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The possible occurrence of crystalline or inhomogeneous phases in the QCD phase diagram at large chemical potential has been under investigation for over thirty years. Such phases are present in models of QCD such as the Gross-Neveu model…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
A recently developed variational resummation technique incorporating renormalization group properties has been shown to solve the scale dependence problem that plagues the evaluation of thermodynamical quantities, e.g., within the framework…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
This is an edited version of an unpublished 1979 EFI (U. Chicago) preprint: "The U(N) lattice gauge theory in 2-dimensions can be considered as the statistical mechanics of a Coulomb gas on a circle in a constant electric field. The large N…
A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer.…
A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. Based on detailed balance, reaction rates are proposed for the system. The static behavior of the system is investigated. It is shown…
We use scale invariant scattering theory to obtain the exact equations determining the renormalization group fixed points of the two-dimensional $CP^{N-1}$ model, for $N$ real. Also due to special degeneracies at $N=2$ and 3, the space of…
A scaling hypothesis for the n-particle spectral densities of the O(3) nonlinear sigma-model is described. It states that for large particle numbers the n-particle spectral densities are ``self-similar'' in being basically rescaled copies…
We discuss the (non)-restoration of global and local symmetries at high temperature. First, we analyze a two-scalar model with $Z_2 \times Z_2$ symmetry using the exact renormalization group. We conclude that inverse symmetry breaking is…
Inhomogeneous cosmological models are often reported to suffer from a fine-tuning problem because of the observer's location. We study if this is a generic feature in the Lema\^{i}tre-Tolman (LT) models, by investigating if there are models…
We study the $O(N)$ nonlinear $\sigma$ model on a three-dimensional compact space $S^1 \times S^2$ (of radii $L$ and $R$ respectively) by means of large $N$ expansion, focusing on the finite size effects and conformal symmetries of this…
We consider thermal QCD in the large N_C limit, mainly in 1+1 dimensions. The gauge coupling is only taken into account to minimal order, by projection onto colour singlets. An expression for the free energy, exact as N_C goes to infinity,…
We analyze a microscopic RNA model, which includes two widely used models as limiting cases, namely it contains terms for bond as well as for stacking energies. We numerically investigate possible changes in the qualitative and quantitative…
Convergence of the solutions of nonhomogeneous linear singularly perturbed systems to that of the corresponding reduced singular system on the half-line [0, $\infty $) is considered. To include the situation on a neighborhood of initial…
We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval $I$, under Dirichlet conditions in the exterior of $I$. This model is strictly related to the…
We have simulated the asymptotically free two-dimensional O(3) model at nonzero chemical potential using the model's dual representation. We first demonstrate how the latter solves the sign (complex action) problem. The system displays a…
A one-phase Stefan problem for a semi-infinite material is investigated for special functional forms of the thermal conductivity and specific heat depending on the temperature of the phase-change material. Using the similarity…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…