Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual article within multiparticle collisions. In the multiparticle collisions we included the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analysing simple simulations we found that in the strong repulsive state binary collisions dominate. However, within multiparticle collisions weak repulsion is observed to be much stronger. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.Comment: 17 pages, 8 figures, 1 table; In review process of Physical Review

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

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

Variational Problems with Fractional Derivatives: Euler-Lagrange Equations

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense

Towards operational use of aircraft‐derived observations: a case study at London Heathrow airport

Mode-Selective Enhanced Surveillance (Mode-S EHS) aircraft reports can be collected at a low-cost, and are readily available around busy airports. The new work presented here demonstrates that observations derived from Mode-S EHS reports can be used to study the evolution of temperature inversions since the data have a high spatial and temporal frequency. This is illustrated by a case study centred around London Heathrow airport for the period 4 to 5 January 2015. Using Mode-S EHS reports from multiple aircraft and after applying quality control criteria, vertical temperature profiles are constructed by aggregating these reports at discrete intervals between the surface and 3000m. To improve these derived temperatures, four smoothing methods using low-pass filters are evaluated. The effect of smoothing reduces the variance in the aircraft derived temperature by approximately half. After smoothing, the temperature variance between the altitudes 3000m and 1000m is 1K to 2K; and below 1000m it is 2K to 4K. While the differences between the four smoothing methods are small, exponential smoothing is favoured because it uses all available Mode-S EHS reports. The resulting vertical profiles may be useful in operational meteorology for identifying elevated temperature inversions above 1000m. However, below 1000m they are less useful because of the reduced precision of the reported Mach number. A better source of in situ temperature observations would be for aircraft to use the meteorological reporting function of their automatic dependent surveillance (ADS) system

Fractional dynamics of coupled oscillators with long-range interaction

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power-wise interaction. The corresponding term in dynamical equations is proportional to $1/|n-m|^{\alpha+1}$. It is shown that the equation of motion in the infrared limit can be transformed into the medium equation with the Riesz fractional derivative of order $\alpha$, when $0<\alpha<2$. We consider few models of coupled oscillators and show how their synchronization can appear as a result of bifurcation, and how the corresponding solutions depend on $\alpha$. The presence of fractional derivative leads also to the occurrence of localized structures. Particular solutions for fractional time-dependent complex Ginzburg-Landau (or nonlinear Schrodinger) equation are derived. These solutions are interpreted as synchronized states and localized structures of the oscillatory medium.Comment: 34 pages, 18 figure

TID and SEE Response of an Advanced Samsung 4G NAND Flash Memory

Initial total ionizing dose (TID) and single event heavy ion test results are presented for an unhardened commercial flash memory, fabricated with 63 nm technology. Results are that the parts survive to a TID of nearly 200 krad (SiO2), with a tractable soft error rate of about 10(exp -l2) errors/bit-day, for the Adams Ten Percent Worst Case Environment

Anomalous diffusion and the first passage time problem

We study the distribution of first passage time (FPT) in Levy type of anomalous diffusion. Using recently formulated fractional Fokker-Planck equation we obtain three results. (1) We derive an explicit expression for the FPT distribution in terms of Fox or H-functions when the diffusion has zero drift. (2) For the nonzero drift case we obtain an analytical expression for the Laplace transform of the FPT distribution. (3) We express the FPT distribution in terms of a power series for the case of two absorbing barriers. The known results for ordinary diffusion (Brownian motion) are obtained as special cases of our more general results.Comment: 25 pages, 4 figure

Spontaneous emission from a two-level atom in anisotropic one-band photonic crystals: a fractional calculus approach

Spontaneous emission (SE) from a two-level atom in a photonic crystal (PC) with anisotropic one-band model is investigated using the fractional calculus. Analytically solving the kinetic equation in terms of the fractional exponential function, the dynamical discrepancy of SE between the anisotropic and isotropic systems is discussed on the basis of different photon density of states (DOS) and the existence of incoherent diffusion field that becomes even more clearly as the atomic transition frequency lies close to the band edge. With the same atom-field coupling strength and detuning in the forbidden gap, the photon-atom bound states in the isotropic system turn into the unbound ones in the anisotropic system that is consistent with the experimental observation in $Phys.$ $Rev.$ $Lett.$ \textbf{96}, 243902 (2006). Dynamics along different wavevectors with various curvatures of dispersion is also addressed with the changes of the photon DOS and the appearance of the diffusion fields.Comment: 16 pages, 4 figure