Search results for "Exponential function"
showing 10 items of 173 documents
Application of the relativistic mean-field mass model to ther-process and the influence of mass uncertainties
2008
A new mass table calculated by the relativistic mean-field approach with the state-dependent BCS method for the pairing correlation is applied for the first time to study r-process nucleosynthesis. The solar r-process abundance is well reproduced within a waiting-point approximation approach. Using an exponential fitting procedure to find the required astrophysical conditions, the influence of mass uncertainty is investigated. The r-process calculations using the FRDM, ETFSI-Q, and HFB-13 mass tables have been used for that purpose. It is found that the nuclear physical uncertainty can significantly influence the deduced astrophysical conditions for the r-process site. In addition, the infl…
Photorefractive amplifier-converter and coherent oscillator with nonexponential gain
2001
For some parametric interactions with identically zero exponential gain for the signal wave the intensity of the idler wave can grow as a second power of the propagation coordinate. Such an amplification is revealed for the parametric mixing of four copropagating waves in BaTiO3; two of them are ordinarily polarized and the two others are extraordinarily polarized. This mixing is used to build up a coherent oscillator. A reasonable qualitative agreement of the experimental results with the calculated data is demonstrated.
A pedagogical approach to the Magnus expansion
2010
Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrodinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.
Pulse-driven near-resonant quantum adiabatic dynamics: lifting of quasi-degeneracy
2004
We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power law rising. This allows us to determine approximative formulas for the lineshape of resonant excitation by various forms of pulses such as truncated trig-pulses. We also analyze and explain the various superpositions of states that can be obtained by the Half Stark Chirped Rapid Adiabat…
Multi-hadron spectroscopy in a large physical volume
2017
We demonstrate the efficacy of the stochastic LapH method to treat all-to-all quark propagation on a $N_f = 2+1$ CLS ensemble with large linear spatial extent $L = 5.5$ fm, allowing us to obtain the benchmark elastic isovector p-wave pion-pion scattering amplitude to good precision already on a relatively small number of gauge configurations. These results hold promise for multi-hadron spectroscopy at close-to-physical pion mass with exponential finite-volume effects under control.
Continuum limit in random sequential adsorption.
1991
We develop analytical estimates of the late-stage (long-time) asymptotic behavior of the coverage in the D-dimensional lattice models of irreversible deposition of hypercube-shaped particles. Our results elucidate the crossover from the exponential time dependence for the lattice case to the power-law behavior with a multiplicative logarithmic factor, in the continuum deposition. Numerical Monte Carlo results are reported for the two-dimensional (2D) deposition, both lattice and continuum. Combined with the exact 1D results, they are used to test the general theoretical expectations for the late-stage deposition kinetics. New accurate estimates of the jamming coverages in 2D rule out some e…
Legri Background. Short Term Variability
2001
Background modelling for LEO satellites with high orbital inclination is not an easy task. The diffuse background component is dominated by the background coming from strong interactions with Earth magnetosphere trapped particles. Magnetic shielding is variable along the orbits and crosses through the SAA induce high radioactivity decay counting ratios. The aim of this paper is to present a model for the background total counting ratio of the 17 operative CdZnTe detectors on LEGRI in the short time scales and for observing periods outside crosses through SAA having enough time to cool LEGRI after the last SAA transit. Fluxes measured have been modelled in terms of the Mcllwain parameter L u…
Dynamic fragmentation of a two-dimensional brittle material with quenched disorder
1997
Fragmentation of a two-dimensional brittle material caused by a rapid impact has been analyzed. Computer simulations together with simple arguments are used to obtain a qualitative understanding of crack formation, which is then used to derive an exponential fragment size distribution valid in the large fragment size limit. In the limit of small fragments this distribution is solved numerically, and it is found to obey a scaling law with the exponent {minus}1.5. These results suggest that two different mechanisms are operative in the fragmentation process: branching of propagating cracks determines the small fragment size limit, and merging of the nucleated cracks determines the large size …
A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
2001
A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional +/-J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100^2 down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential and not as a power law as T -> Tc = 0.
Multicanonical Simulations of the Tails of the Order-Parameter Distribution of the Two-Dimensional Ising Model
2005
We report multicanonical Monte Carlo simulations of the tails of the order-parameter distribution of the two-dimensional Ising model for fixed boundary conditions. Clear numerical evidence for "fat" stretched exponential tails is found below the critical temperature, indicating the possible presence of fat tails at the critical temperature.