SISSA PreprintsSISSA authors' not-referred manuscripts of the research outputhttp://preprints.sissa.it:8180/xmlui/handle/1963/352812020-08-03T09:32:35Z2020-08-03T09:32:35ZA Vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlersGidoni, PaoloRiva, Filippohttp://preprints.sissa.it:8180/xmlui/handle/1963/353882020-07-21T23:20:31Z2020-07-21T00:00:00ZA Vanishing inertia analysis for finite dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers
Gidoni, Paolo; Riva, Filippo
We study the approximation of quasistatic evolutions, formulated as abstract finite-dimensional rate-independent systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamical solutions to the quasistatic one, employing the concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy.
Contents: 1. Introduction and motivation. 2. Setting of the problem and main result.
3. Existence of solutions for the dynamic problem. 4. R-absolutely continuous functions and functions of bounded R-variation. 5. Differential and energetic solutions for the quasistatic problem. 6. Quasistatic limit. 7. Applications and examples. References.
2020-07-21T00:00:00ZOn a Phase-field model of damage for hybrid laminates with cohesive interfacesBonetti, ElenaCavaterra, CeciliaFreddi, FrancescoRiva, Filippohttp://preprints.sissa.it:8180/xmlui/handle/1963/353872020-07-17T23:20:32Z2020-07-17T00:00:00ZOn a Phase-field model of damage for hybrid laminates with cohesive interfaces
Bonetti, Elena; Cavaterra, Cecilia; Freddi, Francesco; Riva, Filippo
In this paper we investigate a rate{independent model for hybrid laminates described by a damage phase field approach on two layers coupled with a cohesive law governing
the behaviour of their interface. For the analysis we adopt the notion of energetic evolution,
based on global minimisation of the involved energy. Due to the presence of the cohesive zone, as already emerged in literature, compactness mathematical issues lead to the introduction of a fictitious variable replacing the physical one which represents the maximal opening of the interface displacement discontinuity reached during the evolution. A new strategy which allows to recover the equivalence between the fictitious and the real variable under general loading-unloading regimes is illustrated. The argument is based on temporal regularity of energetic evolutions. This regularity is achieved by means of a careful balance between the convexity of the elastic energy of the layers and the natural concavity of the cohesive energy of the interface.
2020-07-17T00:00:00ZA Dynamic model for viscoelasticity in domains with time-dependent cracksSapio, Francescohttp://preprints.sissa.it:8180/xmlui/handle/1963/353542020-06-03T23:20:32Z2020-06-03T00:00:00ZA Dynamic model for viscoelasticity in domains with time-dependent cracks
Sapio, Francesco
In this paper, we prove the existence of solutions for a class of viscoelastic dynamic systems on time–dependent cracking domains. Finally we exhibit an example which shows that our model overcomes the viscoelastic crack paradox; indeed, the energy-dissipation balance is satisfied provided we take into account the additional dissipative term due to crack growth.
2020-06-03T00:00:00ZSuperconformal indices at large N and the entropy of AdS5 × SE5 black holesBenini, FrancescoColombo, EdoardoSoltani, SamanZaffaroni, AlbertoZhang, Ziruohttp://preprints.sissa.it:8180/xmlui/handle/1963/353532020-05-28T23:20:29Z2020-05-01T00:00:00ZSuperconformal indices at large N and the entropy of AdS5 × SE5 black holes
Benini, Francesco; Colombo, Edoardo; Soltani, Saman; Zaffaroni, Alberto; Zhang, Ziruo
The large N limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS5 black holes only in the particular case of equal angular momenta. Using the Bethe Ansatz formulation, we compute the index at large N with arbitrary chemical potentials for all charges and angular momenta, for general N = 1 four-dimensional conformal theories with a holographic dual. We con-jecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large N. For N = 4 SYM, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS5 × S5 for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS5 × SE5, where SE5 is a Sasaki-Einstein manifold. We ﬁrst check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr-Newman black holes in AdS5 × T 1,1, charged under the baryonic symmetry of the conifold theory and with equal angular mo-menta. We compute the entropy of these black holes using the attractor mechanism and we ﬁnd complete agreement with the ﬁeld theory predictions.
SISSA, Via Bonomea 265, 34136 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy, ICTP, Strada Costiera 11, 34151 Trieste, Italy, Dipartimento di Fisica, Universit`a di Milano-Bicocca, I-20126 Milano, Italy, INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy
2020-05-01T00:00:00Z