State Vector: A New Approach to Prediction of the Failure of Brittle Heterogeneous Media and Large Earthquakes

The concept of state vector stems from statistical physics, where it is usually used to describe activity patterns of a physical field in its manner of coarsegrain. In this paper, we propose an approach by which the state vector was applied to describe quantitatively the damage evolution of the brittle heterogeneous systems, and some interesting results are presented, i.e., prior to the macro-fracture of rock specimens and occurrence of a strong earthquake, evolutions of the four relevant scalars time series derived from the state vectors changed anomalously. As retrospective studies, some prominent large earthquakes occurred in the Chinese Mainland (e.g., the M 7.4 Haicheng earthquake on February 4, 1975, and the M 7.8 Tangshan earthquake on July 28, 1976, etc) were investigated. Results show considerable promise that the time-dependent state vectors could serve as a kind of precursor to predict earthquakes.

Modification of Bertrand's theorem and extended Runge-Lenz vector

It is shown that for a particle with suitable angular moments in the screened Coulomb potential or isotropic harmonic potential, there still exist closed orbits rather than ellipse, characterized by the conserved aphelion and perihelion vectors, i.e. extended Runge-Lenz vector, which implies a higher dynamical symmetry than the geometrical symmetry O-3. The closeness of a planar orbit implies the radial and angular motional frequencies are commensurable.

Divergence-free vector-field and reduction

By the Lie symmetry group, the reduction for divergence-free vector-fields (DFVs) is studied, and the following results are found. A n-dimensional DFV can be locally reduced to a (n - 1)-dimensional DFV if it admits a one-parameter symmetry group that is spatial and divergenceless. More generally, a n-dimensional DFV admitting a r-parameter, spatial, divergenceless Abelian (commutable) symmetry group can be locally reduced to a (n - r)-dimensional DFV.

Comparison Between Lurr And State Vector Analysis Before Strong Earthquakes In Southern California Since 1980

There are seven strong earthquakes with M >= 6.5 that occurred in southern California during the period from 1980 to 2005. In this paper, these earthquakes were studied by the LURR (Load/Unload Response Ratio) method and the State Vector method to detect if there are anomalies before them. The results show that LURR anomalies appeared before 6 earthquakes out of 7 and State Vector anomalies appeared before all 7 earthquakes. For the LURR method, the interval between maximum LURR value and the forthcoming earthquake is 1 to 19 months, and the dominant mean interval is about 10.7 months. For the State Vector method, the interval between the maximum modulus of increment State Vector and the forthcoming earthquake is from 3 to 27 months, but the dominant mean interval between the occurrence time of the maximum State Vector anomaly and the forthcoming earthquake is about 4.7 months. The results also show that the minimum valid space window scale for the LURR and the State Vector is a circle with a radius of 100 km and a square of 3 degrees 3 degrees, respectively. These results imply that the State Vector method is more effective for short-term earthquake prediction than the LURR method, however the LURR method is more effective for location prediction than the State Vector method.

The vector fields admitting one-parameter spatial symmetry group and their reduction

For a n-dimensional vector fields preserving some n-form, the following conclusion is reached by the method of Lie group. That is, if it admits an one-parameter, n-form preserving symmetry group, a transformation independent of the vector field is constructed explicitly, which can reduce not only dimesion of the vector field by one, but also make the reduced vector field preserve the corresponding ( n - 1)-form. In partic ular, while n = 3, an important result can be directly got which is given by Me,ie and Wiggins in 1994.

Gain saturation effects of a flowing chemical oxygen-iodine laser

A new oxygen-iodine medium gain model is developed to include pumping and deactivation of the upper laser levels of the iodine atoms, hyperfine and translation relaxation, as well as the flowing effect. The rate equations for gain of a supersonic flowing cw oxygen-iodine laser (COIL) are described when the medium is stimulated by a single-mode field. The general solution of the self-consistency integral equation is obtained. The result shows that the saturation behaviour in low pressure of the COIL differs from both the inhomogeneous and homogeneous broadening, and exhibits an 'anomalous' saturation phenomenon.

NUMERICAL ANALYSIS OF THE FLOWFIELD IN A SUPERSONIC COIL WITH AN INTERLEAVED JET CONFIGURATION AND ITS EFFECT ON THE GAIN DISTRIBUTION

In a supersonic chemical oxygen-iodine laser (COIL) operating without primary buffer gas, the features of flowfield have significant effects on the Laser efficiency and beam quality. In this paper three-dimensional, multi-species, chemically reactive CFD technology was used to study the flowfield in mixing nozzle implemented with a supersonic interleaving jet configuration. The features of the flowfield as well as its effect on the spatial distribution of small signal gain were analyzed.

Numerical analysis of spatial evolution of the small signal gain in a chemical oxygen-iodine laser operating without primary buffer gas

A chemical oxygen iodine laser (COIL) that operates without primary buffer gas has become a new way of facilitating the compact integration of laser systems. To clarify the properties of spatial gain distribution, three-dimensional (3-D) computational fluid dynamics (CFD) technology was used to study the mixing and reactive flow in a COIL nozzle with an interleaving jet configuration in the supersonic section. The results show that the molecular iodine fraction in the secondary flow has a notable effect on the spatial distribution of the small signal gain. The rich iodine condition produces some negative gain regions along the jet trajectory, while the lean iodine condition slows down the development of the gain in the streamwise direction. It is also found that the new configuration of an interleaving jet helps form a reasonable gain field under appropriate operation conditions. (c) 2007 Elsevier Ltd. All rights reserved.

Gain saturation in gas flow and chemical lasers

A theoretical model for gain saturation in gas flow and chemical lasers is presented. The theory is applicable to all possible numerical values of τ/τc, where τ is the characteristie flow time for the flowing gas to move across the laser action region and τc is the characteristic collision relaxation time. The saturation effects of the convection and the "source flow" of the inverted population are revealed. A general relation of gain coefficient and some new gain saturation laws are obtained. For the special case of τ/τc1, the present theoretical results agree with the experimental results on the "anomalous" saturation phenomena in the supersonic diffusion HF chemical laser determined recently by Gross and Coffer[8]. The theory also agrees with the measured results of saturation intensity varying with τ/τc in gas flow CO2 lasers[7]. For the special case of τ/τc1, the present theory is consistent with both the standard theory[1] for gas lasers where the gas has no macroscopic motion and the known gain saturation theory[2-5] for gas flow and chemical lasers.

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.

Broadband high-gain optical parametric chirped-pulse amplification near 780 nm with LBO-I near-degenerate near-collinear phase match

Near-degenerative near-collinear phase-match geometry for broadband optical parametric chirped-pulse amplification (OPCPA) at approximate to 780 nm is calculated in comparison with nondegenerate noncollinear phase-match geometry. In an experiment on LBO-I near-degenerate near-collinear OPCPA, high gain with broad gain bandwidth (approximate to 71 nm, FWHM) at approximate to 780 nm is achieved by using an approximate to 390-nm pumping pulse. The stretched broadband chirped signal pulse near 780 nm is amplified to approximate to 412 mu J with a pumping energy of approximate to 15 mJ, and the total gain is > 3.7 X 10(6), which agrees well with the calculation. For a broadband (covering approximate to 100 nm) chirped signal pulse, the theoretical gain bandwidth has been attained experimentally for the first time. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

Broadband high-gain optical parametric chirped-pulse amplification near 780 nm with LBO-I near-degenerate near-collinear phase match

Near-degenerative near-collinear phase-match geometry for broadband optical parametric chirped-pulse amplification (OPCPA) at approximate to 780 nm is calculated in comparison with nondegenerate noncollinear phase-match geometry. In an experiment on LBO-I near-degenerate near-collinear OPCPA, high gain with broad gain bandwidth (approximate to 71 nm, FWHM) at approximate to 780 nm is achieved by using an approximate to 390-nm pumping pulse. The stretched broadband chirped signal pulse near 780 nm is amplified to approximate to 412 mu J with a pumping energy of approximate to 15 mJ, and the total gain is > 3.7 X 10(6), which agrees well with the calculation. For a broadband (covering approximate to 100 nm) chirped signal pulse, the theoretical gain bandwidth has been attained experimentally for the first time. (c) 2005 Society of Photo-Optical Instrumentation Engineers.

Compact 120 TW Ti: sapphire laser system with a high gain final amplifier

A 120TW/36fs laser system based on Ti:sapphire chirped-pulse amplification (CPA) has been successfully established in our lab. The final four pass Ti:sapphire amplifier pumped by an energetic single-shot Nd:YAG-Nd:glass laser was designed and optimized. With 24J/8ns pump energy at 532 nm, 300 mJ/220 ps chirped pulse was amplified to 5.98 J in this amplifier, and a total saturated gain of similar to 20 was achieved. The focused intensity of compressed beam could reach to 10(20) W/cm(2) with the M-2 of similar to 2.0. (c) 2005 Elsevier Ltd. All rights reserved.

Optical gain at 1550 nm from colloidal solution of Er3+-Yb3+ codoped NaYF4 nanocubes

We demonstrated optical amplification at 1550 nm with a carbon tetrachloride solution of Er3+-Yb3+ codoped NaYF4 nanocubes synthesized with solvo-thermal route. Upon excitation with a 980 nm laser diode, the nanocube solution exhibited strong near-infrared emission by the I-4(13/2) -> I-4(15/2) transition of Er3+ ions due to energy transfer from Yb3+ ions. We obtained the highest optical gain coefficient at 1550 nm of 0.58 cm(-1) for the solution with the pumping power of 200 mW. This colloidal solution might be a promising candidate as a liquid medium for optical amplifier and laser at the optical communication wavelength. (C) 2009 Optical Society of America