Statistical multi-moment bifurcations in random delay coupled swarms

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments

Numerical methods for analyzing electromagnetic scattering

Numerical methods to analyze electromagnetic scattering are presented. The dispersions and attenuations of the normal modes in a circular waveguide coated with lossy material were completely analyzed. The radar cross section (RCS) from a circular waveguide coated with lossy material was calculated. The following is observed: (1) the interior irradiation contributes to the RCS much more than does the rim diffraction; (2) at low frequency, the RCS from the circular waveguide terminated by a perfect electric conductor (PEC) can be reduced more than 13 dB down with a coating thickness less than 1% of the radius using the best lossy material available in a 6 radius-long cylinder; (3) at high frequency, a modal separation between the highly attenuated and the lowly attenuated modes is evident if the coating material is too lossy, however, a large RCS reduction can be achieved for a small incident angle with a thin layer of coating. It is found that the waveguide coated with a lossy magnetic material can be used as a substitute for a corrugated waveguide to produce a circularly polarized radiation yield

Numerical methods for analyzing electromagnetic scattering

Attenuation properties of the normal modes in an overmoded waveguide coated with a lossy material were analyzed. It is found that the low-order modes, can be significantly attenuated even with a thin layer of coating if the coating material is not too lossy. A thinner layer of coating is required for large attenuation of the low-order modes if the coating material is magnetic rather than dielectric. The Radar Cross Section (RCS) from an uncoated circular guide terminated by a perfect electric conductor was calculated and compared with available experimental data. It is confirmed that the interior irradiation contributes to the RCS. The equivalent-current method based on the geometrical theory of diffraction (GTD) was chosen for the calculation of the contribution from the rim diffraction. The RCS reduction from a coated circular guide terminated by a PEC are planned schemes for the experiments are included. The waveguide coated with a lossy magnetic material is suggested as a substitute for the corrugated waveguide

Wave attenuation and mode dispersion in a waveguide coated with lossy dielectric material

The modal attenuation constants in a cylindrical waveguide coated with a lossy dielectric material are studied as functions of frequency, dielectric constant, and thickness of the dielectric layer. A dielectric material best suited for a large attenuation is suggested. Using Kirchhoff's approximation, the field attenuation in a coated waveguide which is illuminated by a normally incident plane wave is also studied. For a circular guide which has a diameter of two wavelengths and is coated with a thin lossy dielectric layer (omega sub r = 9.1 - j2.3, thickness = 3% of the radius), a 3 dB attenuation is achieved within 16 diameters

THE RESPONSE OF WHOLE BODY VIBRATION ON TAI CHI AND WEIGHT-LIFTING ATHLETES

Whole body vibration (WBV) is a new technique which may improve leg muscle strength. Many researchers have studied the effect of whole body vibration recently. But study of effects of vibration stimulus to different activity type athletes, such as Tai Chi (N=12) and Weight-lifting (N=15) athletes is lacking. In this study we examine that question. The subjects were asked to stand in a half-squat posture without additional load on a vibration platform with 7 vibration frequencies (5, 9, 12, 16, 20, 24, 30 Hz) at 4 mm amplitude and maintained for 30 seconds. The effect of WBV would be different on different sport subjects’ perceived exertion. We discovered that the subject’s perception may be related with the acceleration of the subject’s head. Using whole body vibration training to improve muscle power and strength depends on the particular sport’s training emphasis to setup the appropriate training protocol such as amplitude and frequency

First passage times and asymmetry of DNA translocation

Motivated by experiments in which single-stranded DNA with a short hairpin loop at one end undergoes unforced diffusion through a narrow pore, we study the first passage times for a particle, executing one-dimensional brownian motion in an asymmetric sawtooth potential, to exit one of the boundaries. We consider the first passage times for the case of classical diffusion, characterized by a mean-square displacement of the form $\sim t$, and for the case of anomalous diffusion or subdiffusion, characterized by a mean-square displacement of the form $\sim t^{\gamma}$ with $0<\gamma<1$. In the context of classical diffusion, we obtain an expression for the mean first passage time and show that this quantity changes when the direction of the sawtooth is reversed or, equivalently, when the reflecting and absorbing boundaries are exchanged. We discuss at which numbers of `teeth' $N$ (or number of DNA nucleotides) and at which heights of the sawtooth potential this difference becomes significant. For large $N$, it is well known that the mean first passage time scales as $N^2$. In the context of subdiffusion, the mean first passage time does not exist. Therefore we obtain instead the distribution of first passage times in the limit of long times. We show that the prefactor in the power relation for this distribution is simply the expression for the mean first passage time in classical diffusion. We also describe a hypothetical experiment to calculate the average of the first passage times for a fraction of passage events that each end within some time $t^*$. We show that this average first passage time scales as $N^{2/\gamma}$ in subdiffusion.Comment: 10 pages, 4 figures We incorporated reviewers' suggestions from Physical Review E. We reformulated a few paragraphs in the introduction and further clarified the issue of the (a)symmetry of passage times. In the results section, we re-expressed the results in a form that manifest the important features. We also added a few references concerning anomalous diffusion. The look (but not the content) of figure 1 was also change