47,968 research outputs found

    Circuits, Perfect Matchings and Paths in Graphs

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    We primarily consider the problem of finding a family of circuits to cover a bidgeless graph (mainly on cubic graph) with respect to a given weight function defined on the edge set. The first chapter of this thesis is going to cover all basic concepts and notations will be used and a survey of this topic.;In Chapter two, we shall pay our attention to the Strong Circuit Double Cover Conjecture (SCDC Conjecture). This conjecture was verified for some graphs with special structure. As the complement of two factor in cubic graph, the Berge-Fulkersen Conjecture was introduced right after SCDC Conjecture. In Chapter three, we shall present a series of conjectures related to perfect matching covering and point out their relationship.;In last chapter, we shall introduce the saturation number, in contrast to extremal number (or known as Turan Number), and describe the edge spectrum of saturation number for small paths, where the spectrum was consisted of all possible integers between saturation number and Turan number

    Toward the Semiclassical Theory of the High Energy Heavy Ion Collisions

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    Sudden deposition of energy at the early stage of high energy heavy ion collisions makes virtual gluon fields real. The same is true for virtual vacuum fields underunder the topological barrier, excited to real states atat or aboveabove the barrier, gluomagnetic clusters of particular structure related to the sphaleronssphalerons of the electroweak theory. Semiclassically, these states play the role of the {\em ``turning points''}. After being produced they explode into a spherical shell of coherent field which then turn into several outgoing gluons. Furthermore, this explosions promptly produce quark pairs, as seen from explicit solution of the Dirac equation. The masses of such clusters depend on their size, and are expected to peak at M∼3GeVM\sim 3 GeV. After we briefly review those consepts in a non-technical manner, we discuss what observable consequences the production of such clusters would make in the context of heavy ion collisions, especially at the RHIC energies. We discuss entropy and especially quark production, event-by-event fluctuations in collective effects like radial and elliptic flows and J/ψJ/\psi suppression. Coherent fields and their geometry increase the jet quenching, and we also point out the existene of ``explosive edge'' which jump-start collective effects and may affect unusual phenomena seen at RHIC at large ptp_t.Comment: Third version, substantially changed adding new sections and eliminating large part on jet quenching of the paper which brunched into a separate pape

    Phonon transport in large scale carbon-based disordered materials: Implementation of an efficient order-N and real-space Kubo methodology

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    We have developed an efficient order-N real-space Kubo approach for the calculation of the phonon conductivity which outperforms state-of-the-art alternative implementations based on the Green's function formalism. The method treats efficiently the time-dependent propagation of phonon wave packets in real space, and this dynamics is related to the calculation of the thermal conductance. Without loss of generality, we validate the accuracy of the method by comparing the calculated phonon mean free paths in disordered carbon nanotubes (isotope impurities) with other approaches, and further illustrate its upscalability by exploring the thermal conductance features in large width edge-disordered graphene nanoribbons (up to ~20 nm), which is out of the reach of more conventional techniques. We show that edge-disorder is the most important scattering mechanism for phonons in graphene nanoribbons with realistic sizes and thermal conductance can be reduced by a factor of ~10.Comment: Accepted for publication in Physical Review B - Rapid Communication

    A Closed-Form Shave from Occam's Quantum Razor: Exact Results for Quantum Compression

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    The causal structure of a stochastic process can be more efficiently transmitted via a quantum channel than a classical one, an advantage that increases with codeword length. While previously difficult to compute, we express the quantum advantage in closed form using spectral decomposition, leading to direct computation of the quantum communication cost at all encoding lengths, including infinite. This makes clear how finite-codeword compression is controlled by the classical process' cryptic order and allows us to analyze structure within the length-asymptotic regime of infinite-cryptic order (and infinite Markov order) processes.Comment: 21 pages, 13 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/eqc.ht

    Signatures of disorder in the minimum conductivity of graphene

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    Graphene has been proposed as a promising material for future nanoelectronics because of its unique electronic properties. Understanding the scaling behavior of this new nanomaterial under common experimental conditions is of critical importance for developing graphene-based nanoscale devices. We present a comprehensive experimental and theoretical study on the influence of edge disorder and bulk disorder on the minimum conductivity of graphene ribbons. For the first time, we discovered a strong non-monotonic size scaling behavior featuring a peak and saturation minimum conductivity. Through extensive numerical simulations and analysis, we are able to attribute these features to the amount of edge and bulk disorder in graphene devices. This study elucidates the quantum transport mechanisms in realistic experimental graphene systems, which can be used as a guideline for designing graphene-based nanoscale devices with improved performance.Comment: Article: 14 pages, 4 figures. Supporting information: 8 pages, 3 figure

    Phonon transport in large scale carbon-based disordered materials: Implementation of an efficient order-N and real-space Kubo methodology

    Get PDF
    We have developed an efficient order-N real-space Kubo approach for the calculation of the phonon conductivity which outperforms state-of-the-art alternative implementations based on the Green's function formalism. The method treats efficiently the time-dependent propagation of phonon wave packets in real space, and this dynamics is related to the calculation of the thermal conductance. Without loss of generality, we validate the accuracy of the method by comparing the calculated phonon mean free paths in disordered carbon nanotubes (isotope impurities) with other approaches, and further illustrate its upscalability by exploring the thermal conductance features in large width edge-disordered graphene nanoribbons (up to ~20 nm), which is out of the reach of more conventional techniques. We show that edge-disorder is the most important scattering mechanism for phonons in graphene nanoribbons with realistic sizes and thermal conductance can be reduced by a factor of ~10.Comment: Accepted for publication in Physical Review B - Rapid Communication
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