1,755 research outputs found

    Maximum Edge-Disjoint Paths in kk-sums of Graphs

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    We consider the approximability of the maximum edge-disjoint paths problem (MEDP) in undirected graphs, and in particular, the integrality gap of the natural multicommodity flow based relaxation for it. The integrality gap is known to be Ω(n)\Omega(\sqrt{n}) even for planar graphs due to a simple topological obstruction and a major focus, following earlier work, has been understanding the gap if some constant congestion is allowed. In this context, it is natural to ask for which classes of graphs does a constant-factor constant-congestion property hold. It is easy to deduce that for given constant bounds on the approximation and congestion, the class of "nice" graphs is nor-closed. Is the converse true? Does every proper minor-closed family of graphs exhibit a constant factor, constant congestion bound relative to the LP relaxation? We conjecture that the answer is yes. One stumbling block has been that such bounds were not known for bounded treewidth graphs (or even treewidth 3). In this paper we give a polytime algorithm which takes a fractional routing solution in a graph of bounded treewidth and is able to integrally route a constant fraction of the LP solution's value. Note that we do not incur any edge congestion. Previously this was not known even for series parallel graphs which have treewidth 2. The algorithm is based on a more general argument that applies to kk-sums of graphs in some graph family, as long as the graph family has a constant factor, constant congestion bound. We then use this to show that such bounds hold for the class of kk-sums of bounded genus graphs

    Theory of Thermodynamic Magnetic Oscillations in Quasi-One-Dimensional Conductors

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    The second order correction to free energy due to the interaction between electrons is calculated for a quasi-one-dimensional conductor exposed to a magnetic field perpendicular to the chains. It is found that specific heat, magnetization and torque oscillate when the magnetic field is rotated in the plane perpendicular to the chains or when the magnitude of magnetic filed is changed. This new mechanism of thermodynamic magnetic oscillations in metals, which is not related to the presence of any closed electron orbits, is applied to explain behavior of the organic conductor (TMTSF)2_2ClO4_4.Comment: 11 pages + 5 figures (included

    Via Hexagons to Squares in Ferrofluids: Experiments on Hysteretic Surface Transformations under Variation of the Normal Magnetic Field

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    We report on different surface patterns on magnetic liquids following the Rosensweig instability. We compare the bifurcation from the flat surface to a hexagonal array of spikes with the transition to squares at higher fields. From a radioscopic mapping of the surface topography we extract amplitudes and wavelengths. For the hexagon--square transition, which is complex because of coexisting domains, we tailor a set of order parameters like peak--to--peak distance, circularity, angular correlation function and pattern specific amplitudes from Fourier space. These measures enable us to quantify the smooth hysteretic transition. Voronoi diagrams indicate a pinning of the domains. Thus the smoothness of the transition is roughness on a small scale.Comment: 17 pages, 14 figure

    Spectroscopy of 18^{18}Na: Bridging the two-proton radioactivity of 19^{19}Mg

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    The unbound nucleus 18^{18}Na, the intermediate nucleus in the two-proton radioactivity of 19^{19}Mg, was studied by the measurement of the resonant elastic scattering reaction 17^{17}Ne(p,17^{17}Ne)p performed at 4 A.MeV. Spectroscopic properties of the low-lying states were obtained in a R-matrix analysis of the excitation function. Using these new results, we show that the lifetime of the 19^{19}Mg radioactivity can be understood assuming a sequential emission of two protons via low energy tails of 18^{18}Na resonances

    Destruction of density-wave states by a pseudo-gap in high magnetic fields: application to (TMTSF)2_2ClO4_4

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    A model is presented for the destruction of density-wave states in quasi-one-dimensional crystals by high magnetic fields. The model is consistent with previously unexplained properties of the organic conductors (TMTSF)2_2ClO4_4 and (BEDT-TTF)2_2MHg(SCN)4_4 (M=K,Rb,Tl). As the magnetic field increases quasi-one-dimensional density-wave fluctuations increase, producing a pseudo-gap in the electronic density of states near the transition temperature. When the pseudo-gap becomes larger than the mean-field transition temperature formation of a density-wave state is not possible.Comment: 4 pages, RevTeX, 2 figures in uuencoded compressed tar file. Small changes to text and Figure 1. Final version to appear in Physical Review Letter

    Theoretical study of the two-proton halo candidate 17^{17}Ne including contributions from resonant continuum and pairing correlations

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    With the relativistic Coulomb wave function boundary condition, the energies, widths and wave functions of the single proton resonant orbitals for 17^{17}Ne are studied by the analytical continuation of the coupling constant (ACCC) approach within the framework of the relativistic mean field (RMF) theory. Pairing correlations and contributions from the single-particle resonant orbitals in the continuum are taken into consideration by the resonant Bardeen-Cooper-Schrieffer (BCS) approach, in which constant pairing strength is used. It can be seen that the fully self-consistent calculations with NL3 and NLSH effective interactions mostly agree with the latest experimental measurements, such as binding energies, matter radii, charge radii and densities. The energy of π\pi2s1/2_{1/2} orbital is slightly higher than that of π1d5/2\pi1d_{5/2} orbital, and the occupation probability of the (π(\pi2s1/2)2_{1/2})^2 orbital is about 20%, which are in accordance with the shell model calculation and three-body model estimation

    Developing effective practice learning for tomorrow's social workers

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    This paper considers some of the changes in social work education in the UK, particularly focusing on practice learning in England. The changes and developments are briefly identified and examined in the context of what we know about practice learning. The paper presents some findings from a small scale qualitative study of key stakeholders involved in practice learning and education in social work and their perceptions of these anticipated changes, which are revisited at implementation. The implications for practice learning are discussed
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