47,968 research outputs found
Circuits, Perfect Matchings and Paths in Graphs
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
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 the topological barrier,
excited to real states or the barrier, gluomagnetic clusters of
particular structure related to the 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
. 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
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
.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
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
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
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
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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