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Makarov P.V.,RAS Institute of Strength Physics and Materials Science
Physical Mesomechanics | Year: 2010

The paper considers common nonlinear characteristics of inelastic deformation and fracture of loaded solids and similarity of numerical solutions of a nonlinear system of relevant partial differential equations. The self-similarity of inelastic strain and damage accumulation in the entire hierarchy of scales-from interatomic distances up to tectonic faults of many thousands of kilometers in the Earth crust-ensures qualitative similarity of fracture scenarios whatever the scale of deformation and rheology of a medium. The common properties of deformed systems are spatial localization of inelastic strain and damage accumulation in the entire hierarchy of scales, further temporal strain localization as a superfast autocatalytic blow-up process, slow dynamics (deformation fronts or slow motions), and strain activity migration due to long-range space-time correlations over the entire hierarchy of scales. Thus, fracture evolves as a sequence of catastrophes of increasing scales up to macroscales. It is shown that self-organized criticality of any deformed system does not exclude the possibility to predict the time and the place of a future catastrophic event. Precursors of similar large-scale events can be (i) frozen strain activity in the immediate vicinity of a formed main crack or fault and (ii) generation of trains of deformation fronts (damage fronts) in this region and their flow toward the site of a formed main crack (fault). © 2010.

Reshetnyak A.A.,RAS Institute of Strength Physics and Materials Science
Physics of Particles and Nuclei | Year: 2010

The spectrum of superstring theory on the AdS5 × S5 Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux Y(s1, s2). We review the details of a gauge-invariant Lagrangian description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group. © 2010 Pleiades Publishing, Ltd.

Li Q.,TU Berlin | Popov M.,TU Berlin | Dimaki A.,RAS Institute of Strength Physics and Materials Science | Filippov A.E.,NASU Institute of Physics | And 2 more authors.
Physical Review Letters | Year: 2013

In this Letter, we study the friction between a one-dimensional elastomer and a one-dimensional rigid body having a randomly rough surface. The elastomer is modeled as a simple Kelvin body and the surface as self-affine fractal having a Hurst exponent H in the range from 0 to 1. The resulting frictional force as a function of velocity always shows a typical structure: it first increases linearly, achieves a plateau and finally drops to another constant level. The coefficient of friction on the plateau depends only weakly on the normal force. At lower velocities, the coefficient of friction depends on two dimensionless combinations of normal force, sliding velocity, shear modulus, viscosity, rms roughness, rms surface gradient, the linear size of the system, and the Hurst exponent. We discuss the physical nature of different regions of the law of friction and suggest an analytical relation describing the coefficient of friction in a wide range of loading conditions. An important implication of the analytical result is the extension of the well-known "master curve procedure" to the dependencies on the normal force and the size of the system. © 2013 American Physical Society.

Buchbinder I.L.,Federal University of Juiz de fora | Buchbinder I.L.,Tomsk State Pedagogical University | Reshetnyak A.,RAS Institute of Strength Physics and Materials Science
Nuclear Physics B | Year: 2012

We construct a Lagrangian description of irreducible integer higher spin representations of the Poincaré-group with an arbitrary Young tableaux having k rows, on a basis of the universal BRST approach. Starting with a description of bosonic mixed-symmetry higher spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with special Poincaré module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincaré-group representations) into a first-class constraint system. For this purpose, we find, for the first time, auxiliary representations of the constraint subalgebra, to be isomorphic due to Howe duality to sp(2k) algebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We propose a universal procedure of constructing unconstrained gauge-invariant Lagrangians with reducible gauge symmetries describing the dynamics of both massless and massive bosonic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by the constraints corresponding to an irreducible Poincaré-group representation. As examples of the general procedure, we formulate the method of Lagrangian construction for bosonic fields subject to arbitrary Young tableaux having 3 rows and derive the gauge-invariant Lagrangian for new model of massless rank-4 tensor field with spin (2,1,1) and second stage reducible gauge symmetries. © 2012 Elsevier B.V.

Chertova N.V.,RAS Institute of Strength Physics and Materials Science
Physical Mesomechanics | Year: 2013

The mechanisms of plane harmonic wave propagation in homogeneous and interfaced elastic-viscoplastic media are considered using the field theory of defects with kinematic identities of a dislocation-containing elastic continuum and dynamic equations of the gauge theory of dislocations. The reflection and refraction coefficients were determined for displacement waves and defect field waves with the defect field characterized by the dislocation density tensor and flux density tensor. The dependence of the coefficients on the parameters of the interfaced media is analyzed. © 2013 Pleiades Publishing, Ltd.

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