Asymptotically optimal interruptible service policies for?scheduling jobs in a diffusion regime with?nondegenerate slowdown

A?parallel server system is considered, with I customer classes and many servers, operating in a heavy traffic diffusion regime where the queueing delay and service time are of the same order of magnitude. Denoting by $\widehat{X}^{n}$ and $\widehat{Q}^{n}$ , respectively, the diffusion scale deviation of the headcount process from the quantity corresponding to the underlying fluid model and the diffusion scale queue-length, we consider minimizing r.v.??s of the form $c^{n}_{X}=\int_{0}^{u}C(\widehat{X}^{n}(t))\,dt$ and $c^{n}_{Q}=\int_{0}^{u}C(\widehat{Q}^{n}(t))\,dt$ over policies that allow for service interruption. Here, C:? ^I ???₊ is continuous, and u>0. Denoting by ?? the so-called workload vector, it is assumed that $C^{*}(w):=\min\{C(q):q\in\mathbb{R}_{+}^{\mathbf{I}},\theta\cdot q=w\}$ is attained along a continuous curve as w varies in ?₊. We show that any weak limit point of $c^{n}_{X}$ stochastically dominates the r.v. $\int_{0}^{u}C^{*}(W(t))\,dt$ for a suitable reflected Brownian motion W and construct a sequence of policies that asymptotically achieve this lower bound. For $c^{n}_{Q}$ , an analogous result is proved when, in addition, C ^? is convex. The construction of the policies takes full advantage of the fact that in this regime the number of servers is of the same order as the typical queue-length.     

Creating nonclassical states of Bose-Einstein condensates by dephasing collisions

We show, using an exactly solvable model, that nonlinear dynamics is induced in a double-well Bose-Einstein condensate (BEC) by collisions with a thermal reservoir. This dynamics can facilitate the creation of phase or number squeezing and, at longer times, the creation of macroscopic nonclassical superposition states. Enhancement of these effects is possible by loading the reservoir atoms into an optical lattice.     

Einstein-Podolsky-Rosen correlations of ultracold atomic gases

We demonstrate that collective continuous variables of two species of trapped ultracold bosonic gases can be Einstein-Podolsky-Rosen-correlated (entangled) via inherent interactions between the species. We propose two different schemes for creating these correlations--a dynamical scheme and a static scheme analogous to two-mode squeezing in quantum optics. We quantify the correlations by using known measures of entanglement and study the effect of finite temperature on these quantum correlations.     

Nonsymmetrized Hyperspherical Harmonics with Realistic NN Potentials

The Schrödinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is based on the formalism developed by Gattobigio et al. (Phys Rev A 79:032513, 2009; Few-Body Syst 45:127, 2009; Phys Rev C 83:024001, 2011), where it was applied to four- and six-body systems using central and central spin dependent potentials. In addition we include isospin dependence and noncentral forces in order to be able to make calculations also with more realistic NN potential models. Furthermore, a more efficient procedure to determine the fermionic spectrum is used. The approach is applied to four- and six-body nuclei (⁴He,⁶Li) with various NN potential models including for ⁴He the realistic AV18 potential. It is shown that the results for ground-state energy and radius agree well with those from the literature.     

Morphology and infrared spectroscopy of strongly interacting polymer blends: EVOH/copolyamide-6/6.9

The presence of aliphatic hydroxyl groups in poly(ethylene-co-vinylaleohol) (EVOH) suggests that these copolymers have the potential of forming miscible blends, within certain composition ranges, with a variety of polymers containing complementary functional groups. Hydrogen bonding in EVOH involves a wide variety of inter- and intramolecular species and plays an important role in the phase behavior of EVOH blends. Polymer blends of two random copolymers, EVOH with different ethylene contents and copolyamide-6/6.9 (COPA) at an approximately 1:1 comonomer ratio, were investigated using Fourier transform infrared (FTIR), near-IR, transmission electron microscopy (TEM), and scanning electron microscopy (SEM) methods. The blends were found to be partially miscible due to intermolecular hydrogen bonding between the OH group of the EVOH and the amide group of the copolyamide. The EVOH-rich blends exhibit much lower miscibility compared with the copolyamide-rich blends.     

Edge Kempe equivalence of regular graph covers

Let $G$ be a finite $d$-regular graph with a proper edge coloring. An edge Kempe switch is a new proper edge coloring of $G$ obtained by switching the two colors along some bichromatic cycle. We prove that any other edge coloring can be obtained by performing finitely many edge Kempe switches, provided that $G$ is replaced with a suitable finite covering graph. The required covering degree is bounded above by a constant depending only on $d$.     

Application of the Finite Cell Method to patient-specific femur simulations

Standard methods for predicting the mechanical response of a human femur bone from quantitative computer-tomography (qCT) scans are classically based on the h-version of the finite element method. These methods are often limited in accuracy and efficiency due to the need for segmentation and the slow convergence rate. With the Finite Cell Method (FCM) a high-order fictitious domain method has been developed that overcomes the aforementioned problems and provides accurate results when compared to high-order finite element methods and experimental results. Herein the FCM applied to the analysis of a patient-specific femur is presented. The femur model is determined based on qCT-scans and the elastic response under compression is presented in terms of strains and displacements. The results are compared with a p-FE analysis and validated by results from an in-vitro test of the modeled femur. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On groups of central type,non-degenerate and bijective cohomology classes

A finite group G is of central type (in the non-classical sense) if it admits a non-degenerate cohomology class [c] ∈ H ²(G, ℂ*) (G acts trivially on ℂ*). Groups of central type play a fundamental role in the classification of semisimple triangular complex Hopf algebras and can be determined by their representation-theoretical properties. Suppose that a finite group Q acts on an abelian group A so that there exists a bijective 1-cocycle π ∈ Z ¹(Q,Ǎ), where Ǎ = Hom(A, ℂ*) is endowed with the diagonal Q-action. Under this assumption, Etingof and Gelaki gave an explicit formula for a non-degenerate 2-cocycle in Z ²(G, ℂ*), where G:= A × Q. Hence, the semidirect product G is of central type. In this paper, we present a more general correspondence between bijective and non-degenerate cohomology classes. In particular, given a bijective class [π] ∈ H ¹(Q,Ǎ) as above, we construct non-degenerate classes [cπ] ∈ H ²(G,ℂ*) for certain extensions 1 → A → G → Q → 1 which are not necessarily split. We thus strictly extend the above family of central type groups.