2,658 research outputs found
Chaotic and pseudochaotic attractors of perturbed fractional oscillator
We consider a nonlinear oscillator with fractional derivative of the order
alpha. Perturbed by a periodic force, the system exhibits chaotic motion called
fractional chaotic attractor (FCA). The FCA is compared to the ``regular''
chaotic attractor. The properties of the FCA are discussed and the
``pseudochaotic'' case is demonstrated.Comment: 20 pages, 7 figure
Convex Independence in Permutation Graphs
A set C of vertices of a graph is P_3-convex if every vertex outside C has at
most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest
P_3-convex set that contains A. A set M is convexly independent if for every
vertex x \in M, x \notin \sigma(M-x). We show that the maximal number of
vertices that a convexly independent set in a permutation graph can have, can
be computed in polynomial time
On the Order Dimension of Convex Geometries
We study the order dimension of the lattice of closed sets for a convex
geometry. Further, we prove the existence of large convex geometries realized
by planar point sets that have very low order dimension. We show that the
planar point set of Erdos and Szekeres from 1961 which is a set of 2^(n-2)
points and contains no convex n-gon has order dimension n - 1 and any larger
set of points has order dimension strictly larger than n - 1.Comment: 12 pages, 2 figure
On the possibility to supercool molecular hydrogen down to superfluid transition
Recent calculations by Vorobev and Malyshenko (JETP Letters, 71, 39, 2000)
show that molecular hydrogen may stay liquid and superfluid in strong electric
fields of the order of . I demonstrate that strong local
electric fields of similar magnitude exist beneath a two-dimensional layer of
electrons localized in the image potential above the surface of solid hydrogen.
Even stronger local fields exist around charged particles (ions or electrons)
if surface or bulk of a solid hydrogen crystal is statically charged.
Measurements of the frequency shift of the photoresonance transition
in the spectrum of two-dimensional layer of electrons above positively or
negatively charged solid hydrogen surface performed in the temperature range 7
- 13.8 K support the prediction of electric field induced surface melting. The
range of surface charge density necessary to stabilize the liquid phase of
molecular hydrogen at the temperature of superfluid transition is estimated.Comment: 5 pages, 2 figure
Probability of local bifurcation type from a fixed point: A random matrix perspective
Results regarding probable bifurcations from fixed points are presented in
the context of general dynamical systems (real, random matrices), time-delay
dynamical systems (companion matrices), and a set of mappings known for their
properties as universal approximators (neural networks). The eigenvalue spectra
is considered both numerically and analytically using previous work of Edelman
et. al. Based upon the numerical evidence, various conjectures are presented.
The conclusion is that in many circumstances, most bifurcations from fixed
points of large dynamical systems will be due to complex eigenvalues.
Nevertheless, surprising situations are presented for which the aforementioned
conclusion is not general, e.g. real random matrices with Gaussian elements
with a large positive mean and finite variance.Comment: 21 pages, 19 figure
Distributions of flux vacua
We give results for the distribution and number of flux vacua of various
types, supersymmetric and nonsupersymmetric, in IIb string theory compactified
on Calabi-Yau manifolds. We compare this with related problems such as counting
attractor points.Comment: 43 pages, 7 figures. v2: improved discussion of finding vacua with
discrete flux, references adde
Lattice congruences of the weak order
We study the congruence lattice of the poset of regions of a hyperplane
arrangement, with particular emphasis on the weak order on a finite Coxeter
group. Our starting point is a theorem from a previous paper which gives a
geometric description of the poset of join-irreducibles of the congruence
lattice of the poset of regions in terms of certain polyhedral decompositions
of the hyperplanes. For a finite Coxeter system (W,S) and a subset K of S, let
\eta_K:w \mapsto w_K be the projection onto the parabolic subgroup W_K. We show
that the fibers of \eta_K constitute the smallest lattice congruence with
1\equiv s for every s\in(S-K). We give an algorithm for determining the
congruence lattice of the weak order for any finite Coxeter group and for a
finite Coxeter group of type A or B we define a directed graph on subsets or
signed subsets such that the transitive closure of the directed graph is the
poset of join-irreducibles of the congruence lattice of the weak order.Comment: 26 pages, 4 figure
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