Related papers: A density theorem for asymptotically hyperbolic in…
A new framework is introduced for examining and evaluating the fundamental limits of lossless data compression, that emphasizes genuinely non-asymptotic results. The {\em sample complexity} of compressing a given source is defined as the…
This paper concerns the large time asymptotic behavior of solutions to the free boundary problem of the compressible primitive equations in atmospheric dynamics with physical vacuum. Up to second order of the perturbations of an…
The asymptotic form of the energy density for a gas of particles surrounding a sphere of mass $M$ and radius $R$ is studied using Einstein's equations. It is shown that if the pressure of the gas $p$ varies linearly with the energy density…
Given positive integers $a_1,\ldots,a_k$, we prove that the set of primes $p$ such that $p \not\equiv 1 \bmod{a_i}$ for $i=1,\ldots,k$ admits asymptotic density relative to the set of all primes which is at least $\prod_{i=1}^k…
In this note, we show that the Local Molecular Field theory of Weeks et. al. can be re-derived as an extremum problem for an approximate Helmholtz free energy. Using the resulting free energy as a classical, fluid density functional yields…
We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
We determine the asymptotic density $\delta_k$ of the set of ordered $k$-tuples $(n_1,...,n_k)\in \N^k, k\ge 2$, such that there exists no prime power $p^a$, $a\ge 1$, appearing in the canonical factorization of each $n_i$, $1\le i\le k$,…
We consider Gowdy spacetimes under the assumption that the spatial hypersurfaces are diffeomorphic to the torus. The relevant equations are then wave map equations with the hyperbolic space as a target. In an article by Grubisic and…
We study sufficient conditions for local asymptotic mixed normality. We weaken the sufficient conditions in Theorem 1 of Jeganathan (Sankhya Ser. A 1982) so that they can be applied to a wider class of statistical models including a…
It is argued that the use of the initial Gaussian energy density profile for hydrodynamics leads to much better uniform description of the RHIC heavy-ion data than the use of the standard initial condition obtained from the Glauber model.…
We provide a Hilbert manifold structure {\`a} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{\'e} and Korn type inequalities for AH…
A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of…
For an asymptotically flat initial-data set in general relativity, the total mass-momentum may be interpreted as a Hermitian quadratic form on the complex, two-dimensional vector space of ``asymptotic spinors''. We obtain a generalization…
We construct families of asymptotically locally hyperbolic Riemannian metrics with constant scalar curvature (i.e., time symmetric vacuum general relativistic initial data sets with negative cosmological constant), with prescribed topology…
In 2012, inspired by developments in group theory and complexity, Jockusch and Schupp introduced generic computability, capturing the idea that an algorithm might work correctly except for a vanishing fraction of cases. However, we observe…
It was shown recently that the constraints on the initial data for Einstein's equations may be posed as an evolutionary problem [9]. In one of the proposed two methods the constraints can be replaced by a first order symmetrizable…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
The Eigenstate Thermalization Hypothesis implies that for a thermodynamically large system in one of its eigenstates, the reduced density matrix describing any finite subsystem is determined solely by a set of {\it relevant} conserved…
The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…