2,950 research outputs found

    Constraint Satisfaction with Counting Quantifiers

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    We initiate the study of constraint satisfaction problems (CSPs) in the presence of counting quantifiers, which may be seen as variants of CSPs in the mould of quantified CSPs (QCSPs). We show that a single counting quantifier strictly between exists^1:=exists and exists^n:=forall (the domain being of size n) already affords the maximal possible complexity of QCSPs (which have both exists and forall), being Pspace-complete for a suitably chosen template. Next, we focus on the complexity of subsets of counting quantifiers on clique and cycle templates. For cycles we give a full trichotomy -- all such problems are in L, NP-complete or Pspace-complete. For cliques we come close to a similar trichotomy, but one case remains outstanding. Afterwards, we consider the generalisation of CSPs in which we augment the extant quantifier exists^1:=exists with the quantifier exists^j (j not 1). Such a CSP is already NP-hard on non-bipartite graph templates. We explore the situation of this generalised CSP on bipartite templates, giving various conditions for both tractability and hardness -- culminating in a classification theorem for general graphs. Finally, we use counting quantifiers to solve the complexity of a concrete QCSP whose complexity was previously open

    Vortex energy and vortex bending for a rotating Bose-Einstein condensate

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    For a Bose-Einstein condensate placed in a rotating trap, we give a simplified expression of the Gross-Pitaevskii energy in the Thomas Fermi regime, which only depends on the number and shape of the vortex lines. Then we check numerically that when there is one vortex line, our simplified expression leads to solutions with a bent vortex for a range of rotationnal velocities and trap parameters which are consistent with the experiments.Comment: 7 pages, 2 figures. submitte

    Compaction dynamics in ductile granular media

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    Ductile compaction is common in many natural systems, but the temporal evolution of such systems is rarely studied. We observe surprising oscillations in the weight measured at the bottom of a self-compacting ensemble of ductile grains. The oscillations develop during the first ten hours of the experiment, and usually persist through the length of an experiment (one week). The weight oscillations are connected to the grain--wall contacts, and are directly correlated with the observed strain evolution and the dynamics of grain--wall contacts during the compaction. Here, we present the experimental results and characteristic time constants of the system, and discuss possible reasons for the measured weight oscillations.Comment: 11 pages, 14 figure

    Early-type galaxies in the Chandra COSMOS Survey

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    We study a sample of 69 X-ray detected Early Type Galaxies (ETGs), selected from the Chandra COSMOS survey, to explore the relation between the X-ray luminosity of hot gaseous halos (L_X, gas) and the integrated stellar luminosity (L_K) of the galaxies, in a range of redshift extending out to z=1.5. In the local universe a tight steep relationship has been stablished between these two quantities (L_X,gas~ L_K^4.5) suggesting the presence of largely virialized halos in X-ray luminous systems. We use well established relations from the study of local universe ETGs, together with the expected evolution of the X-ray emission, to subtract the contribution of low mass X-ray binary populations (LMXBs) from the X-ray luminosity of our sample. Our selection minimizes the presence of active galactic nuclei (AGN), yielding a sample representative of normal passive COSMOS ETGs; therefore the resulting luminosity should be representative of gaseous halos, although we cannot exclude other sources such as obscured AGN, or enhanced X-ray emission connected with embedded star formation in the higher z galaxies. We find that most of the galaxies with estimated L_X<10^42 erg/s and z<0.55 follow the L_X,gas- L_K relation of local universe ETGs. For these galaxies, the gravitational mass can be estimated with a certain degree of confidence from the local virial relation. However, the more luminous (10^42<L_X<10^43.5 erg/s) and distant galaxies present significantly larger scatter; these galaxies also tend to have younger stellar ages. The divergence from the local L_X,gas - L_K relation in these galaxies implies significantly enhanced X-ray emission, up to a factor of 100 larger than predicted from the local relation. We discuss the implications of this result for the presence of hidden AGN, and the evolution of hot halos, in the presence of nuclear and star formation feedback.Comment: 29 pages, 10 figures, accepted for publication on ApJ on May 27 201

    Shape deformations and angular momentum transfer in trapped Bose-Einstein condensates

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    Angular momentum can be transferred to a trapped Bose-Einstein condensate by distorting its shape with an external rotating field, provided the rotational frequency is larger than a critical frequency fixed by the energy and angular momentum of the excited states of the system. By using the Gross-Pitaevskii equation and sum rules, we explore the dependence of such a critical frequency on the multipolarity of the excitations and the asymmetry of the confining potential. We also discuss its possible relevance for vortex nucleation in rotating traps.Comment: 4 pages revtex, 2 figures include

    Fracture Surfaces as Multiscaling Graphs

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    Fracture paths in quasi-two-dimenisonal (2D) media (e.g thin layers of materials, paper) are analyzed as self-affine graphs h(x)h(x) of height hh as a function of length xx. We show that these are multiscaling, in the sense that nthn^{th} order moments of the height fluctuations across any distance â„“\ell scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasi-static fracture passes this test.Comment: 4 pages, 5 figure

    Quality Aspects of Butter Marketing in South Dakota

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    The future well-being of the dairy industry in South Dakota may depend to a large extent on progress made in improving butter quality. About two-thirds of the dairy output in the state is exported to other states, mostly as bulk butter. Little of this butter qualifies as Grade A, and a sizeable proportion of it is below Grade B. Improvement in quality is necessary if South Dakota butter is to command top prices on the wholesale markets. It is particularly important in the light of the increasing competition which butter faces from margarine as a spread. Data for the study were gathered from a sample of 20 creameries in 1950 and from all of the South Dakota creameries in 1951. These data shed some light on the relationship between butter quality and prices received by creameries. The data also provide information on the relationship between the different measures of butter quality and various cream procurement, processing, and butter marketing methods prevailing in South Dakota at the time of the surveys
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