110,658 research outputs found
On the uniform generation of modular diagrams
In this paper we present an algorithm that generates -noncrossing,
-modular diagrams with uniform probability. A diagram is a labeled
graph of degree over vertices drawn in a horizontal line with arcs
in the upper half-plane. A -crossing in a diagram is a set of
distinct arcs with the property . A diagram without any
-crossings is called a -noncrossing diagram and a stack of length
is a maximal sequence
. A diagram is
-modular if any arc is contained in a stack of length at least
. Our algorithm generates after preprocessing time,
-noncrossing, -modular diagrams in time and space
complexity.Comment: 21 pages, 7 figure
Shapes of topological RNA structures
A topological RNA structure is derived from a diagram and its shape is
obtained by collapsing the stacks of the structure into single arcs and by
removing any arcs of length one. Shapes contain key topological, information
and for fixed topological genus there exist only finitely many such shapes. We
shall express topological RNA structures as unicellular maps, i.e. graphs
together with a cyclic ordering of their half-edges. In this paper we prove a
bijection of shapes of topological RNA structures. We furthermore derive a
linear time algorithm generating shapes of fixed topological genus. We derive
explicit expressions for the coefficients of the generating polynomial of these
shapes and the generating function of RNA structures of genus . Furthermore
we outline how shapes can be used in order to extract essential information of
RNA structure databases.Comment: 27 pages, 11 figures, 2 tables. arXiv admin note: text overlap with
arXiv:1304.739
Off-fault tensile cracks: A link between geological fault observations, lab experiments, and dynamic rupture models
We examine the local nature of the dynamic stress field in the vicinity of the tip of a semi-infinite sub-Rayleigh (slower than the Rayleigh wave speed, c_R) mode II crack with a velocity-weakening cohesive zone. We constrain the model using results from dynamic photoelastic experiments, in which shear ruptures were nucleated spontaneously in Homalite-100 plates along a bonded, precut, and inclined interface subject to a far-field uniaxial prestress. During the experiments, tensile cracks grew periodically along one side of the shear rupture interface at a roughly constant angle relative to the shear rupture interface. The occurrence and inclination of the tensile cracks are explained by our analytical model. With slight modifications, the model can be scaled to natural faults, providing diagnostic criteria for interpreting velocity, directivity, and static prestress state associated with past earthquakes on exhumed faults. Indirectly, this method also allows one to constrain the velocity-weakening nature of natural ruptures, providing an important link between field geology, laboratory experiments, and seismology
Remark on approximation in the calculation of the primordial spectrum generated during inflation
We re-examine approximations in the analytical calculation of the primordial
spectrum of cosmological perturbation produced during inflation. Taking two
inflation models (chaotic inflation and natural inflation) as examples, we
numerically verify the accuracy of these approximations.Comment: 10 pages, 6 figures, to appear in PR
Magneto-controlled nonlinear optical materials
We exploit theoretically a magneto-controlled nonlinear optical material
which contains ferromagnetic nanoparticles with a non-magnetic metallic
nonlinear shell in a host fluid. Such an optical material can have anisotropic
linear and nonlinear optical properties and a giant enhancement of
nonlinearity, as well as an attractive figure of merit.Comment: 11 pages, 2 figures. To be published in Appl. Phys. Let
Non-Thermal Production of WIMPs and the Sub-Galactic Structure of the Universe
There is increasing evidence that conventional cold dark matter (CDM) models
lead to conflicts between observations and numerical simulations of dark matter
halos on sub-galactic scales. Spergel and Steinhardt showed that if the CDM is
strongly self-interacting, then the conflicts disappear. However, the
assumption of strong self-interaction would rule out the favored candidates for
CDM, namely weakly interacting massive particles (WIMPs), such as the
neutralino. In this paper we propose a mechanism of non-thermal production of
WIMPs and study its implications on the power spectrum. We find that the
non-vanishing velocity of the WIMPs suppresses the power spectrum on small
scales compared to what it obtained in the conventional CDM model. Our results
show that, in this context, WIMPs as candidates for dark matter can work well
both on large scales and on sub-galactic scales.Comment: 6 pages, 2 figures; typo corrected; to appear in PR
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