Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Numerical simulation of gel electrophoresis of DNA knots in weak and strong electric fields.

Gel electrophoresis allows one to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots, being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a Monte Carlo algorithm, the dependence of the electrophoretic migration of the DNA molecules on the knot type and on the electric field intensity is investigated. The results are in qualitative and quantitative agreement with electrophoretic experiments done under conditions of low and high electric fields.

Numerical investigation of iso-spectral cavities built from trinagles

We present computational approaches as alternatives to a recent microwave cavity experiment by S. Sridhar and A. Kudrolli [Phys. Rev. Lett. 72, 2175 (1994)] on isospectral cavities built from triangles. A straightforward proof of isospectrality is given, based on the mode-matching method. Our results show that the experiment is accurate to 0.3% for the first 25 states. The level statistics resemble those of a Gaussian orthogonal ensemble when the integrable part of the spectrum is removed.

Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

The relativistic distorted-wave Born approximation is used to calculate differential and total cross sections for inner shell ionization of neutral atoms by electron and positron impact. The target atom is described within the independent-electron approximation using the self-consistent Dirac-Fock-Slater potential. The distorting potential for the projectile is also set equal to the Dirac-Fock-Slater potential. For electrons, this guarantees orthogonality of all the orbitals involved and simplifies the calculation of exchange T-matrix elements. The interaction between the projectile and the target electrons is assumed to reduce to the instantaneous Coulomb interaction. The adopted numerical algorithm allows the calculation of differential and total cross sections for projectiles with kinetic energies ranging from the ionization threshold up to about ten times this value. Algorithm accuracy and stability are demonstrated by comparing differential cross sections calculated by our code with the distorting potential set to zero with equivalent results generated by a more robust code that uses the conventional plane-wave Born approximation. Sample calculation results are presented for ionization of K- and L-shells of various elements and compared with the available experimental data.

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations.

Phase-field model for Hele-Shaw flows with arabitrary contrast II: numerical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit, and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

Elastic scattering of fast electrons and positrons by atoms

Elastic scattering of relativistic electrons and positrons by atoms is considered in the framework of the static field approximation. The scattering field is expressed as a sum of Yukawa terms to allow the use of various approximations. Accurate phase shifts have been computed by combining Bühring¿s power-series method with the WKB and Born approximations. This combined procedure allows the evaluation of differential cross sections for kinetic energies up to several tens of MeV. Numerical results are used to analyze the validity of several approximate methods, namely the first- and second-order Born approximations and the screened Mott formula, which are frequently adopted as the basis of multiple scattering theories and Monte Carlo simulations of electron and positron transport.

Intensity correlation functions of dye lasers: Comparison of colored-gain-noise and colored-loss-noise models

The intensity correlation functions C(t) for the colored-gain-noise model of dye lasers are analyzed and compared with those for the loss-noise model. For correlation times ¿ larger than the deterministic relaxation time td, we show with the use of the adiabatic approximation that C(t) values coincide for both models. For small correlation times we use a method that provides explicit expressions of non-Markovian correlation functions, approximating simultaneously short- and long-time behaviors. Comparison with numerical simulations shows excellent results simultaneously for short- and long-time regimes. It is found that, when the correlation time of the noise increases, differences between the gain- and loss-noise models tend to disappear. The decay of C(t) for both models can be described by a time scale that approaches the deterministic relaxation time. However, in contrast with the loss-noise model, a secondary time scale remains for large times for the gain-noise model, which could allow one to distinguish between both models.

Numerical algorithm for spectroscopic ellipsometry of thick transparent films

We present a numerical method for spectroscopic ellipsometry of thick transparent films. When an analytical expression for the dispersion of the refractive index (which contains several unknown coefficients) is assumed, the procedure is based on fitting the coefficients at a fixed thickness. Then the thickness is varied within a range (according to its approximate value). The final result given by our method is as follows: The sample thickness is considered to be the one that gives the best fitting. The refractive index is defined by the coefficients obtained for this thickness.

Using numerical classification of profiles based on Vis-NIR spectra to distinguish soils from the Piracicaba Region, Brazil

Considering that information from soil reflectance spectra is underutilized in soil classification, this paper aimed to evaluate the relationship of soil physical, chemical properties and their spectra, to identify spectral patterns for soil classes, evaluate the use of numerical classification of profiles combined with spectral data for soil classification. We studied 20 soil profiles from the municipality of Piracicaba, State of São Paulo, Brazil, which were morphologically described and classified up to the 3rd category level of the Brazilian Soil Classification System (SiBCS). Subsequently, soil samples were collected from pedogenetic horizons and subjected to soil particle size and chemical analyses. Their Vis-NIR spectra were measured, followed by principal component analysis. Pearson's linear correlation coefficients were determined among the four principal components and the following soil properties: pH, organic matter, P, K, Ca, Mg, Al, CEC, base saturation, and Al saturation. We also carried out interpretation of the first three principal components and their relationships with soil classes defined by SiBCS. In addition, numerical classification of the profiles based on the OSACA algorithm was performed using spectral data as a basis. We determined the Normalized Mutual Information (NMI) and Uncertainty Coefficient (U). These coefficients represent the similarity between the numerical classification and the soil classes from SiBCS. Pearson's correlation coefficients were significant for the principal components when compared to sand, clay, Al content and soil color. Visual analysis of the principal component scores showed differences in the spectral behavior of the soil classes, mainly among Argissolos and the others soils. The NMI and U similarity coefficients showed values of 0.74 and 0.64, respectively, suggesting good similarity between the numerical and SiBCS classes. For example, numerical classification correctly distinguished Argissolos from Latossolos and Nitossolos. However, this mathematical technique was not able to distinguish Latossolos from Nitossolos Vermelho férricos, but the Cambissolos were well differentiated from other soil classes. The numerical technique proved to be effective and applicable to the soil classification process.

On the efficient evaluation of ruin probabilities for completely monotone claim size distributions

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed in [2]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show that under weaker assumptions on the claim size distribution, the method may still perform reasonably well in some cases. This in particular provides an efficient alternative to a related method proposed in [3]. A number of numerical illustrations for the performance of this procedure is provided for both completely monotone and other types of random variables.

Flow structures at an idealized bifurcation : a numerical experiment

River bifurcations are key nodes within braided river systems controlling the flow and sediment partitioning and therefore the dynamics of the river braiding process. Recent research has shown that certain geometrical configurations induce instabilities that lead to downstream mid-channel bar formation and the formation of bifurcations. However, we currently have a poor understanding of the flow division process within bifurcations and the flow dynamics in the downstream bifurcates, both of which are needed to understand bifurcation stability. This paper presents results of a numerical sensitivity experiment undertaken using computational fluid dynamics (CFD) with the purpose of understanding the flow dynamics of a series of idealized bifurcations. A geometric sensitivity analysis is undertaken for a range of channel slopes (0.005 to 0.03), bifurcation angles (22 degrees to 42 degrees) and a restricted set of inflow conditions based upon simulating flow through meander bends with different curvature on the flow field dynamics through the bifurcation. The results demonstrate that the overall slope of the bifurcation affects the velocity of flow through the bifurcation and when slope asymmetry is introduced, the flow structures in the bifurcation are modified. In terms of bifurcation evolution the most important observation appears to be that once slope asymmetry is greater than 0.2 the flow within the steep bifurcate shows potential instability and the potential for alternate channel bar formation. Bifurcation angle also defines the flow structures within the bifurcation with an increase in bifurcation angle increasing the flow velocity down both bifurcates. However, redistributive effects of secondary circulation caused by upstream curvature can very easily counter the effects of local bifurcation characteristics. Copyright (C) 2011 John Wiley & Sons, Ltd.