Multisymplectic Geometry and Noether Symmetries for the Field Theories and the Relativistic Mechanics

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.

Analysis of Vortex-Induced Vibration Characteristics for a Three-Dimensional Flexible Tube

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.

Heart Rate Variability Analysis for Early Stage Prediction of Sudden Cardiac Death

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.

Poincaré Plot for Heart Rate Variability

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.

Dynamics and Control of a Chaotic Electromagnetic System

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.

Effects of Input Speed on the Dynamic Response of Planar Multi-body Systems with Differently Located Frictionless Revolute Clearance Joints

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.

Computer Software Applicable in Rehabilitation, Cardiology and Molecular Biology

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.

Global Behavior in (Q-xy)2 Potential

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.