A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure

A methodology for determining amino-acid substitution matrices from set covers

We introduce a new methodology for the determination of amino-acid substitution matrices for use in the alignment of proteins. The new methodology is based on a pre-existing set cover on the set of residues and on the undirected graph that describes residue exchangeability given the set cover. For fixed functional forms indicating how to obtain edge weights from the set cover and, after that, substitution-matrix elements from weighted distances on the graph, the resulting substitution matrix can be checked for performance against some known set of reference alignments and for given gap costs. Finding the appropriate functional forms and gap costs can then be formulated as an optimization problem that seeks to maximize the performance of the substitution matrix on the reference alignment set. We give computational results on the BAliBASE suite using a genetic algorithm for optimization. Our results indicate that it is possible to obtain substitution matrices whose performance is either comparable to or surpasses that of several others, depending on the particular scenario under consideration

Systematic model behavior of adsorption on flat surfaces

A low density film on a flat surface is described by an expansion involving the first four virial coefficients. The first coefficient (alone) yields the Henry's law regime, while the next three correct for the effects of interactions. The results permit exploration of the idea of universal adsorption behavior, which is compared with experimental data for a number of systems

Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation

The phase-turbulent (PT) regime for the one dimensional complex Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large systems and long integration times, using an efficient new integration scheme. Particular attention is paid to solutions with a non-zero phase gradient. For fixed control parameters, solutions with conserved average phase gradient $\nu$ exist only for $|\nu|$ less than some upper limit. The transition from phase to defect-turbulence happens when this limit becomes zero. A Lyapunov analysis shows that the system becomes less and less chaotic for increasing values of the phase gradient. For high values of the phase gradient a family of non-chaotic solutions of the CGLE is found. These solutions consist of spatially periodic or aperiodic waves travelling with constant velocity. They typically have incommensurate velocities for phase and amplitude propagation, showing thereby a novel type of quasiperiodic behavior. The main features of these travelling wave solutions can be explained through a modified Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the PT phase. The latter explains also the behavior of the maximal Lyapunov exponents of chaotic solutions.Comment: 16 pages, LaTeX (Version 2.09), 10 Postscript-figures included, submitted to Phys. Rev.

Band-gaps in long Josephson junctions with periodic phase-shifts

We investigate analytically and numerically a long Josephson junction on an infnite domain, having arbitrary periodic phase shift of k, that is, the so-called 0-k long Josephson junction. The system is described by a one-dimensional sine-Gordon equation and has relatively recently been proposed as artificial atom lattices. We discuss the existence of periodic solutions of the system and investigate their stability both in the absence and presence of an applied bias current. We find critical values of the phase-discontinuity and the applied bias current beyond which a solution switches to its complementary counterpart. Due to the periodic discontinuity in the phase, the system admits regions of allowed and forbidden bands. We perturbatively investigate the Arnold tongues that separate the region of allowed and forbidden bands, and discuss the effect of an applied bias current on the band-gap structure. We present numerical simulations to support our analytical results

Recurrent dynamical symmetry breaking and restoration by Wilson lines at finite densities on a torus

In this paper we derive the general expression of a one-loop effective potential of the nonintegrable phases of Wilson lines for an SU(N) gauge theory with a massless adjoint fermion defined on the spactime manifold $R^{1,d-3}\times T^2$ at finite temperature and fermion density. The Phase structure of the vacuum is presented for the case with $d=4$ and N=2 at zero temperature. It is found that gauge symmetry is broken and restored alternately as the fermion density increases, a feature not found in the Higgs mechanism. It is the manifestation of the quantum effects of the nonintegrable phases.Comment: 17 pages, 2 figure

Some aspects of the Liouville equation in mathematical physics and statistical mechanics

This paper presents some mathematical aspects of Classical Liouville theorem and we have noted some mathematical theorems about its initial value problem. Furthermore, we have implied on the formal frame work of Stochastic Liouville equation (SLE)

Provenance, transport and composition of Dendê Coast beach sands in Bahia, central coast of Brazil

The great physiographic diversity of the Dendê Coast favors the production of different beach sediment types, including bioclastic components. In this study 74 beach samples collected at 2 km intervals were used to evaluate beach sediment composition. For each sample, 300 grains were identified for each grain size class coarser than 0.125 mm, using a binocular microscope. The beach sediments of the Dendê Coast are essentially siliciclastic (80-100%). Quartz is the major component (70-100%). Only at the Tinharé and Boipeba islands bioclasts are major components of beach sands reaching up to 80-100%. These sediments are made up essentially of fragments of Halimeda, reaching percentages up to 70%. Coralline algae and mollusks also contribute significantly to these sediments (up to 30%). The results obtained show that the spatial distribution of the bioclastic components provide important information on the environmental conditions present at the shoreline (energy levels, availability of hard substrates and protected areas, pattern of sediment dispersion) and on the sediment sources as well. The composition of the beach sediments on the Dendê Coast reflects the present day environmental conditions and show that these sediments do not experience significant lateral transport. This situation is favored by an impeded longshore transport that characterizes most of the region. Although, in general, the rivers that discharge on the Dendê Coast appear to transport few sediments to the coastal zone, the presence of heavy minerals, micas and feldspars suggests river contributions to the beach sediments. On the other hand, the coral and coralline algae reefs, besides offering a natural protection to the shoreline, also represent an important source of beach sands.A grande diversidade fisiográfica da Costa do Dendê favorece a deposição de diferentes tipos de sedimentos em suas praias, inclusive sedimentos ricos em carbonato de cálcio. Neste estudo 86 amostras de sedimento foram coletadas, em intervalos de 2 km, para avaliação da composição dos sedimentos praiais. Para cada amostra foram identificados 300 grãos por fração granulométrica maior que 0.125mm, usando uma lupa binocular. Os sedimentos das praias da Costa do Dendê são essencialmente siliciclásticos (80 -100%). O quartzo é o principal componente (70 -100%). Apenas nas ilhas de Tinharé e Boipeba, os bioclastos são os principais componentes alcançando teores entre 80 e 100%. Estes sedimentos são compostos essencialmente de fragmentos de Halimeda, com teores de até 70%. Algas coralinas e moluscos também contribuem significativamente para a composição das areias deste trecho (com teores acima de até 30%). Os resultados obtidos mostram que a análise da distribuição espacial dos componentes bioclásticos fornece informações importantes sobre as condições ambientais na linha de costa (níveis de energia, disponibilidade de substratos duros e suprimento de sedimento), assim como sobre as possíveis fontes de sedimento para a praia. A composição dos sedimentos das praias da Costa do Dendê reflete as condições ambientais atuais, e evidenciam que estes sedimentos não experimentam transporte lateral. Essa situação é favorecida pela situação de transporte litorâneo impedido que caracteriza a maior parte da região. Embora, os rios da região pareçam transportar poucos sedimentos para a zona costeira, a presença de minerais pesados, micas e feldspatos sugerem contribuições fluviais para os sedimentos das praias. Por outro lado, os recifes de coral e algas coralinas, além de oferecerem uma proteção natural para a linha de costa, também representam uma importante fonte de sedimentos para as praias