Related papers: Aggregation-diffusion in heterogeneous environment…
Moving-habitat models track the density of a population whose suitable habitat shifts as a consequence of climate change. Whereas most previous studies in this area consider 1-dimensional space, we derive and study a spatially 2-dimensional…
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
Understanding current energy consumption behavior in communities is critical for informing future energy use decisions and enabling efficient energy management. Urban energy models, which are used to simulate these energy use patterns,…
How diffusion impacts on ecological dynamics under the Allee effect and spatial constraints? That is the question we address. Employing a microscopic minimal model in a metapopulation (without imposing nonlinear birth and death rates) we…
We overview recent developments in the study of alignment hydrodynamics, driven by a general class of symmetric communication kernels. A main question of interest is to characterize the emergent behavior of such systems, which we quantify…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
A generic aggregate forming system in two dimensions (2D) is studied using canonical ensemble constant temperature molecular dynamics simulation. The aggregates form due to the competition between short range attraction and long range…
Spatial structure and species interactions jointly shape the dynamics and biodiversity of ecological systems, yet most theoretical models either neglect spatial heterogeneity or sacrifice analytical tractability. Here, we provide a unified…
The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here we study the influence of finite-sized…
This paper presents a homogenisation-based constitutive model to describe the effective tran- sient diffusion behaviour in heterogeneous media in which there is a large contrast between the phase diffusivities. In this case mobile species…
This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or…
Two-dimensional (2D) particulate aggregates formed due to competing interactions exhibit a range of non-equilibrium steady state morphologies from finite-size compact crystalline structures to non-compact string-like conformations. We…
The hindered diffusion model is introduced. It is a continuum model giving the dynamics of a conserved density. Similar to the spin-facilitated models, the kinetics are hindered by a fluctuating diffusion coefficient that decreases as the…
We show that heterogeneity in self-propulsion speed can lead to the emergence of a robust effective short-range repulsion among active particles interacting via long-range attractive potentials. Using the example of harmonically coupled…
When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…
Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to…
Active matter deals with systems whose particles consume energy at the individual level in order to move. To unravel features such as the emergence of collective structures several models have been suggested, such as the on-lattice model of…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…