Quasi-matter bounce and inflation in the light of the CSL model

The Continuous Spontaneous Localization (CSL) model has been proposed as a possible solution to the quantum measurement problem by modifying the Schr\"{o}dinger equation. In this work, we apply the CSL model to two cosmological models of the early Universe: the matter bounce scenario and slow roll inflation. In particular, we focus on the generation of the classical primordial inhomogeneities and anisotropies that arise from the dynamical evolution, provided by the CSL mechanism, of the quantum state associated to the quantum fields. In each case, we obtained a prediction for the shape and the parameters characterizing the primordial spectra (scalar and tensor), i.e. the amplitude, the spectral index and the tensor-to-scalar ratio. We found that there exist CSL parameter values, allowed by other non-cosmological experiments, for which our predictions for the angular power spectrum of the CMB temperature anisotropy are consistent with the best fit canonical model to the latest data released by the Planck Collaboration.Comment: 27 pages, including 6 figures, 2 tables and one Appendix. Final version. Accepted in EPJ

Quasi-Langmuir-Blodgett Thin Film Deposition of Carbon Nanotubes

The handling and manipulation of carbon nanotubes continues to be a challenge to those interested in the application potential of these promising materials. To this end, we have developed a method to deposit pure nanotube films over large flat areas on substrates of arbitrary composition. The method bears some resemblance to the Langmuir-Blodgett deposition method used to lay down thin organic layers. We show that this redeposition technique causes no major changes in the films' microstructure and that they retain the electronic properties of as-deposited film laid down on an alumina membrane.Comment: 3 pages, 3 figures, submitted Journal of Applied Physic

A modified semi--implict Euler-Maruyama Scheme for finite element discretization of SPDEs with additive noise

We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDE) driven by additive space-time noise. We introduce a new modified scheme using a linear functional of the noise with a semi--implicit Euler--Maruyama method in time and in space we analyse a finite element method (although extension to finite differences or finite volumes would be possible). We prove convergence in the root mean square $L^{2}$ norm for a diffusion reaction equation and diffusion advection reaction equation. We present numerical results for a linear reaction diffusion equation in two dimensions as well as a nonlinear example of two-dimensional stochastic advection diffusion reaction equation. We see from both the analysis and numerics that the proposed scheme has better convergence properties than the standard semi--implicit Euler--Maruyama method

On competitive discrete systems in the plane. I. Invariant Manifolds

Let $T$ be a $C^{1}$ competitive map on a rectangular region $R\subset \mathbb{R}^{2}$. The main results of this paper give conditions which guarantee the existence of an invariant curve $C$, which is the graph of a continuous increasing function, emanating from a fixed point $\bar{z}$. We show that $C$ is a subset of the basin of attraction of $\bar{z}$ and that the set consisting of the endpoints of the curve $C$ in the interior of $R$ is forward invariant. The main results can be used to give an accurate picture of the basins of attraction for many competitive maps. We then apply the main results of this paper along with other techniques to determine a near complete picture of the qualitative behavior for the following two rational systems in the plane. $$x_{n+1}=\frac{\alpha_{1}}{A_{1}+y_{n}},\quad y_{n+1}=\frac{\gamma_{2}y_{n}}{x_{n}},\quad n=0,1,...,$$ with $\alpha_1,A_{1},\gamma_{2}>0$ and arbitrary nonnegative initial conditions so that the denominator is never zero. $$x_{n+1}=\frac{\alpha_{1}}{A_{1}+y_{n}},\quad y_{n+1}=\frac{y_{n}}{A_{2}+x_{n}},\quad n=0,1,...,$$ with $\alpha_1,A_{1},A_{2}>0$ and arbitrary nonnegative initial conditions.Comment: arXiv admin note: text overlap with arXiv:0905.1772 by other author

The War Against Chinese Restaurants

Chinese restaurants are a cultural fixture—as American as cherry pie. Startlingly, however, there was once a national movement to eliminate Chinese restaurants, using innovative legal methods to drive them out. Chinese restaurants were objectionable for two reasons. First, Chinese restaurants competed with “American” restaurants, thus threatening the livelihoods of white owners, cooks, and servers and motivating unions to fight them. Second, Chinese restaurants threatened white women, who were subject to seduction by Chinese men taking advantage of intrinsic female weakness and nefarious techniques such as opium addiction. The efforts were creative. Chicago used anti-Chinese zoning, Los Angeles restricted restaurant jobs to citizens, Boston authorities denied Chinese restaurants licenses, and the New York Police Department simply ordered whites out of Chinatown. Perhaps the most interesting technique was a law, endorsed by the American Federation of Labor for adoption in all jurisdictions, prohibiting white women from working in Asian restaurants. Most measures failed or were struck down. The unions, of course, did not eliminate Chinese restaurants, but Asians still lost because unions achieved their more important goal by extending the federal immigration policy of excluding Chinese immigrants to all Asian immigrants. The campaign is of more than historical interest today. As current anti-immigration sentiments and efforts show, even now the idea that white Americans should have a privileged place in the economy, or that nonwhites are culturally incongruous, persists among some