arXiv subjects

A. Moura

Publications and source records attributed to A. Moura.

3 recordsLinked to original sources

arXiv2004

Branched Crystals and Category O

In this paper we describe a theory of (branched) crystals which is adapted to the study of representations in the BGG category $\cal O$ and which generalizes the theory of normal crystals of Kashiwara. In the case of $sl_2$ we show that one can associate (uniquely up to isomorphism) to every module in $\cal O$ a branched crystal . We show that the indecomposable modules in \cal O$ correspond to "indecomposable" branched crystals. We also define the tensor product of these crystals and show that for $sl_2$ the indecomposable components of the tensor product of branched crystals are the same as the crystals associated to the indecomposable summands of the tensor product of the corresponding modules.

math.RT↗

arXiv2004

Self-Similar Law of Energy Release before Materials Fracture

A general law of energy release is derived for stressed heterogeneous materials, being valid from the starting moment of loading till the moment of materials fracture. This law is obtained by employing the extrapolation technique of the self-similar approximation theory. Experiments are accomplished measuring the energy release for industrial composite samples. The derived analytical law is confronted with these experimental data as well as with the known experimental data for other materials.

cond-mat.mtrl-sci↗

arXiv2003

Self-Similar Extrapolation for the Law of Acoustic Emission Before Failure of Heterogeneous Materials

Acoustic emission before the failure of heterogeneous materials is studied as a function of applied hydrostatic pressure. A formula for the energy release is suggested, which is valid in the whole diapason of pressures, from zero to the critical pressure of rupture. This formula is obtained by employing the extrapolation technique of the self-similar approximation theory. The result is fitted to experiment in order to demonstrate the correct general behaviour of the obtained expression for the energy release.

cond-mat↗