Related papers: Nonlocal cross-diffusion systems for multi-species…
The present paper studies existence and distributional uniqueness of subclasses of stationary hard-core particle systems arising as thinnings of stationary particle processes. These subclasses are defined by natural maximality criteria. We…
We study numerically the population transfer protocol on the Quantum Random Energy Model and its relation to quantum computing, for system sizes of $n\leq 20$ quantum spins. We focus on the energy matching problem, i.e. finding multiple…
We show that locally bounded, local weak solutions to certain nonlocal, nonlinear diffusion equations modeled on the fractional porous media and fast diffusion equations given by \begin{align*} \partial_t u + (-\Delta)^s(|u|^{m-1}u) = 0…
Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one…
Predicting species persistence within ecological communities is a fundamental challenge for both empirical and theoretical ecology. Existing methods span from mechanistic models, whose parameters are difficult to estimate from data, to…
In this work, we introduce a cross-diffusion model that couples population density and occupied area to investigate how internal pressure drives growth and motility. By blending nonlinear nonlocal interactions with porous-medium diffusion…
In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and…
A novel strategy that combines a given collection of $\pi$-reversible Markov kernels is proposed. At each Markov transition, one of the available kernels is selected via a state-dependent probability distribution. In contrast to random-scan…
We consider a class of cross diffusion systems with degenerate (or porous media type) diffusion which is inspired by models in mathematical biology/ecology with zero self diffusions. Known techniques for scalar equations are no longer…
We investigate the long-time behavior of phenotype-structured models describing evolutionary dynamics of asexual populations, and analyze the joint effects of nonlocal interactions and spatial resource distributions on the global dynamics…
We investigate the (generalized) Walsh decomposition of point-to-point effective resistances on countable random electric networks with i.i.d. resistances. We show that it is concentrated on low levels, and thus point-to-point effective…
We study the convenience of a nonlocal dispersal strategy in a reaction-diffusion system with a fractional Laplacian operator. We show that there are circumstances - namely, a precise condition on the distribution of the resource - under…
The nonlocal Fisher equation is a diffusion-reaction equation with a nonlocal quadratic competition, which describes the reaction between distant individuals. This equation arises in evolutionary biological systems, where the arena for the…
We introduce a generalized concept of solutions for reaction-diffusion systems and prove their global existence. The only restriction on the reaction function beyond regularity, quasipositivity and mass control is special in that it merely…
We introduce the notion, and develop the theory of local-noise spectroscopy (LNS) - a tool to study the properties of systems far from equilibrium by means of flux density correlations. As a test bed, we apply it to biased molecular…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…
The existence of a global martingale solution to a cross-diffusion system with multiplicative Wiener noise in a bounded domain with no-flux boundary conditions is shown. The model describes the dynamics of population densities of different…
Nonlocal correlations created in networks with multiple independent sources enable surprising phenomena in quantum information and quantum foundations. The presence of independent sources, however, makes the analysis of network nonlocality…
Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit…