Related papers: Density Functional Theory for Hard Particles in N …
In geometry, there are several challenging problems studying numbers associated to convex bodies. For example, the packing density problem, the kissing number problem, the covering density problem, the packing-covering constant problem,…
We study the virial expansion of mixtures of countably many different types of particles. The main tool is the Lagrange-Good inversion formula, which has other applications such as counting coloured trees or studying probability generating…
In various stereological problems an $n$-dimensional convex body is intersected with an $(n-1)$-dimensional Isotropic Uniformly Random (IUR) hyperplane. In this paper the cumulative distribution function associated with the…
We derive the bosonic sector of the AdS$_3$/CFT$_2$ correspondence from the $(1+1)$-dimensional Gross-Neveu (GN) model with $N$ fermion species and a local quartic interaction, with no stringy or geometric input. A Bargmann-Wigner fusion…
We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…
We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the s- and t-channel expansions) can be thought of as a vector equation in an…
When two bodies get into contact, only a small portion of the apparent area is actually involved in producing contact and friction forces, because of the surface roughnesses. It is therefore crucial to accurately describe the morphology of…
The partition function on the three-sphere of N=3 Chern-Simons-matter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N=2 supersymmetry, the partition function corresponds to a gas of…
We show that properties of hypergeometric class equations and functions become transparent if we derive them from appropriate 2nd order differential equations with constant coefficients. More precisely, properties of the hypergeometric and…
Non-integer dimensionality is central to fractal and complex systems, yet it is rarely represented as an explicit lattice on which classical statistical-mechanical models can be directly simulated. Here we introduce random-h fractional…
A density functional theory for a mixture of hard rods and polymers modeled as chains built of hard tangent spheres is proposed by combining the functional due to Yu and Wu for the polymer mixtures [J. Chem. Phys. {\bf 117}, 2368 (2002)]…
To advance the foundation of one-particle reduced density matrix functional theory (1RDMFT) we refine and relate some of its fundamental features and underlying concepts. We define by concise means the scope of a 1RDMFT, identify its…
A nef-partition for a weighted complete intersection is a combinatorial structure on its weights and degrees which is important for Mirror Symmetry. It is known that nef-partitions exist for smooth well-formed Fano weighted complete…
In this work we present an alternative method to obtain a distribution of particles over an hyper surface, such that they obey a rest-mass density distribution $\rho(x^i)$. We use density profiles that can be written as…
We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at…
We prove the universality of correlation functions of chiral complex matrix models in the microscopic limit (N->\infty, z->0, N z=fixed) which magnifies the crossover region around the origin of the eigenvalue distribution. The proof…
We introduce a geometric path integral definition of wormhole partition functions in a general class of 1D quantum systems obtained by quantizing a phase space. We compute the wormhole partition function in a semi-classical limit and in…
The exact universal functional of integer charge leads to an extension to fractional charge asymptotically when it is applied to a system made of asymptotically separated densities. The extended functional is asymptotically local and is…
An expansion of a density field or particle distribution in basis functions which solve the Poisson equation both provides an easily parallelized n-body force algorithm and simplifies perturbation theories. The expansion converges quickly…
We consider a three dimensional system consisting of a large number of small spherical particles, distributed in a range of sizes and heights (with uniform distribution in the horizontal direction). Particles move vertically at a…