Analysis of error growth and stability for the numerical integration of the equations of chemical kinetics

Error growth and stability analyzed for numerical integration of differential equations in chemical kinetic

Taming the Yukawa potential singularity: improved evaluation of bound states and resonance energies

Using the tools of the J-matrix method, we absorb the 1/r singularity of the Yukawa potential in the reference Hamiltonian, which is handled analytically. The remaining part, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. Analysis of resonance energies and bound states spectrum is performed using the complex scaling method, where we show their trajectories in the complex energy plane and demonstrate the remarkable fact that bound states cross over into resonance states by varying the potential parameters.Comment: 8 pages, 2 tables, 1 figure. 2 mpg videos and 1 pdf table file are available upon request from the corresponding Autho

Breathers in the weakly coupled topological discrete sine-Gordon system

Existence of breather (spatially localized, time periodic, oscillatory) solutions of the topological discrete sine-Gordon (TDSG) system, in the regime of weak coupling, is proved. The novelty of this result is that, unlike the systems previously considered in studies of discrete breathers, the TDSG system does not decouple into independent oscillator units in the weak coupling limit. The results of a systematic numerical study of these breathers are presented, including breather initial profiles and a portrait of their domain of existence in the frequency-coupling parameter space. It is found that the breathers are uniformly qualitatively different from those found in conventional spatially discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely rewritte

Lagrange-mesh calculations in momentum space

The Lagrange-mesh method is a powerful method to solve eigenequations written in configuration space. It is very easy to implement and very accurate. Using a Gauss quadrature rule, the method requires only the evaluation of the potential at some mesh points. The eigenfunctions are expanded in terms of regularized Lagrange functions which vanish at all mesh points except one. It is shown that this method can be adapted to solve eigenequations written in momentum space, keeping the convenience and the accuracy of the original technique. In particular, the kinetic operator is a diagonal matrix. Observables in both configuration space and momentum space can also be easily computed with a good accuracy using only eigenfunctions computed in the momentum space. The method is tested with Gaussian and Yukawa potentials, requiring respectively a small or a great mesh to reach convergence.Comment: Extended versio

Existence of the Stark-Wannier quantum resonances

In this paper we prove the existence of the Stark-Wannier quantum resonances for one-dimensional Schrodinger operators with smooth periodic potential and small external homogeneous electric field. Such a result extends the existence result previously obtained in the case of periodic potentials with a finite number of open gaps.Comment: 30 pages, 1 figur

Generating functions for generalized binomial distributions

In a recent article a generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal expressions was a key-point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties: the constraints of nonnegativeness are automatically fulfilled, a complete characterization in terms of generating functions is given and a large number of analytical examples becomes available.Comment: PDFLaTex, 27 pages, 5 figure

Solitary wave dynamics in time-dependent potentials

We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schr\"odinger equation. We then show that in the {\it space-adiabatic} regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. We finally remark on two physical applications of our analysis. The first is adiabatic transportation of solitons, and the second is Mathieu instability of trapped solitons due to time-periodic perturbations.Comment: 38 pages, some typos corrected, one reference added, one remark adde

Path integral for a relativistic Aharonov-Bohm-Coulomb system

The path integral for the relativistic spinless Aharonov-Bohm-Coulomb system is solved, and the energy spectra are extracted from the resulting amplitude.Comment: 6 pages, Revte

Crack Growth Studies in a welded Ni-base superalloy

It is well known that the introduction of sustained tensile loads during high-temperature fatigue (dwell-fatigue) significantly increases the crack propagation rates in many superalloys. One such superalloy is the Ni-Fe based Alloy 718, which is a high-strength corrosion resistant alloy used in gas turbines and jet engines. As the problem is typically more pronounced in fine-grained materials, the main body of existing literature is devoted to the characterization of sheets or forgings of Alloy 718. However, as welded components are being used in increasingly demanding applications, there is a need to understand the behavior. The present study is focused on the interaction of the propagating crack with the complex microstructure in Alloy 718 weld metal during cyclic and dwell-fatigue loading at 550 °C and 650 °C

Room temperature plasticity in sub-micrometer thermally grown oxide scales

Thermally grown oxides (TGOs) are generally considered to be brittle, capable of sustaining very limited plastic deformation before fracture. As they are prone to exhibit different forms of defects, the fracture toughness, typically measured to be some 1–2 MPa m1/2 [1], is typically reached well before sufficiently high stresses to induce plasticity can be applied [2]. This is particularly true at room temperature, where possible low-stress thermally activated creep mechanisms are suppressed. However, the occurrence of plasticity in e.g. Al2O3 single crystals at room temperature can occur for samples in the micrometer range [3]. Most measurements of the deformation of TGOs have been made on relatively thick scales, (\u3e1 micrometer), which are limited by the fracture originating from inherent defects. Furthermore, the studies have been limited in resolution and sensitivity, as the scales were adherent to the substrates and tested as a composite. Recently, micro-mechanical testing has been introduced as a method to evaluate mechanical behavior of TGOs on a ferritic/martensitic steel [4], where micro-cantilever bending was used to test specimen extracted from different layers in a 5–10 micrometers thick oxide. Still, the cantilever cross-section was typically several micrometers, and the very similar fracture stresses for notched and un-notched cantilevers seems to indicate that the deformation is still limited by inherent defects. Please click Additional Files below to see the full abstract