Related papers: Isolation effects in a system of two mutually comm…
The main result of this article is the determination of the minimal size for the general case of problems with two identical patches. This solution is presented in the explicit form, which allows to recuperate all the cases found in the…
This paper starts from the Fisher-Kolmogorov-Petrovskii-Piskunov equation to model diffusive populations. The main result, according to this model, is that two connected patches in a system do not always contribute to each other.…
The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density; in the systems with power-law interactions, the…
We study the coupling of a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation to a separate, advection-only transport process. We find that the front dynamics can be described by an FKPP-like equation only at sufficiently fast diffusion…
The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov (SFKPP) equation. We derive here an individual based, stochastic model founded on the…
We propose a simple model unifying two major approaches to the analysis of large multicomponent systems: interacting particle systems (IPS) and couple map lattices (CML) and show that in the weak interaction limit depending on fine…
In this paper we consider a system of Brownian particles with proliferation whose rate depends on the empirical measure. The dependence is more local than a mean field one and has been called moderate interaction by Oelschlager [17], [18].…
We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A <-> A$ on the lattice when only a particle is allowed per site.…
Systems under external confinement and constraints often show interesting properties. In this thesis, we study some systems under external confinement. We begin by finding out the probability distribution of end-to-end separation of a Worm…
The spectral properties of a disordered system with few interacting three-dimensional spinless fermions are investigated. We show the existence of a critical spacings distribution which is invariant upon increase of the system size, but…
We study the quantum corrections to the polarizability of isolated metallic mesoscopic systems using the loop-expansion in diffusive propagators. We show that the difference between connected (grand-canonical ensemble) and isolated…
This paper improves understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays. Using the "floating sphere at emitter-plate potential" (FSEPP) model, it re-examines the electrostatics…
The Falicov-Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a…
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled…
We introduce a meta-population version of models of asymmetric exclusion models, consisting of a spatial arrangement of patches. Patches are of a specific size, indicating the maximal number of particles they can hold. We use an expansion…
We compare two singularly perturbed elliptic systems modeling partially phase segregation. Although the formulations are fundamentally different, we prove that their limiting configurations have identical free boundaries. The result shows…
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a "microscopic" model, in which the master…
On the basis of the thermodynamic theory of the excluded volume effects, we show that the size exponent varies abruptly, depending on the change of the segment concentration. For linear polymers, the exponent changes discontinuously from…
This paper builds upon the methods developed in [22] and [15] to investigate the large population behavior of non exchangeable systems of N diffusive particles when the interaction matrix converges (in some sense) to a graphon. We first…
Operator spreading provides a new characterization of quantum chaos beyond the semi-classical limit. There are two complementary views of how the characteristic size of an operator, also known as the butterfly light cone, grows under…