8,275 research outputs found
Random trees between two walls: Exact partition function
We derive the exact partition function for a discrete model of random trees
embedded in a one-dimensional space. These trees have vertices labeled by
integers representing their position in the target space, with the SOS
constraint that adjacent vertices have labels differing by +1 or -1. A
non-trivial partition function is obtained whenever the target space is bounded
by walls. We concentrate on the two cases where the target space is (i) the
half-line bounded by a wall at the origin or (ii) a segment bounded by two
walls at a finite distance. The general solution has a soliton-like structure
involving elliptic functions. We derive the corresponding continuum scaling
limit which takes the remarkable form of the Weierstrass p-function with
constrained periods. These results are used to analyze the probability for an
evolving population spreading in one dimension to attain the boundary of a
given domain with the geometry of the target (i) or (ii). They also translate,
via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main
modifications in Sect. 5-6 and conclusio
High energy cosmic ray signature of quark nuggets
It has been recently proposed that dark matter in the Universe might consist of nuggets of quarks which populate the nuclear desert between nucleons and neutron star matter. It is further suggested that the Centauro events which could be the signature of particles with atomic mass A approx. 100 and energy E approx. 10 to 15th power eV might also be related to debris produced in the encounter of two neutron stars. A further consequence of the former proposal is examined, and it is shown that the production of relativistic quark nuggets is accompanied by a substantial flux of potentially observable high energy neutrinos
On the arithmetic of Krull monoids with infinite cyclic class group
Let be a Krull monoid with infinite cyclic class group and let denote the set of classes containing prime divisors. We study under
which conditions on some of the main finiteness properties of
factorization theory--such as local tameness, the finiteness and rationality of
the elasticity, the structure theorem for sets of lengths, the finiteness of
the catenary degree, and the existence of monotone and of near monotone chains
of factorizations--hold in . In many cases, we derive explicit
characterizations
Directed force chain networks and stress response in static granular materials
A theory of stress fields in two-dimensional granular materials based on
directed force chain networks is presented. A general equation for the
densities of force chains in different directions is proposed and a complete
solution is obtained for a special case in which chains lie along a discrete
set of directions. The analysis and results demonstrate the necessity of
including nonlinear terms in the equation. A line of nontrivial fixed point
solutions is shown to govern the properties of large systems. In the vicinity
of a generic fixed point, the response to a localized load shows a crossover
from a single, centered peak at intermediate depths to two propagating peaks at
large depths that broaden diffusively.Comment: 18 pages, 12 figures. Minor corrections to one figur
Confluence of geodesic paths and separating loops in large planar quadrangulations
We consider planar quadrangulations with three marked vertices and discuss
the geometry of triangles made of three geodesic paths joining them. We also
study the geometry of minimal separating loops, i.e. paths of minimal length
among all closed paths passing by one of the three vertices and separating the
two others in the quadrangulation. We concentrate on the universal scaling
limit of large quadrangulations, also known as the Brownian map, where pairs of
geodesic paths or minimal separating loops have common parts of non-zero
macroscopic length. This is the phenomenon of confluence, which distinguishes
the geometry of random quadrangulations from that of smooth surfaces. We
characterize the universal probability distribution for the lengths of these
common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding
paragraph and one reference added, and several other small correction
Are Children with High-Functioning Autism Better at Syntax than Typically Developing Children? The Case of Dutch Object Relative Clauses
The influence of cognitive abilities on article choice and scrambling performance in Dutch-speaking children with autism
The influence of cognitive abilities on article choice and scrambling performance in Dutch-speaking children with autism
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