IEPT RAS

The Geophysical Journal International published an article by Doctor of Physical and Mathematical Sciences G. Molchan and his Italian colleagues, devoted to the theoretical analysis of the productivity of seismic events. The productivity of a magnitude m event can be characterized in term of triggered events of magnitude above m – Δ: it is the number of direct ‘descendants’ νΔ and the number of all ‘descendants’ VΔ. There is evidence in favour of the discrete exponential distribution for both νΔ and VΔ with a dominant initial magnitude m (the case of aftershock cluster). We consider the general Epidemic Type Aftershock Sequence model adapted to any distribution of νΔ. Our first result shows that models with branching aftershock structure do not allow for the coincidence of distribution types of νΔ and VΔ (say, the discrete exponential, as in the scientific literature). The second problem is related to the tail behaviour of the VΔ distribution. We show the fundamental difference in tail behaviour of the VΔ – distributions for general-type clusters and clusters with a dominant initial magnitude: the tail is heavy in the former case and light in the latter. The real data demonstrate the possibilities of this kind.

Source: G. Molchan, E. Varini, A. Peresan Productivity within the epidemic-type seismicity model Geophysical Journal International, Volume 231, Issue 3, December 2022, Pages 1545–1557,DOI: 10.1093/gji/ggac269, Published: 22 July 2022

In «Mathematics» (Web of Science Q1, Scopus Q2, Impact Factor: 2.592) издательства MDPI published an article «Nonlinear large-scale perturbations of steady thermal convective dynamo regimes in a plane layer of electrically conducting fluid rotating about the vertical axis». This is a joint work of scientists from the IEPT RAS and the University of Porto (Portugalia) Simon Ranjith Jeyabalan, Roman Chertovskih, Silvio Gama и Vladislav Zheligovsky.

The paper titled “Phaseless inverse scattering with background information” was published in “Inverse Problems” (Q1 WoS) journal. Doctor of Physical and Mathematical sciences, Senior Researcher of IEPT RAS Novikov R.G. is one of coauthors.

The work deals with phaseless inverse scattering for the multidimensional Schrödinger equation with unknown potential v using the method of known background scatterers.

In particular, in dimension d ⩾ 2, the authors show that |f₁|² at high energies uniquely determines v via explicit formulas, where f₁ is the scattering amplitude for v + w₁, where w₁ is an a priori known nonzero background scatterer, under the condition that supp v and supp w₁ are sufficiently disjoint.

The Wiley-VCH journal “Zeitschrift für Angewandte Mathematik und Mechanik” (Web of Science Q3, Scopus Q2, Impact Factor JCR: 1.103) published an article “A strip with constant stresses on the cut: exact solutions”. Among the authors are employees of the IEPT RAS: senior researcher, Ph.D. A.P. Kerzhaev and senior researcher, Ph.D. I.V. Menshov.

We construct exact solutions of three boundary value problems in the theory of elasticity for an infinite strip with a central transverse cut on which constant normal stresses are specified (even-symmetric deformation). We consider three variants of homogeneous boundary conditions on the strip sides: (1) free sides, (2) firmly clamped sides, and (3) there are identical stiffeners on the strip sides. The solutions of all problems are represented as series in Papkovich–Fadle eigenfunctions whose coefficients are determined from simple closed formulas.

The problem of estimation the maximum possible magnitude of regional earthquakes Mmax is examined. Statistical and paleoseismological approaches to this problem are combined. Within the framework of the statistical approach, the method of statistical moments, the Bayes method, the method based on the theory of extreme values ​​(EVT) are examined and compared.

Determining the thermal stresses in elastic plates is a necessary component in strength calculations of elements of thin-walled structures, for example, the skin of aircraft and rockets in aerodynamic heating conditions.

Knowledge of the magnitude and nature of the action of thermal stresses is necessary for a comprehensive analysis of the strength of the structure. Thermal stresses in themselves and in combination with mechanical stresses from external forces can cause cracks and destruction of structures made of materials with increased fragility.