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We present the first analytical superposition of a charged black hole with an annular disk of extremal dust. In order to obtain the solutions, we first solve the Einstein-Maxwell field equations for sources that represent disk-like configurations of matter in confomastatic spacetimes by assuming a functional dependence among the metric function, the electric potential and an auxiliary function,which is taken as a solution of the Laplace equation. We then employ the Lord Kelvin Inversion Method applied to models of finite extension in order to obtain annular disks. The structures obtained extend to infinity, but their total masses are finite and all the energy conditions are satisfied. Finally, we observe that the extremal Reissner-Nordstr\"{o}m black hole can be embedded into the center of the disks by adding a boundary term in the inversion.
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arxiv:1009.1005
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Effect of irradiation on graphene oxide by sunlight, UV light and KrF excimer laser has been investigated in detail. Both sunlight and ultraviolet light reduce graphene oxide well after prolonged irradiation, but laser irradiation produces graphene with negligible oxygen functionalities within a short time. Laser irradiation is also useful for one-step synthesis of metal particle decorated graphene. Laser irradiation of graphene oxide appears to be an efficient procedure for large-scale synthesis of graphene.
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arxiv:1009.1028
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The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high-frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently-developed colored-noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nos\'e-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.
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arxiv:1009.1045
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We analyze the simultaneous time-optimal control of two-spin systems. The two non coupled spins which differ in the value of their chemical offsets are controlled by the same magnetic fields. Using an appropriate rotating frame, we restrict the study to the case of opposite shifts. We then show that the optimal solution of the inversion problem in a rotating frame is composed of a pulse sequence of maximum intensity and is similar to the optimal solution for inverting only one spin by using a non-resonant control field in the laboratory frame. An example is implemented experimentally using techniques of Nuclear Magnetic Resonance.
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arxiv:1009.1077
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We study the spectrum of the integrable open XXX Heisenberg spin chain subject to non-diagonal boundary magnetic fields. The spectral problem for this model can be formulated in terms of functional equations obtained by separation of variables or, equivalently, from the fusion of transfer matrices. For generic boundary conditions the eigenvalues cannot be obtained from the solution of finitely many algebraic Bethe equations. Based on careful finite size studies of the analytic properties of the underlying hierarchy of transfer matrices we devise two approaches to analyze the functional equations. First we introduce a truncation method leading to Bethe type equations determining the energy spectrum of the spin chain. In a second approach the hierarchy of functional equations is mapped to an infinite system of non-linear integral equations of TBA type. The two schemes have complementary ranges of applicability and facilitate an efficient numerical analysis for a wide range of boundary parameters. Some data are presented on the finite size corrections to the energy of the state which evolves into the antiferromagnetic ground state in the limit of parallel boundary fields.
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arxiv:1009.1081
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A foliated manifold (M,F) is minimizable if there exists a Riemannian metric g on M such that every leaf of F is a minimal submanifold of (M,g). Alvarez Lopez defined a cohomology class of degree 1 called the Alvarez class of (M,F) whose triviality characterizes the minimizability of (M,F), when M is closed and F is Riemannian. In this paper, we show that the family of the Alvarez classes of a smooth family of Riemannian foliations is continuous with respect to the parameter. Since the Alvarez class has algebraic rigidity under certain topological conditions on (M,F) as the author showed in arXiv:0909.1125, we show that the minimizability of Riemannian foliations is invariant under deformation under the same topological conditions.
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arxiv:1009.1098
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The question of invisibility for bodies with mirror surface is studied in the framework of geometrical optics. We construct bodies that are invisible/have zero resistance in two mutually orthogonal directions, and prove that there do not exist bodies which are invisible/have zero resistance in all possible directions of incidence.
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arxiv:1009.1104
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We present a general scheme for treating particle beams as many particle systems. This includes the full counting statistics and the requirements of Bose/Fermi symmetry. In the stationary limit, i.e., for longer and longer beams, the total particle number diverges, and a description in Fock space is no longer possible. We therefore extend the formalism to include stationary beams. These beams exhibit a well-defined "local" counting statistics, by which we mean the full counting statistics of all clicks falling into any given finite interval. We treat in detail a model of a source, creating particles in a fixed state, which then evolve under the free time evolution, and we determine the resulting stationary beam in the far field. In comparison to the one-particle picture we obtain a correction due to Bose/Fermi statistics, which depends on the emission rate. We also consider plane waves as stationary many particle states, and determine the distribution of intervals between successive clicks in such a beam.
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arxiv:1009.1109
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M-Learning is a new learning paradigm of the new social structure with mobile and wireless technologies.Smart school is one of the four flagship applications for Multimedia Super Corridor (MSC) under Malaysian government initiative to improve education standard in the country. With the advances of mobile devices technologies, mobile learning could help the government in realizing the initiative. This paper discusses the prospect of implementing mobile learning for primary school students. It indicates significant and challenges and analysis of user perceptions on potential mobile applications through a survey done in primary school context. The authors propose the m-Learning for mathematics by allowing the extension of technology in the traditional classroom in term of learning and teaching.
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arxiv:1009.1170
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The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Gr\"unbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages, arXiv:1007.4327]. In this study, a simple proof of the necessary and sufficient condition of orthogonality is given for a general case.
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arxiv:1009.1203
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We study the beam energy dependence of equilibration process and space-time characteristics of participant and spectator matter. For this, we simulated the semi-central collisions of $^{40}Ca+ ^{40}Ca$ at incident energies of 400, 600 and 1000 AMeV within the \emph{quantum molecular dynamics} (QMD) approach. Our numerical calculations based on the molecular dynamics approach show that incident energy of the projectile influences the reaction observables drastically. The effect is more visible for transverse expansion of the nuclear matter and transparency behavior. The degree of thermalization of participant matter, however, remains independent of the incident energy. The characteristics of the trajectories followed by the nucleons suffering maximal and minimal binary collisions are also analyzed.
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arxiv:1009.1249
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We present spherically symmetric boson stars as black hole mimickers based on the power spectrum of a simple accretion disk model. The free parameters of the boson star are the mass of the boson and the fourth order self-interaction coefficient in the scalar field potential. We show that even if the mass of the boson is the only free parameter it is possible to find a configuration that mimics the power spectrum of the disk due to a black hole of the same mass. We also show that for each value of the self-interaction a single boson star configuration can mimic a black hole at very different astrophysical scales in terms of the mass of the object and the accretion rate. In order to show that it is possible to distinguish one of our mimickers from a black hole we also study the deflection of light.
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arxiv:1009.1250
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We find the logarithmic small ball asymptotics for the $L_2$-norm with respect to a degenerate self-similar measures of a certain class of Gaussian processes including Brownian motion, Ornstein - Uhlenbeck process and their integrated counterparts.
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arxiv:1009.1252
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We complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to derived equivalence.
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arxiv:1009.1259
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I describe the parton picture at strong coupling emerging from the gauge/gravity duality, with emphasis on the universality of the phenomenon of parton saturation. I discuss several consequences of this picture for the phenomenology of a strongly coupled quark-gluon plasma, which are potentially relevant for heavy ion collisions at RHIC and LHC.
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arxiv:1009.1278
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Bosonic atom-trimer scattering is studied in the unitary limit using momentum-space equations for four-particle transition operators. The impact of the Efimov effect on the atom-trimer scattering observables is explored and a number of universal relations is established. Positions and widths of tetramer resonances are determined. Trimer relaxation rate constant is calculated.
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arxiv:1009.1295
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The Spectral and Photometric Imaging Receiver (SPIRE) on Herschel has been carrying out deep extragalactic surveys, one of whose aims is to establish spectral energy distributions (SED)s of individual galaxies spanning the infrared/submillimeter (IR/SMM) wavelength region. We report observations of the (IR/SMM) emission from the Lockman North field (LN) and Great Observatories Origins Deep Survey field North (GOODS-N). Because galaxy images in the wavelength range covered by Herschel generally represent a blend with contributions from neighboring galaxies, we present sets of galaxies in each field especially free of blending at 250, 350, and 500 microns. We identify the cumulative emission of these galaxies and the fraction of the far infrared cosmic background radiation they contribute. Our surveys reveal a number of highly luminous galaxies at redshift z ~< 3 and a novel relationship between infrared and visible emission that shows a dependence on luminosity and redshift.
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arxiv:1009.1371
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Analytical calculations based on a Landau Level (LL) picture are reported for an interface (with a finite-width Quantum Well (QW)) and for a fully three-dimensional charged quantum electronic system in an external magnetic field. They lead to a sequence of previously unnoticed singular features in global magnetization and magnetic susceptibility that lead to nontrivial corrections to the standard de Haas - van Alphen periods. Additional features due to Zeeman splitting are also reported (such as new energy minima that originate from the interplay of QW, Zeeman and LL Physics) that are possibly useful for the design of quantum devices. A corresponding calculation in a Composite Fermion picture leads to new predictions on magnetic response properties of a fully-interacting electron liquid in a finite-width interface.
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arxiv:1009.1390
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We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new results. Our approach relies on the commutation of a Hankel operator with some differential operator of second order.
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arxiv:1009.1391
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Here, we present a de Haas-van Alphen (dHvA) effect1 study on the newly discovered LaFeAsO1-xFx compounds2,3 in order to unveil the topography of the Fermi surface associated with their antiferromagnetic and superconducting phases, which is essential for understanding their magnetism, pairing symmetry and superconducting mechanism. Calculations 4 and surface-sensitive measurements 5,6,7 provided early guidance, but lead to contradictory results, generating a need for a direct experimental probe of their bulk Fermi surface. In antiferromagnetic LaFeAsO1-xFx 8,9 we observe a complex pattern in the Fourier spectrum of the oscillatory component superimposed onto the magnetic torque signal revealing a reconstructed Fermi surface, whose geometry is not fully described by band structure calculations. Surprisingly, several of the same frequencies, or Fermi surface cross-sectional areas, are also observed in superconducting LaFeAsO1-xFx (with a superconducting transition temperature Tc ~ 15 K). Although one could attribute this to inhomogeneous F doping, the corresponding effective masses are largely enhanced with respect to those of the antiferromagnetic compound. Instead, this implies the microscopic coexistence of superconductivity and antiferromagnetism on the same Fermi surface in the underdoped region of the phase diagram of the LaFeAsO1-xFx series. Thus, the dHvA-effect reveals a more complex Fermi surface topography than that predicted by band structure calculations4 upon which the currently proposed superconducting pairing scenarios10,11,12,13 are based, which could be at the origin of their higher Tcs when compared to their phosphide analogs.
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arxiv:1009.1408
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We devise a nonlocal correlation energy functional that describes the entire range of dispersion interactions in a seamless fashion using only the electron density as input. The new functional is considerably simpler than its predecessors of a similar type. The functional has a tractable and robust analytic form that lends itself to efficient self-consistent implementation. When paired with an appropriate exchange functional, our nonlocal correlation model yields accurate interaction energies of weakly-bound complexes, not only near the energy minima but also far from equilibrium. Our model exhibits an outstanding precision at predicting equilibrium intermonomer separations in van der Waals complexes. It also gives accurate covalent bond lengths and atomization energies. Hence the functional proposed in this work is a computationally inexpensive electronic structure tool of broad applicability.
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arxiv:1009.1421
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We show a microscopic derivation of a quantum master equation with counting terms which describes the electron statistics. A localized spin behaves as a probe whose precession angle monitors the net electron current by the magnetic-moment interaction. The probe Hamiltonian is proportional to the current, and is determined self-consistently for a model of a quantum dot. Then it turns out that the quantum master equation for the spin-precession contains the counting terms. As an application, we show the fluctuation theorem for the electron current.
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arxiv:1009.1428
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By using coupling method, a Bismut type derivative formula is established for the Markov semigroup associated to a class of hyperdissipative stochastic Navier-Stokes/Burgers equations. As applications, gradient estimates, dimension-free Harnack inequality, strong Feller property, heat kernel estimates and some properties of the invariant probability measure are derived.
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arxiv:1009.1464
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In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold $(M, <, >)$. We then draw some geometric conclusions with the aid of the maximum principle.
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arxiv:1009.1480
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Investigations of photoluminescence (PL) in the magnetic field of quantum structures based on the ZnSe quantum well with asymmetrical ZnBeMnSe and ZnBeSe barriers reveal that the introduction of Be into semimagnetic ZnMnSe causes a decrease of the exchange integrals for conductive and valence bands as well as the forming of a complex based on Mn, degeneration of an energy level of which with the energy levels of the V band of ZnBeMnSe or ZnSe results in spin-flip electron transitions.
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arxiv:1009.1490
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Tollefson described a variant of normal surface theory for 3-manifolds, called Q-theory, where only the quadrilateral coordinates are used. Suppose $M$ is a triangulated, compact, irreducible, boundary-irreducible 3-manifold. In Q-theory, if $M$ contains an essential surface, then the projective solution space has an essential surface at a vertex. One interesting situation not covered by this theorem is when $M$ is boundary reducible, e.g. $M$ is an unknot complement. We prove that in this case $M$ has an essential disc at a vertex of the Q-projective solution space.
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arxiv:1009.1500
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Planning for the next generation of light-shining-through-wall experiments has started. It is therefore timely to investigate possible ways to optimize their setups. The goals are to improve the sensitivity towards smaller couplings and increase the mass range to which the experiments are sensitive. We discuss possible magnet arrangements and the effects of the unavoidable gaps in the magnetic field profile. Furthermore, we discuss requirements on the diameter of the laser beam and aperture of the magnets in order to achieve high-quality cavities.
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arxiv:1009.1519
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This paper aims to propose a significant way of remote access and real time monitoring of a particular geographic area by integrating wireless sensor clouds with existing Telecom infrastructure and applications built around them through a gateway. This utility is very potent for environment monitoring in harsh and inaccessible places like mines, nuclear reactors, etc. We demonstrate a scaled down version of multi-hop network of wireless sensor nodes and its integration with existing telecom network infrastructure via a gateway. The kind of results achieved like temperature monitoring etc. gives a glimpse of an enormous step ahead in mine safety.
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arxiv:1009.1526
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We present a search for the rare decays B+ -> K+ nu nubar and B0 -> K0 nu nubar using 459 million BBbar pairs collected with the BaBar detector at the SLAC National Accelerator Laboratory. Flavor-changing neutral-current decays such as these are forbidden at tree level but can occur through one-loop diagrams in the Standard Model (SM), with possible contributions from new physics at the same order. The presence of two neutrinos in the final state makes identification of signal events challenging, so reconstruction in the semileptonic decay channels B -> D(*) l nu of the B meson recoiling from the signal B is used to suppress backgrounds. We set an upper limit at the 90% confidence level of 1.3 x 10^{-5} on the total branching fraction for B+ -> K+ nu nubar, and 5.6 x 10^{-5} for B0 -> K0 nu nubar. We additionally report partial branching fractions in two ranges of di-neutrino mass squared for B+ -> K+ nu nubar.
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arxiv:1009.1529
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We obtain analitically the $v^2$ dependence of the drag force on a falling sphere close to the drag crisis, as well as the drag coefficient at the drag crisis, with excellent agreement with experiment. We take into account the effects of viscosity in creating a turbulent boundary layer and perform the calculations using the Navier-Stokes equation.
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arxiv:1009.1536
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Achieving coherent population transfer in the solid-state is challenging compared to atomic systems due to closely spaced electronic states and fast decoherence. Here, within an atomistic pseudopotential theory, we offer recipes for the stimulated Raman adiabatic passage in embedded silicon and germanium nanocrystals. The transfer efficiency spectra displays characteristic Fano resonances. By exploiting the Stark effect, we predict that transfer can be switched off with a dc voltage. As the population transfer is highly sensitive to structural variations, with a choice of a sufficiently small two-photon detuning bandwidth, it can be harnessed for addressing individual nanocrystals within an ensemble.
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arxiv:1009.1538
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We study the attenuation of long-wavelength shear sound waves propagating through model jammed packings of frictionless soft spheres interacting with repulsive springs. The elastic attenuation coefficient, $\alpha(\omega)$, of transverse phonons of low frequency, $\omega$, exhibits power law scaling as the packing fraction $\phi$ is lowered towards $\phi_c$, the critical packing fraction below which rigidity is lost. The elastic attenuation coefficient is inversely proportional to the scattering mean free path and follows Rayleigh law with $\alpha(\omega)\sim \omega^4 (\phi - \phi_c)^{-5/2}$ for $\omega$ much less than $\omega^* \sim (\phi - \phi_c)^{1/2}$, the characteristic frequency scale above which the energy diffusivity and density of states plateau. This scaling of the attenuation coefficient, consistent with numerics, is obtained by assuming that a jammed packing can be viewed as a mosaic composed of domains whose characteristic size $\ell^ * \sim (\phi-\phi_c) ^{-1/2}$ diverges at the transition.
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arxiv:1009.1541
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We report experiments on hard sphere colloidal glasses that reveal a type of shear banding hitherto unobserved in soft glasses. We present a scenario that relates this to an instability arising from shear-concentration coupling, a mechanism previously thought unimportant in this class of materials. Below a characteristic shear rate $\dot\gamma_c$ we observe increasingly non-linear velocity profiles and strongly localized flows. We attribute this trend to very slight concentration gradients (likely to evade direct detection) arising in the unstable flow regime. A simple model accounts for both the observed increase of $\dot\gamma_c$ with concentration, and the fluctuations observed in the flow.
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arxiv:1009.1579
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We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to $\R^{n}\setminus \Omega, n\ge 3$, and so that their boundary is a minimal hypersurface. (Here, $\Omega\subset \R^{n}$ is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by $(V/\beta_{n})^{(n-2)/n}$, where $V$ is the Euclidean volume of $\Omega$ and $\beta_{n}$ is the volume of the Euclidean unit $n$-ball. This gives a partial proof to a conjecture of Bray and Iga \cite{brayiga}. Surprisingly, we do not require the boundary to be outermost.
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arxiv:1009.1587
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Efficient resource discovery and availability improvement are very important issues in unstructured P2P networks. In this paper, a bio-inspired resource discovery scheme inspired by the principle of elephants migration is proposed. A replication scheme based on Q-learning and erasure codes is also introduced. Simulation results show that the proposed schemes significantly increases query success rate and availability, and reduces the network traffic as the resources are effectively distributed to well-performing nodes.
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arxiv:1009.1685
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We tested the Ho\u{r}ava Lifshitz (HL) quantum gravity model by using the L{\" u}, Mei and Pope solutions for primordial black holes (PBHs) and the observational upper bounds of the PBH density parameters. We found that, although the HL model is severely constrained, it is not ruled out. When our analysis is combined with that of Dutta and Saridakis the observed value of the density parameter $\Omega_{PBH}$ might rise by several percent as the running energy parameter $\lambda$ increases.
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arxiv:1009.1703
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We compute the sparticle mass spectrum in the minimal four-dimensional construction that interpolates between gaugino mediation and ordinary gauge mediation.
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arxiv:1009.1714
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In their comment[1] on our Letter [arXiv:0907.0767], Leggett and Garg claim that they have introduced in their original paper (LG1) a dependence on measurement times. They also claim that Eqs.(HMDR1) and (LG2a) can therefore not be linked in such a way that the arguments of [arXiv:0907.0767] can be transcribed. However, (LG1) distinguishes only three time differences, and all experimental results corresponding to the same time differences are identically labeled and therefore treated as mathematically identical. We therefore cannot agree with the argumentation of Leggett and Garg: except for a change of nomenclature Eqs.(HMDR1) and (LG2a) are the same. A more extensive discussion of this point can be found in [arXiv:0901.2546].
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arxiv:1009.1717
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In this paper, an original result in terms of a sufficient condition to test identifiability of nonlinear delayed-differential models with constant delays and multi-inputs is given. The identifiability is studied for the linearized system and a criterion for linear systems with constant delays is provided, from which the identifiability of the original nonlinear system can be proved. This result is obtained by combining a classical identifiability result for nonlinear ordinary differential systems due to M.S. Grewal and K. Glover (1976) with the identifiability of linear delayed-differential models developed by Y. Orlov et al. (2002). This paper is a generalization of the results provided by L. Denis-Vidal, C. Jauberthie, G. Joly-Blanchard (2006), which deal with the specific case of nonlinear delayed-differential models with two delays and a single input.
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arxiv:1009.1742
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The question is discussed of what is the speed of gravity (at the fundamental non-perturbative level). The question is important, if nowhere else, in discussing the problem of information "lost" in black holes. It turns out that the duly defined "gravitational signal" generally may be causal, superluminal and "semi-superluminal". In the class of globally hyperbolic spacetimes the two last varieties coincide. And if some (often imposed, but not always satisfied) conditions hold, the signals may be \emph{only} causal. In this sense the speed of gravity does not exceed the speed of light.
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arxiv:1009.1761
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Void of any inherent structure in classical physics, the vacuum has revealed to be incredibly crowded with all sorts of processes in relativistic quantum physics. Yet, its direct effects are usually so subtle that its structure remains almost as evasive as in classical physics. Here, in contrast, we report on the discovery of a novel effect according to which the vacuum is compelled to play an unexpected central role in an astrophysical context. We show that the formation of relativistic stars may lead the vacuum energy density of a quantum field to an exponential growth. The vacuum-driven evolution which would then follow may lead to unexpected implications for astrophysics, while the observation of stable neutron-star configurations may teach us much on the field content of our Universe.
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arxiv:1009.1771
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We probe for statistical and Coulomb induced spin textures among the low-lying states of repulsively-interacting particles confined to potentials that are both rotationally and time-reversal invariant. In particular, we focus on two-dimensional quantum dots and employ configuration-interaction techniques to directly compute the correlated many-body eigenstates of the system. We produce spatial maps of the single-particle charge and spin density and verify the annular structure of the charge density and the rotational invariance of the spin field. We further compute two-point spin correlations to determine the correlated structure of a single component of the spin vector field. In addition, we compute three-point spin correlation functions to uncover chiral structures. We present evidence for both chiral and quasi-topological spin textures within energetically degenerate subspaces in the three- and four-particle system.
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arxiv:1009.1784
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The energetics of mixing and defect ordering in solid solutions of fluorite-structured ThO$_{2}$ with oxides of trivalent cations (Sc, In, Y, Nd, La) are investigated by electronic density-functional-theory (DFT). Through DFT calculations of structures enumerated by lattice-algebra techniques, we identify the lowest-energy patterns for defect clustering for four separate dopant concentrations. The most stable structures are characterized by a repulsive interaction between nearest-neighbor vacancies on the oxygen sublattice. The enthalpies of formation with respect to constituent oxides are positive for all dopants considered, and show a tendency to decrease in magnitude as the size and electronegativity of the trivalent dopant decrease. Due to the small positive formation enthalpies and low oxygen-vacancy binding energy with La dopants, La$_{2}$O$_{3}$-ThO$_{2}$ solid solutions are predicted to have relatively high ionic conductivities relative to those for the other aliovalent dopants considered. Our results are compared with those for the more widely studied ZrO$_{2}$ and CeO$_{2}$ fluorite-structured solid solutions with trivalent cations.
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arxiv:1009.1850
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We consider the asymmetric simple exclusion process (ASEP) on the integers in which the initial density at a site (the probability that it is occupied) is given by a periodic function on the positive integers. (When the function is constant this is the step Bernoulli initial condition.) Starting with a result in earlier work we find a formula for the probability distribution for a given particle at a given time which is a sum over positive integers k of integrals of order k.
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arxiv:1009.1863
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Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in $\mathcal{T}$ is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in $\mathbb{R}^d$. We use these partitions with slack for embedding ultrametrics into $d$-dimensional Euclidean space: we give a $\mathop{\rm polylog}(\Delta)$-approximation algorithm for embedding $n$-point ultrametrics into $\mathbb{R}^d$ with minimum distortion, where $\Delta$ denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in $n$. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.
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arxiv:1009.1866
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Often the result of a scientific experiment is given by the difference of measurements in two configurations, denoted by A and B. Since the measurements are not obtained simultaneously, drift of the zero-point can bias the result. In practice measurement patterns are used to minimize this bias. The time sequence AB followed by BA, for example, would cancel a linear drift in the average difference A-B. We propose taking data with an alternating series ABAB.., and removing drift with a post-hoc analysis. We present an analysis method that removes bias from the result for drift up to polynomial order p. A statistical cost function c(N) is introduced to compare the uncertainty in the end result with that from using a raw data average. For a data set size N>30 the statistical cost is negligible. For N<30 the cost is plotted as a function of N and filter order p and the trade off between the size of the data set and p is discussed.
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arxiv:1009.1894
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We consider a macroscopic two-sate system based on persistent current states of a Bose-Einstein condensate (BEC) of interacting neutral atoms confined in a ring with a weak Josephson link. We demonstrate that macroscopic superpositions of different BEC flows are energetically favorable in this system. Moreover, a macroscopic two-state dynamics emerges in the low energy limit. We also investigate fundamental limitations due to the noise inherent to the interacting BEC of Josephson-ring geometry. We show that the coherent macroscopic dynamics is readily measurable for an experimentally accessible range of parameters.
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arxiv:1009.1901
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We find the novel effect on the decay of a false vacuum in view of quantum field theory, which is induced by a field coupling to the scalar field related to a first-order phase transition. This effect of the environment can never be included in the traditional method using the effective potential, and, in fact, acts as dissipative and fluctuation effects on tunneling phenomena. We show that the decay of the false vacuum is drastically either enhanced or suppressed. It is also clarified what kind of interaction enhance or suppress the tunneling probability.
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arxiv:1009.1927
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Using ATLAS data corresponding to 70 +- 8 nb^-1 of integrated luminosity from the 7 TeV proton-proton collisions at the LHC, distributions of relevant supersymmetry-sensitive variables are shown for the final state containing jets, missing transverse momentum and one isolated electron or muon. With increased integrated luminosities, selections based on these distributions will be used in the search for supersymmetric particles: it is thus important to show that the Standard Model backgrounds to these searches are under good control.
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arxiv:1009.1951
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We continue an analysis, started in [10], of some issues related to the incompressible Euler or Navier-Stokes (NS) equations on a d-dimensional torus T^d. More specifically, we consider the quadratic term in these equations; this arises from the bilinear map (v, w) -> v . D w, where v, w : T^d -> R^d are two velocity fields. We derive upper and lower bounds for the constants in some inequalities related to the above bilinear map; these bounds hold, in particular, for the sharp constants G_{n d} = G_n in the Kato inequality | < v . D w | w >_n | <= G_n || v ||_n || w ||^2_n, where n in (d/2 + 1, + infinity) and v, w are in the Sobolev spaces H^n, H^(n+1) of zero mean, divergence free vector fields of orders n and n+1, respectively. As examples, the numerical values of our upper and lower bounds are reported for d=3 and some values of n. When combined with the results of [10] on another inequality, the results of the present paper can be employed to set up fully quantitative error estimates for the approximate solutions of the Euler/NS equations, or to derive quantitative bounds on the time of existence of the exact solutions with specified initial data; a sketch of this program is given.
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arxiv:1009.2051
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We construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kind of trees or forests, and some more general classes of graphs, ranging from the Connes-Kreimer algebra to an algebra of labelled forests isomorphic to the Hopf algebra of parking functions, and to a new noncommutative algebra based on endofunctions admitting many interesting subalgebras and quotients.
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arxiv:1009.2067
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This paper analyzes the sensitivity of antineutrino count rate measurements to changes in the fissile content of civil power reactors. Such measurements may be useful in IAEA reactor safeguards applications. We introduce a hypothesis testing procedure to identify statistically significant differences between the antineutrino count rate evolution of a standard 'baseline' fuel cycle and that of an anomalous cycle, in which plutonium is removed and replaced with an equivalent fissile worth of uranium. The test would allow an inspector to detect anomalous reactor activity, or to positively confirm that the reactor is operating in a manner consistent with its declared fuel inventory and power level. We show that with a reasonable choice of detector parameters, the test can detect replacement of 73 kg of plutonium in 90 days with 95% probability, while controlling the false positive rate at 5%. We show that some improvement on this level of sensitivity may be expected by various means, including use of the method in conjunction with existing reactor safeguards methods. We also identify a necessary and sufficient daily antineutrino count rate to achieve the quoted sensitivity, and list examples of detectors in which such rates have been attained.
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arxiv:1009.2123
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Two widely proposed kt-dependent gluon distributions in the small-x saturation regime are investigated using two particle back-to-back correlations in high energy scattering processes. The Weizsacker-Williams gluon distribution, interpreted as the number density of gluon inside the nucleus, is studied in the quark-antiquark jet correlation in deep inelastic scattering. On the other hand, the unintegrated gluon distribution, defined as the Fourier transform of the color-dipole cross section, is probed in the direct photon-jet correlation in pA collisions. Dijet-correlation in pA collisions depends on both gluon distributions through combination and convolution in the large Nc limit.
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arxiv:1009.2141
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A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally $O(n^{-1/2})$ and can be very considerable when the distribution is heavily biased or skew. This note shows how one may reduce this error to $O(n^{-(j+1)/2})$, where $j$ is a given integer. The case considered is when the statistic is the mean of the sample values from a continuous one-parameter distribution, after the sample has undergone an initial transformation.
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arxiv:1009.2190
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Feynman perturbation theory for nonabelian gauge theory in light-like gauge is investigated. A lattice along two space-like directions is used as a gauge invariant ultraviolet regularization. For preservation of the polinomiality of action we use as independent variables arbitrary (non-unitary) matrices related to the link of the lattice. The action of the theory is selected in such a way to preserve as much as possible the rotational invariance, which remains after introduction of the lattice, as well as to make superfluous degrees of freedom vanish in the limit of removing the regularization. Feynman perturbation theory is constructed and diagrams which does not contain ultraviolet divergences are analyzed. The scheme of renormalization of this theory is discussed.
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arxiv:1009.2238
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Within the Machian model of the universe the dark energy is identified with the Machian energy of collective gravitational interactions of all particles inside the horizon. It is shown that the fine structure constant can be expressed in terms of the observed radiative, baryon and dark energy densities of the universe and the densities of various matter components are interrelated via it.
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arxiv:1009.2266
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The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a compact metric space. The theorem stating that a weakly mixing and strongly transitive system is $\Delta$-transitive is extended to a non-invertible case with a simple proof. Two examples are constructed, answering the questions posed by Moothathu [Colloq. Math. 120 (2010), no. 1, 127--138]. The first one is a multi-transitive non weakly mixing system, and the second one is a weakly mixing non multi-transitive system. The examples are special spacing shifts. The later shows that the assumption of minimality in the Multiple Recurrence Theorem can not be replaced by weak mixing.
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arxiv:1009.2277
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Lowering the operating voltage of electrooptic modulators is desirable for a variety of applications, most notably in analog photonics , and digital data communications . In particular for digital systems such as CPUs, it is desirable to develop modulators that are both temperature-insensitive and compatible with typically sub-2V CMOS electronics ; however, drive voltages in silicon-based MZIs currently exceed 6.5V . Here we show an MZI modulator based on an electrooptic polymer-clad silicon slot waveguide, with a halfwave voltage of only 0.69V, and a bandwidth of 500 MHz. We also show that there are also paths to significantly improve both the bandwidth and drive voltage . Our silicon-organic modulator has an intrinsic power consumption less than 0.66 pJ/bit, nearly an order of magnitude improvement over the previous lowest energy silicon MZI .
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arxiv:1009.2336
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We present the solutions of equations of degrees 3 and 4 using Galois theory and some simple Fourier analysis for finite groups, together with historical comments on these and other solution methods.
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arxiv:1009.2373
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We study kinetic mixing between massless U(1)s in toroidal orbifolds with D3-branes at orbifold singularities. We focus in particular on C^3/Z_4 singularities but also study C^3/Z_6 and C^3/Z'_6 singularities. We find kinetic mixing can be present and describe the conditions for it to occur. Kinetic mixing comes from winding modes in the N=2 sector of the orbifold. If kinetic mixing is present its size depends only on the complex structure modulus of the torus and is independent of the K\"ahler moduli. We also study gauge threshold corrections for local Z_M x Z_N orbifold models finding that, consistent with previous studies, gauge couplings run from the bulk winding scale rather than the string scale.
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arxiv:1009.2380
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Tverberg's theorem asserts that every (k-1)(d+1)+1 points in R^d can be partitioned into k parts, so that the convex hulls of the parts have a common intersection. Calder and Eckhoff asked whether there is a purely combinatorial deduction of Tverberg's theorem from the special case k=2. We dash the hopes of a purely combinatorial deduction, but show that the case k=2 does imply that every set of O(k^2 log^2 k) points admits a Tverberg partition into k parts.
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arxiv:1009.2384
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Motivated by recent experimental progress to read out quantum bits implemented in superconducting circuits via the phenomenon of dynamical bifurcation, transitions between steady orbits in a driven anharmonic oscillator, the Duffing oscillator, are analyzed. In the regime of weak dissipation a consistent master equation in the semiclassical limit is derived to capture the intimate relation between finite tunneling and reflection and bath induced quantum fluctuations. From the corresponding steady state distributions analytical expressions for the switching probabilities are obtained. It is shown that a reduction of the transition rate due to finite reflection at the phase-space barrier is overcompensated by an increase due to environmental quantum fluctuations that are specific for diffusion processes over dynamical barriers. Moreover, it is revealed that close to the bifurcation threshold the escape dynamics enters an overdamped domain such that the quantum mechanical energy scale associated with friction even exceeds the thermal energy scale.
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arxiv:1009.2401
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It has been suggested that consciousness plays an important role in quantum mechanics as it is necessary for the collapse of wave function during the measurement. Furthermore, this idea has spawned a symmetrical proposal: a possibility that quantum mechanics explains the emergence of consciousness in the brain. Here we formulated several predictions that follow from this hypothetical relationship and that can be empirically tested. Some of the experimental results that are already available suggest falsification of the first hypothesis. Thus, the suggested link between human consciousness and collapse of wave function does not seem viable. We discuss the constraints implied by the existing evidence on the role that the human observer may play for quantum mechanics and the role that quantum mechanics may play in the observer's consciousness.
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arxiv:1009.2404
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Two special calorimeters are foreseen for the instrumentation of the very forward region of the ILC detector, a luminometer designed to measure the rate of low angle Bhabha scattering events with a precision better than 10-3 and a low polar angle calorimeter, adjacent to the beam-pipe. The latter will be hit by a large amount of beamstrahlung remnants. The amount and shape of these depositions will allow a fast luminosity estimate and the determination of beam parameters. The sensors of this calorimeter must be radiation hard. Both devices will improve the hermeticity of the detector in the search for new particles. Finely segmented and very compact calorimeters will match the requirements. Due to the high occupancy fast front-end electronics is needed. The design of the calorimeters developed and optimised with Monte Carlo simulations is presented. Sensors and readout electronics ASICs have been designed and prototypes are available. Results on the performance of these major components are summarised.
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arxiv:1009.2433
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We present results for the next-to-leading order calculation of single-top Wt-channel production interfaced to Shower Monte Carlo programs, implemented according to the POWHEG method. A comparison with MC@NLO is carried out. Results obtained using the PYTHIA shower are also shown and the effect of typical cuts is briefly discussed.
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arxiv:1009.2450
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We study a certain cycle map defined on finite dimensional modules for the W-algebra with regular integral central character. Via comparison with the theory in postive characteristic, we show that this map injects into the top Borel-Moore homology group of a Springer fibre. This is the first result in a larger program to completely desribe the finite dimensional modules for the W algebras.
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arxiv:1009.2456
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We determine the valence parton distribution function of the pion by performing a new analysis of data for the Drell-Yan process $\pi^- N\to \mu^+\mu^-X$. Compared to previous analyses, we include next-to-leading-logarithmic threshold resummation effects in the calculation of the Drell-Yan cross section. As a result of these, we find a considerably softer valence distribution at high momentum fractions $x$ than obtained in previous next-to-leading order analyses, in line with expectations based on perturbative-QCD counting rules or Dyson-Schwinger equations.
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arxiv:1009.2481
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Analytical arguments suggest that a large class of scalar field potentials permit the existence of oscillons -- pseudo-stable, non-topological solitons -- in three spatial dimensions. In this paper we numerically explore oscillon solutions in three dimensions. We confirm the existence of these field configurations as solutions to the Klein-Gorden equation in an expanding background, and verify the predictions of Amin and Shirokoff for the characteristics of individual oscillons for their model. Further, we demonstrate that significant numbers of oscillons can be generated via fragmentation of the inflaton condensate, consistent with the analysis of Amin. These emergent oscillons can easily dominate the post-inflationary universe. Finally, both analytic and numerical results suggest that oscillons are stable on timescales longer than the post-inflationary Hubble time. Consequently, the post-inflationary universe can contain an effective matter-dominated phase, during which it is dominated by localized concentrations of scalar field matter.
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arxiv:1009.2505
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We study first-passage properties for a particle that diffuses either inside or outside of generalized paraboloids, defined by y=a(x_1^2+...+x_{d-1}^2)^{p/2} where p>1, with absorbing boundaries. When the particle is inside the paraboloid, the survival probability S(t) generically decays as a stretched exponential, ln(S) ~ -t^{(p-1)/(p+1)}, independent of the spatial dimensional. For a particle outside the paraboloid, the dimensionality governs the asymptotic decay, while the exponent p specifying the paraboloid is irrelevant. In two and three dimensions, S ~ t^{-1/4} and S ~(ln t)^{-1}, respectively, while in higher dimensions the particle survives with a finite probability. We also investigate the situation where the interior of a paraboloid is uniformly filled with non-interacting diffusing particles and estimate the distance between the closest surviving particle and the apex of the paraboloid.
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arxiv:1009.2530
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Let $\lambda^{*}>0$ denote the largest possible value of $\lambda$ such that $$ \{{array}{lllllll} \Delta^{2}u=\frac{\lambda}{(1-u)^{p}} & \{in}\ \ B, 0<u\leq 1 & \{in}\ \ B, u=\frac{\partial u}{\partial n} =0 & \{on}\ \ \partial B. {array} . $$ has a solution, where $B$ is the unit ball in $R^{n}$ centered at the origin, $p>1$ and $n$ is the exterior unit normal vector. We show that for $\lambda=\lambda^{*}$ this problem possesses a unique weak solution $u^{*}$, called the extremal solution. We prove that $u^{*}$ is singular when $n\geq 13$ for $p$ large enough and $1-C_{0}r^{\frac{4}{p+1}}\leq u^{*}(x)\leq 1-r^{\frac{4}{p+1}}$ on the unit ball, where $ C_{0}:=(\lambda^{*}/\bar{\lambda})^{\frac{1}{p+1}}$ and $\bar{\lambda}:=\frac{8(p-1)}{(p+1)^{2}}[n-\frac{2(p-1)}{p+1}][n-\frac{4p}{p+1}]$. Our results actually complete part of the open problem which \cite{D} lef
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arxiv:1009.2546
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Three separate questions of relevance to Major League Baseball are investigated from a physics perspective. First, can a baseball be hit farther with a corked bat? Second, is there evidence that the baseball is more lively today than in earlier years? Third, can storing baseballs in a temperature- or humidity-controlled environment significantly affect home run production? Each of these questions is subjected to a physics analysis, including an experiment, an interpretation of the data, and a definitive answer. The answers to the three questions are no, no, and yes.
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arxiv:1009.2549
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We show that the evaluation of an integral considered by Boros and Moll is a special case of a convolution result about Student t-densities obtained by the authors in 2008.
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arxiv:1009.2598
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The design of a scheduling scheme is crucial for the efficiency and user-fairness of wireless networks. Assuming that the quality of all user channels is available to a central controller, a simple scheme which maximizes the utility function defined as the sum logarithm throughput of all users has been shown to guarantee proportional fairness. However, to acquire the channel quality information may consume substantial amount of resources. In this work, it is assumed that probing the quality of each user's channel takes a fraction of the coherence time, so that the amount of time for data transmission is reduced. The multiuser diversity gain does not always increase as the number of users increases. In case the statistics of the channel quality is available to the controller, the problem of sequential channel probing for user scheduling is formulated as an optimal stopping time problem. A joint channel probing and proportional fair scheduling scheme is developed. This scheme is extended to the case where the channel statistics are not available to the controller, in which case a joint learning, probing and scheduling scheme is designed by studying a generalized bandit problem. Numerical results demonstrate that the proposed scheduling schemes can provide significant gain over existing schemes.
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arxiv:1009.2602
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In this paper, we investigate the relations between the pitch, the angle of pitch and drall of parallel ruled surface of a closed curve in dual Lorentzian space.
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arxiv:1009.2625
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We review the prospects for Central Exclusive Diffractive (CED) production of Higgs bosons in the SM with a fourth generation of fermions at the LHC using forward proton detectors installed at 220m and 420m distance around ATLAS and / or CMS. We discuss the determination of Higgs spin-parity and coupling structures at the LHC and show that the forward proton mode would provide a critical information on the CP properties of the Higgs bosons.
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arxiv:1009.2680
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We have used Virtual Observatory technology to analyse the disk scale length and central surface brightness for a sample of 29955 bright disk galaxies from the Sloan Digital Sky Survey. We use the results in the r-band and revisit the relation between these parameters and the galaxy morphology, and find the average disk surface brightness of 20.2(0.7) mag/arcsec^2. We confirm that late type spirals populate the lower left corner of the scale length-mu0 plane and that the early and intermediate spirals are mixed in this diagram, with disky ellipticals at the top left corner. We further investigate the Freeman Law and affirm that it indeed defines an upper limit for the disk central surface brightness in bright galaxies, and that disks in late type spirals have fainter central surface brightness. Our results are based on a volume corrected sample of galaxies in the local universe (z < 0.3) that is two orders of magnitudes larger than any sample previously studied, and deliver statistically significant implications that provide a comprehensive test bed for future theoretical studies and numerical simulations of galaxy formation and evolution.
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arxiv:1009.2692
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The existence of bound states in the continuum was predicted at the dawn of quantum mechanics by von Neumann and Wigner. In this work we discuss the mechanism of formation of these exotic states and the feasibility to observe them experimentally in symmetrical heterostructures composed by segments of graphene ribbons with different widths forming a graphene quantum dot. We identify the existence of bound states in the continuum in these graphene quantum dot systems by means of local density of states and electronic conductance calculations.
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arxiv:1009.2711
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The production of doubly charged Higgs bosons (H^{\pm\pm}) at the CERN LHC can give rise to distinctive multi-lepton signatures. The discovery potential of H^{\pm\pm} can be optimized by considering a search strategy which is sensitive to both of the dominant production mechanisms, q\bar q\to H^{++}H^{--} and q\bar {q'}\to H^{\pm\pm}H^{\mp}. We compare the discovery potential for the signatures of exactly four leptons and at least three leptons in the final state, using the same set of cuts. We have carried out fast detector simulations at the LHC for both signal and backgrounds for a wide range of values of the charged Higgs mass. We find that the use of the latter channel can substantially improve the detection prospects of the doubly charged Higgs boson at the LHC.
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arxiv:1009.2780
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Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the sensors. One of the established methods for achieving this is to iteratively maximize a likelihood function (ML), which requires initialization with an approximate solution to avoid convergence towards local extrema. This paper develops methods for handling both Gaussian and Laplacian noise, the latter modeling the presence of outliers in some practical ranging systems that adversely affect the performance of localization algorithms designed for Gaussian noise. A modified Euclidean Distance Matrix (EDM) completion problem is solved for a block of target range measurements to approximately set up initial sensor/target positions, and the likelihood function is then iteratively refined through Majorization-Minimization (MM). To avoid the computational burden of repeatedly solving increasingly large EDM problems in time-recursive operation an incremental scheme is exploited whereby a new target/node position is estimated from previously available node/target locations to set up the iterative ML initial point for the full spatial configuration. The above methods are first derived under Gaussian noise assumptions, and modifications for Laplacian noise are then considered. Analytically, the main challenges to be overcome in the Laplacian case stem from the non-differentiability of $\ell_1$ norms that arise in the various cost functions. Simulation results confirm that the proposed algorithms significantly outperform existing methods for SLAT in the presence of outliers, while offering comparable performance for Gaussian noise.
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arxiv:1009.2786
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We consider a system where a waveguide is coupled to a cavity embedded with a two-level system (TLS), and study the effects when a two-photon quantum state is injected into the waveguide. The wave function of two outgoing photons is exactly solved using the Lehmann-Symanzik-Zimmermann (LSZ) reduction formalism. Our results explicitly exhibit the photon blockade effects in the strong atom-cavity coupling regime. The quantum statistical characters of the outgoing photons, including the photon bunching and anti-bunching behaviors, are also investigated in both the strong and weak coupling regimes. These results agree with the observations of recent experiments.
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arxiv:1009.2828
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Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\'nski and G\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and prove nonlinear versions of the HVZ theorem, in the spirit of works of Friesecke. In the last section we study translation-invariant many-body systems comprising a nonlinear term, which effectively describes the interactions with a second system. As an example, we prove the existence of the multi-polaron in the Pekar-Tomasevich approximation, for certain values of the coupling constant.
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arxiv:1009.2836
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We investigate various quantum phase transitions of attractive two-species bosons in a square lattice. Using the algorithm based on the tensor product states, the phase boundaries of the pair superfluid states with nonzero pair condensate density \emph{and} vanishing atomic condensate density are determined. Various quantum phase transitions across the phase boundaries are characterized. Our work thus provides guides to the experimental search of the pair superfluid phase in lattice boson systems.
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arxiv:1009.2841
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Let $\F_q$ be a field of characteristic $p$ with $q$ elements. It is known that the degrees of the irreducible characters of the Sylow $p$-subgroup of $GL_n(\F_q)$ are powers of $q$ by Issacs. On the other hand Sangroniz showed that this is true for a Sylow $p$-subgroup of a classical group defined over $\F_q$ if and only if $p$ is odd. For the classical groups of Lie type $B$, $C$ and $D$ the only bad prime is 2. For the exceptional groups there are others. In this paper we construct irreducible characters for the Sylow $p$-subgroups of the Chevalley groups $D_4(q)$ with $q=2^f$ of degree $q^3/2$. Then we use an analogous construction for $E_6(q)$ with $q=3^f$ to obtain characters of degree $q^7/3$, and for $E_8(q)$ with $q=5^f$ to obtain characters of degree $q^{16}/5.$ This helps to explain why the primes 2, 3 and 5 are bad for the Chevalley groups of type $E$ in terms of the representation theory of the Sylow $p$-subgroup.
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arxiv:1009.2864
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CeCoIn5 is a heavy fermion Type-II superconductor which exhibits clear indications of Pauli-limited superconductivity. A variety of measurements give evidence for a transition at high magnetic fields inside the superconducting state, when the field is applied either parallel to or perpendicular to the c axis. When the field is perpendicular to the c axis, antiferromagnetic order is observed on the high-field side of the transition, with a magnetic wavevector of (q q 0.5), where q = 0.44 reciprocal lattice units. We show that this order remains as the magnetic field is rotated out of the basal plane, but the associated moment eventually disappears above 17 degrees, indicating that the anomalies seen with the field parallel to the c axis are not related to this magnetic order. We discuss the implications of this finding.
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arxiv:1009.2883
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The measurement of the mass of the W boson is one of the prime goals of the Tevatron experiments. In this contribution, a review is given of the most recent determinations of the W boson mass (mW) at the Tevatron. The combined Tevatron result, mW = 80.420 +/- 0.031 GeV, is now more precise than the combined LEP result, leading to a world average value of mW = 80.399 +/- 0.023 GeV.
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arxiv:1009.2903
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Many systems in nature, society and technology can be described as networks, where the vertices are the system's elements and edges between vertices indicate the interactions between the corresponding elements. Edges may be weighted if the interaction strength is measurable. However, the full network information is often redundant because tools and techniques from network analysis do not work or become very inefficient if the network is too dense and some weights may just reflect measurement errors, and shall be discarded. Moreover, since weight distributions in many complex weighted networks are broad, most of the weight is concentrated among a small fraction of all edges. It is then crucial to properly detect relevant edges. Simple thresholding would leave only the largest weights, disrupting the multiscale structure of the system, which is at the basis of the structure of complex networks, and ought to be kept. In this paper we propose a weight filtering technique based on a global null model (GloSS filter), keeping both the weight distribution and the full topological structure of the network. The method correctly quantifies the statistical significance of weights assigned independently to the edges from a given distribution. Applications to real networks reveal that the GloSS filter is indeed able to identify relevantconnections between vertices.
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arxiv:1009.2913
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Inelastic neutron scattering is used to investigate the collective magnetic excitations of the high-temperature superconductor parent antiferromagnet La2CuO4. We find that while the lower energy excitations are well described by spin-wave theory, including one- and two-magnon scattering processes, the high-energy spin waves are strongly damped near the (1/2,0) position in reciprocal space and merge into a momentum dependent continuum. This anomalous damping indicates the decay of spin waves into other excitations, possibly unbound spinon pairs.
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arxiv:1009.2915
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This paper investigates the Poisson geometry associated to a cluster algebra over the complex numbers, and its relationship to compatible torus actions. We show, under some assumptions, that each Noetherian cluster algebra has only finitely many torus invariant Poisson prime ideals and we show how to obtain using the exchange matrix of an initial seed. In fact, these ideals are independent of the choice of compatible Poisson structure. In many interesting cases the ideals can be described more explicitly.
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arxiv:1009.2936
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A continuously monitored quantum system prepared in an excited state will decay to its ground state with an abrupt jump. The jump occurs stochastically on a characteristic time scale T1, the lifetime of the excited state. These quantum jumps, originally envisioned by Bohr, have been observed in trapped atoms and ions, single molecules, photons, and single electrons in cyclotrons. Here we report the first observation of quantum jumps in a macroscopic quantum system, in our case a superconducting "artificial atom" or quantum bit (qubit) coupled to a superconducting microwave cavity. We use a fast, ultralow-noise parametric amplifier to amplify the microwave photons used to probe the qubit state, enabling continuous high-fidelity monitoring of the qubit. This technique represents a major step forward for solid state quantum information processing, potentially enabling quantum error correction and feedback, which are essential for building a quantum computer. Our technology can also be readily integrated into hybrid circuits involving molecular magnets, nitrogen vacancies in diamond, or semiconductor quantum dots.
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arxiv:1009.2969
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Observations of relativistic jets from black holes systems suggest that particle acceleration often occurs at fixed locations within the flow. These sites could be associated with critical points that allow the formation of standing shock regions, such as the magnetosonic modified fast point. Using the self-similar formulation of special relativistic magnetohydrodynamics by Vlahakis & K\"onigl, we derive a new class of flow solutions that are both relativistic and cross the modified fast point at a finite height. Our solutions span a range of Lorentz factors up to at least 10, appropriate for most jets in X-ray binaries and active galactic nuclei, and a range in injected particle internal energy. A broad range of solutions exists, which will allow the eventual matching of these scale-free models to physical boundary conditions in the analysis of observed sources.
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arxiv:1009.3031
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We study the behavior of the quarter-filled Kondo lattice model on a triangular lattice by combining a zero-temperature variational approach and finite-temperature Monte-Carlo simulations. For intermediate coupling between itinerant electrons and classical moments ${\bf S}_j$, we find a thermodynamic phase transition into an exotic spin ordering with uniform scalar spin chirality and $< {\bf S}_j >=0$. The state exhibits spontaneous quantum Hall effect. We also study how its properties are affected by application of an external magnetic field.
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arxiv:1009.3059
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We present deep optical integral-field spectroscopic observations of the nearby (z ~ 0.01) brightest cluster galaxy NGC 4696 in the core of the Centaurus Cluster, made with the Wide Field Spectrograph (WiFeS) on the ANU 2.3m telescope at Siding Spring Observatory. We investigate the morphology, kinematics, and excitation of the emission-line filaments and discuss these in the context of a model of a minor merger. We suggest that the emission-line filaments in this object have their origin in the accretion of a gas-rich galaxy and that they are excited by v ~100-200 km/s shocks driven into the cool filament gas by the ram pressure of the transonic passage of the merging system through the hot halo gas of NGC 4696.
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arxiv:1009.3070
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Using an exact integrodifferential equation we study the properties of the gauge invariant quark Green's function, defined with a path-ordered gluon field phase factor along a straight line, in two-dimensional QCD in the large-N_c limit. The Green's function is found to be infrared finite with singularities represented by an infinite number of threshold type branch points with a power equal to -3/2, starting at positive mass squared values. The solution is analytically determined.
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arxiv:1009.3107
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Two particle correlations are used to extract information about the characteristic size of the system for proton-proton collisions at 900 GeV measured by the ALICE (A Large Ion Collider experiment) detector at CERN. The correlation functions obtained show the expected Bose-Einstein effect for identical particles, but there are also long range correlations present that shift the baseline from the expected flat behavior. A possible source of these correlations is the conservation of energy and momentum, especially for small systems, where the energy available for particle production is limited. A new technique, first introduced by the STAR collaboration, of quantifying these long range correlations using energy-momentum conservation considerations is presented here. It is shown that the baseline of the two particle correlation function can be described using this technique.
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arxiv:1009.3157
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We obtain geometric characterizations of isospectral minimal Riemannian Legendre foliations on compact Sasakian manifolds of constant $\phi$-sectional curvature.
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arxiv:1009.3194
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The existing polar continuum theory contains unresolved indeterminacies in the spherical part of the couple-stress tensor. This severely restricts its applicability in the study of micro and nano-scale solid and fluid mechanics and, perhaps more importantly, in the investigation of fluid turbulence phenomena, which involve a broad range of scales. In this paper, we rely on the energy equation, along with some kinematical considerations, to establish a consistent couple-stress theory for polar continua that resolves all indeterminacies. After presenting the general formulation and obtaining conservation laws, we concentrate exclusively on couple stress theory for polar fluid mechanics. We specialize the theory for linear viscous flow and consider several boundary value problems in couple-stress fluid mechanics. More generally, the resulting theory presented here may provide a basis for fundamental continuum-level studies at the finest scales.
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arxiv:1009.3252
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This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal Lagrangian for a system of differential equations whose the number of equations is equal to or lower than the number of dependent variables are defined. It is proved that the system given by an equation and its adjoint is associated with a variational problem (with or without classical Lagrangian) and inherits all Lie-point and generalized symmetries from the original equation. Accordingly, a Noether theorem for conservation laws can be formulated.
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arxiv:1009.3261
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We study the effect of any uneven voltage distribution on two close cylindrical conductors with parallel axes that are slightly shifted in the radial and by any length in the axial direction. The investigation is especially motivated by certain precision measurements, such as the Satellite Test of the Equivalence Principle (STEP). By energy conservation, the force can be found as the energy gradient in the vector of the shift, which requires determining potential distribution and energy in the gap. The boundary value problem for the potential is solved, and energy is thus found to the second order in the small transverse shift, and to lowest order in the gap to cylinder radius ratio. The energy consists of three parts: the usual capacitor part due to the uniform potential difference, the one coming from the interaction between the voltage patches and the uniform voltage difference, and the energy of patch interaction, entirely independent of the uniform voltage. Patch effect forces and torques in the cylindrical configuration are derived and analyzed in the next two parts of this work.
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arxiv:1009.3292
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In this paper we determine topologically the canonical component of the $SL_2(\mathbb{C})$ character variety of the Whitehead link complement.
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arxiv:1009.3323
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It is well known that links in CSMA wireless networks are prone to starvation. Prior works focused almost exclusively on equilibrium starvation. In this paper, we show that links in CSMA wireless networks are also susceptible to temporal starvation. Specifically, although some links have good equilibrium throughputs and do not suffer from equilibrium starvation, they can still have no throughput for extended periods from time to time. Given its impact on quality of service, it is important to understand and characterize temporal starvation. To this end, we develop a "trap theory" to analyze temporal throughput fluctuation. The trap theory serves two functions. First, it allows us to derive new mathematical results that shed light on the transient behavior of CSMA networks. For example, we show that the duration of a trap, during which some links receive no throughput, is insensitive to the distributions of the backoff countdown and transmission time (packet duration) in the CSMA protocol. Second, we can develop analytical tools for computing the "degrees of starvation" for CSMA networks to aid network design. For example, given a CSMA network, we can determine whether it suffers from starvation, and if so, which links will starve. Furthermore, the likelihood and durations of temporal starvation can also be computed. We believe that the ability to identify and characterize temporal starvation as established in this paper will serve as an important first step toward the design of effective remedies for it.
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arxiv:1009.3415
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