Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

Certain physical and chemical changes of Grimes Apples during ripening and storage pr

These studies of changes in Grimes Apples, incident to ripening and storage, include rate of softening, increase in size, color changes of fruit and seeds, other common tests used by the growr to determine time of picking, and chemical analyses of changes within the apple

Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk

We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random walk of microscopic particles and a discrete vector field which defines the time evolution of the particles. The cellular automaton thus obtained can retain isotropy and therefore reproduces the patterns found in the numerical solutions of the reaction-diffusion equation. As a specific example, we apply the method to the Belousov-Zhabotinsky reaction in excitable media

Does a nonlinear mating preference predict nonlinear benefits to offspring?: Avoiding bad mates to obtain good genes

Abstract only availableFemale Hyla versicolor (gray tree frogs) strongly prefer choosing mates with long or medium call lengths, avoiding the shorter callers. The development of their offspring is hypothesized to mirror this nonlinear preference, in that the long and medium caller progeny will develop at a similar rate that is faster than that of the short callers. Using past data, twenty-seven males with long, medium, and short call lengths were chosen and mated (in vitro) with random field-caught females. Five hundred and forty tadpoles were raised in individual containers. The tadpoles were subjected to high and low food treatments to test an environmental effect on their development. At three weeks, the tadpoles were weighed. These data were compared for the offspring of the long, medium, and short father's call according to food treatment as well as tadpole growth according to food treatment. Both the long calling and the medium calling progeny developed at a faster rate then the short calling progeny, but at a similar rate compared to each other. Tadpoles subjected to high food treatments developed at a faster rate than the low food treatment tadpoles. The dates of metamorphosis will also be recorded and later compared in the future. As the tadpoles of shorter calling fathers develop at a slower rate than the longer calling progeny, they are more at risk for environmental dangers and predation before they undergo metamorphosis. By researching female choices regarding length of calls and its effect on offspring development, we can examine how natural selection affects the evolution of female mating behavior.NSF grant to A. Welc

Integrated Diamond Optics for Single Photon Detection

Optical detection of single defect centers in the solid state is a key element of novel quantum technologies. This includes the generation of single photons and quantum information processing. Unfortunately the brightness of such atomic emitters is limited. Therefore we experimentally demonstrate a novel and simple approach that uses off-the-shelf optical elements. The key component is a solid immersion lens made of diamond, the host material for single color centers. We improve the excitation and detection of single emitters by one order of magnitude, as predicted by theory.Comment: 10 pages, 3 figure

Validation and Calibration of Models for Reaction-Diffusion Systems

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numerical integration of diffusion and reaction-diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite $\Delta x$ and $\Delta t$, if the parameter $\gamma_N=D \Delta t/(\Delta x)^2$ assumes a fixed constant value, where $N$ is an odd positive integer parametrizing the alghorithm. The error between the solutions of the discrete and the continuous equations goes to zero as $(\Delta x)^{2(N+2)}$ and the values of $\gamma_N$ are dimension independent. With these new integration methods, anisotropy effects resulting from the finite differences are minimized, defining a standard for validation and calibration of numerical solutions of diffusion and reaction-diffusion equations. Comparison between numerical and analytical solutions of reaction-diffusion equations give global discretization errors of the order of $10^{-6}$ in the sup norm. Circular patterns of travelling waves have a maximum relative random deviation from the spherical symmetry of the order of 0.2%, and the standard deviation of the fluctuations around the mean circular wave front is of the order of $10^{-3}$.Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao

A new approach to functional and software structure for engine management systems

ABSTRACT This paper describes the new Engine Management System (EMS) ME7. Torque and A/F demands for modern EMS result from both, internal functions (i.e. engine start, idle speed control, catalyst heating) and external systems (i.e. driver's request, transmission or vehicle dynamic control). With ME7 these demands are processed to the optimized actions of the actuators by a centrally coordinated torque and A/F management. The design of the functions is physically based to provide optimum portability and minimum calibration time. Examples are given for the physical manifold pressure model and the cylinder charge control of ME7 with electronic throttle control. The real time operating system "ERCOS" and a layer based software architecture enable the implementation of these functions in a flexible family of products for current and future systems. Topics, such as warm-up strategies for catalysts in conventional port injection systems, gasoline direct injection systems (with their switch-over strategies between stoichiometric and stratified operation), NOx catalyst control, and the requirements of future integrated drive train management systems, all require maximum flexibility and expandability. The introduction of the ME7 is an important step towards this future. The design represents a good basis for development sharing with customers and is also an important prerequisite for the vehicle management system CARTRONIC

Convex Functions and Spacetime Geometry

Convexity and convex functions play an important role in theoretical physics. To initiate a study of the possible uses of convex functions in General Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an initial data set $(\Sigma, h_{ij}, K_{ij})$ admitting a suitably defined convex function. We show how the existence of a convex function on a spacetime places restrictions on the properties of the spacetime geometry.Comment: 26 pages, latex, 7 figures, improved version. some claims removed, references adde

Sexual selection and population divergence III : interspecific and intraspecific variation in mating signals

Funding: Orthopterists' Society, Natural Environment Research Council (Grant Number(s): NE/G00949X/1, NE/G014906/1, NE/L011255/1), ARC (Grant Number(s): DP180101708).A major challenge for studying the role of sexual selection in divergence and speciation is understanding the relative influence of different sexually selected signals on those processes in both intra‐ and interspecific contexts. Different signals may be more or less susceptible to co‐option for species identification depending on the balance of sexual and ecological selection acting upon them. To examine this, we tested three predictions to explain geographic variation in long‐ versus short‐range sexual signals across a 3,500 + km transect of two related Australian field cricket species (Teleogryllus spp.): (a) selection for species recognition, (b) environmental adaptation and (c) stochastic divergence. We measured male calling song and male and female cuticular hydrocarbons (CHCs) in offspring derived from wild populations, reared under common garden conditions. Song clearly differentiated the species, and no hybrids were observed suggesting that hybridization is rare or absent. Spatial variation in song was not predicted by geography, genetics or climatic factors in either species. In contrast, CHC divergence was strongly associated with an environmental gradient supporting the idea that the climatic environment selects more directly upon these chemical signals. In light of recently advocated models of diversification via ecological selection on secondary sexual traits, the different environmental associations we found for song and CHCs suggest that the impact of ecological selection on population divergence, and how that influences speciation, might be different for acoustic versus chemical signals.Publisher PDFPeer reviewe