Two-Step-Model of Photosensitivity in Cerium-doped Fibers

The photosensitivity of various cerium-doped fibers has been experimentally investigated for both excimer- and femtosecond-laser illumination. The results of single-pulse, few-pulse and multi-pulse inscription of fiber-Bragg-gratings with both laser systems and the thermal aging of those gratings demonstrated the restrictions of the conventional color center model for cerium-doped fibers. To explain the short-term stability of single-pulse gratings against long-term stability of multi-pulse gratings, an extension into a two-step-model was deduced

Semiclassical two-step model for strong-field ionization

We present a semiclassical two-step model for strong-field ionization that accounts for path interferences of tunnel-ionized electrons in the ionic potential beyond perturbation theory. Within the framework of a classical trajectory Monte-Carlo representation of the phase-space dynamics, the model employs the semiclassical approximation to the phase of the full quantum propagator in the exit channel. By comparison with the exact numerical solution of the time-dependent Schr\"odinger equation for strong-field ionization of hydrogen, we show that for suitable choices of the momentum distribution after the first tunneling step, the model yields good quantitative agreement with the full quantum simulation. The two-dimensional photoelectron momentum distributions, the energy spectra, and the angular distributions are found to be in good agreement with the corresponding quantum results. Specifically, the model quantitatively reproduces the fan-like interference patterns in the low-energy part of the two-dimensional momentum distributions as well as the modulations in the photoelectron angular distributions.Comment: 31 pages, 7 figure

"Two-step" model of molecular diffusion in silicalite

The influence of the particle "memory" on long-range diffusion in the channel network of silicalite is taken into account by considering pairs of subsequent steps between the channel intersections. It is shown that in this case the correlation rule between the principal elements of the diffusion tensor has to be modified by including an additional term, which takes account of the deviation of molecular propagation from complete randomness. The obtained relations are discussed in terms of molecular dynamics simulations of ethane in silicalite

Critical Behaviour of the Two Dimensional Step Model

We use finite--size scaling of Lee--Yang partition function zeroes to study the critical behaviour of the two dimensional step or sgn $O(2)$ model. We present evidence that, like the closely related $XY$--model, this has a phase transition from a disordered high temperature phase to a low temperature massless phase where the model remains critical. The critical parameters (including logarithmic corrections) are compatible with those of the $XY$--model indicating that both models belong to the same universality class.Comment: 6 pages latex, 3 postscript figures, compressed and uuencoded (revised remarks on Lee_Yang theorem, version to appear in Phys Rev B

The Operating Diagram for a Two-Step Anaerobic Digestion Model

The Anaerobic Digestion Model No. 1 (ADM1) is a complex model which is widely accepted as a common platform for anaerobic process modeling and simulation. However, it has a large number of parameters and states that hinder its analytical study. Here, we consider the two-step reduced model of anaerobic digestion (AM2) which is a four-dimensional system of ordinary differential equations. The AM2 model is able to adequately capture the main dynamical behavior of the full anaerobic digestion model ADM1 and has the advantage that a complete analysis for the existence and local stability of its steady states is available. We describe its operating diagram, which is the bifurcation diagram which gives the behavior of the system with respect to the operating parameters represented by the dilution rate and the input concentrations of the substrates. This diagram, is very useful to understand the model from both the mathematical and biological points of view

Two-Step Model of Fusion for Synthesis of Superheavy Elements

A new model is proposed for fusion mechanisms of massive nuclear systems where so-called fusion hindrance exists. The model describes two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to $^{48}$Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. Combined with the statistical decay theory, residue cross sections for the superheavy elements can be readily calculated. Examples are given.Comment: 4 pages, 4 figure

Two-step Liquid Drop Model for Binary, Metal-rich Clusters

It is shown that differences observed between the ionization potentials of the molecular-doped metallic clusters and those corresponding to the bare metallic ones can be explained by a two-step approach of the classical Liquid Drop Model. This approach takes into account the distinct physical properties of the interface between the molecular core and the metallic shell. Also, it is shown that the presence of the molecular core may act in the determination of the predominant channel of the coulombic fission.Comment: 8 page

Oracally Efficient Two-Step Estimation of Generalized Additive Model

Generalized additive models (GAM) are multivariate nonparametric regressions for non-Gaussian responses including binary and count data. We propose a spline-backfitted kernel (SBK) estimator for the component functions. Our results are for weakly dependent data and we prove oracle efficiency. The SBK techniques is both computational expedient and theoretically reliable, thus usable for analyzing high-dimensional time series. Inference can be made on component functions based on asymptotic normality. Simulation evidence strongly corroborates with the asymptotic theory.Bandwidths, B spline, knots, link function, mixing, Nadaraya-Watson estimator

Two-Step Acceleration Model of Cosmic Rays at Middle-Aged SNR

Recent gamma-ray observations of middle-aged supernova remnants revealed a mysterious broken power-law spectrum. Using three-dimensional magnetohydrodynamics simulations, we show that the interaction between a supernova blast wave and interstellar clouds formed by thermal instability generates multiple reflected shocks. The typical Mach numbers of the reflected shocks are shown to be M ~ 2 depending on the density contrast between the diffuse intercloud gas and clouds. These secondary shocks can further energize cosmic-ray particles originally accelerated at the blast-wave shock. This "two-step" acceleration scenario reproduces the observed gamma-ray spectrum and predicts the high-energy spectral index ranging approximately from 3 to 4.Comment: 4 pages, 2 figures, accepted by ApJ Letter