相关论文: Pattern formation for a local/nonlocal interaction…
We consider a scalar field theory with quartic self interaction, Yukawa coupled to fermions in the inflationary de Sitter spacetime background. The scalar has a classical background plus quantum fluctuations, whereas the fermions are taken…
We investigate a homogenization problem related to a non-local interface energy with a periodic forcing term. We show the existence of planelike minimizers for such energy. Moreover, we prove that, under suitable assumptions on the…
We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define…
In this paper we characterise the minimisers of a one-parameter family of nonlocal and anisotropic energies $I_\alpha$ defined on probability measures in $\R^n$, with $n\geq 3$. The energy $I_\alpha$ consists of a purely nonlocal term of…
We investigate the structure of a binary mixture of particles interacting via purely repulsive (point) Yukawa pair potentials with a common inverse screening length $\lambda$. Using the hyper-netted chain closure to the Ornstein-Zernike…
We propose and investigate a Yukawa model featuring a dynamical scalar field coupled to relativistic Luttinger fermions. Using the functional renormalization group (RG) as well as large-$N_{\text{f}}$ or perturbative expansions, we observe…
We introduce a new screening function which is useful for the few-body Coulomb scattering problem in ``screening and renormalization'' scheme. The new renormalization phase factor of the screening function is analytically shown. The Yukawa…
Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC) for the local volume fraction and the correlation function are derived from the DFT…
When canonical Hamiltonians of local quantum field theories are transformed using a renormalization group procedure for effective particles, the resulting interaction terms are non-local. The range of their non-locality depends on the…
We study a class of integral functionals known as nonlocal perimeters, which, intuitively, express a weighted interaction between a set and its complement. The weight is provided by a positive kernel K, which might be singular. In the first…
We study the lowest energy configurations of an equimolar binary mixture of classical pointlike particles with charges $Q_1$ and $Q_2$, such that $q=Q_2/Q_1\in [0,1]$. The particles interact pairwisely via 3D Coulomb potential and are…
We derive two versions of an effective model to describe dynamical effects of the Yukawa interaction among Dirac electrons in the plane. Such short-range interaction is obtained by introducing a mass term for the intermediate particle,…
The formation of colloidal gels is strongly dependent on the volume fraction of the system and the strength of the interactions between the colloids. Here we explore very dilute solutions by the means of numerical simulations, and show…
The phase diagram of crystalline bilayers of particles interacting via a Yukawa potential is calculated for arbitrary screening lengths and particle densities. Staggered rectangular, square, rhombic and triangular structures are found to be…
Atmospheric pressure helium plasmas are investigated through molecular dynamics simulations at room temperature (300 K) for various ionization fractions ($\chi_i = 10^{-1} - 10^{-5}$) in the strongly coupled regime (ion coupling parameter,…
We consider the minimization of an energy functional given by the sum of a crystalline perimeter and a nonlocal interaction of Riesz type, under volume constraint. We show that, in the small mass regime, if the Wulff shape of the…
We have investigated the pattern formation in systems described by the nonlocal Fisher--Kolmogorov--Petrovskii--Piskunov equation for the cases where the dimension of the pattern concentration area is less than that of independent variables…
Phase diagram of microcanonical ensembles of self-attracting particles is studied for two types of short-range potential regularizations: self-gravitating fermions and classical particles interacting via attractive soft…
A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg-Landau energy…
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in 1-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear…