One-dimensional trapped atoms: critical coupling parameter and critical number of particles

In this paper we consider the case of a Bose gas in low dimension in order to illustrate the applicability of a method that allows us to construct analytical relations, valid for a broad range of coupling parameters, for a function which asymptotic expansions are known. The method is well suitable to investigate the problem of stability of a collection of Bose particles trapped in one- dimensional configuration for the case where the scattering length presents a negative value. The eigenvalues for this interacting quantum one-dimensional many particle system become negative when the interactions overcome the trapping energy and, in this case, the system becomes unstable. Here we calculate the critical coupling parameter and apply for the case of Lithium atoms obtaining the critical number of particles for the limit of stability.

The effect of the negative coupling parameter on the spectrum of a trapped Bose gas

The interest in attractive Bose-Einstein Condensates arises due to the chemical instabilities generate when the number of trapped atoms is above a critical number. In this case, recombination process promotes the collapse of the cloud. This behavior is normally geometry dependent. Within the context of the mean field approximation, the system is described by the Gross-Pitaevskii equation. We have considered the attractive Bose-Einstein condensate, confined in a nonspherical trap, investigating numerically and analytically the solutions, using controlled perturbation and self-similar approximation methods. This approximation is valid in all interval of the negative coupling parameter allowing interpolation between weak-coupling and strong-coupling limits. When using the self-similar approximation methods, accurate analytical formulas were derived. These obtained expressions are discussed for several different traps and may contribute to the understanding of experimental observations.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

Foam pore size is a critical interface parameter of suction-based wound healing devices.

BACKGROUND: Suction-based wound healing devices with open-pore foam interfaces are widely used to treat complex tissue defects. The impact of changes in physicochemical parameters of the wound interfaces has not been investigated. METHODS: Full-thickness wounds in diabetic mice were treated with occlusive dressing or a suction device with a polyurethane foam interface varying in mean pore size diameter. Wound surface deformation on day 2 was measured on fixed tissues. Histologic cross-sections were analyzed for granulation tissue thickness (hematoxylin and eosin), myofibroblast density (α-smooth muscle actin), blood vessel density (platelet endothelial cell adhesion molecule-1), and cell proliferation (Ki67) on day 7. RESULTS: Polyurethane foam-induced wound surface deformation increased with polyurethane foam pore diameter: 15 percent (small pore size), 60 percent (medium pore size), and 150 percent (large pore size). The extent of wound strain correlated with granulation tissue thickness that increased 1.7-fold in small pore size foam-treated wounds, 2.5-fold in medium pore size foam-treated wounds, and 4.9-fold in large pore size foam-treated wounds (p < 0.05) compared with wounds treated with an occlusive dressing. All polyurethane foams increased the number of myofibroblasts over occlusive dressing, with maximal presence in large pore size foam-treated wounds compared with all other groups (p < 0.05). CONCLUSIONS: The pore size of the interface material of suction devices has a significant impact on the wound healing response. Larger pores increased wound surface strain, tissue growth, and transformation of contractile cells. Modification of the pore size is a powerful approach for meeting biological needs of specific wounds.

Determination of the critical coupling for oscillators in a ring

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Critical coupling for dynamical chiral-symmetry breaking with an infrared finite gluon propagator

We compute the critical coupling constant for the dynamical chiral-symmetry breaking in a model of quantum chromodynamics, solving numerically the quark self-energy using infrared finite gluon propagators found as solutions of the Schwinger-Dyson equation for the gluon, and one gluon propagator determined in numerical lattice simulations. The gluon mass scale screens the force responsible for the chiral breaking, and the transition occurs only for a larger critical coupling constant than the one obtained with the perturbative propagator. The critical coupling shows a great sensibility to the gluon mass scale variation, as well as to the functional form of the gluon propagator.

Critical coupling for chiral symmetry breaking in QCD motivated models

We determine the critical coupling constant above which dynamical chiral symmetry breaking occurs in a class of QCD motivated models where the gluon propagator has an enhanced infrared behavior. Using methods of bifurcation theory we find that the critical value of the coupling constant is always smaller than the one obtained for QCD. ©2000 The American Physical Society.

Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbor coupling. Upon analyzing the behavior of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.

Synchronization and Basins of Synchronized in Two-Dimensional Piecewise Maps Via Coupling Three Pieces of One-Dimensional Maps

This paper is devoted to the synchronization of a dynamical system defined by two different coupling versions of two identical piecewise linear bimodal maps. We consider both local and global studies, using different tools as natural transversal Lyapunov exponent, Lyapunov functions, eigenvalues and eigenvectors and numerical simulations. We obtain theoretical results for the existence of synchronization on coupling parameter range. We characterize the synchronization manifold as an attractor and measure the synchronization speed. In one coupling version, we give a necessary and sufficient condition for the synchronization. We study the basins of synchronization and show that, depending upon the type of coupling, they can have very different shapes and are not necessarily constituted by the whole phase space; in some cases, they can be riddled.

C-H and C-D interbond coupling in CHDCl2

Laser photoacoustic spectra of vapour phase CHDCl2 reveal the presence of an interaction which has been ascribed to interbond coupling between C-H and C-D local modes. The absolute value of the interbond coupling parameter for the CHD group, determined from a fit of a model local mode hamiltonian to the experimental data, is shown to be given approximately by the geometric mean of the interbond coupling parameters of the CH2 and CD2 groups recently derived from similar studies of CH2Cl2 and CD2Cl2. Such behaviour is understood in terms of a simple analysis in which kinetic coupling effects dominate. It is suggested that C-H stretch/bend Fermi resonance is responsible for some weaker features in the spectra and modelling calculations are described which allow an order of magnitude estimate of the size of the coupling parameter involved.

Time-dependent orientation coupling in equilibrium polymer melts

The motion in concentrated polymer systems is described by either the Rouse or the reptation model, which both assume that the relaxation of each polymer chain is independent of the surrounding chains. This, however, is in contradiction with several experiments. In this Letter, we propose a universal description of orientation coupling in polymer melts in terms of the time-dependent coupling parameter κ(t). We use molecular dynamics simulations to show that the coupling parameter increases with time, reaching about 50% at long times, independently of the chain length or blend composition. This leads to predictions of component dynamics in mixtures of different molecular weights from the knowledge of monodisperse dynamics for unentangled melts. Finally, we demonstrate that entanglements do not play a significant role in the observed coupling. © 2010 The American Physical Society

Electrochemical single-molecule transistors with optimized gate coupling

Electrochemical gating at the single molecule level of viologen molecular bridges in ionic liquids is examined. Contrary to previous data recorded in aqueous electrolytes, a clear and sharp peak in the single molecule conductance versus electrochemical potential data is obtained in ionic liquids. These data are rationalized in terms of a two-step electrochemical model for charge transport across the redox bridge. In this model the gate coupling in the ionic liquid is found to be fully effective with a modeled gate coupling parameter, ξ, of unity. This compares to a much lower gate coupling parameter of 0.2 for the equivalent aqueous gating system. This study shows that ionic liquids are far more effective media for gating the conductance of single molecules than either solid-state three-terminal platforms created using nanolithography, or aqueous media.

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)