2,819 research outputs found
Infinitely Many Stochastically Stable Attractors
Let f be a diffeomorphism of a compact finite dimensional boundaryless
manifold M exhibiting infinitely many coexisting attractors. Assume that each
attractor supports a stochastically stable probability measure and that the
union of the basins of attraction of each attractor covers Lebesgue almost all
points of M. We prove that the time averages of almost all orbits under random
perturbations are given by a finite number of probability measures. Moreover
these probability measures are close to the probability measures supported by
the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure
On stochastic sea of the standard map
Consider a generic one-parameter unfolding of a homoclinic tangency of an
area preserving surface diffeomorphism. We show that for many parameters
(residual subset in an open set approaching the critical value) the
corresponding diffeomorphism has a transitive invariant set of full
Hausdorff dimension. The set is a topological limit of hyperbolic sets
and is accumulated by elliptic islands.
As an application we prove that stochastic sea of the standard map has full
Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure
On two-dimensional surface attractors and repellers on 3-manifolds
We show that if is an -diffeomorphism with a surface
two-dimensional attractor or repeller and is a
supporting surface for , then and
there is such that: 1) is a union
of disjoint tame surfaces such that every is
homeomorphic to the 2-torus . 2) the restriction of to
is conjugate to Anosov automorphism of
High-throughput on-the-fly scanning ultraviolet-visible dual-sphere spectrometer
We have developed an on-the-fly scanning spectrometer operating in the UV-visible and near-infrared that can simultaneously perform transmission and total reflectance measurements at the rate better than 1 sample per second. High throughput optical characterization is important for screening functional materials for a variety of new applications. We demonstrate the utility of the instrument for screening new light absorber materials by measuring the spectral absorbance, which is subsequently used for deriving band gap information through Tauc plot analysis
Periodic Orbits and Escapes in Dynamical Systems
We study the periodic orbits and the escapes in two different dynamical
systems, namely (1) a classical system of two coupled oscillators, and (2) the
Manko-Novikov metric (1992) which is a perturbation of the Kerr metric (a
general relativistic system). We find their simple periodic orbits, their
characteristics and their stability. Then we find their ordered and chaotic
domains. As the energy goes beyond the escape energy, most chaotic orbits
escape. In the first case we consider escapes to infinity, while in the second
case we emphasize escapes to the central "bumpy" black hole. When the energy
reaches its escape value a particular family of periodic orbits reaches an
infinite period and then the family disappears (the orbit escapes). As this
family approaches termination it undergoes an infinity of equal period and
double period bifurcations at transitions from stability to instability and
vice versa. The bifurcating families continue to exist beyond the escape
energy. We study the forms of the phase space for various energies, and the
statistics of the chaotic and escaping orbits. The proportion of these orbits
increases abruptly as the energy goes beyond the escape energy.Comment: 28 pages, 23 figures, accepted in "Celestial Mechanics and Dynamical
Astronomy
Polymorphisms in the WNK1 gene are asociated with blood pressure variation and urinary potassium excretion
WNK1 - a serine/threonine kinase involved in electrolyte homeostasis and blood pressure (BP) control - is an excellent candidate gene for essential hypertension (EH). We and others have previously reported association between WNK1 and BP variation. Using tag SNPs (tSNPs) that capture 100% of common WNK1 variation in HapMap, we aimed to replicate our findings with BP and to test for association with phenotypes relating to WNK1 function in the British Genetics of Hypertension (BRIGHT) study case-control resource (1700 hypertensive cases and 1700 normotensive controls). We found multiple variants to be associated with systolic blood pressure, SBP (7/28 tSNPs min-p = 0.0005), diastolic blood pressure, DBP (7/28 tSNPs min-p = 0.002) and 24 hour urinary potassium excretion (10/28 tSNPs min-p = 0.0004). Associations with SBP and urine potassium remained significant after correction for multiple testing (p = 0.02 and p = 0.01 respectively). The major allele (A) of rs765250, located in intron 1, demonstrated the strongest evidence for association with SBP, effect size 3.14 mmHg (95%CI:1.23–4.9), DBP 1.9 mmHg (95%CI:0.7–3.2) and hypertension, odds ratio (OR: 1.3 [95%CI: 1.0–1.7]).We genotyped this variant in six independent populations (n = 14,451) and replicated the association between rs765250 and SBP in a meta-analysis (p = 7×10−3, combined with BRIGHT data-set p = 2×10−4, n = 17,851). The associations of WNK1 with DBP and EH were not confirmed. Haplotype analysis revealed striking associations with hypertension and BP variation (global permutation p10 mmHg reduction) and risk for hypertension (OR<0.60). Our data indicates that multiple rare and common WNK1 variants contribute to BP variation and hypertension, and provide compelling evidence to initiate further genetic and functional studies to explore the role of WNK1 in BP regulation and EH
Piecewise Linear Models for the Quasiperiodic Transition to Chaos
We formulate and study analytically and computationally two families of
piecewise linear degree one circle maps. These families offer the rare
advantage of being non-trivial but essentially solvable models for the
phenomenon of mode-locking and the quasi-periodic transition to chaos. For
instance, for these families, we obtain complete solutions to several questions
still largely unanswered for families of smooth circle maps. Our main results
describe (1) the sets of maps in these families having some prescribed rotation
interval; (2) the boundaries between zero and positive topological entropy and
between zero length and non-zero length rotation interval; and (3) the
structure and bifurcations of the attractors in one of these families. We
discuss the interpretation of these maps as low-order spline approximations to
the classic ``sine-circle'' map and examine more generally the implications of
our results for the case of smooth circle maps. We also mention a possible
connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request
Knowledge protection in firms: A conceptual framework and evidence from HP Labs
This paper proposes a simple framework to examine organizational methods of knowledge protection. The framework highlights a basic trade‐off between improving decision‐making and innovation through communication and mitigating security risks by imposing restrictions on communication flows. The trade‐off is mediated by factors such as the sensitivity of information, the degree to which employees can be trusted to handle sensitive information appropriately, and firms’ investments in legal protection mechanisms. Evidence from HP Labs supports the basic predictions of the model, in particular the importance of employee trustworthiness and internalized codes of behavior in promoting open communication. Our interviews also suggest a potential conflict between two of the most important appropriability mechanisms: secrecy and lead‐time advantage
Polynomial diffeomorphisms of C^2, IV: The measure of maximal entropy and laminar currents
This paper concerns the dynamics of polynomial automorphisms of .
One can associate to such an automorphism two currents and the
equilibrium measure . In this paper we study some
geometric and dynamical properties of these objects. First, we characterize
as the unique measure of maximal entropy. Then we show that the measure
has a local product structure and that the currents have a
laminar structure. This allows us to deduce information about periodic points
and heteroclinic intersections. For example, we prove that the support of
coincides with the closure of the set of saddle points. The methods used
combine the pluripotential theory with the theory of non-uniformly hyperbolic
dynamical systems
Sensitivity of a tonne-scale NEXT detector for neutrinoless double beta decay searches
The Neutrino Experiment with a Xenon TPC (NEXT) searches for the neutrinoless
double-beta decay of Xe-136 using high-pressure xenon gas TPCs with
electroluminescent amplification. A scaled-up version of this technology with
about 1 tonne of enriched xenon could reach in less than 5 years of operation a
sensitivity to the half-life of neutrinoless double-beta decay decay better
than 1E27 years, improving the current limits by at least one order of
magnitude. This prediction is based on a well-understood background model
dominated by radiogenic sources. The detector concept presented here represents
a first step on a compelling path towards sensitivity to the parameter space
defined by the inverted ordering of neutrino masses, and beyond.Comment: 22 pages, 11 figure
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