Abstract: The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used. In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in qi, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.
Abstract: Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×104. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.
Abstract: In present scenario, cardiovascular problems are growing challenge for researchers and physiologists. As heart disease have no geographic, gender or socioeconomic specific reasons; detecting cardiac irregularities at early stage followed by quick and correct treatment is very important. Electrocardiogram is the finest tool for continuous monitoring of heart activity. Heart rate variability (HRV) is used to measure naturally occurring oscillations between consecutive cardiac cycles. Analysis of this variability is carried out using time domain, frequency domain and non-linear parameters. This paper presents HRV analysis of the online dataset for normal sinus rhythm (taken as healthy subject) and sudden cardiac death (SCD subject) using all three methods computing values for parameters like standard deviation of node to node intervals (SDNN), square root of mean of the sequences of difference between adjacent RR intervals (RMSSD), mean of R to R intervals (mean RR) in time domain, very low-frequency (VLF), low-frequency (LF), high frequency (HF) and ratio of low to high frequency (LF/HF ratio) in frequency domain and Poincare plot for non linear analysis. To differentiate HRV of healthy subject from subject died with SCD, k –nearest neighbor (k-NN) classifier has been used because of its high accuracy. Results show highly reduced values for all stated parameters for SCD subjects as compared to healthy ones. As the dataset used for SCD patients is recording of their ECG signal one hour prior to their death, it is therefore, verified with an accuracy of 95% that proposed algorithm can identify mortality risk of a patient one hour before its death. The identification of a patient’s mortality risk at such an early stage may prevent him/her meeting sudden death if in-time and right treatment is given by the doctor.
Abstract: Heart is the most important part in the body of living
organisms. It affects and is affected by any factor in the body.
Therefore, it is a good detector for all conditions in the body. Heart
signal is a non-stationary signal; thus, it is utmost important to study
the variability of heart signal. The Heart Rate Variability (HRV) has
attracted considerable attention in psychology, medicine and has
become important dependent measure in psychophysiology and
behavioral medicine. The standards of measurements, physiological
interpretation and clinical use for HRV that are most often used were
described in many researcher papers, however, remain complex
issues are fraught with pitfalls. This paper presents one of the nonlinear
techniques to analyze HRV. It discusses many points like, what
Poincaré plot is and how Poincaré plot works; also, Poincaré plot's
merits especially in HRV. Besides, it discusses the limitation of
Poincaré cause of standard deviation SD1, SD2 and how to overcome
this limitation by using complex correlation measure (CCM). The
CCM is most sensitive to changes in temporal structure of the
Poincaré plot as compared toSD1 and SD2.
Abstract: In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method of Lyapunov exponents to show the occurrence of chaotic motion and to verify those numerical simulation results. Finally, two cases of a chaotic electromagnetic system being effectively controlled by a reference signal or being synchronized to another nonlinear electromagnetic system are presented.
Abstract: This paper numerically investigates the effects of input
speed on the overall dynamic characteristics of a multi-body system
with differently located revolute clearance joints without friction. A
typical planar slider-crank mechanism is used as a demonstration case
in which the effects of the input speed on the dynamic performance
of the mechanism with a revolute clearance joint between the crank
and connecting rod, and between the connecting rod and slider are
separately investigated with comprehensive observations numerically
presented. It is observed that, changing the driving speed of a multibody
system makes the behavior of the system to change from
either periodic to chaotic, or chaotic to periodic depending on which
joint has clearance. The location of the clearance revolute joint and
the operating speed of a multi-body system play a crucial role in
predicting accurately the dynamic responses of the system. Therefore
the dynamic behavior of one clearance revolute joint cannot be used
as a general case for a mechanical system.
Abstract: We have developed a computer program consisting of
6 subtests assessing the children hand dexterity applicable in the
rehabilitation medicine. We have carried out a normative study on a
representative sample of 285 children aged from 7 to 15 (mean age
11.3) and we have proposed clinical standards for three age groups
(7-9, 9-11, 12-15 years). We have shown statistical significance of
differences among the corresponding mean values of the task time
completion. We have also found a strong correlation between the task
time completion and the age of the subjects, as well as we have
performed the test-retest reliability checks in the sample of 84
children, giving the high values of the Pearson coefficients for the
dominant and non-dominant hand in the range 0.740.97 and
0.620.93, respectively.
A new MATLAB-based programming tool aiming at analysis of
cardiologic RR intervals and blood pressure descriptors, is worked
out, too. For each set of data, ten different parameters are extracted: 2
in time domain, 4 in frequency domain and 4 in Poincaré plot
analysis. In addition twelve different parameters of baroreflex
sensitivity are calculated. All these data sets can be visualized in time
domain together with their power spectra and Poincaré plots. If
available, the respiratory oscillation curves can be also plotted for
comparison. Another application processes biological data obtained
from BLAST analysis.
Abstract: The general global behavior of particle S a non-linear (Q - xy)2 potential cannot be revealed a Poincare surface of section method (PSS) because inost trajectories take practically infinitely long time to integrate numerically before they come back to the surface. In this study as an alternative to PSS, a multiple scale perturbation is applied to analyze global adiabatic, non-adiabatic and chaotic behavior of particles in this potential. It was found that the results can be summarized as a form of a Fermi-like map. Additionally, this method gives a variation of global stochasticity criteria with Q.