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[en] I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics

[en] As discovered by recent quasi-static and dynamic resonance experiments, the classical nonlinear theory fails in describing the hysteretic behaviour of nonlinear mesoscopic materials like rocks, concrete, etc. The paper applies the local interaction simulation approach (LISA) for studying such kind of nonclassical nonlinearity. To this purpose, in the LISA treatment of ultrasonic wave propagation has been included a phenomenological model, based on the PM space approach, of the local mesoscopic features of rocks and other materials with localized damages. A quantitative comparison of simulation and experimental results in quasi-static experiments is also presented

[en] Dynamic partitioning or substructuring is the reduction of degrees of freedom by neglecting the dynamical influence of higher modes of certain substructure. One of the major reasons for these techniques not being widely accepted is the lack of criteria to judge the accuracy of the computed data. So far as natural frequencies are concerned a theorem is formulated which gives upper bounds for the error due to dynamic substructuring. The theorem is tested by applying it to a special statically exact substructuring method which is gained from a fixed-mode approach. The error estimation turns out to be strict enough to decide on the validity of DOF-reduction. (orig.)

[en] Classical contact transformation theory is reconstructed from the concept of explicit rather than implicit transformation equations. This proves the existence of contact transformations from any given Hamiltonian to any prescribed Hamiltonian

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[en] Preface The present volume of the Journal of Physics: Conference Series represents contributions from participants of the All-Russian Conference with international participation «Modern problems of continuum mechanics and explosion physics» dedicated to the 60th anniversary of Lavrentyev Institute of Hydrodynamics SB RAS held at the Technopark of Novosibirsk Akademgorodok, Russia, September, 4-8 2017, organised by the Lavrentyev Institute of Hydrodynamics. The conference is traditional and attracts attention of mathematicians and physicists. Scientific activities of the Conference include a discussion of a wide range of problems: mathematical problems of continuum mechanics, physics and mechanics of high-energy processes, fluid mechanics and mechanics of solids. The program of conference included 18 plenary presentations (30 minutes), 170 oral presentations (15 minutes) and 50 posters given by more than 220 participants from 23 cities of Russia (Moscow, Novosibirsk, Vladivostok, Tomsk, Yakutsk, Perm, Novokuznetsk, Biisk, Lys’va, Kemerovo, Snezhinsk, Volgograd, Tyumen, Barnaul, Yekaterinburg, Krasnoyarsk, Irkutsk), Portugal (Lisbon), Kazakhstan (Almaty), Thailand (Nakhon Ratchasima), Denmark (Lyngby), Spain (Oviedo) and France (Marseille). A significant part of talks (about 25 %) were presented by young researchers and postgraduate students. We would like to thank the Speakers for their significant contributions to the conference. We also would like to thank the members of the Organizing Committee. We cannot end without expressing our many thanks to our sponsors (Federal Agency for Scientific Organizations (FASO Russia), Russian Foundation for Basic Research and Technology Company Schlumberger, International Mathematical Center of Novosibirsk State University) for their financial support. Novosibirsk, September 2017 Alexander Chesnokov, Eduard Pruuel, Vladimir Shelukhin (paper)

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