The cutoff-dependence of the Casimir force within an inhomogeneous medium

We consider the ground state energy of the electromagnetic field in a piston geometry. In the idealised case, where the piston and the walls of the chamber are taken as perfect mirrors, the Casimir pressure on the piston is finite and independent of the small scale physics of the media that compose the mirrors; the Casimir-energy of the system can be regularised and is cutoff-independent. Yet we find that, when the body of the piston is filled with an inhomogeneous dielectric medium, the Casimir energy is cutoff-dependent, and the value of the pressure is thus inextricably dependent on the detailed behaviour of the mirror and the medium at large wave-vectors. This result is inconsistent with recent proposals for regularising Casimir forces in inhomogeneous media.Comment: 6 pages, 2 figure

Non-Filippov dynamics arising from the smoothing of nonsmooth systems, and its robustness to noise

Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth functions, such as step functions. Consistent modelling requires that piecewise-smooth and smooth dynamical systems have similar dynamics, but the conditions for such similarity are not well understood. Here we show that by smoothing out a piecewise-smooth system one may obtain dynamics that is inconsistent with the accepted wisdom --- so-called Filippov dynamics --- at a discontinuity, even in the piecewise-smooth limit. By subjecting the system to white noise, we show that these discrepancies can be understood in terms of potential wells that allow solutions to dwell at the discontinuity for long times. Moreover we show that spurious dynamics will revert to Filippov dynamics, with a small degree of stochasticity, when the noise magnitude is sufficiently large compared to the order of smoothing. We apply the results to a model of a dry-friction oscillator, where spurious dynamics (inconsistent with Filippov's convention or with Coulomb's model of friction) can account for different coefficients of static and kinetic friction, but under sufficient noise the system reverts to dynamics consistent with Filippov's convention (and with Coulomb-like friction).Comment: submitted to: Nonlinear Dynamic

The fate of NOx emissions due to nocturnal oxidation at high latitudes: 1-D simulations and sensitivity experiments

The fate of nitrogen oxide pollution during high-latitude winter is controlled by reactions of dinitrogen pentoxide (N2O5) and is highly affected by the competition between heterogeneous atmospheric reactions and deposition to the snowpack. MISTRA (MIcrophysical STRAtus), a 1-D photochemical model, simulated an urban pollution plume from Fairbanks, Alaska to investigate this competition of N2O5 reactions and explore sensitivity to model parameters. It was found that dry deposition of N2O5 made up a significant fraction of N2O5 loss near the snowpack, but reactions on aerosol particles dominated loss of N2O5 over the integrated atmospheric column. Sensitivity experiments found the fate of NOx emissions were most sensitive to NO emission flux, photolysis rates, and ambient temperature. The results indicate a strong sensitivity to urban area density, season and clouds, and temperature, implying a strong sensitivity of the results to urban planning and climate change. Results suggest that secondary formation of particulate (PM2.5) nitrate in the Fairbanks downtown area does not contribute significant mass to the total PM2.5 concentration, but appreciable amounts are formed downwind of downtown due to nocturnal NOx oxidation and subsequent reaction with ammonia on aerosol particles

Stochastic Perturbations of Periodic Orbits with Sliding

Vector fields that are discontinuous on codimension-one surfaces are known as Filippov systems and can have attracting periodic orbits involving segments that are contained on a discontinuity surface of the vector field. In this paper we consider the addition of small noise to a general Filippov system and study the resulting stochastic dynamics near such a periodic orbit. Since a straight-forward asymptotic expansion in terms of the noise amplitude is not possible due to the presence of discontinuity surfaces, in order to quantitatively determine the basic statistical properties of the dynamics, we treat different parts of the periodic orbit separately. Dynamics distant from discontinuity surfaces is analyzed by the use of a series expansion of the transitional probability density function. Stochastically perturbed sliding motion is analyzed through stochastic averaging methods. The influence of noise on points at which the periodic orbit escapes a discontinuity surface is determined by zooming into the transition point. We combine the results to quantitatively determine the effect of noise on the oscillation time for a three-dimensional canonical model of relay control. For some parameter values of this model, small noise induces a significantly large reduction in the average oscillation time. By interpreting our results geometrically, we are able to identify four features of the relay control system that contribute to this phenomenon.Comment: 44 pages, 9 figures, submitted to: J Nonlin. Sc

A digital technique to compensate for time- base error in magnetic tape recording

Digital technique for compensation of time base error in magnetic tape recorder dat

Models of collective cell spreading with variable cell aspect ration: a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multiscale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (PME). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the PME to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models

Tradeoff analysis of technology needs for public service helicopters

The design requirements for a family or type of Public Service Helicopter (PSH) is examined which will satisfy the needs of municipal and state governments in the following mission areas: Emergency Medical Service--Airborne Rescue Squad; Law Enforcement; Search and Rescue; and Environmental Control (Fire Fighting, Pollution, Resource Management). The report compares both design and performance requirements as specified by the PSH user's group against current technological capabilities, RTOPS and US Army LHX design requirements. The study explores various design trade-offs and options available to the aircraft designer/manufacturer in order to meet the several criteria specified by the PSH user's group. In addition, the report includes a brief assessment of the feasibility of employing certain advanced rotorcraft designs to meet the stringent combination of operational capabilities desired by the Public Service Helicopter Users