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

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

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

Considerations for the design of an onboard air traffic situation display

The basic concept of remoting information to the cockpit is used to design and develop a computerized airborne traffic situation display device that automatically selects and presents segments of a controller's scope to the aircraft pilot via a narrow band digital data link. These data are integrated with aircraft heading and navigation information to provide a display useful in congested air space. The display can include alphanumerical symbols, air route maps, and controller instructions

Development of Replacement Heifers using Combinations of Three Forage Types and Feed Supplements (with or without Broiler Litter)

The proper management of replacement heifers is an essential component of successful cow/calf operations. The level of management and nutrition applied to replacement heifers as calves and yearlings can impact their subsequent reproductive performance and productivity

Vacuum-UV negative photoion spectroscopy of CF3Cl, CF3Br and CF3I

Using synchrotron radiation negative ions have been detected by mass spectrometry following vacuum-UV photoexcitation of trifluorochloromethane (CF$_3$Cl), trifluorobromomethane (CF$_3$Br) and trifluoroiodomethane (CF$_3$I). The anions F$^-$, X$^-$, F$_2^-$, FX$^-$, CF$^-$, CF$_2^-$ and CF$_3^-$ were observed from all three molecules, where X = Cl, Br or I, and their ion yields recorded in the range 8-35 eV. With the exception of Br$^-$ and I$^-$, the anions observed show a linear dependence of signal with pressure, showing that they arise from unimolecular ion-pair dissociation. Dissociative electron attachment, following photoionization of CF$_3$Br and CF$_3$I as the source of low-energy electrons, is shown to dominate the observed Br$^-$ and I$^-$ signals, respectively. Cross sections for ion-pair formation are put on to an absolute scale by calibrating the signal strengths with those of F$^-$ from both SF$_6$ and CF$_4$. These anion cross sections are normalized to vacuum-UV absorption cross sections, where available, and the resulting quantum yields are reported. Anion appearance energies are used to calculate upper limits to 298 K bond dissociation energies for $D^0$(CF$_3$-X) which are consistent with literature values. We report new data for $D^0$(CF$_2$I$^-$-F) ≤ 2.7 ± 0.2 eV and $\Delta_fH^0_{298}$ (CF$_2$I$^+$) ≤ (598 ± 22) kJ mol$^{-1}$. No ion-pair formation is observed below the ionization energy of the parent molecule for CF$_3$Cl and CF$_3$Br, and only weak signals (in both I$^-$ and F$^-$) are detected for CF$_3$I. These observations suggest neutral photodissociation is the dominant exit channel to Rydberg state photoexcitation at these lower energies