Solitons in the noisy Burgers equation

We investigate numerically the coupled diffusion-advective type field equations originating from the canonical phase space approach to the noisy Burgers equation or the equivalent Kardar-Parisi-Zhang equation in one spatial dimension. The equations support stable right hand and left hand solitons and in the low viscosity limit a long-lived soliton pair excitation. We find that two identical pair excitations scatter transparently subject to a size dependent phase shift and that identical solitons scatter on a static soliton transparently without a phase shift. The soliton pair excitation and the scattering configurations are interpreted in terms of growing step and nucleation events in the interface growth profile. In the asymmetrical case the soliton scattering modes are unstable presumably toward multi soliton production and extended diffusive modes, signalling the general non-integrability of the coupled field equations. Finally, we have shown that growing steps perform anomalous random walk with dynamic exponent z=3/2 and that the nucleation of a tip is stochastically suppressed with respect to plateau formation.Comment: 11 pages Revtex file, including 15 postscript-figure

Motion of a driven tracer particle in a one-dimensional symmetric lattice gas

We study the dynamics of a tracer particle subject to a constant driving force $E$ in a one-dimensional lattice gas of hard-core particles whose transition rates are symmetric. We show that the mean displacement of the driven tracer grows in time, $t$, as $\sqrt{\alpha t}$, rather than the linear time dependence found for driven diffusion in the bath of non-interacting (ghost) particles. The prefactor $\alpha$ is determined implicitly, as the solution of a transcendental equation, for an arbitrary magnitude of the driving force and an arbitrary concentration of the lattice gas particles. In limiting cases the prefactor is obtained explicitly. Analytical predictions are seen to be in a good agreement with the results of numerical simulations.Comment: 21 pages, LaTeX, 4 Postscript fugures, to be published in Phys. Rev. E, (01Sep, 1996

Persistence in a Stationary Time-series

We study the persistence in a class of continuous stochastic processes that are stationary only under integer shifts of time. We show that under certain conditions, the persistence of such a continuous process reduces to the persistence of a corresponding discrete sequence obtained from the measurement of the process only at integer times. We then construct a specific sequence for which the persistence can be computed even though the sequence is non-Markovian. We show that this may be considered as a limiting case of persistence in the diffusion process on a hierarchical lattice.Comment: 8 pages revte

Renormalization group and nonequilibrium action in stochastic field theory

We investigate the renormalization group approach to nonequilibrium field theory. We show that it is possible to derive nontrivial renormalization group flow from iterative coarse graining of a closed-time-path action. This renormalization group is different from the usual in quantum field theory textbooks, in that it describes nontrivial noise and dissipation. We work out a specific example where the variation of the closed-time-path action leads to the so-called Kardar-Parisi-Zhang equation, and show that the renormalization group obtained by coarse graining this action, agrees with the dynamical renormalization group derived by directly coarse graining the equations of motion.Comment: 33 pages, 3 figures included in the text. Revised; one reference adde

Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics

When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical example to a universality class in critical phenomena. A quarter century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing a seemingly trivial modification to the Ising lattice gas, they took it into the vast realms of non-equilibrium statistical mechanics. An abundant variety of unexpected behavior emerged and caught many of us by surprise. We present a brief review of some of the new insights garnered and some of the outstanding puzzles, as well as speculate on the model's role in the future of non-equilibrium statistical physics.Comment: 3 figures. Proceedings of 100th Statistical Mechanics Meeting, Rutgers, NJ (December, 2008

Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.Comment: The original publication is available at www.springerlink.com/content/8528v8563r7u2742

Efeitos da nutrição mineral sobre o crescimento, aspecto, composição elementar e fixação de nitrogênio em Azolla

The mineral nutrition of Azolla feliculoides Lam was studied in solutions deficient in phosphorus, potassium, calcium, magnesium, sulfur, iron and molybdenum, and in excess of Mn and Al. Dry weight, N2 fixation and mineral composition of Azolla were determined after 3 weeks. Phosphorus, potassium, calcium and magnesium deficiencies and excess of manganese and aluminium decressed growth severely and also depressed the activity of nitrogenase. Phosphorus deficiency improved the uptake of iron and zinc. Potassium deficiency increased the levels of phosphorus in dry matter. Magnesium deficiency caused lower uptake of K and better uptake of Ca, Fe and Mn. Sulfur deficiency reduced aluminium uptake and promoted the best growth. Positive correlations were found between: N content and dry matter, nitrogenase activity and N content.Azolla filiculoides Lam foi cultivado em solução nutritiva arejada, sempre desprovida de N combinado, sendo submetida aos seguintes tratamentos: omissão de P, K, Ca, Mg, S, Fe e Mo, excesso de Mn e Al. As plantas foram colhidas depois de 3 semanas da inoculação. Verificou-se que as deficiências de P, K, Ca e Mg provocaram diminuição na produção de matéria seca e na atividade de nitrogenase. A análise mineral mostrou que: a falta de um elemento provoca redução no seu teor; grande acumulo de Mo; diminuição no teor de Al (do inóculo ou contaminação) no tratamento menos S que garantiu o maior crescimento; efeitos inibitórios ou sinergísticos semelhantes aos descritos no caso de plantas superiores. A toxidez de Al e Mn causou, principalmente a primeira, redução no crescimento e na atividade da nitrogenase. Houve correlações positivas entre: N total e crescimento, atividade de nitrogenase e N total

Sulphate Preconcentration By Anion Exchange Resin In Flow Injection And Its Turbidimetric Determination In Water

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)A preconcentration procedure was established for sulphate determination in rain waters at the mg/l level, employing a small column packed with the AG1-X8 (200-400 mesh) anionic resin inserted into a flow injection system. Sulphate determination was performed by using the turbidimetric method based on reaction with barium. For concentrations within 0.10 and 2.0 MgSO2- 4/l, a throughput of 50 determinations/hr was achieved, and the relative standard deviation of results was better than 2%. © 1993.401015291534Brazilian Computer Society (SBC),Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq),et al.,FAPESP,Google,Microsoft ResearchFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Ruzicka, Hansen, (1988) Flow Injection Analysis, , 2nd ed., John Wiley, New YorkKrug, Zagatto, Reis, Fo, Jacintho, Jorgensen, (1983) Anal. Chim. Acta, 145, p. 179Band, Linares, Castro, Valcarcel, (1991) Analyst, 116, p. 305Reis, Giné, Kronka, (1989) Quim. Nova, 12, p. 82Reis, Giné, Kronka, (1992) Quim. Nova, 15, p. 231Filha, Reis, Fo, Baccan, (1992) Anal. Chim. Acta, 261, p. 339Zagatto, Arruda, Jacintho, Mattos, (1990) Anal. Chim. Acta, 234, p. 153Strong anion exchange resin instruction manual, Bio-Rad Laboratories, 1414 Harbour Way South, Richmond, CA 94804Karlsson, Persson, Möller, (1991) Anal. Chim. Acta, 244, p. 10