Similarity Solutions of a Class of Perturbative Fokker-Planck Equation

In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the Fokker-Planck equations and the Schrodinger equations. In this work, we further explore the possibility of similarity solutions of such a class of Fokker-Planck equations. These solutions possess definite scaling behaviors, and are obtained by means of the so-called similarity method

Far-infrared spectroelectrochemistry: a study of linear molybdenum/iron/sulfur clusters

The far-infrared spectroelectrochemistry of linear M/Fe/S (M=Mo, W) complexes was investigated in methylene chloride and dichloroethane. With CsI as spectral windows, bands above 200 cm−1 can be observed in methylene chloride, except for a weak methylene chloride band at 450 cm−1. Substitution of dichloroethane for methylene chloride, solvents of nearly identical electrochemical properties, allows one to observe solute bands in the 450-cm−1 region. The far-infrared spectroelectrochemistry of [MoFe2S4Cl4]2− and its tungsten analogue was investigated. The disappearance of the oxidation bands and the appearance of bands due to the reduced product could be clearly observed. The origin of the vibrational bands could be clearly identified using 34S-substituted complexes. In addition to the far-infrared bands, the resonance Raman spectroelectrochemistry of the oxidized and reduced complex, along with the 34S-substituted complexes was obtained. Far-infrared and resonance Raman spectroelectrochemistry can be combined to understand the electrochemical mechanism of transition metal complexes. The far-infrared spectroelectrochemistry of [MoFe2S4Cl4]2− and its tungsten analogue was investigated. The disappearance of the initial bands and the appearance of bands due to the reduced product could be clearly observed. Resonance Raman spectroscopy and the use of 34S-substituted complexes were used for characterization of the reactant and products

Statistical properties of the method of regularization with periodic Gaussian reproducing kernel

The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization. We show in the white noise model setting, that in function spaces of very smooth functions, such as the infinite-order Sobolev space and the space of analytic functions, the method under consideration is asymptotically minimax; in finite-order Sobolev spaces, the method is rate optimal, and the efficiency in terms of constant when compared with the minimax estimator is reasonably high. The smoothing parameters in the periodic Gaussian regularization can be chosen adaptively without loss of asymptotic efficiency. The results derived in this paper give a partial explanation of the success of the Gaussian reproducing kernel in practice. Simulations are carried out to study the finite sample properties of the periodic Gaussian regularization.Comment: Published by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Statistics (http://www.imstat.org/aos/) at http://dx.doi.org/10.1214/00905360400000045

Nonlocal Kirchhoff superlinear equations with indefinite nonlinearity and lack of compactness

We study the following Kirchhoff equation $$- \left(1 + b \int_{\mathbb{R}^3} |\nabla u|^2 dx \right) \Delta u + V(x) u = f(x,u), \ x \in \mathbb{R}^3.$$ A special feature of this paper is that the nonlinearity $f$ and the potential $V$ are indefinite, hence sign-changing. Under some appropriate assumptions on $V$ and $f$, we prove the existence of two different solutions of the equation via the Ekeland variational principle and Mountain Pass Theorem

Concrete: Potential material for Space Station

To build a permanent orbiting space station in the next decade is NASA's most challenging and exciting undertaking. The space station will serve as a center for a vast number of scientific products. As a potential material for the space station, reinforced concrete was studied, which has many material and structural merits for the proposed space station. Its cost-effectiveness depends on the availability of lunar materials. With such materials, only 1 percent or less of the mass of a concrete space structure would have to be transported from earth

Thermalization and temperature distribution in a driven ion chain

We study thermalization and non-equilibrium dynamics in a dissipative quantum many-body system -- a chain of ions with two points of the chain driven by thermal bath under different temperature. Instead of a simple linear temperature gradient as one expects from the classical heat diffusion process, the temperature distribution in the ion chain shows surprisingly rich patterns, which depend on the ion coupling rate to the bath, the location of the driven ions, and the dissipation rates of the other ions in the chain. Through simulation of the temperature evolution, we show that these unusual temperature distribution patterns in the ion chain can be quantitatively tested in experiments within a realistic time scale.Comment: 5 pages, 5 figure

Superradiance in spin-JJ particles: Effects of multiple levels

We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-$j$ particle with $j$ an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems, and compare the results based on a novel approach we have developed in {[}Yelin \textit{et al.}, arXiv:quant-ph/0509184{]}. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-$j$ particles, taking into account the coherence of transitions between different atomic levels. We find that the superradiance, which is well-known as a many-body phenomenon, can also be modified by multiple level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have multi-level structure which is partially harmonic.Comment: 11 pages, 7 figure