Long time motion of NLS solitary waves in a confining potential

We study the motion of solitary-wave solutions of a family of focusing generalized nonlinear Schroedinger equations with a confining, slowly varying external potential, $V(x)$. A Lyapunov-Schmidt decomposition of the solution combined with energy estimates allows us to control the motion of the solitary wave over a long, but finite, time interval. We show that the center of mass of the solitary wave follows a trajectory close to that of a Newtonian point particle in the external potential $V(x)$ over a long time interval.Comment: 42 pages, 2 figure

Numerical Simulation of the Kinetics of Radical Decay in Single-Pulse High-Energy Electron-Irradiated Polymer Aqueous Solutions

A new method for the numerical simulation of the radiation chemistry of aqueous polymer solutions is introduced. The method makes use of a deterministic approach combining the conventional homogeneous radiation chemistry of water with the chemistry of polymer radicals and other macromolecular species. The method is applied on single-pulse irradiations of aqueous polymer solutions. The speciation of macromolecular species accounts for the variations in the number of alkyl radicals per chain, molecular weight, and number of internal loops (as a consequence of an intramolecular radical-radical combination). In the simulations, the initial polymer molecular weight, polymer concentration, and dose per pulse (function of pulse length and dose rate during the pulse) were systematically varied. In total, 54 different conditions were simulated. The results are well in line with the available experimental data for similar systems. At a low polymer concentration and a high dose per pulse, the kinetics of radical decay is quite complex for the competition between intra- and intermolecular radical-radical reactions, whereas at a low dose per pulse the kinetics is purely second-order. The simulations demonstrate the limitations of the polymer in scavenging all the radicals generated by water radiolysis when irradiated at a low polymer concentration and a high dose per pulse. They also show that the radical decay of lower-molecular-weight chains is faster and to a larger extent dominated by intermolecular radical-radical reactions, thus explaining the mechanism behind the experimentally observed narrowing of molecular weight distributions

A theory of normed simulations

In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general purpose theorem provers. Moreover, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a lower-level specification can be simulated by at most one step in the higher-level one, for any related pair of states. In earlier work we demonstrated that normed simulations are quite useful as a vehicle for the formalization of refinement proofs via theorem provers. Here we show that normed simulations also have pleasant theoretical properties: (1) under some reasonable assumptions, it is decidable whether a given relation is a normed forward simulation, provided tautology checking is decidable for the underlying logic; (2) at the semantic level, normed forward and backward simulations together form a complete proof method for establishing behavior inclusion, provided that the higher-level specification has finite invisible nondeterminism.Comment: 31 pages, 10figure

Scaling and Correlation Functions in a Model of a Two-dimensional Earthquake Fault

We study numerically a two-dimensional version of the Burrige-Knopoff model. We calculate spatial and temporal correlation functions and compare their behavior with the results found for the one-dimensional model. The Gutenberg-Richter law is only obtained for special choices of parameters in the relaxation function. We find that the distribution of the fractal dimension of the slip zone exhibits two well-defined peaks coeersponding to intermediate size and large events.Comment: 14 pages, 23 Postscript figure

Long-Time Dynamics of Variable Coefficient mKdV Solitary Waves

We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We study the long time behaviour of solutions with initial conditions close to a stable, B=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function B(t,x), plus an H^1-small fluctuation.Comment: 19 page

Balloon-borne radiometer measurement of Northern Hemisphere mid-latitude stratospheric HNO3 profiles spanning 12 years

Low-resolution atmospheric thermal emission spectra collected by balloon-borne radiometers over the time span of 1990–2002 are used to retrieve vertical profiles of HNO3, CFC-11 and CFC-12 volume mixing ratios between approximately 10 and 35 km altitude. All of the data analyzed have been collected from launches from a Northern Hemisphere mid-latitude site, during late summer, when stratospheric dynamic variability is at a minimum. The retrieval technique incorporates detailed forward modeling of the instrument and the radiative properties of the atmosphere, and obtains a best fit between modeled and measured spectra through a combination of onion-peeling and global optimization steps. The retrieved HNO3 profiles are consistent over the 12-year period, and are consistent with recent measurements by the Atmospheric Chemistry Experiment-Fourier transform spectrometer satellite instrument. This suggests that, to within the errors of the 1990 measurements, there has been no significant change in the HNO3 summer mid-latitude profile

Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films

The dynamical vortex response of a two-dimensional array of the resistively shunted Josephson junctions in a perpendicular magnetic field is inferred from simulations. It is found that, as the magnetic field is increased at a fixed temperature, the response crosses over from normal to anomalous, and that this crossover can be characterized by a single dimensionless parameter. It is described how this crossover should be reflected in measurements of the complex impedance for Josephson junction arrays and superconducting films.Comment: 4 pages including 5 figures in two columns, final versio

Avaliação da toxicidade do diflubenzuron e P-cloroanilina em indicadores bioquímicos de organismos não-alvo aquáticos.

Resumo: O uso de produtos agrícolas vem sendo a principal forma de combater parasitas na aquicultura, sendo que o Diflubenzuron, (DFB) é o mais utilizado. Este composto inibe a síntese de quitina, componente do exoesqueleto dos parasitas, e apresenta baixa toxicidade aos peixes. Porém, no ambiente aquático, o DFB pode ser tóxico às espécies não-alvo e, quando degradado, gera p-cloroanilina, (PCA), metabólito potencialmente cancerígeno e mutagênico para o ser humano. Tendo em vista a necessidade de se obter mais informações sobre a toxicidade destes compostos nos organismos aquáticos não-alvo, a proposta deste trabalho foi analisar a atividade enzimática de fosfatases ácida (FAT) e alcalina (Fale), catalase (CAT) e superoxido dismutase (SOD) de microalga Pseudokirchneriella subcapitata, microcrustáceo Daphnia similis e o peixe Oreochromis niloticus com base na concentração efetiva 50% (CE50) com vistas a suprir a necessidade de dados na literatura acerca da toxicidade destes produtos e analisar o possível uso da análise enzimática como indicador de poluição de recursos hídricos em programas de biomonitoramento

Hydrogen transport in superionic system Rb3H(SeO4)2: a revised cooperative migration mechanism

We performed density functional studies of electronic properties and mechanisms of hydrogen transport in Rb3H(SeO4)2 crystal which represents technologically promising class M3H(XO4)2 of proton conductors (M=Rb,Cs, NH4; X=S,Se). The electronic structure calculations show a decisive role of lattice dynamics in the process of proton migration. In the obtained revised mechanism of proton transport, the strong displacements of the vertex oxygens play a key role in the establishing the continuous hydrogen transport and in the achieving low activation energies of proton conduction which is in contrast to the standard two-stage Grotthuss mechanism of proton transport. Consequently, any realistic model description of proton transport should inevitably involve the interactions with the sublattice of the XO4 groups.Comment: 11 pages, 11 figures, to appear in Physical Review