Related papers: Infinite volume limit for the dipole gas
When the intensity of turbulence is increased (by increasing the Reynolds number, e.g. by reducing the viscosity of the fluid), the rate of the dissipation of kinetic energy decreases but does not tend asymptotically to zero: it levels off…
This note provides a simple proof for the equality between the normalized volume of a convex polytope with $m$ vertices and the mixed volume of $m$ simplices and thus shows the seemingly restrictive problem of computing mixed volume of…
Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are…
We propose an upwind finite volume method for a system of two kinetic equations in one dimension that are coupled through nonlocal interaction terms. These cross-interaction systems were recently obtained as the mean-field limit of a…
Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical…
We show that for $n \neq 1,4$ the simplicial volume of an inward tame triangulable open $n$-manifold $M$ with amenable fundamental group at infinity at each end is finite; moreover, we show that if also $\pi_1(M)$ is amenable, then the…
In an earlier paper Almeida and Frenkel considered the calculation of the pressure in g\phi^3 theory in 6 dimensions via the Schwinger--Dyson equation. They found, under certain approximations, that a finite result ensues in the infrared…
The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic…
The Casimir energy of a dilute dielectric cylinder, with the same light-velocity as in its surrounding medium, is evaluated exactly to first order in $\xi^2$ and numerically to higher orders in $\xi^2$. The first part is carried out using…
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases we…
We consider liquid-vapor systems in finite volume $V\subset\R^d$ at parameter values corresponding to phase coexistence and study droplet formation due to a fixed excess $\delta N$ of particles above the ambient gas density. We identify a…
Considering the fundamental cutoff applied by the uncertainty relations' limit on virtual particles' frequency in the quantum vacuum, it is shown that the vacuum energy density is proportional to the inverse of the forth power of the…
We revisit the topic of a dipolar condensate with the recently derived more rigorous pseudo-potential for dipole-dipole interaction [A. Derevianko, Phys. Rev. A {\bf 67}, 033607 (2003)]. Based on the highly successful variational technique,…
We analyze the stability of super- and subradiant states in a system of identical two-level atoms in the near-Dicke limit, i.e., when the atoms are very close to each other compared to the wavelength of resonant light. The dynamics of the…
The entropy of a classical thermally isolated Hamiltonian system is given by the logarithm of the measure of phase space enclosed by the constant energy hyper-surface, also known as volume entropy. It has been shown that on average the…
We consider two- and three-dimensional gravity and gravity-capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves…
A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time,…
Liquid-gas equilibrium is considered using the global isomorphism with the Ising-like (lattice gas) model. Such an approach assumes the existence of the order parameter in terms of which the symmetry of binodal is restored not only in the…
Extrapolations of numerical data obtained from finite cluster calculations to the infinite volume limit can often give incorrect results. We discuss four separate cases: (a) the intensity of the lowest two-photon absorption in the infinite…
We point out that a special case of an ideal gas exhibits concentration of the volume of its phase space, which is a sphere, around its equator in the thermodynamic limit. The rate of approach to the thermodynamic limit is determined. Our…