728 research outputs found
Stability boundary approximation of periodic dynamics
We develop here the method for obtaining approximate stability boundaries in
the space of parameters for systems with parametric excitation. The monodromy
(Floquet) matrix of linearized system is found by averaging method. For system
with 2 degrees of freedom (DOF) we derive general approximate stability
conditions. We study domains of stability with the use of fourth order
approximations of monodromy matrix on example of inverted position of a
pendulum with vertically oscillating pivot. Addition of small damping shifts
the stability boundaries upwards, thus resulting to both stabilization and
destabilization effects.Comment: 9 pages, 2 figure
Hamilton-Jacobi Theory and Information Geometry
Recently, a method to dynamically define a divergence function for a
given statistical manifold by means of the
Hamilton-Jacobi theory associated with a suitable Lagrangian function
on has been proposed. Here we will review this
construction and lay the basis for an inverse problem where we assume the
divergence function to be known and we look for a Lagrangian function
for which is a complete solution of the associated
Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to
replace probability distributions with probability amplitudes.Comment: 8 page
Study on the ecology of the peregrine falcon (Falco peregrinus Tunstall, 1771) in the Chusovaya River Nature Park
Numerical instability of the Akhmediev breather and a finite-gap model of it
In this paper we study the numerical instabilities of the NLS Akhmediev
breather, the simplest space periodic, one-mode perturbation of the unstable
background, limiting our considerations to the simplest case of one unstable
mode. In agreement with recent theoretical findings of the authors, in the
situation in which the round-off errors are negligible with respect to the
perturbations due to the discrete scheme used in the numerical experiments, the
split-step Fourier method (SSFM), the numerical output is well-described by a
suitable genus 2 finite-gap solution of NLS. This solution can be written in
terms of different elementary functions in different time regions and,
ultimately, it shows an exact recurrence of rogue waves described, at each
appearance, by the Akhmediev breather. We discover a remarkable empirical
formula connecting the recurrence time with the number of time steps used in
the SSFM and, via our recent theoretical findings, we establish that the SSFM
opens up a vertical unstable gap whose length can be computed with high
accuracy, and is proportional to the inverse of the square of the number of
time steps used in the SSFM. This neat picture essentially changes when the
round-off error is sufficiently large. Indeed experiments in standard double
precision show serious instabilities in both the periods and phases of the
recurrence. In contrast with it, as predicted by the theory, replacing the
exact Akhmediev Cauchy datum by its first harmonic approximation, we only
slightly modify the numerical output. Let us also remark, that the first rogue
wave appearance is completely stable in all experiments and is in perfect
agreement with the Akhmediev formula and with the theoretical prediction in
terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv
admin note: text overlap with arXiv:1707.0565
Bistability in Apoptosis by Receptor Clustering
Apoptosis is a highly regulated cell death mechanism involved in many
physiological processes. A key component of extrinsically activated apoptosis
is the death receptor Fas, which, on binding to its cognate ligand FasL,
oligomerize to form the death-inducing signaling complex. Motivated by recent
experimental data, we propose a mathematical model of death ligand-receptor
dynamics where FasL acts as a clustering agent for Fas, which form locally
stable signaling platforms through proximity-induced receptor interactions.
Significantly, the model exhibits hysteresis, providing an upstream mechanism
for bistability and robustness. At low receptor concentrations, the bistability
is contingent on the trimerism of FasL. Moreover, irreversible bistability,
representing a committed cell death decision, emerges at high concentrations,
which may be achieved through receptor pre-association or localization onto
membrane lipid rafts. Thus, our model provides a novel theory for these
observed biological phenomena within the unified context of bistability.
Importantly, as Fas interactions initiate the extrinsic apoptotic pathway, our
model also suggests a mechanism by which cells may function as bistable
life/death switches independently of any such dynamics in their downstream
components. Our results highlight the role of death receptors in deciding cell
fate and add to the signal processing capabilities attributed to receptor
clustering.Comment: Accepted by PLoS Comput Bio
Stable Isotope Composition of Fatty Acids in Organisms of Different Trophic Levels in the Yenisei River
We studied four-link food chain, periphytic microalgae and water moss (producers), trichopteran larvae (consumers I), gammarids (omnivorous – consumers II) and Siberian grayling (consumers III) at a littoral site of the Yenisei River on the basis of three years monthly sampling. Analysis of bulk carbon stable isotopes and compound specific isotope analysis of fatty acids (FA) were done. As found, there was a gradual depletion in 13C contents of fatty acids, including essential FA upward the food chain. In all the trophic levels a parabolic dependence of δ13C values of fatty acids on their degree of unsaturation/chain length occurred, with 18:2n-6 and 18:3n-3 in its lowest point. The pattern in the δ13C differences between individual fatty acids was quite similar to that reported in literature for marine pelagic food webs. Hypotheses on isotope fractionation were suggested to explain the findings
Beyond Gross-Pitaevskii Mean Field Theory
A large number of effects related to the phenomenon of Bose-Einstein
Condensation (BEC) can be understood in terms of lowest order mean field
theory, whereby the entire system is assumed to be condensed, with thermal and
quantum fluctuations completely ignored. Such a treatment leads to the
Gross-Pitaevskii Equation (GPE) used extensively throughout this book. Although
this theory works remarkably well for a broad range of experimental parameters,
a more complete treatment is required for understanding various experiments,
including experiments with solitons and vortices. Such treatments should
include the dynamical coupling of the condensate to the thermal cloud, the
effect of dimensionality, the role of quantum fluctuations, and should also
describe the critical regime, including the process of condensate formation.
The aim of this Chapter is to give a brief but insightful overview of various
recent theories, which extend beyond the GPE. To keep the discussion brief,
only the main notions and conclusions will be presented. This Chapter
generalizes the presentation of Chapter 1, by explicitly maintaining
fluctuations around the condensate order parameter. While the theoretical
arguments outlined here are generic, the emphasis is on approaches suitable for
describing single weakly-interacting atomic Bose gases in harmonic traps.
Interesting effects arising when condensates are trapped in double-well
potentials and optical lattices, as well as the cases of spinor condensates,
and atomic-molecular coupling, along with the modified or alternative theories
needed to describe them, will not be covered here.Comment: Review Article (19 Pages) - To appear in 'Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment', Edited by
P.G. Kevrekidis, D.J. Frantzeskakis and R. Carretero-Gonzalez (Springer
Verlag
A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains
In the first (and abstract) part of this survey we prove the unitary
equivalence of the inverse of the Krein--von Neumann extension (on the
orthogonal complement of its kernel) of a densely defined, closed, strictly
positive operator, for some in a Hilbert space to an abstract buckling problem operator.
This establishes the Krein extension as a natural object in elasticity theory
(in analogy to the Friedrichs extension, which found natural applications in
quantum mechanics, elasticity, etc.).
In the second, and principal part of this survey, we study spectral
properties for , the Krein--von Neumann extension of the
perturbed Laplacian (in short, the perturbed Krein Laplacian)
defined on , where is measurable, bounded and
nonnegative, in a bounded open set belonging to a
class of nonsmooth domains which contains all convex domains, along with all
domains of class , .Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144
- …