325 research outputs found
Isomerization dynamics of a buckled nanobeam
We analyze the dynamics of a model of a nanobeam under compression. The model
is a two mode truncation of the Euler-Bernoulli beam equation subject to
compressive stress. We consider parameter regimes where the first mode is
unstable and the second mode can be either stable or unstable, and the
remaining modes (neglected) are always stable. Material parameters used
correspond to silicon. The two mode model Hamiltonian is the sum of a
(diagonal) kinetic energy term and a potential energy term. The form of the
potential energy function suggests an analogy with isomerisation reactions in
chemistry. We therefore study the dynamics of the buckled beam using the
conceptual framework established for the theory of isomerisation reactions.
When the second mode is stable the potential energy surface has an index one
saddle and when the second mode is unstable the potential energy surface has an
index two saddle and two index one saddles. Symmetry of the system allows us to
construct a phase space dividing surface between the two "isomers" (buckled
states). The energy range is sufficiently wide that we can treat the effects of
the index one and index two saddles in a unified fashion. We have computed
reactive fluxes, mean gap times and reactant phase space volumes for three
stress values at several different energies. In all cases the phase space
volume swept out by isomerizing trajectories is considerably less than the
reactant density of states, proving that the dynamics is highly nonergodic. The
associated gap time distributions consist of one or more `pulses' of
trajectories. Computation of the reactive flux correlation function shows no
sign of a plateau region; rather, the flux exhibits oscillatory decay,
indicating that, for the 2-mode model in the physical regime considered, a rate
constant for isomerization does not exist.Comment: 42 pages, 6 figure
Nonlinear modes for the Gross-Pitaevskii equation -- demonstrative computation approach
A method for the study of steady-state nonlinear modes for Gross-Pitaevskii
equation (GPE) is described. It is based on exact statement about coding of the
steady-state solutions of GPE which vanish as by reals. This
allows to fulfill {\it demonstrative computation} of nonlinear modes of GPE
i.e. the computation which allows to guarantee that {\it all} nonlinear modes
within a given range of parameters have been found. The method has been applied
to GPE with quadratic and double-well potential, for both, repulsive and
attractive nonlinearities. The bifurcation diagrams of nonlinear modes in these
cases are represented. The stability of these modes has been discussed.Comment: 21 pages, 6 figure
Initial evidence for the criterion-related and structural validity of the long versions of the direct and meta-perspectives of the Coach-Athlete Relationship Questionnaire
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2010 Taylor & Francis.The aim of the present study was to develop and initially validate a longer version of the direct (Jowett & Ntoumanis, 2004) and meta-perspectives (Jowett, 2009a, 2009b) of the Coach-Athlete Relationship Questionnaire (CART-Q). In Study 1, instruments (e.g. questionnaires, scales, and inventories) that have been used to assess relationship quality in the broader psychological literature were examined and items potentially relevant to the coach-athlete relationship were identified. The content validity of the identified items was then assessed using expert panels. A final questionnaire was subsequently prepared and administered to 693 participants (310 coaches and 383 athletes). Confirmatory factor analysis was employed to assess the multidimensional nature of the questionnaire based on the 3Cs (i.e. closeness, commitment, and complementarity) model of the coach-athlete relationship. The findings indicated that the direct and meta-perspective items of the long versions of the CART-Q approached an adequate data fit. Moreover, evidence for the internal consistency and criterion validity of the new instruments was also obtained. In Study 2, the newly developed measure was administered to an independent sample of 251 individuals (145 athletes and 106 coaches). Further statistical support was gained for the factorial validity and reliability of the longer version of the CART-Q
On the Global Stability of a Generalized Cholera Epidemiological Model
In this paper, we conduct a careful global stability analysis for a generalized cholera epidemiological model originally proposed in [J. Wang and S. Liao, A generalized cholera model and epidemic/endemic analysis, J. Biol. Dyn. 6 (2012), pp. 568-589]. Cholera is a water-and food-borne infectious disease whose dynamics are complicated by the multiple interactions between the human host, the pathogen, and the environment. Using the geometric approach, we rigorously prove the endemic global stability for the cholera model in three-dimensional (when the pathogen component is a scalar) and four-dimensional (when the pathogen component is a vector) systems. This work unifies the study of global dynamics for several existing deterministic cholera models. The analytical predictions are verified by numerical simulation results
Tubular Chemical Reactors: The “Lumping Approximation” and Bifurcation of Oscillatory States
A Nonperturbative Eliasson's Reducibility Theorem
This paper is concerned with discrete, one-dimensional Schr\"odinger
operators with real analytic potentials and one Diophantine frequency. Using
localization and duality we show that almost every point in the spectrum admits
a quasi-periodic Bloch wave if the potential is smaller than a certain constant
which does not depend on the precise Diophantine conditions. The associated
first-order system, a quasi-periodic skew-product, is shown to be reducible for
almost all values of the energy. This is a partial nonperturbative
generalization of a reducibility theorem by Eliasson. We also extend
nonperturbatively the genericity of Cantor spectrum for these Schr\"odinger
operators. Finally we prove that in our setting, Cantor spectrum implies the
existence of a -set of energies whose Schr\"odinger cocycle is not
reducible to constant coefficients
Lin's method for heteroclinic chains involving periodic orbits
We present an extension of the theory known as Lin's method to heteroclinic
chains that connect hyperbolic equilibria and hyperbolic periodic orbits. Based
on the construction of a so-called Lin orbit, that is, a sequence of continuous
partial orbits that only have jumps in a certain prescribed linear subspace,
estimates for these jumps are derived. We use the jump estimates to discuss
bifurcation equations for homoclinic orbits near heteroclinic cycles between an
equilibrium and a periodic orbit (EtoP cycles)
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