Microcanonical temperature for a classical field: Application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.

Charge transport in a quantum electromechanical system

We describe a quantum electromechanical system comprising a single quantum dot harmonically bound between two electrodes and facilitating a tunneling current between them. An example of such a system is a fullerene molecule between two metal electrodes [Park et al., Nature 407, 57 (2000)]. The description is based on a quantum master equation for the density operator of the electronic and vibrational degrees of freedom and thus incorporates the dynamics of both diagonal (population) and off diagonal (coherence) terms. We derive coupled equations of motion for the electron occupation number of the dot and the vibrational degrees of freedom, including damping of the vibration and thermo-mechanical noise. This dynamical description is related to observable features of the system including the stationary current as a function of bias voltage

Three-dimensional solitons in coupled atomic-molecular Bose-Einstein condensates

We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BECs). The soliton solutions to the mean-field equations are obtained in an approximate analytical form by means of a variational approach. We investigate soliton stability within the parameter space described by the atom-molecule conversion coupling, the atom-atom s-wave scattering, and the bare formation energy of the molecular species. In terms of ordinary optics, this is analogous to the process of sub- or second-harmonic generation in a quadratic nonlinear medium modified by a cubic nonlinearity, together with a phase mismatch term between the fields. While the possibility of formation of multidimensional spatiotemporal solitons in pure quadratic media has been theoretically demonstrated previously, here we extend this prediction to matter-wave interactions in BEC systems where higher-order nonlinear processes due to interparticle collisions are unavoidable and may not be neglected. The stability of the solitons predicted for repulsive atom-atom interactions is investigated by direct numerical simulations of the equations of motion in a full 3D lattice. Our analysis also leads to a possible technique for demonstrating the ground state of the Schrodinger-Newton and related equations that describe Bose-Einstein condensates with nonlocal interparticle forces.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

Molecular motion in nanocomposites of poly(ethylene oxide) and montmorillonite

Motion of chains of poly(ethylene oxide) within the interlayer spacing of 2:1 phyllosilicate/montmorillonite was studied with H-1 and C-13 NMR spectroscopy. Measurements of the H-1 NMR line widths and relaxation times across a large temperature range were used to determine the effect of bulk thermal transitions on polymer chain motion within the nanocomposites. The results were consistent with previous reports of low apparent activation energies of motion. Details of the frequency and geometry of motion were obtained from a comparison of the C-13 cross-polarity/magic-angle spinning spectra and relaxation times of the nanocomposite with those of the pure polymer. (C) 2001 John Wiley & Sons, Inc.

Numerical evaluation of the fields induced by body motion in or near high-field MRI scanners

In modern magnetic resonance imaging, both patients and health care workers are exposed to strong. non-uniform static magnetic fields inside and outside of the scanner. In which body movement may be able to induce electric currents in tissues which could be potentially harmful. This paper presents theoretical investigations into the spatial distribution of induced E-fields in a tissue-equivalent human model when moving at various positions around the magnet. The numerical calculations are based on an efficient. quasi-static, finite-difference scheme. Three-dimensional field profiles from an actively shielded 4 T magnet system are used and the body model projected through the field profile with normalized velocity. The simulation shows that it is possible to induce E-fields/currents near the level of physiological significance under some circumstances and provides insight into the spatial characteristics of the induced fields. The methodology presented herein can be extrapolated to very high field strengths for the evaluation of the effects of motion at a variety of field strengths and velocities. (C) 2004 Elsevier Ltd. All rights reserved.

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

A windows program for the derivation of steady-state equations in enzyme systems

Despite the number of computer-assisted methods described for the derivation of steady-state equations of enzyme systems, most of them are focused on strict steady-state conditions or are not able to solve complex reaction mechanisms. Moreover, many of them are based on computer programs that are either not readily available or have limitations. We present here a computer program called WinStes, which derives equations for both strict steady-state systems and those with the assumption of rapid equilibrium, for branched or unbranched mechanisms, containing both reversible and irreversible conversion steps. It solves reaction mechanisms involving up to 255 enzyme species, connected by up to 255 conversion steps. The program provides all the advantages of the Windows programs, such as a user-friendly graphical interface, and has a short computation time. WinStes is available free of charge on request from the authors. (c) 2006 Elsevier Inc. All rights reserved.

Constraints on the spatiotemporal accuracy of interceptive action: effects of target size on hitting a moving object

Results of two experiments are reported that examined how people respond to rectangular targets of different sizes in simple hitting tasks. If a target moves in a straight line and a person is constrained to move along a linear track oriented perpendicular to the targetrsquos motion, then the length of the target along its direction of motion constrains the temporal accuracy and precision required to make the interception. The dimensions of the target perpendicular to its direction of motion place no constraints on performance in such a task. In contrast, if the person is not constrained to move along a straight track, the targetrsquos dimensions may constrain the spatial as well as the temporal accuracy and precision. The experiments reported here examined how people responded to targets of different vertical extent (height): the task was to strike targets that moved along a straight, horizontal path. In experiment 1 participants were constrained to move along a horizontal linear track to strike targets and so target height did not constrain performance. Target height, length and speed were co-varied. Movement time (MT) was unaffected by target height but was systematically affected by length (briefer movements to smaller targets) and speed (briefer movements to faster targets). Peak movement speed (Vmax) was influenced by all three independent variables: participants struck shorter, narrower and faster targets harder. In experiment 2, participants were constrained to move in a vertical plane normal to the targetrsquos direction of motion. In this task target height constrains the spatial accuracy required to contact the target. Three groups of eight participants struck targets of different height but of constant length and speed, hence constant temporal accuracy demand (different for each group, one group struck stationary targets = no temporal accuracy demand). On average, participants showed little or no systematic response to changes in spatial accuracy demand on any dependent measure (MT, Vmax, spatial variable error). The results are interpreted in relation to previous results on movements aimed at stationary targets in the absence of visual feedback.

What's scene and not seen: Influences of movement and task upon what we see

Studies concerning the processing of natural scenes using eye movement equipment have revealed that observers retain surprisingly little information from one fixation to the next. Other studies, in which fixation remained constant while elements within the scene were changed, have shown that, even without refixation, objects within a scene are surprisingly poorly represented. Although this effect has been studied in some detail in static scenes, there has been relatively little work on scenes as we would normally experience them, namely dynamic and ever changing. This paper describes a comparable form of change blindness in dynamic scenes, in which detection is performed in the presence of simulated observer motion. The study also describes how change blindness is affected by the manner in which the observer interacts with the environment, by comparing detection performance of an observer as the passenger or driver of a car. The experiments show that observer motion reduces the detection of orientation and location changes, and that the task of driving causes a concentration of object analysis on or near the line of motion, relative to passive viewing of the same scene.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Preparatory trunk motion accompanies rapid upper limb movement

Evaluation of trunk movements, trunk muscle activation, intra-abdominal pressure and displacement of centres of pressure and mass was undertaken to determine whether trunk orientation is a controlled variable prior to and during rapid bilateral movement of the upper limbs. Standing subjects performed rapid bilateral symmetrical upper limb movements in three directions (flexion, abduction and extension). The results indicated a small (0.4-3.3 degrees) but consistent initial angular displacement between the segments of the trunk in a direction opposite to that produced by the reactive moments resulting from limb movement. Phasic activation of superficial trunk muscles was consistent with this pattern of preparatory motion and with the direction of motion of the centre of mass. In contrast, activation of the deep abdominal muscles was independent of the direction of limb motion, suggesting a non-direction specific contribution to spinal stability. The results support the opinion that feedforward postural responses result in trunk movements, and that orientation of the trunk and centre of mass are both controlled variables in relation to rapid limb movements.

NMR characterization of blends of poly(hydroxybutyrate-co-hydroxyvalerate) with poly(vinyl acetate)

The extent of mixing in blends of poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) (27% HV) and poly(vinyl acetate) (PVAc) has been measured using a number of different techniques, principally solid-state NMR. Differential scanning calorimetry DSC measurements indicated effective mixing of the polymer chains on a scale of several nanometres. The results of H-1 T-1 and H-1 T-1rho. measurements confirm intimate mixing of the chains. A change on blending in the H-1 T-1rho, and the H-1 NMR line width of the signal from the protons of PVAc was consistent with an increase in the amplitude and frequency of motion of this component. The PVAc chains reside within the inter-lamellar space, as confirmed by spin diffusion measurements after H-1 T-1rho preparation. (C) 2003 Society of Chemical Industry.

Characterization of inflammatory responses to eccentric exercise in humans

Eccentric exercise commonly results in muscle damage. The primary sequence of events leading to exercise-induced muscle damage is believed to involve initial mechanical disruption of sarcomeres, followed by impaired excitation-contraction coupling and calcium signaling, and finally, activation of calcium-sensitive degradation pathways. Muscle damage is characterized by ultrastructural changes to muscle architecture, increased muscle proteins and enzymes in the bloodstream, loss of muscular strength and range of motion and muscle soreness. The inflammatory response to exercise-induced muscle damage is characterized by leukocyte infiltration and production of pro-inflammatory cytokines within damaged muscle tissue, systemic release of leukocytes and cytokines, in addition to alterations in leukocyte receptor expression and functional activity. Current evidence suggests that inflammatory responses to muscle damage are dependent on the type of eccentric exercise, previous eccentric loading (repeated bouts), age and gender. Circulating neutrophil counts and systemic cytokine responses are greater after eccentric exercise using a large muscle mass (e.g. downhill running, eccentric cycling) than after other types of eccentric exercise involving a smaller muscle mass. After an initial bout of eccentric exercise, circulating leukocyte counts and cell surface receptor expression are attenuated. Leukocyte and cytokine responses to eccentric exercise are impaired in elderly individuals, while cellular infiltration into skeletal muscle is greater in human females than males after eccentric exercise. Whether alterations in intracellular calcium homeostasis influence inflammatory responses to muscle damage is uncertain. Furthermore, the effects of antioxidant supplements are variable, and the limited data available indicates that anti-inflammatory drugs largely have no influence on inflammatory responses to eccentric exercise. In this review, we compare local versus systemic inflammatory responses, and discuss some of the possible mechanisms regulating the inflammatory responses to exercise-induced muscle damage in humans.

Multifidus muscle recovery is not automatic after resolution of acute, first-episode low back pain

Study Design. A clinical study was conducted on 39 patients with acute, first-episode, unilateral low back pain and unilateral, segmental inhibition of the multifidus muscle. Patients were allocated randomly to a control or treatment group. Objectives. To document the natural course of lumbar multifidus recovery and to evaluate the effectiveness of specific, localized, exercise therapy on muscle recovery. Summary of Background Data. Acute low back pain usually resolves spontaneously, but the recurrence rate is high. Inhibition of multifidus occurs with acute, first-episode, low back pain, and pathologic changes in this muscle have been linked with poor outcome and recurrence of symptoms. Methods. Patients in group 1 received medical treatment only. Patients in group 2 received medical treatment and specific, localized, exercise therapy. Outcome measures for both groups included 4 weekly assessments of pain, disability, range of motion, and size of the multifidus cross-sectional area. Independent examiners were blinded to group allocation. Patients were reassessed at a 10-week follow-up examination. Results. Multifidus muscle recovery was not spontaneous on remission of painful symptoms in patients in group 1. Muscle recovery was more rapid and more complete in patients in group 2 who received exercise therapy (P = 0.0001). Other outcome measurements were similar for the two groups at the 4-week examination. Although they resumed normal levels of activity, patients in group 1 still had decreased multifidus muscle size at the 10-week follow-up examination. Conclusions. Multifidus muscle recovery is not spontaneous on remission of painful symptoms. Lack of localized, muscle support may be one reason for the high recurrence rate of low back pain following the initial episode.