Related papers: Study of Arbitrary Nonlinearities in Convective Po…
We use Molecular Dynamics combined with Dissipative Particle Dynamics to construct a model of a binary mixture where the two species differ only in their dynamic properties (friction coefficients). For an asymmetric mixture of slow and fast…
Reaction-diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many models of biological invasion are extensions of the…
We study semi-linear evolutionary problems where the linear part is the generator of a positive $C_0$-semigroup. The non-linear part is assumed to be quasi-increasing. Given an initial value in between a sub- and a super-solution of the…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
A general class of cross-diffusion systems for two population species in a bounded domain with no-flux boundary conditions and Lotka-Volterra-type source terms is analyzed. Although the diffusion coefficients are assumed to depend linearly…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
The classical 'ballistic' overshoot models show some contradictions and are not consistence with numerical simulations and asteroseismic studies. Asteroseismic studies imply that overshoot is a weak mixing process. Diffusion model is…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation…
We introduce non-linear diffusion in a classical diffusion advection model with non local aggregative coupling on the circle, that exhibits a transition from an uncoherent state to a coherent one when the coupling strength is increased. We…
We study the diffusion of a tracer particle driven out-of-equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…