101,763 research outputs found
Convergence of the Poincare Constant
The Poincare constant R(Y) of a random variable Y relates the L2 norm of a
function g and its derivative g'. Since R(Y) - Var(Y) is positive, with
equality if and only if Y is normal, it can be seen as a distance from the
normal distribution. In this paper we establish a best possible rate of
convergence of this distance in the Central Limit Theorem. Furthermore, we show
that R(Y) is finite for discrete mixtures of normals, allowing us to add rates
to the proof of the Central Limit Theorem in the sense of relative entropy.Comment: 11 page
Holographic Nuclei : Supersymmetric Examples
We provide a dual gravity description of a supersymmetric heavy nucleus,
following the idea of our previous paper arXiv:0809.3141. The supersymmetric
nucleus consists of a merginal bound state of baryons distributed over a
ball in 3 dimensions. In the gauge/string duality, the baryon in N=4 super
Yang-Mills (SYM) theory corresponds to a D5-brane wrapping S^5 of the AdS_5 x
S^5 spacetime, so the nucleus corresponds to a collection of D5-branes. We
take a large and a near horizon limits of a back-reacted geometry generated
by the wrapped D5-branes, where we find a gap in the supergravity
fluctuation spectrum. This spectrum is a gravity dual of giant resonances of
heavy nuclei, in the supersymmetric toy example of QCD.Comment: 9 pages, 6 figures; v2:a refernce adde
Three-dimensional carbon foam nanocomposites for thermal energy storage
This is the final version. Available from Elsevier via the DOI in this record.Nanocomposites consisting of paraffin/graphene nanoplatelets mix embedded in carbon foams via vacuum infiltration were fabricated with the aim of developing new phase change material (PCM) formulation with excellent shape stabilization, improved thermal conductivity and outstanding thermal reliability and structural stability. Physicochemical and thermal properties of the nanocomposites were evaluated using a suite of techniques such as scanning and transmission electron microscopy, X-ray diffraction, attenuated total reflection - Fourier transform infrared spectroscopy, nitrogen adsorption analyzer, differential scanning calorimetry, mechanical tester, Raman spectroscopy, thermal conductivity analyzer and thermogravimetric analyzer. The carbon foams exhibited good cyclic compressive behavior at a strain of up to 95% and kept part of their elastic properties after cyclic testing. Due to the robust mechanical integrity and layered meso-/macroporous morphology of these carbon foams, the nanocomposites are well equipped to cope with volume changes without leaking during thermal cycling. A 141% thermal conductivity enhancement observed for the carbon foam nanocomposite demonstrates the contributing role of the carbon foam in creating effective heat transfer through its conductive 3D network. The results have shown that proper chemical modification and subsequent carbonization of the low cost porous foams can lead to ultralight multifunctional materials with high mechanical and physical properties suitable for thermal energy storage applications.Engineering and Physical Sciences Research Council (EPSRC
Numerical simulation of liquid sloshing in a partially filled container with inclusion of compressibility effects
A numerical scheme of study is developed to model compressible two-fluid flows simulating liquid sloshing in a partially filled tank. For a two-fluid system separated by an interface as in the case of sloshing, not only a Mach-uniform scheme is required, but also an effective way to eliminate unphysical numerical oscillations near the interface. By introducing a preconditioner, the governing equations expressed in terms of primitive variables are solved for both fluids (i.e. water, air, gas etc.) in a unified manner. In order to keep the interface sharp and to eliminate unphysical numerical oscillations in unsteady fluid flows, the non-conservative implicit Split Coefficient Matrix Method (SCMM) is modified to construct a flux difference splitting scheme in the dual time formulation. The proposed numerical model is evaluated by comparisons between numerical results and measured data for sloshing in an 80% filled rectangular tank excited at resonance frequency. Through similar comparisons, the investigation is further extended by examining sloshing flows excited by forced sway motions in two different rectangular tanks with 20% and 83% filling ratios. These examples demonstrate that the proposed method is suitable to capture induced free surface waves and to evaluate sloshing pressure loads acting on the tank walls and ceiling
Superconductivity in the Two-Dimensional - Model at Low Hole Doping
By combining a generalized Lanczos scheme with the variational Monte Carlo
method we can optimize the short- and long-range properties of the groundstate
separately. This allows us to measure the long-range order of the groundstate
of the - model as a function of the coupling constant , and identify
a region of finite d-wave superconducting long-range order. With a lattice size
of 50 sites we can reliably examine hole densities down to 0.16.Comment: 12 pages and 4 PostScript figures, ReVTeX 3.0, ETH-TH/94-1
Shot noise spectrum of superradiant entangled excitons
The shot noise produced by tunneling of electrons and holes into a double dot
system incorporated inside a p-i-n junction is investigated theoretically. The
enhancement of the shot noise is shown to originate from the entangled
electron-hole pair created by superradiance. The analogy to the superconducting
cooper pair box is pointed out. A series of Zeno-like measurements is shown to
destroy the entanglement, except for the case of maximum entanglement.Comment: 5 pages, 3 figures, to appear in Phys. Rev. B (2004
Blow-up solutions for linear perturbations of the Yamabe equation
For a smooth, compact Riemannian manifold (M,g) of dimension N \geg 3, we
are interested in the critical equation where \Delta_g is the Laplace--Beltrami
operator, S_g is the Scalar curvature of (M,g), , and
is a small parameter
Pricing in Social Networks with Negative Externalities
We study the problems of pricing an indivisible product to consumers who are
embedded in a given social network. The goal is to maximize the revenue of the
seller. We assume impatient consumers who buy the product as soon as the seller
posts a price not greater than their values of the product. The product's value
for a consumer is determined by two factors: a fixed consumer-specified
intrinsic value and a variable externality that is exerted from the consumer's
neighbors in a linear way. We study the scenario of negative externalities,
which captures many interesting situations, but is much less understood in
comparison with its positive externality counterpart. We assume complete
information about the network, consumers' intrinsic values, and the negative
externalities. The maximum revenue is in general achieved by iterative pricing,
which offers impatient consumers a sequence of prices over time.
We prove that it is NP-hard to find an optimal iterative pricing, even for
unweighted tree networks with uniform intrinsic values. Complementary to the
hardness result, we design a 2-approximation algorithm for finding iterative
pricing in general weighted networks with (possibly) nonuniform intrinsic
values. We show that, as an approximation to optimal iterative pricing, single
pricing can work rather well for many interesting cases, but theoretically it
can behave arbitrarily bad
Eigenvalues of Ruijsenaars-Schneider models associated with root system in Bethe ansatz formalism
Ruijsenaars-Schneider models associated with root system with a
discrete coupling constant are studied. The eigenvalues of the Hamiltonian are
givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic"
limit, we obtain the spectrum of the corresponding Calogero-Moser systems in
the third formulas of Felder et al [20].Comment: Latex file, 25 page
Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram
The local geometry of a Riemannian symmetric space is described completely by
the Riemannian metric and the Riemannian curvature tensor of the space. In the
present article I describe how to compute these tensors for any Riemannian
symmetric space from the Satake diagram, in a way that is suited for the use
with computer algebra systems. As an example application, the totally geodesic
submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
The submission also contains an example implementation of the algorithms and
formulas of the paper as a package for Maple 10, the technical documentation
for this implementation, and a worksheet carrying out the computations for the
space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical
documentatio
- …