PSI - Issue 32

Available online at www.sciencedirect.com Available online at www.sciencedirect.com Sci nceD rect Structural Integrity Procedia 00 (2021) 000–000 Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2021) 000–000

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Procedia Structural Integrity 32 (2021) 144–151

© 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” Abstract There are two conventionally discussed dispersion relations (DR) in condensed matter: the gapless phonon-like DR and the DR with the energy or frequency gap. The third type of DR has been emerging in different areas of condensed matter physics: the gapped momentum states (GMS) when the DR with the gap in momentum, or k-space. Increasing interest for the gapped momentum states are related to important implications for dynamical and thermodynamic properties of the system (hydrodynamic turbulence, plasticity, failure). Traditionally GMS emerge in the Maxwell-Frenkel approach to liquid or solid viscoelasticity, relate the k-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space. Generalized hydrodynamics seeks to start with hydrodynamic equations for liquid properties and subsequently add non-hydrodynamic effects. GMS can also be obtained starting from solid-like elastic equations and generalizing them by adding hydrodynamic flow effects. Original interpretation of GMS and dispersion properties in condensed matter is developed considering the defects induced criticality (structural-scaling transition) in shocked liquid and solid. The nature of the viscosity limit is discussed analyzing the scenario of GMS in the presence of dynamics of collective modes of defects. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” Keywords: Gapped Momentum States, defects induced criticality, viscosity limit 1. Introduction 1.1. Gaped Momentum States and Dispersion Relations The gapped momentum states (GMS) are often related to dissipation in open systems with specific dynamic and XXIIth Winter School on Continuous Media Mechanics Defects Induced Criticality and Gapped Momentum States in Condensed Matter Naimark O.B. 1 Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science (ICMM UB RAS), Academician Korolev Street, 1 Perm, 614013, Russian Federation Abstract There are two conventionally discussed dispersion relations (DR) in condensed matter: the gapless phonon-like DR and the DR with the energy or frequenc gap. The th rd type of DR has been emerging in different areas of conde sed matter physics: the gapped momentum states (GMS) w n the DR with the gap i ome tum, or k-space. Increasing interest for t e gapped mom ntum sta es are related to important implications for dyna ical and thermody amic properti of t system (hydrodynamic turbul nc , plasticity, failure). Trad tionally GMS emerge in the Maxwell-Frenkel approach to liquid or olid viscoelasticity, relate the k-g p to dissipation and observe how th gaps in DR can continuously change from the energy to mom ntum space. G neralized hydrodynamics seeks to start with hydrodyn mic eq ations for liquid properti s and subsequently add non-hydrodynamic effects. GMS can also be obtaine starting from s lid-like elastic equation generalizing them by adding h drodynamic flow effects. Original interpretation of GMS and dispersion properties in condense matter s developed cons dering the defects induced criticality (structu al-scaling transition) n shocked liquid and s li . The nature of the viscosity limit is discussed analyzing the s enario of GMS in the presence of dynamics of collective mo es of defects. © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review u der re ponsibility of scientific committe of the XXIIth Winter School on Continuous Media Mechanics” Keywords: Gapped Momentum States, defects induced criticality, viscosity limit 1. Introduction 1.1. Gaped Momentum States and Dispersion Relations The gapped momentum states (GMS) are often related to dissipation in open systems with specific dynamic and XXIIth Winter School on Continuous Media Mechanics Defects Induced Criticality and Gapped Momentum States in Condensed Matter Naimark O.B. 1 Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of Science (ICMM UB RAS), Academician Korolev Street, 1 Perm, 614013, Russian Federation

Corresponding author. Tel.: +7-342-2378-389 ; fax: +7-342-2378-487. E-mail address: naimark@icmm.ru Corresponding author. Tel.: +7-342-2378-389 ; fax: +7-342-2378-487. E-mail address: naimark@icmm.ru

2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” 2452-3216 © 2021 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license ( https://creativecommons.org/licenses/by-nc-nd/4.0 ) Peer-review u der responsibility of t e scientific committee of the XXIIth Winter School on Continuous Media Mechanics”

2452-3216 © 2021 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the XXIIth Winter School on Continuous Media Mechanics” 10.1016/j.prostr.2021.09.021