Numerical solution of the non-linear Schroedinger equation : the half-line problem and dynamical systems and bifurcations of vector fields

Solutions to the nonlinear Schrodinger equation with potential V(u) = -λulul2 have been theoretically and numerically calculated, revealing the formation of solitons. In this study the finite element method with linear basis functions, distinguished for its simplicity and effective applicability, is considered and a predictor-corrector scheme is applied to simulate the propagation in time. Numerical experiments include the propagation of a single soliton form, a two-soliton collision, as well as the formation of more than one solitons from non-soliton initial data. The important problem of boundary reflections has been successfully overcome by the implementation of absorbing boundaries, a method that in practice achieves a gradual reduction of the wave amplitude at the end of each time step. The second part of this work deals with dynamical systems of the form [see file]. The dynamics of such systems near their equilibrium point depends strongly on the adjustable parameter μ, as it is possible for the system to lose its hyperbolicity and a bifurcation to occur. After reviewing aspects of linearisation, the prospect of change in the equilibrium solutions has been studied, both for flows and maps, in terms of the eigenvalues of the linearised system. In the study of steady-state bifurcation, elements of saddle-node, transcritical, pitchfork, as well as period-doubling bifurcation are considered. Finally, the case when equilibrium solutions persist, known as Hopf bifurcation, has also been included

Obtaining the basic response pattern of physiological time series data : a comparison of methods

An understanding of the kinetics of physiological variables such as the heart rate or the rate of change of volume of oxygen uptake is fundamental not only to training methodology and competitive success in sport and exercise, but also to our knowledge of cardiovascular health. A correct and efficient means of interpreting and analyzing the data obtained is of vast importance, as exercise testing is routinely used in both of these areas

Connection between performance and body sway/morphology in juvenile Olympic shooters

The objective of the study was to examine, via use of a simple specific test, the correlation between body sway and performance in Juvenile Olympic shooters, to compare the differences in body morphology between different shooting modalities and to know if the anthropometric profile of a shooter influences performance. 38 national level juvenile shooters (24 pistol and 14 rifle) who competed at a pistol and air rifle Young Promises Spanish Championship participated in the study. Body sway (measured in terms of movements of the Centre of Pressure (COP): maximum displacements, maximum and minimum average velocities, rotation angles and total areas) and anthropometric data (age, height and weight) were recorded under competition conditions during shooting simulations. Performance was measured in terms of average points per shot. The variables of stress and experience before competition were also considered. The study was observational and descriptive following a cross-sectional design. The results showed that, in the juvenile category, rifle shooters perform better than pistol shooters, but pistol shooters have less body sway. Performance was found to be statistically related to COP displacements, only in pistol shooters. Body weight was found to be related to body sway but not with performance. Body height was found to be related neither with body sway, nor with performance No anthropometric differences have been found to exist between the different modalities (pistol and rifle)

Geometry and transport in a model of two coupled quadratic nonlinear waveguides

This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled X(2) waveguides is modeled and analyzed in terms of transport and geometry in the phase space. This gives us a transport problem in the phase space resulting from the coupling of the two Hamiltonian systems for each waveguide. In particular, the effect of the presence of partial and complete barriers in the phase space on the transfer of intensity between the waveguides is studied, given a specific input and range of material properties. We show how these barriers break down as the coupling between the waveguides is increased and what the role of resonances in the phase space has in this. We also show how an increase in the coupling can lead to chaos and global transport and what effect this has on the intensity

Simulating heart rate kinetics during incremental and interval training

Study aim: To apply a recently proposed dynamical systems model to simulate, for the first time, the heart rate (HR) response to exercise of time-dependent intensity

Modelling Heart Rate Kinetics

<div><p>The objective of the present study was to formulate a simple and at the same time effective mathematical model of heart rate kinetics in response to movement (exercise). Based on an existing model, a system of two coupled differential equations which give the rate of change of heart rate and the rate of change of exercise intensity is used. The modifications introduced to the existing model are justified and discussed in detail, while models of blood lactate accumulation in respect to time and exercise intensity are also presented. The main modification is that the proposed model has now only one parameter which reflects the overall cardiovascular condition of the individual. The time elapsed after the beginning of the exercise, the intensity of the exercise, as well as blood lactate are also taken into account. Application of the model provides information regarding the individual’s cardiovascular condition and is able to detect possible changes in it, across the data recording periods. To demonstrate examples of successful numerical fit of the model, constant intensity experimental heart rate data sets of two individuals have been selected and numerical optimization was implemented. In addition, numerical simulations provided predictions for various exercise intensities and various cardiovascular condition levels. The proposed model can serve as a powerful tool for a complete means of heart rate analysis, not only in exercise physiology (for efficiently designing training sessions for healthy subjects) but also in the areas of cardiovascular health and rehabilitation (including application in population groups for which direct heart rate recordings at intense exercises are not possible or not allowed, such as elderly or pregnant women).</p></div

Title Page Title: Validating the use of a dumbbell to measure body sway in female Olympic air pistol shooting Other authors&apos; email addresses

Abstract: The present study validates use of a dumbbell to simulate the air pistol in female Olympic shooting, examining, at the same time, the relation between body sway and performance. The study&apos;s participants were 23 senior female Olympic pistol shooters who competed at a Spanish air pistol championship. The participants&apos; performance was measured at competition while their COP movements were recorded during two static bipodal balance tests which were performed the day previous to the competition, during the official training time and at the training stands. During one of the tests a 1.5 kg dumbbell was used to simulate the pistol. The calculated Pearson product moment correlations for all variables that refer to the movement of the COP revealed statistically significant correlations between the two tests. Statistically significant inverse linear correlations were also found between performance and COP movements regarding both tests: strong correlations regarding COP movement amplitudes and moderate correlations regarding COP velocities. The study concludes that a) a dumbbell can be validly used to simulate the pistol in female Olympic air pistol shooting, and b) specific balance training programs should be taken into account in order to improve performance in female air pistol shooting

Example of off-transient beat-to-beat heart rate time series.

<p>Recovery after the exercise of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0118263#pone.0118263.g001" target="_blank">Fig. 1</a>, please refer to Exercise D in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0118263#pone.0118263.s001" target="_blank">S1 Data Set</a>.</p

The repelling function <i>f</i>_<i>min</i>.

<p>Compared to its respective repelling term of normalized <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0118263#pone.0118263.e003" target="_blank">Equation (1)</a>. <i>B</i> = 1.8 and <i>B</i> = 2.5.</p