Related papers: Virial estimates for hard spheres
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
In this work we concentrate on an experimental validation of the Lifshitz theory for van der Waals and Casimir forces in gold-alcohol-glass systems. From this theory weak dispersive forces are predicted when the dielectric properties of the…
Different theoretical approaches for the thermodynamic properties and the equation of state for multicomponent mixtures of nonadditive hard spheres in $d$ dimensions are presented in a unified way. These include the theory by Hamad, our…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
In this work the properties of Q-balls in the complex signum-Gordon model in $d$ spatial dimensions is studied. We obtain a general virial relation for this kind of Q-ball in the higher-dimensional spacetime. We compute the energy and radii…
It is challenging to perform a multiscale analysis of mesoscopic systems exhibiting singularities at the macroscopic scale. In this paper, we study the hydrodynamic limit of the Boltzmann equations $$\mathrm{St} \partial_t F + v\cdot…
We investigate the semiclassical energy spectrum of quantum elliptic billiard. The nearest neighbor spacing distribution, level number variance and spectral rigidity support the notion that the elliptic billiard is a generic integrable…
The quantum dynamics of a chaotic billiard with moving boundary is considered in this work. We found a shape parameter Hamiltonian expansion which enables us to obtain the spectrum of the deformed billiard for deformations so large as the…
We discuss the interplay between the piece-line regular and vertex-angle singular boundary effects, related to integrability and chaotic features in rational polygonal billiards. The approach to controversial issue of regular and irregular…
In this paper, we extend the analysis of the subcritical approximation of the Nirenberg problem on spheres recently conducted in \cite{MM19, MM}. Specifically, we delve into the scenario where the sequence of blowing up solutions exhibits a…
We study the transport properties of a large class of locally confined Hamiltonian systems, in which neighboring particles interact through hard core elastic collisions. When these collisions become rare and the systems large, we derive a…
Determining the flow of rays or particles driven by a force or velocity field is fundamental to modelling many physical processes, including weather forecasting and the simulation of molecular dynamics. High frequency wave energy…
For suspensions of permeable particles, the short-time translational and rotational self-diffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a…
A fluid of N smooth, hard spheres is considered as a model for normal (elastic collisions) and granular (inelastic collisions) fluids. The potential energy is discontinuous for hard spheres so the pairwise forces are singular and the usual…
We prove (adjoint) bilinear restriction estimates for general phases at different scales in the full non-endpoint mixed norm range, and give bounds with a sharp and explicit dependence on the phases. These estimates have applications to…
The collision of a rising bubble with a superhydrophilic horizontal surface is studied numerically using the Cahn-Hilliard diffuse-interface method. For the studied systems, the Bond number, $Bo=\rho R^2 g/\sigma$, varies between 0.25 to…
We discuss the calculation of Casimir forces between a collection of $N$-dielectric spheres. This is done by evaluating directly the force on a sphere constructed from a stress tensor, rather than an interaction energy. Two and three body…
The Casimir and van der Waals forces acting between two metallic plates or a sphere (lens) above a plate are calculated accounting for the finite conductivity of the metals. The simple formalism of surface modes is briefly presented which…
We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed…
The scalar glueball, the lightest state in the gluonic Yang-Mills (YM) sector of QCD, is stable in that framework. The scattering of two scalar glueballs is therefore a well defined process in YM, which can be studied with the tools of…