Near-critical thermodynamics in the hard-sphere (1, 1) electrolyte is well described, at a classical level, by Debye-Hückel (DH) theory with s1, 2d ion pairing and dipolar-pair-ionic-fluid coupling. But DH-based theories do not address density fluctuations. Here density correlations are obtained by functional differentiation of DH theory generalized to nonuniform densities of various species. T...

We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find indications that fluctuation-dissipation relations hold if the system is nonintegrable after the quench...

Abstract For a given multidimensional data set (point cloud), we investigate methods for computing the minimum-volume enclosing ellipsoid (MVEE), which provides an efficient representation of that is useful in many applications, including analysis, optimal design, and computational geometry. Contrary to conventional wisdom, demonstrate careful exploitation problem structure can enable high-orde...

Polymer-nanoparticle composites (PNCs) play an increasing role in technology. Inorganic or organic nanoparticles are usually incorporated into a polymer matrix to improve material properties. Polyurea is a spontaneously occurring PNC, exhibiting a phase segregated structure with hard nanodomains embedded in a soft (elastically compliant) matrix. This system shows two glass transitions at Tg1 an...

We present a new event-driven molecular dynamics (MD) algorithm for measuring the free energy of nearly jammed packings of spherical and non-spherical hard particles. This Bounding Cell Molecular Dynamics (BCMD) algorithm exactly calculates the free-energy of a single-occupancy cell (SOC) model in which each particle is restricted to a neighborhood of its initial position using a hard-wall boun...

This paper presents a complete proof of the fact 1 that the ellipsoid with minimal volume containing the regular simplex is a sphere (lemma 4). It is shown also that the proof can be used to build and compute easily minimal volume ellipsoids around irregular simplex (Theorem 1). Some consequences are presented. The first two lemmas deal with the wellknown (see [2],[3]) Steiner and Swarz symmetr...

RECIST (Response Evaluation Criteria in Solid Tumors) is a linear measure intended to predict tumor size in medical computed tomography (CT). In this work, using purely geometrical considerations, we estimate how well RECIST can predict the volume of randomly-oriented tumor models, each composed of the union of ellipsoids. The principal conclusion is that RECIST is likely to work less well for ...