Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is \C_+. $F$ is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C^{m,\al}, $m\ge4$.Comment: 9 pages, v2:final version, to be publishe

Combining gravity with the forces of the standard model on a cosmological scale

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the underlying spacetime is a Friedman universe with flat spatial slices and where the matter fields are comprised of the strong interaction, with \SU(3) replaced by a general \SU(n), $n\ge 2$, and the electro-weak interaction. The wave functions are maps from $\R[4n+10]$ to a subspace of the antisymmetric Fock space, and one noteworthy result is that, whenever the electro-weak interaction is involved, the image of an eigenfunction is in general not one dimensional, i.e., in general it makes no sense specifying a fermion and looking for an eigenfunction the range of which is contained in the one dimensional vector space spanned by the fermion.Comment: 53 pages, v6: some typos correcte

Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

In the presence of a uniform field the one-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model develops zero frequency excitations at field-dependent 'soft mode' momenta. We determine three types of critical quantities, which we extract from the finite-size dependence of the lowest excitation energies, the singularities in the static structure factors and the infrared singularities in the dynamical structure factors at the soft mode momenta. We also compare our results with the predictions of conformal field theory.Comment: 12 pages, REVTEX, 7 figures, submitted to Physical Review

Technology and politics: The regional airport experience

The findings of a comparative study of the following six regional airports were presented: Dallas/Fort Worth, Kansas City, Washington, D.C., Montreal, Tampa, and St. Louis. Each case was approached as a unique historical entity, in order to investigate common elements such as: the use of predictive models in planning, the role of symbolism to heighten dramatic effects, the roles of community and professional elites, and design flexibility. Some of the factors considered were: site selection, consolidation of airline service, accessibility, land availability and cost, safety, nuisance, and pollution constraints, economic growth, expectation of regional growth, the demand forecasting conundrum, and design decisions. The hypotheses developed include the following: the effect of political, social, and economic conflicts, the stress on large capacity and dramatic, high-technology design, projections of rapid growth to explain the need for large capital outlays

Ultrafast circular polarization oscillations in spin-polarized vertical-cavity surface-emitting laser devices

Spin-polarized lasers offer new encouraging possibilities for future devices. We investigate the polarization dynamics of electrically pumped vertical-cavity surface-emitting lasers after additional spin injection at room temperature. We find that the circular polarization degree exhibits faster dynamics than the emitted light. Moreover the experimental results demonstrate a strongly damped ultrafast circular polarization oscillation due to spin injection with an oscillation frequency of approximately 11GHz depending on the birefringence in the VCSEL device. We compare our experimental results with theoretical calculations based on rate-equations. This allows us to predict undamped long persisting ultrafast polarization oscillations, which reveal the potential of spin-VCSELs for ultrafast modulation applications

Alternative way to characterize a q-gaussian distribution by a robust heavy tail measurement

The q-Gaussians are a class of stable distributions which are present in many scientific fields, and that behave as heavy tailed distributions for an especific range of q values. The identification of these values, which are used in the description of systems, is sometimes a hard task. In this work the identification of a q-Gaussian distribution from empirical data was done by a measure of its tail weight using robust statistics. Numerical methods were used to generate artificial data, to find out the tail weight -- medcouple, and also to adjust the curve between medcouple and the q value. We showed that the medcouple value remains unchanged when the calculation is applied to data which have long memory. A routine was made to calculate the q value and its standard deviation, when applied to empirical data. It is possible to identify a q-Gaussian by the proposed methods with higher precision than in the literature for the same data sample, or as precise as found in the literature. However, in this case, it is required a smaller sample of data. We hope that this method will be able to open new ways for identifying physical phenomena that belongs to nonextensive frameworks.Comment: Added references. Corrected typos. Improved in introduction, conclusion, results unchange

Birefringence controlled room-temperature picosecond spin dynamics close to the threshold of vertical-cavity surface-emitting laser devices

We analyze the spin-induced circular polarization dynamics at the threshold of vertical-cavity surface-emitting lasers at room-temperature using a hybrid excitation combining electrically pumping without spin preference and spin-polarized optical injection. After a short pulse of spin-polarized excitation, fast oscillations of the circular polarization degree (CPD) are observed within the relaxation oscillations. A theoretical investigation of this behavior on the basis of a rate equation model shows that these fast oscillations of CPD could be suppressed by means of a reduction of the birefringence of the laser cavity

The Panchromatic Starburst Intensity Limit At Low And High Redshift

The integrated bolometric effective surface brightness S_e distributions of starbursts are investigated for samples observed in 1. the rest frame ultraviolet (UV), 2. the far-infrared and H-alpha, and 3. 21cm radio continuum emission. For the UV sample we exploit a tight empirical relationship between UV reddening and extinction to recover the bolometric flux. Parameterizing the S_e upper limit by the 90th percentile of the distribution, we find a mean S_{e,90} = 2.0e11 L_{sun}/kpc^2 for the three samples, with a factor of three difference between the samples. This is consistent with what is expected from the calibration uncertainties alone. We find little variation in S_{e,90} with effective radii for R_e ~ 0.1 - 10 kpc, and little evolution out to redshifts z ~ 3. The lack of a strong dependence of S_{e,90} on wavelength, and its consistency with the pressure measured in strong galactic winds, argue that it corresponds to a global star formation intensity limit (\dot\Sigma_{e,90} ~ 45 M_{sun}/kpc^2/yr) rather than being an opacity effect. There are several important implications of these results: 1. There is a robust physical mechanism limiting starburst intensity. We note that starbursts have S_e consistent with the expectations of gravitational instability models applied to the solid body rotation portion of galaxies. 2. Elliptical galaxies and spiral bulges can plausibly be built with maximum intensity bursts, while normal spiral disks can not. 3. The UV extinction of high-z galaxies is significant, implying that star formation in the early universe is moderately obscured. After correcting for extinction, the observed metal production rate at z ~ 3 agrees well with independent estimates made for the epoch of elliptical galaxy formation.Comment: 31 pages Latex (aas2pp4.sty,psfig.sty), 9 figures, accepted for publication in the Astronomical Journa

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