165,176 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
Crossover from one to three dimensions for a gas of hard-core bosons
We develop a variational theory of the crossover from the one-dimensional
(1D) regime to the 3D regime for ultra-cold Bose gases in thin waveguides.
Within the 1D regime we map out the parameter space for fermionization, which
may span the full 1D regime for suitable transverse confinement.Comment: 4 pages, 2 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
On the formation of current sheets in response to the compression or expansion of a potential magnetic field
The compression or expansion of a magnetic field that is initially potential
is considered. It was recently suggested by Janse & Low [2009, ApJ, 690, 1089]
that, following the volumetric deformation, the relevant lowest energy state
for the magnetic field is another potential magnetic field that in general
contains tangential discontinuities (current sheets). Here we examine this
scenario directly using a numerical relaxation method that exactly preserves
the topology of the magnetic field. It is found that of the magnetic fields
discussed by Janse & Low, only those containing magnetic null points develop
current singularities during an ideal relaxation, while the magnetic fields
without null points relax toward smooth force-free equilibria with finite
non-zero current.Comment: Accepted for publication in Ap
Segue Between Favorable and Unfavorable Solvation
Solvation of small and large clusters are studied by simulation, considering
a range of solvent-solute attractive energy strengths. Over a wide range of
conditions, both for solvation in the Lennard-Jones liquid and in the SPC model
of water, it is shown that the mean solvent density varies linearly with
changes in solvent-solute adhesion or attractive energy strength. This behavior
is understood from the perspective of Weeks' theory of solvation [Ann. Rev.
Phys. Chem. 2002, 53, 533] and supports theories based upon that perspective.Comment: 8 pages, 7 figure
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