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 $x\to+\infty$ 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

Interactions between Plasmodium falciparum skeleton-binding protein 1 and the membrane skeleton of malaria-infected red blood cells

During development inside red blood cells (RBCs), Plasmodium falciparum malaria parasites export proteins that associate with the RBC membrane skeleton. These interactions cause profound changes to the biophysical properties of RBCs that underpin the often severe and fatal clinical manifestations of falciparum malaria. P. falciparum erythrocyte membrane protein 1 (PfEMP1) is one such exported parasite protein that plays a major role in malaria pathogenesis since its exposure on the parasitised RBC surface mediates their adhesion to vascular endothelium and placental syncytioblasts. En route to the RBC membrane skeleton, PfEMP1 transiently associates with Maurer\u27s clefts (MCs), parasite-derived membranous structures in the RBC cytoplasm. We have previously shown that a resident MC protein, skeleton-binding protein 1 (SBP1), is essential for the placement of PfEMP1 onto the RBC surface and hypothesised that the function of SBP1 may be to target MCs to the RBC membrane. Since this would require additional protein interactions, we set out to identify binding partners for SBP1. Using a combination of approaches, we have defined the region of SBP1 that binds specifically to defined sub-domains of two major components of the RBC membrane skeleton, protein 4.1R and spectrin. We show that these interactions serve as one mechanism to anchor MCs to the RBC membrane skeleton, however, while they appear to be necessary, they are not sufficient for the translocation of PfEMP1 onto the RBC surface. The N-terminal domain of SBP1 that resides within the lumen of MCs clearly plays an essential, but presently unknown role in this process

Three-Fold Diffraction Symmetry in Epitaxial Graphene and the SiC Substrate

The crystallographic symmetries and spatial distribution of stacking domains in graphene films on SiC have been studied by low energy electron diffraction (LEED) and dark field imaging in a low energy electron microscope (LEEM). We find that the graphene diffraction spots from 2 and 3 atomic layers of graphene have 3-fold symmetry consistent with AB (Bernal) stacking of the layers. On the contrary, graphene diffraction spots from the buffer layer and monolayer graphene have apparent 6-fold symmetry, although the 3-fold nature of the satellite spots indicates a more complex periodicity in the graphene sheets.Comment: An addendum has been added for the arXiv version only, including one figure with five panels. Published paper can be found at http://link.aps.org/doi/10.1103/PhysRevB.80.24140