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This paper is concerned with an age-structured model in population dynamics. We investigate the uniqueness of solution for this type of nonlinear reaction-diffusion problem when the source term depends on the density, indicating the…
We consider an initial-boundary value problem for the Maxwell's system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver-Muller-type boundary feedback mechanism…
We study (unrooted) random forests on a graph where the probability of a forest is multiplicatively weighted by a parameter $\beta>0$ per edge. This is called the arboreal gas model, and the special case when $\beta=1$ is the uniform forest…
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…
Biological systems are majorly dependent on their property of bistability in order to exhibit nongenetic heterogeneity in terms of cellular morphology and physiology. Spatial patterns of phenotypically heterogeneous cells, arising due to…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
Understanding epidemic dynamics in urban environments requires models that capture interactions across space and time while incorporating biological constraints. In this work, we propose a probabilistic spatiotemporal framework based on…
We investigate the phenomenology emerging from a 2-species dynamics under the scenario of a quasi-neutral competition within a metapopulation framework. We employ stochastic and deterministic approaches, namely spatially-constrained…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
Despite the fact that the theory of mixtures has been part of non-equilibrium thermodynamics and engineering for a long time, it is far from complete. While it is well formulated and tested in the case of mechanical equilibrium (where only…
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis…
Tree-size distribution is one of the most investigated subjects in plant population biology. The forestry literature reports that tree-size distribution trajectories vary across different stands and/or species, while the metabolic scaling…
Declines in resilience have been observed in several climate tipping elements over the past decades, including the Atlantic Meridional Overturning Circulation (AMOC) and the Amazon rainforest (AR). Large-scale nonlinear and possibly…
We investigate a diffusion process in heterogeneous media where particles stochastically reset to their initial positions at a constant rate. The heterogeneous media is modeled using a spatial-dependent diffusion coefficient with a…
We study the response of one dimensional diffusive systems, consisting of particles interacting via symmetric or asymmetric exclusion, to time-periodic driving from two reservoirs coupled to the ends. The dynamical response of the system…
Many forest management planning decisions are based on information about the number of trees by species and diameter per unit area. This information is commonly summarized in a stand table, where a stand is defined as a group of forest…
The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the "hockey-stick" upward trend of human technological evolution, where an explosion in the number of produced items with…
Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail…
Current questions in ecology revolve around instabilities in the dynamics on spatial networks and particularly the effect of node heterogeneity. We extend the Master Stability Function formalism to inhomogeneous biregular networks having…
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…