Related papers: Simple equation of state for hard disks on the hyp…
A proposal to link the equation of state of a monocomponent hard-disk fluid to the equation of state of a polydisperse hard-disk mixture is presented. Event-driven molecular dynamics simulations are performed to obtain data for the…
The available virial coefficients for the 2D hard disks model are transformed into a matrix representation of the thermodynamic potentials, which allows for an accurate description of the whole fluid phase, up to the phase transition. We…
For any given natural number $k$, this paper gives upper bounds on the radius of a packing of a complete hyperbolic surface of finite area by $k$ equal-radius disks in terms of the surface's topology. We show that the bounds given here are…
An equation of state for a multicomponent mixture of non-additive hard spheres in $d$ dimensions is proposed. It yields a rather simple density dependence and constitutes a natural extension of the equation of state for additive hard…
We use video microscopy to study a two-dimensional (2D) model fluid of charged colloidal particles suspended in water and compute the pressure from the measured particle configurations. Direct experimental control over the particle density…
An accurate description of a columnar liquid crystal of hard disks at high packing fractions is presented using an improved free-volume theory. It is shown that the orientational entropy of the disks in the one-dimensional fluid direction…
A two-dimensional system of 10000 hard disks with square periodic boundary conditions, at a density in the middle of the 2-phase region predicted from equation-of-state data, when subjected to a weak external uniform force, is seen to phase…
The theory of weak solutions for nonlinear conservation laws is now well developed in the case of scalar equations [3] and for one-dimensional hyperbolic systems [1, 2]. For systems in several space dimensions, however, even the global…
The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and both of its ends grow…
The question of whether the known virial coefficients are enough to determine the packing fraction $\eta_\infty$ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived…
Recent values for virial coefficients up to B12, when expressed in powers of density relative to maximum close packing,lead to a closed equation-of-state for the equilibrium fluid. The series obtained converges for all densities;it becomes…
A general equation of state for the hard-body reference system of real fluid has been developed from first principles, statistical mechanical arguments using metric differential geometry to describe the "available volume," V0, and its…
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions…
In many cases, analytic solutions of partial differential equations may not be possible. For practical problems, it is more reasonable to carry out computational solutions. However, the standard grid in the finite difference approximation…
We show there exists a nontrivial $H^1_0$ solution to the steady Stokes equation on the 2D exterior domain in the hyperbolic plane. Hence we show there is no Stokes paradox in the hyperbolic setting. We also show the existence of a…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
Answering a question left open in \cite{MZ2}, we show for general symmetric hyperbolic boundary problems with constant coefficients, including in particular systems with characteristics of variable multiplicity, that the uniform Lopatinski…
The asymptotic expansion method is extended by using currently available accurate values for the first ten virial coefficients for hard sphere fluids. It is then used to yield an equation of state for hard sphere fluids, which accurately…
In this article an analytical solution of equations of motion of a rigid disk of finite thickness rolling on its edge on a perfectly rough horizontal plane under the action of gravity is given. The solution is given in terms of Gauss…
We prove stability for a coefficient determination problem for a two velocity 2x2 system of hyperbolic PDEs in one space dimension.