4,696 research outputs found
Computational Discovery of A New Rhombohedral Diamond Phase
We identify by first-principles calculations a new diamond phase in R¯3c (D63d) symmetry, which has a 16-atom rhombohedral primitive cell, thus termed R16 carbon. This rhombohedral diamond comprises a characteristic all-sp3 six-membered-ring bonding network, and it is energetically more stable than previously identified diamondlike six-membered-ring bonded BC8 and BC12 carbon phases. A phonon mode analysis verifies the dynamic structural stability of R16 carbon, and electronic band calculations reveal that it is an insulator with a direct band gap of 4.45 eV. Simulated x-ray diffraction patterns provide an excellent match to recently reported distinct diffraction peaks found in milled fullerene soot, suggesting a viable experimental synthesis route. These findings pave the way for further exploration of this new diamond phase and its outstanding properties
Self-organized critical behavior: the evolution of frozen spin networks model in quantum gravity
In quantum gravity, we study the evolution of a two-dimensional planar open
frozen spin network, in which the color (i.e. the twice spin of an edge)
labeling edge changes but the underlying graph remains fixed. The mainly
considered evolution rule, the random edge model, is depending on choosing an
edge randomly and changing the color of it by an even integer. Since the change
of color generally violate the gauge invariance conditions imposed on the
system, detailed propagation rule is needed and it can be defined in many ways.
Here, we provided one new propagation rule, in which the involved even integer
is not a constant one as in previous works, but changeable with certain
probability. In random edge model, we do find the evolution of the system under
the propagation rule exhibits power-law behavior, which is suggestive of the
self-organized criticality (SOC), and it is the first time to verify the SOC
behavior in such evolution model for the frozen spin network. Furthermore, the
increase of the average color of the spin network in time can show the nature
of inflation for the universe.Comment: 5 pages, 5 figure
Two-dimensional small-world networks: navigation with local information
Navigation process is studied on a variant of the Watts-Strogatz small world
network model embedded on a square lattice. With probability , each vertex
sends out a long range link, and the probability of the other end of this link
falling on a vertex at lattice distance away decays as .
Vertices on the network have knowledge of only their nearest neighbors. In a
navigation process, messages are forwarded to a designated target. For and , a scaling relation is found between the average actual
path length and , where is the average length of the additional long
range links. Given , dynamic small world effect is observed, and the
behavior of the scaling function at large enough is obtained. At and 3, this kind of scaling breaks down, and different functions of the
average actual path length are obtained. For , the average actual
path length is nearly linear with network size.Comment: Accepted for publication in Phys. Rev.
Long range random walks and associated geometries on groups of polynomial growth
In the context of countable groups of polynomial volume growth, we consider a
large class of random walks that are allowed to take long jumps along multiple
subgroups according to power law distributions. For such a random walk, we
study the large time behavior of its probability of return at time in terms
of the key parameters describing the driving measure and the structure of the
underlying group. We obtain assorted estimates including near-diagonal
two-sided estimates and the H\"older continuity of the solutions of the
associated discrete parabolic difference equation. In each case, these
estimates involve the construction of a geometry adapted to the walk.Comment: 51 page
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