39,494 research outputs found
Exact Meander Asymptotics: a Numerical Check
This note addresses the meander enumeration problem: "Count all topologically
inequivalent configurations of a closed planar non self-intersecting curve
crossing a line through a given number of points". We review a description of
meanders introduced recently in terms of the coupling to gravity of a
two-flavored fully-packed loop model. The subsequent analytic predictions for
various meandric configuration exponents are checked against exact enumeration,
using a transfer matrix method, with an excellent agreement.Comment: 48 pages, 24 figures, tex, harvmac, eps
Virtual Knot Theory --Unsolved Problems
This paper is an introduction to the theory of virtual knots and links and it
gives a list of unsolved problems in this subject.Comment: 33 pages, 7 figures, LaTeX documen
SU(N) Meander Determinants
We propose a generalization of meanders, i.e., configurations of
non-selfintersecting loops crossing a line through a given number of points, to
SU(N). This uses the reformulation of meanders as pairs of reduced elements of
the Temperley-Lieb algebra, a SU(2)-related quotient of the Hecke algebra, with
a natural generalization to SU(N). We also derive explicit formulas for SU(N)
meander determinants, defined as the Gram determinants of the corresponding
bases of the Hecke algebra.Comment: TeX using harvmac.tex and epsf.tex, 60 pages (l-mode), 5 figure
On the birth of limit cycles for non-smooth dynamical systems
The main objective of this work is to develop, via Brower degree theory and
regularization theory, a variation of the classical averaging method for
detecting limit cycles of certain piecewise continuous dynamical systems. In
fact, overall results are presented to ensure the existence of limit cycles of
such systems. These results may represent new insights in averaging, in
particular its relation with non smooth dynamical systems theory. An
application is presented in careful detail
Fixation, transient landscape and diffusion's dilemma in stochastic evolutionary game dynamics
Agent-based stochastic models for finite populations have recently received
much attention in the game theory of evolutionary dynamics. Both the ultimate
fixation and the pre-fixation transient behavior are important to a full
understanding of the dynamics. In this paper, we study the transient dynamics
of the well-mixed Moran process through constructing a landscape function. It
is shown that the landscape playing a central theoretical "device" that
integrates several lines of inquiries: the stable behavior of the replicator
dynamics, the long-time fixation, and continuous diffusion approximation
associated with asymptotically large population. Several issues relating to the
transient dynamics are discussed: (i) multiple time scales phenomenon
associated with intra- and inter-attractoral dynamics; (ii) discontinuous
transition in stochastically stationary process akin to Maxwell construction in
equilibrium statistical physics; and (iii) the dilemma diffusion approximation
facing as a continuous approximation of the discrete evolutionary dynamics. It
is found that rare events with exponentially small probabilities, corresponding
to the uphill movements and barrier crossing in the landscape with multiple
wells that are made possible by strong nonlinear dynamics, plays an important
role in understanding the origin of the complexity in evolutionary, nonlinear
biological systems.Comment: 34 pages, 4 figure
The Nature of Cima Dome
In the Mojave Desert of southeasternmost California is a remarkably
smooth, symmetrical rock-alluvial dome which takes its name
from Cima on the Union Pacific Railroad. Lawson (1915, pp. 26, 33)
cited Cima Dome as a prime example of a panfan, but Thompson
(1929, p. 550) later showed that its upper part is bare rock. Davis
(1933, pp. 240-243) considered it a fine example of a convex desert
dome evolved from back-wearing of a fault block, but this concept
is contradicted by the geological relations (Hewett, 1954), which
throw more light on the nature and origin of Cima Dome than do
geomorphological theories
- …