Direct dynamical test for deterministic chaos

We present a direct and dynamical method to distinguish low-dimensional deterministic chaos from noise. We define a series of time-dependent curves which are closely related to the largest Lyapunov exponent. For a chaotic time series, there exists an envelope to the time-dependent curves, while for a white noise or a noise with the same power spectrum as that of a chaotic time series, the envelope cannot be defined. When a noise is added to a chaotic time series, the envelope is eventually destroyed with the increasing of the amplitude of the noise.

Local exponential divergence plot and optimal embedding of a chaotic time-series

we propose here a local exponential divergence plot which is capable of providing a new means of characterizing chaotic time series. The suggested plot defines a time dependent exponent LAMBDA and a ''plus'' exponent LAMBDA+ which serves as a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time and the largest Lyapunov exponent.

Spatio-Temporal Scanning and Statistical Test of the Accelerating Moment Release (AMR) Model Using Australian Earthquake Data

The Accelerating Moment Release (AMR) preceding earthquakes with magnitude above 5 in Australia that occurred during the last 20 years was analyzed to test the Critical Point Hypothesis. Twelve earthquakes in the catalog were chosen based on a criterion for the number of nearby events. Results show that seven sequences with numerous events recorded leading up to the main earthquake exhibited accelerating moment release. Two occurred near in time and space to other earthquakes preceded by AM R. The remaining three sequences had very few events in the catalog so the lack of AMR detected in the analysis may be related to catalog incompleteness. Spatio-temporal scanning of AMR parameters shows that 80% of the areas in which AMR occurred experienced large events. In areas of similar background seismicity with no large events, 10 out of 12 cases exhibit no AMR, and two others are false alarms where AMR was observed but no large event followed. The relationship between AMR and Load-Unload Response Ratio (LURR) was studied. Both methods predict similar critical region sizes, however, the critical point time using AMR is slightly earlier than the time of the critical point LURR anomaly.

Numerical Analysis of the Effects of Free-Stream Thermo-Chemical State on the Test Model Flow Field in High-Enthalpy Tunnel

The effects of the free-stream thermo-chemical state on the test model flow field in the high-enthalpy tunnel are studied numerically. The properties of the free-stream, which is in thermo-chemical non-equilibrium, are determined by calculating the nozzle flow field. A free-stream with total enthalpy equal to the real one in the tunnel while in thermo-chemical equilibrium is constructed artificially to simulate the natural atmosphere condition. The flow fields over the test models (blunt cone and Apollo command capsule model) under both the non-equilibrium and the virtual equilibrium free-stream conditions are calculated. By comparing the properties including pressure, temperature, species concentration and radiation distributions of these two types of flow fields, the effects of the non-equilibrium state of the free-stream in the high-enthalpy shock tunnel are analyzed.

A block SPP algorithm for multidimensional tridiagonal equations with optimal message vector length

A parallel strategy for solving multidimensional tridiagonal equations is investigated in this paper. We present in detail an improved version of single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication cost. We show the resulting block SPP can achieve good speedup for a wide range of message vector length (MVL), especially when the number of grid points in the divided direction is large. Instead of only using the largest possible MVL, we adopt numerical tests and modeling analysis to determine an optimal MVL so that significant improvement in speedup can be obtained.

On optimal message vector length for block single parallel partition algorithm in a three-dimensional ADI solver

It has long been recognized that many direct parallel tridiagonal solvers are only efficient for solving a single tridiagonal equation of large sizes, and they become inefficient when naively used in a three-dimensional ADI solver. In order to improve the parallel efficiency of an ADI solver using a direct parallel solver, we implement the single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication costs. The measured performances show that the longest allowable message vector length (MVL) is not necessarily the best choice. To understand this observation and optimize the performance, we propose an improved model that takes the cache effect into consideration. The optimal MVL for achieving the best performance is shown to depend on number of processors and grid sizes. Similar dependence of the optimal MVL is also found for the popular block pipelined method.

Optimal feedback control of two-photon fluorescence based on genetic algorithm

An optimal feedback control of two-photon fluorescence in the ethanol solution of 4-dicyanomethylene-2-methyl-6-p-dimethyl-amiiiostryryl-4H-pyran (DCM) using pulse-shaping technique based on genetic algorithm is demonstrated experimentally. The two-photon fluorescence of the DCM ethanol solution is enhanced in intensity of about 23%. The second harmonic generation frequency-resolved optical gating (SHG-FROG) trace indicates that the effective population transfer arises from the positively chirped pulse. The experimental results appear the potential applications of coherent control to the complicated molecular system.

Optimal feedback control of two-photon fluorescence in Coumarin 515 based on genetic algorithm

An optimal feedback control of two-photon fluorescence in the Coumarin 515 ethanol solution excited by shaping femtosecond laser pulses based on genetic algorithm is demonstrated experimentally. The two-photon fluorescence intensity can be enhanced by similar to 20%. Second harmonic generation frequency-resolved optical gating traces indicate that the optimal laser pulses are positive chirp, which are in favor of the effective population transfer of two-photon transitions. The dependence of the two-photon fluorescence signal on the laser pulse chirp is investigated to validate the theoretical model for the effective population transfer of two-photon transitions. The experimental results appear the potential applications in nonlinear spectroscopy and molecular physics. (c) 2005 Elsevier B.V. All rights reserved.