Non-Markovian Levy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure

RF MEMS Switches with SiC Microbridges for Improved Reliability

Radio frequency (RF) microelectromechanical (MEMS) switches offer superior performance when compared to the traditional semiconductor devices such as PIN diodes or GaAs transistors. MEMS switches have a return loss (RL) better than -25 dB, negligible insertion loss (IL), isolation better than -30 dB, and near zero power consumption. However, RF MEMS switches have several drawbacks the most serious being long-term reliability. The ability for the switch to operate for millions or even billions of cycles is a major concern and must be addressed. MEMS switches are basically grouped in two categories, capacitive and metal-to-metal contact. The capacitive type switch consists of a movable metal bridge spanning a fixed electrode and separated by a narrow air gap and thin insulating material. The metal-to-metal contact type utilizes the same basic design but without the insulating material. After prolonged operation the metal bridges, in most of these switches, begin to sag and eventually fail to actuate. For the metal-to-metal type, the two metal layers may actually fuse together. Also if the switches are not packaged properly or protected from the environment moisture may build up and cause stiction between the top and bottom electrodes rendering them useless. Many MEMS switch designs have been developed and most illustrate fairly good RF characteristics. Nevertheless very few have demonstrated both great RF performance and ability to perform millions/billions of switching cycles. Of these, nearly all are of metal-to-metal type so as the frequency increases RF performance decreases

State transition of a non-Ohmic damping system in a corrugated plane

Anomalous transport of a particle subjected to non-Ohmic damping of the power $\delta$ in a tilted periodic potential is investigated via Monte Carlo simulation of generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locking state and the running state. Under the surrounding of sub-Ohmic damping ($0<\delta<1$), the particle should transfer into a running state from a locking state only when local minima of the potential vanish; hence the particle occurs a synchronization oscillation in its mean displacement and mean square displacement (MSD). In particular, the two motion modes are allowed to coexist in the case of super-Ohmic damping ($1<\delta<2$) for moderate driving forces, namely, where exists double centers in the velocity distribution. This induces the particle having faster diffusion, i.e., its MSD reads $= 2D^{(\delta)}_{eff} t^{\delta_{eff}}$. Our result shows that the effective power index $\delta_{\textmd{eff}}$ can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture effect of the two motion modes also leads to a breakdown of hysteresis loop of the mobility.Comment: 7 pages,7 figure

Altered dynamic postural control during gait termination following concussion

Impaired postural control is a cardinal symptom following concussion. Planned gait termination (GT) is a non-novel, dynamic task that challenges postural control in individuals with neurological deficits, and it could be an impactful measure for identifying dynamic postural control impairments following concussion. Therefore, the purpose of this study was to assess acute post-concussion dynamic postural control utilizing a planned GT task. The concussion participants (n= 19, age: 19.0 ± 0.8 years, height: 177.0 ± 10.1 cm, weight: 83.3 ± 20.0 kg) completed five planned GT trials during preseason baseline testing (Baseline) and on Day 1 post-concussion (Day-1). Healthy control participants (n=19, age: 20.4 ± 1.2 years, height: 173.8 ± 8.9 cm, weight: 80.2 ± 17.6 kg) completed the same trials a week apart. The dependent variables of interest included COP displacement and velocity in the mediolateral (ML) and anteroposterior (AP) axes during the three phases (braking, transitional, stabilization) of planned GT. There were significant interactions observed in both the braking ML and transitional AP displacement (p= 0.042, p= 0.030) and velocity (p= 0.027, p= 0.030). These results suggest a conservative post-concussion motor control strategy during planned GT. Further, these results support the use of dynamic postural control tasks as measures of post-concussion impairments

Infrared spectroscopy of diatomic molecules - a fractional calculus approach

The eigenvalue spectrum of the fractional quantum harmonic oscillator is calculated numerically solving the fractional Schr\"odinger equation based on the Riemann and Caputo definition of a fractional derivative. The fractional approach allows a smooth transition between vibrational and rotational type spectra, which is shown to be an appropriate tool to analyze IR spectra of diatomic molecules.Comment: revised + extended version, 9 pages, 6 figure

Anomalous Rotational Relaxation: A Fractional Fokker-Planck Equation Approach

In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has a fractional form for complex disordered systems, which indicates relaxation has non-exponential character obeys to Kohlrausch-William-Watts law, following the Mittag-Leffler decay.Comment: Revtex4, 9 pages. Paper was revised. References adde

Effect of Radiation Exposure on the Retention of Commercial NAND Flash Memory

We have compared the data retention of irradiated commercial NAND flash memories with that of unirradiated controls. Under some circumstanc es, radiation exposure has a significant effect on the retention of f lash memories

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

Spectral Asymptotics of Eigen-value Problems with Non-linear Dependence on the Spectral Parameter

We study asymptotic distribution of eigen-values $\omega$ of a quadratic operator polynomial of the following form $(\omega^2-L(\omega))\phi_\omega=0$, where $L(\omega)$ is a second order differential positive elliptic operator with quadratic dependence on the spectral parameter $\omega$. We derive asymptotics of the spectral density in this problem and show how to compute coefficients of its asymptotic expansion from coefficients of the asymptotic expansion of the trace of the heat kernel of $L(\omega)$. The leading term in the spectral asymptotics is the same as for a Laplacian in a cavity. The results have a number of physical applications. We illustrate them by examples of field equations in external stationary gravitational and gauge backgrounds.Comment: latex, 20 page

Hyperbolic subdiffusive impedance

We use the hyperbolic subdiffusion equation with fractional time derivatives (the generalized Cattaneo equation) to study the transport process of electrolytes in media where subdiffusion occurs. In this model the flux is delayed in a non-zero time with respect to the concentration gradient. In particular, we obtain the formula of electrochemical subdiffusive impedance of a spatially limited sample in the limit of large and of small pulsation of the electric field. The boundary condition at the external wall of the sample are taken in the general form as a linear combination of subdiffusive flux and concentration of the transported particles. We also discuss the influence of the equation parameters (the subdiffusion parameter and the delay time) on the Nyquist impedance plots.Comment: 10 pages, 5 figure