A method for estimation of elastic wave velocity anisotropy based on ultrasonic sounding data during rock-sample loading was developed. The subject matter of the method is approximation of ultrasonic sounding data by triaxial velocity ellipsoid. The applicability of proposed method was verified on investigation of anisot ropic rock samples. Laboratory loading of migmatite samples was realized under various mutual orientations between acting force direction and rock foliation - perpendicular, parallel and under 45°. P-ve velocity of ultrasound waves was monitored by 8 sensors network. The velocity ellipsoid was computed and changes of sizes and waorientation its main axes during loading were analyzed for separate experiments with regard to loading level. It was found, that independently to mutual orientation between rock foliation and loading direction, the minimum velocity vector turns to perpendicular direction to final rupture plane and maximum velocity vector turns to the plane of final rupture., Matěj Petružálek, Jan Vilhelm, Tomáš Lokajíček and Vladimír Rudajev., and Obsahuje bibliografické odkazy
We show that dynamical systems in inverse problems are sometimes foliated if the embedding dimension is greater than the dimension of the manifold on which the system resides. Under this condition, we end up reaching different leaves of the foliation if we start from different initial conditions. For some of these cases we have found a method by which we can asymptotically guide the system to a specific leaf even if we start from an initial condition which corresponds to some other leaf. We demonstrate the method by two examples. In the chosen cases of the harmonic oscillator and Duffing's oscillator we find an alternative set of equations which represent a collapsed foliation, such that no matter what initial conditions we choose, the system would asymptotically reach the same desired sub-manifold of the original system. This process can lead to cases for which a system begins in a chaotic region, but is guided to a periodic region and vice versa. It may also happen that we could move from an orbit of one period to an orbit of another period.