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.

Long-distant contribution and chi(c1) radiative decays to light vector meson

The discrepancy between the PQCD calculation and the CLEO data for chi (c1)->gamma V (V=rho (0), omega, phi) stimulates our interest in exploring other mechanisms of chi (c1) decay. In this work, we apply an important non-perturbative QCD effect, i.e., the hadronic loop mechanism, to study chi (c1)->gamma V radiative decay. Our numerical result shows that the theoretical results including the hadronic loop contribution and the PQCD calculation of chi (c1)->gamma V are consistent with the corresponding CLEO data of chi (c1)->gamma V. We expect further experimental measurement of chi (c1)->gamma V, which will be helpful to test the hadronic loop effect on chi (c1) decay.