Related papers: Capacity bounds on integral flows and the Kostant …

Let $\bar{p}(n)$ denote the overpartition function. In this paper, we study the asymptotic higher order $\log$-concavity property of the overpatition function in a similar framework done by Hou and Zhang for the partition function. This…

One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…

The study of the well-known partition function $p(n)$ counting the number of solutions to $n = a_{1} + \dots + a_{\ell}$ with integers $1 \leq a_{1} \leq \dots \leq a_{\ell}$ has a long history in combinatorics. In this paper, we study a…

It is shown that the canonical problem of classical statistical thermodynamics, the computation of the partition function, is in the case of +/-J Ising spin glasses a particular instance of certain simple sums known as quadratically signed…

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…

We construct the polynomial induction functor, which is the right adjoint to the restriction functor from the category of polynomial representations of a general linear group to the category of representations of its Weyl group. This…

Part I of this paper presented a systematic derivation of the Stokes Dirac structure underlying the port-Hamiltonian model of ideal fluid flow on Riemannian manifolds. Starting from the group of diffeomorphisms as a configuration space for…

Gradient flows are a powerful tool for optimizing functionals in general metric spaces, including the space of probabilities endowed with the Wasserstein metric. A typical approach to solving this optimization problem relies on its…

We obtain large N asymptotics for the Hermitian random matrix partition function \[Z_N(V)=\int_{\mathbb R^N}\prod_{i<j}(x_i-x_j)^2 \prod_{j=1}^N e^{-N V(x_j)}dx_j,\] in the case where the external potential $V$ is a polynomials such that…

We use the Circle Method to derive asymptotic formulas for functions related to the number of parts of partitions in particular residue classes.

Let $Z$ be a Boolean model based on a stationary Poisson process $\eta$ of compact, convex particles in Euclidean space ${\mathbb{R}}^d$. Let $W$ denote a compact, convex observation window. For a large class of functionals $\psi$, formulas…

We propose a novel feasible-path algorithm to solve the optimal power flow (OPF) problem for real-time use cases. The method augments the seminal work of Dommel and Tinney with second-order derivatives to work directly in the reduced space…

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function,also…

A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…

Particles on Demand formulation of kinetic theory [B. Dorschner, F. B\"{o}sch and I. V. Karlin, {\it Phys. Rev. Lett.} {\bf 121}, 130602 (2018)] is used to simulate a variety of compressible flows with strong discontinuities in density,…

The Enskog-like kinetic approach, recently introduced by us to study strongly inhomogeneous flu- ids, is reconsidered in order to improve the description of the transport coefficients. The approach is based on a separation of the…

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

Ray flow methods provide efficient tools for modelling wave energy transport in complex systems at high-frequencies. We compare two Petrov-Galerkin discretizations of a phase-space boundary integral model for stationary wave energy…

We independently assign a non-negative value, as a capacity for the quantity of flows per unit time, with a distribution F to each edge on the Z^d lattice. We consider the maximum flows through the edges of two disjoint sets, that is from a…

In this paper, we consider the local well-posedness of the Prandtl boundary layer equations that describe the behavior of boundary layer in the small viscosity limit of the compressible isentropic Navier-Stokes equations with non-slip…