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The aim of this work is an analysis of distal and non-distal behavior in dense pairs of o-minimal structures. A characterization of distal types is given through orthogonality to a generic type in $M^{\operatorname{eq}}$, non-distality is…
We provide a proof of mean-field convergence of first-order dissipative or conservative dynamics of particles with Riesz-type singular interaction (the model interaction is an inverse power $s$ of the distance for any $0<s<d$) when assuming…
The mean field equation involving the $N$-Laplace operator and an exponential nonlinearity is considered in dimension $N\geq2$ on bounded domains with homogenoeus Dirichlet boundary condition. By a detailed asymptotic analysis we derive a…
In this paper, we investigate the dynamics of two two-level atoms interacting with a two-mode field inside an optical cavity, in presence of a nonlinear Kerr-like medium as well as the Stark shift. We derive the exact analytical solution of…
This paper investigates a system of nonlocal continuity equations modelling the interaction of two species coupled through Riesz-type potentials. The model incorporates self- and cross-interaction kernels of possibly different fractional…
We present an extension of the previously proposed mean-field renormalization method to model Hamiltonians which are characterized by more than just one type of interaction. The method rests on scaling assumptions about the magnetization of…
The contact angle of a fluid droplet on an heterogeneous surface is analysed using the statistical dynamics of the spreading contact line. The statistical properties of the final droplet radius and contact angle are obtained through…
The aim of this paper is to study the asymptotic behavior of a system of birth and death processes in mean field type interaction in discrete space. We first establish the exponential convergence of the particle system to equilibrium for a…
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in…
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local…
In this paper we numerically investigate the breakup dynamics of droplets in an emulsion flowing in a tapered microchannel with a narrow constriction. The mesoscale approach for multicomponent fluids with near contact interactions is shown…
We examine metastable configurations of a two-dimensional system of interacting particles on a quenched random potential landscape and ask how the configurational pair correlation function is related to the particle interactions and the…
We study the pairwise interactions of drops in an applied uniform DC electric field within the framework of the leaky dielectric model. We develop three-dimensional numerical simulations using the boundary integral method and an analytical…
We theoretically investigate the apparent contact angle of droplets on liquid infused surfaces as a function of the relative size of the wetting ridge and the deposited droplet. We provide an intuitive geometrical interpretation whereby the…
We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model,…
We study systems of $n$ points in the Euclidean space of dimension $d \ge 1$ interacting via a Riesz kernel $|x|^{-s}$ and confined by an external potential, in the regime where $d-2\le s<d$. We also treat the case of logarithmic…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
We study the static and dynamic behavior of the one dimensional pair contact process with diffusion. Several critical exponents are found to vary with the diffusion rate, while the order-parameter moment ratio m=\bar{rho^2} /\bar{rho}^2…
In the field of microdroplet manipulation, optical tweezers have been used to form and grow droplets, to transport them, or to measure forces between droplet pairs. However, the exploration of out-of-equilibrium phenomena in optically…
In this paper we study a mean field model for the dynamics of an interacting Bose-Einstein condensate in two dimensional pseudo-relativistic materials. This model is relatively simple, but contains stable solutions called oscillons which…