Approach to Nonrigid Body Metamorphosis Using Generalized Morph-translation

An approach of morphing by decomposing two objects into sets of individual convex sub objects respectively and contructing the mapping between two sets is presented The Minkvski addition of two convex sub-objects according to their mapping ralationship is calculated, then all the Minkovski additions are combined to obtain the final result. Nonrigid body motion can be divided into nonrigid body metamorphosis and rigid body rotation A novel method for describing nonrigid body motion based on generalized morph-translation is proposed. This method can solve the metamorphosis problem of two non-homotopic objects. Experiments show tha this method can generate natural, high quality metamorphosis results with simple computation. This method can also be used in interpolation between two keyframes in 2D and 3D computer animation automatically.

Generalized flyby trajectories around elongated minor celestial bodies as a rotating mass dipole

The aim of this paper is to understand the common characteristics of the generalized flyby trajectory around natural elongated bodies. Such flyby trajectories provide a short-term mechanism to clear away vicinal objects or temporally capture ejecta into circling orbits. The gravitational potential of elongated bodies is described by a unified approximate model, i.e., the rotating mass dipole which is two point masses connected with a constant massless rod The energy power is used to illustrate the flyby effect in terms of the instantaneous orbital energy. The essential of the single flyby trajectory is studied analytically, and the relationship between the flyby trajectory and its Jacobi integral is also illustrated. Sample trajectories are given to show the variational trend of the energy increment with respect to differen orbital periapsides. The distribution of natural ejecting orbits is presented by varying the parameters of the approximate model.

Theoretical analysis of the spatio-temporal evolution of the bulk-strain field based on a rheologic inclusion model

Based on the theoretical expression of the three-dimension rheologic inclusion model, we analyze in detail the spatio-temporal changes on the ground of the bulk-strain produced by a spherical rheologic inclusion in a semi-infinite rheologic medium. The results show that the spatio-temporal change of bulk-strain produced by the hard inclusion has three stages of different characteristics, which are similar to most of those geodetic deformation curves, but those by a soft inclusion do not. The α-stage is a long stage in which the precursors in both the near source region and the far field develop from the focal region to the periphery. The β-stage indicates a very rapid propagation of the precursors, so that they almost appear everywhere. During the γ-stage, the precursors in the far-field converge from the periphery, and the precursors in the near source region develop outwards. The theoretical results have been used to explain tentatively the stage characteristics of the spatio-temporal change of earthquake precursors.

On seismic strengthening area before strong and great shocks and its mechanism

By systematically studying seismic strengthening areas before 85 earthquakes with M>=6.0 in China, some results have been extracted. 1) Earthquake active strengthening area exists universally before strong shock or great earthquake; 2) The size of the strengthening area and its appearing time will increase when the earthquake magnitude increases; 3) The rate between the size of seismic strengthening area and the size of the source region decreases when earthquake magnitude increases; 4) The appearing time of the earthquake active strengthening region in the eastern part of China is longer than that in the western part of China. The above characteristics have been preliminarily explained qualitatively and half-quantitatively by applying the strong body earthquake generating model and the hard inclusion theory. Then applying the seismic strengthening area, we have obtained long-term predictions of 2 earthquakes, so the seismic strengthening area before strong earthquake or great earthquakes is a universal phenomenon, which has some mechanical base.

Paterns and regularity of ring distribution of seismic activity before great earthquakes in China

A systematic study on ″ring phenomena″ frequently occurring before great earthquakes has made in this paper, which has analyzed the features of ring distributions before 16 great earthquakes and part of large earthquakes in China and its boundary areas, and discussed their features of generality, regularity and predictive meaning. The results have showed that moderate earthquakes or larger earthquakes distribute around the epicenter like a ring from decades to hundred years before the great earthquakes of magnitude more than 7, which is a general phenomenon of great earthquakes without an exception. The active ring generally occurs in the areas from hundreds to thousands of kilometers from the epicenter(according to the magnitude). The seismicity in the ring has three basic stages with different features. in the first stage, seismicity remains at low level and the earthquakes distribute scatteredly, while the source area of the future great earthquake remains quiet; in the second stage, the seismicity strengthens, whose frequency, intensity, concentrated degree, released rate of strain and ratio of distributed area etc. increase, while the quiet area decreases or disappears; in the third stage, the seismicity is weaker than in the former stage, and the quiet area appears again. The source area surrounded by the active ring might have three periods of activity(called as early term, medium term and late term foreshocks activity). The length of the quiet area undergoes the process from large to small, then to large. Therefore, we can estimate the occurring place, magnitude and seismogenic stage of great earthquake according to the area,length and the seismicity in the active ring, which is valuable to make a long term prediction of great earthquakes. At last, we had a preliminary discussion on the mechanism of active ring formation.

Generalized Intersection Bodies with Parameter

In 2005, the classical intersection bodies and L_p intersection bodies were extended. Afterwards, the concept of gen-eral L_p intersection bodies and the generalized intersection bodies was introduced. In this paper, we define the generalized bodies with parameter. Besides, we establish the extremal values for volume, Brunn-Minkowski type inequality for radial combination and L_p harmonic Blaschke combination of this notion.