Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

Ozone formation potentials of volatile organic compounds and ozone sensitivity to their emission in the megacity of Sao Paulo, Brazil

In the present study, a three-dimensional Eulerian photochemical model was employed to estimate the impact that organic compounds have on tropospheric ozone formation in the Metropolitan Area of Sao Paulo (MASP). In the year 2000, base case simulations were conducted in two periods: August 22-24 and March 13-15. Based on the pollutant concentrations calculated by the model, the correlation coefficient relative to observations for ozone ranged from 0.91 to 0.93 in both periods. In the simulations employed to evaluate the ozone potential of individual VOCs, as well as the sensitivity of ozone to the VOC/NO(x) emission ratio, the variation in anthropogenic emissions was estimated at 15% (according to tests performed previously variations of 15% were stable). Although there were significant differences between the two periods, ozone concentrations were found to be much more sensitive to VOCs than to NO(x) in both periods and throughout the study domain. In addition, considering their individual rates of emission from vehicles, the species/classes that were most important for ozone formation were as follows: aromatics with a kOH>2x 10(4) ppm(-1) min(-1); olefins with a kOH 7 x 10(4) ppm(-1) min(-1); olefins with a kOH 7 x 10(4) ppm(-1) min(-1); ethene; and formaldehyde, which are the principal species related to the production, transport, storage and combustion of fossil fuels.

A collocation method for solving singular integro-differential equations

This paper describes a collocation method for numerically solving Cauchy-type linear singular integro-differential equations. The numerical method is based on the transformation of the integro-differential equation into an integral equation, and then applying a collocation method to solve the latter. The collocation points are chosen as the Chebyshev nodes. Uniform convergence of the resulting method is then discussed. Numerical examples are presented and solved by the numerical techniques.

A singular integro-differential equation model for dryout in LMFBR boiler tubes

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem Appropriate boundary conditions for the now are discussed The resulting non-lineal singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques) Predictions for the length to the dryout point from the entry of the annular regime are made The influence of both the traction tau provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter eta on the dryout length is investigated

Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension

We show that the Hausdorff dimension of the spectral measure of a class of deterministic, i.e. nonrandom, block-Jacobi matrices may be determined with any degree of precision, improving a result of Zlatos [Andrej Zlatos,. Sparse potentials with fractional Hausdorff dimension, J. Funct. Anal. 207 (2004) 216-252]. (C) 2010 Elsevier Inc. All rights reserved.

Limitation of double folding potentials to simulate the polarization in reactions involving halo nuclei

In this work, we investigate the limitation of the use of strength coefficients on double folding potentials to study the presence of the threshold anomaly in the elastic scattering of halo nuclei at near barrier energies. For this purpose, elastic angular distributions and reaction cross sections for the He-6 on Bi-209 are studied. (c) 2008 Elsevier B.V. All rights reserved.

A further exploration of a nucleophilicity index based on the gas-phase ionization potentials

An empirical nucleophilicity index based on the gas-phase ionization potentials has been recently shown to be useful categorizing and settling the nucleophilicity power of a series of captodative ethylenes reacting in cycloaddition reactions (L.R. Domingo, E. Chamorro, P. Perez, Journal of Organic Chemistry 73 (2008) 4615-4624). In the present work, the applicability of such model is tested within a broader series of substituted alkenes, substituted aromatic compounds and simple nucleophilic molecules. This index obtained within a Koopman`s theorem framework has been evaluated here in both gas and solution phases for several well-known nucleophiles. These results are found to be linearly correlated. Finally, the feasibility of the predictive character of this index has been discussed in comparison to the available experimental nucleophilicities of some amines in water. These results further support and validate the usefulness of such approximation in the modeling of the global nucleophilicity. (C) 2008 Elsevier B.V. All rights reserved.

Conservation laws and tachyon potentials in the sliver frame

Conservation laws have provided an elegant and efficient tool to evaluate the open string field theory interaction vertex, they have been originally implemented in the case where the string field is expanded in the Virasoro basis. In this work we derive conservation laws in the case where the string field is expanded in the so-called sliver L(0)-basis. As an application of this new set of conservation laws, we compute the open string field action relevant to the tachyon condensation and in order to present not only an illustration but also an additional information, we evaluate the action without imposing a gauge choice.

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabasi-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks. Copyright (C) EPLA, 2009

Bose systems in spatially random or time-varying potentials

Bose systems, subject to the action of external random potentials, are considered. For describing the system properties, under the action of spatially random potentials of arbitrary strength, the stochastic mean-field approximation is employed. When the strength of disorder increases, the extended Bose-Einstein condensate fragments into spatially disconnected regions, forming a granular condensate. Increasing the strength of disorder even more transforms the granular condensate into the normal glass. The influence of time-dependent external potentials is also discussed. Fastly varying temporal potentials, to some extent, imitate the action of spatially random potentials. In particular, strong time-alternating potential can induce the appearance of a nonequilibrium granular condensate.

ON CLOSED GEODESICS IN THE LEAF SPACE OF SINGULAR RIEMANNIAN FOLIATIONS

In this paper we prove the existence of closed geodesics in the leaf space of some classes of singular Riemannian foliations (s.r.f.), namely s.r.fs. that admit sections or have no horizontal conjugate points. We also investigate the shortening process with respect to Riemannian foliations.

Desingularization of singular Riemannian foliation

Let F be a singular Riemannian foliation on a compact Riemannian manifold M. By successive blow-ups along the strata of F we construct a regular Riemannian foliation (F) over cap on a compact Riemannian manifold (M) over cap and a desingularization map (rho) over cap : (M) over cap -> M that projects leaves of (F) over cap into leaves of F. This result generalizes a previous result due to Molino for the particular case of a singular Riemannian foliation whose leaves were the closure of leaves of a regular Riemannian foliation. We also prove that, if the leaves of F are compact, then, for each small epsilon > 0, we can find (M) over cap and (F) over cap so that the desingularization map induces an epsilon-isometry between M/F and (M) over cap/(F) over cap. This implies in particular that the space of leaves M/F is a Gromov-Hausdorff limit of a sequence of Riemannian orbifolds {((M) over cap (n)/(F) over cap (n))}.

Spectroscopic evidences of the presence of hydrogenated species on the surface of copper during CO(2) electroreduction at low cathodic potentials

Carbon dioxide electroreduction on copper electrode was studied by surface enhanced Raman scattering (SERS) in K(2)SO(4) aqueous solutions with different pH values. CO(2) was bubbled into the solution at 0 V vs. Ag/AgCl, i.e., on an oxidized copper surface. In acidic solutions (pH around 2.5), at -0.2 V, bands indicative of the presence of ethylene on the electrode surface were detected. Although ethylene is knowledgably a product of CO(2) electroreduction on copper, it was not experimentally identified on the electrode`s surface at such a low cathodic potential in prior works. In solutions with pH around 2.5, CO bands were not observed, suggesting that hydrocarbons could be formed by a pathway that does not occur via adsorbed CO. In solutions with higher pHs, a complex spectral pattern, between 800 and 1700 cm(-1), was observed at approximately -0.4 V. The observed spectrum closely resembles those reported in the literature for adsorption of monocarboxylic acids with small chains. The spectral features indicate the presence of a structure containing a double C=C bond. a carboxyl group, and C-H bonds on the electrode`s surface. SERS spectra obtained in CO-saturated solution are also presented. However, in this case, no SERS bands were observed in the region between 800 and 1700 cm(-1) at low cathodic potentials. (c) 2009 Elsevier B.V. All rights reserved.