 2D Boundary Element Method (BEM) modeling of the thermal diffusion-controlled growth of a vapor bubble attached to a heating surface during saturated pool boiling. The transient heat conduction problem is solved in a liquid that…
Atomic heating is a fundamental phenomenon governed by the thermal spike effect during energetic deposition. This work presented another insight into thermal spike using a coupled classical oscillator model instead of a typical heat…
Scattering of electromagnetic fields by a defect layer embedded in a slow-light periodically layered ambient medium exhibits phenomena markedly different from typical scattering problems. In a slow-light periodic medium, constructed by…
The increasing frequency and severity of wildfires highlight the need for accurate fire and plume spread models. We introduce an approach that effectively isolates and tracks fire and plume behavior across various spatial and temporal…
We propose and analyze a deterministic mathematical model for the transmission of food-borne diseases in a population consisting of humans and flies. We employ the Caputo operator to examine the impact of governmental actions and online…
PT symmetric Aubry-Andre model describes an array of N coupled optical waveguides with position dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of disorder for small number of lattice…
This study presents a probabilistic surrogate model for localized wildfire spread based on a conditional flow matching algorithm. The approach models fire progression as a stochastic process by learning the conditional distribution of fire…
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…
Tidal disruptions of stars by supermassive black holes produce multi-wavelength emission, of which the optical emission is of ambiguous origin. A unification scenario of tidal disruption events (TDEs) has been proposed to explain the…
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…
We present a statistical model which shows the influence of turbulence on a thermonuclear flame propagating in C+O white dwarf matter. Based on a Monte Carlo description of turbulence, it provides a method for investigating the physics in…
We consider random dynamics on a uniform random recursive tree with $n$ vertices. Successively, in a uniform random order, each edge is either set on fire with some probability $p_n$ or fireproof with probability $1-p_n$. Fires propagate in…
I examine some analytical properties of a nonlinear reaction-diffusion system that has been used to model the propagation of a wildfire. I establish global-in-time existence and uniqueness of bounded mild solutions to the Cauchy problem for…
We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for…
This work deals with two problems arising in mathematical ecology. The first problem is concerned with diploid branching particle models and its behavior when rapid stirring is added to the interaction. The particle models involve two types…
We show that a large class of 1D first-order conservation PDEs can be probabilistically represented using multi-type branching processes. The representation holds when the initial conditions are linear combinations of negative exponentials.…
Invasive pest establishment is a pervasive threat to global ecosystems, agriculture, and public health. The recent establishment of the invasive spotted lanternfly in the northeastern United States has proven devastating to farms and…
Oscillation and collective behavior of diffusion flames is a fascinating phenomena. Considering candle bundles with different sizes in variable oxygen concentration, the flickering dynamics of the flames are experimentally and theoretically…
We introduce a two-type internal DLA model which is an example of a non-unary abelian network. Starting with n "oil" and n "water" particles at the origin, the particles diffuse in Z according to the following rule: whenever some site x has…
In this paper we analyze a new temperature-dependent model for adhesive contact that encompasses nonlocal adhesive forces and damage effects, as well as nonlocal heat flux contributions on the contact surface. The related PDE system…