arXiv subjects

Corrado Rainone

Publications and source records attributed to Corrado Rainone.

28 records · Page 2Linked to original sources

arXiv2017

Shear bands as manifestation of a criticality in yielding amorphous solids

Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterwards exhibiting a steady state with a constant mean stress. In stress controlled experiments the system simply breaks when pushed beyond this mean stress. The ubiquity of this phenomenon over a huge variety of amorphous solids calls for a generic theory that is free of microscopic details. Here we offer such a theory: the mechanical yield is a thermodynamic phase transition, where yield occurs as a spinodal phenomenon. At the spinodal point there exists a divergent correlation length which is associated with the system-spanning instabilities (known also as shear bands) which are typical to the mechanical yield. The theory, the order parameter used and the correlation functions which exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.

cond-mat.dis-nn↗

arXiv2016

Breakdown of Nonlinear Elasticity in Amorphous Solids at Finite Temperatures

It is known by now that amorphous solids at zero temperature do not possess a nonlinear elasticity theory: besides the shear modulus which exists, all the higher order coefficients do not exist in the thermodynamic limit. Here we show that the same phenomenon persists up to temperatures comparable to the glass transition. The zero temperature mechanism due to the prevalence of dangerous plastic modes of the Hessian matrix is replaced by anomalous stress fluctuations that lead to the divergence of the variances of the higher order elastic coefficients. The conclusion is that in amorphous solids elasticity can never be decoupled from plasticity: the nonlinear response is very substantially plastic.

cond-mat.soft↗

arXiv2016

Mechanical Yield in Amorphous Solids: a First-Order Phase Transition

Amorphous solids yield at a critical value of the strain (in strain controlled experiments); for larger strains the average stress can no longer increase - the system displays an elasto-plastic steady state. A long standing riddle in the materials community is what is the difference between the microscopic states of the material before and after yield. Explanations in the literature are material specific, but the universality of the phenomenon begs a universal answer. We argue here that there is no fundamental difference in the states of matter before and after yield, but the yield is a bona-fide first order phase transition between a highly restricted set of possible configurations residing in a small region of phase space to a vastly rich set of configurations which include many marginally stable ones. To show this we employ an order parameter of universal applicability, independent of the microscopic interactions, that is successful in quantifying the transition in an unambiguous manner.

cond-mat.soft↗

arXiv2016

Following the evolution of metastable glassy states under external perturbations: compression and shear-strain

This thesis sums up the research work I performed as a PhD student in Sapienza Università di Roma, and École Normale Supérieure, Paris, under the joint supervision of Prof. Giorgio Parisi and Dr. Francesco Zamponi. The thesis focuses on the theoretical study of metastable glasses prepared through non-equilibrium protocols. The first two chapters contain a review of the phenomenology of equilibrium supercooled liquids and non-equilibrium glasses, along with an exposition of the theoretical tools used up to now to approach the glass problem; the third chapter contains a review of the theoretical tools which are employed in the following of the thesis; the following two chapters contain our main result, namely a mean-field and first-principles theory of metastable glassy states which, as we show, is both able to reproduce known observations and to formulate new predictions and insights into the very nature of the glass phase, with tangible consequences in terms of behavior at high densities (or equivalently, low temperatures) and elasto-plastic response under strain; the last two chapters contain a numerical check of some of the results, and our conclusions and proposals for further research. The results I report in the present work have been for the most part already published, but here they are presented in a consistent and (as much as possible) self-contained manner.

cond-mat.soft↗

arXiv2015

Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution

The state-following technique allows the study of metastable glassy states under external perturbations. Here we show how this construction can be used to study the behavior of glassy states of Hard Spheres in infinite dimensions under compression or shear strain. In a preceding work it has been shown that in both cases, when the external perturbation is sufficiently strong, glassy states undergo a second-order transition, called the Gardner transition, whereupon a hierarchical structure of marginal micro-states manifests within the original glass state. The purpose of this work is to study the solution of the state-following construction in this marginal phase. We show that upon compression, close to the jamming transition, the metastable states are described by a scaling solution characterized by a set of non-trivial critical exponents that agree with the results obtained in a preceding work, and we compute the value of the final jamming density for various glassy states. Moreover we show that under the action of the shear strain, beyond the Gardner point, the metastable states can be followed in the marginal phase and we detect an overshoot in the stress-strain curve in agreement with numerical and experimental observations. Finally we further characterize the Gardner transition point by computing both the critical 4-point susceptibility and the exponents that characterize the critical slowing down of the dynamics within a glassy state close to the transition.

cond-mat.soft↗

arXiv2015

Dynamical arrest with zero complexity: the unusual behavior of the spherical Blume Emery Griffiths disordered model

The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field approximation of a spin-$1$ model with $p$-body quenched disordered interaction, with $p>2$, termed spherical Blume-Emery-Griffiths models. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of a different nature. In specific regions of the phase diagram coexistence of low density and high density paramagnets can occur, as well as the coexistence of spin-glass and paramagnetic phases. The exact static solution for the glassy phase is known to be obtained by the one-step replica symmetry breaking ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include: (i) the usual random first- order transition (Kauzmann-like) for mean-field glasses preceded by a dynamic transition, (ii) a thermodynamic first-order transition with phase coexistence and latent heat and (iii) a regime of apparent inversion of static transition line and dynamic transition lines, the latter defined as a non-zero complexity line. The latter inversion, though, turns out to be preceded by a novel dynamical arrest line at higher temperature. Crossover between different regimes is analyzed by solving mode coupling theory equations throughout the space of external thermodynamic parameters and the relationship with the underlying statics is discussed.

cond-mat.dis-nn↗

arXiv2015

Numerical detection of the Gardner transition in a mean-field glass former

Recent theoretical advances predict the existence, deep into the glass phase, of a novel phase transition, the so-called Gardner transition. This transition is associated with the emergence of a complex free energy landscape composed of many marginally stable sub-basins within a glass metabasin. In this study, we explore several methods to detect numerically the Gardner transition in a simple structural glass former, the infinite-range Mari-Kurchan model. The transition point is robustly located from three independent approaches: (i) the divergence of the characteristic relaxation time, (ii) the divergence of the caging susceptibility, and (iii) the abnormal tail in the probability distribution function of cage order parameters. We show that the numerical results are fully consistent with the theoretical expectation. The methods we propose may also be generalized to more realistic numerical models as well as to experimental systems.

cond-mat.dis-nn↗

arXiv2015

The replica method in liquid theory: from the basics to explicit computations

In these notes we introduce briefly the fundamentals of the replica method in the context of liquid theory and the structural glass problem. In particular, we explain and show its usefulness as a computation framework in the context of the Random First Order Transition (RFOT) theory of the glass transition, whose defining points the reader is assumed to know. We shall give the intuitive idea of how and why the replica method is suitable for the description of the glass transition (the dynamical glass transition in particular) in real liquids, and then show how it can be used to make explicit computations and predictions that can be compared to experiments and numerical simulations.

cond-mat.soft↗

arXiv2014

Calorimetric glass transition in a mean field theory approach

The study of the properties of glass-forming liquids is difficult for many reasons. Analytic solutions of mean field models are usually available only for systems embedded in a space with an unphysically high number of spatial dimensions; on the experimental and numerical side, the study of the properties of metastable glassy states requires to thermalize the system in the supercooled liquid phase, where the thermalization time may be extremely large. We consider here an hard-sphere mean field model which is solvable in any number of spatial dimensions; moreover we easily obtain thermalized configurations even in the glass phase. We study the three dimensional version of this model and we perform Monte Carlo simulations which mimic heating and cooling experiments performed on ultra-stable glasses. The numerical findings are in good agreement with the analytical results and qualitatively capture the features of ultra-stable glasses observed in experiments.

cond-mat.dis-nn↗

arXiv2014

Following the evolution of glassy states under external perturbations: compression and shear-strain

We consider the adiabatic evolution of glassy states under external perturbations. Although the formalism we use is very general, we focus here on infinite-dimensional hard spheres where an exact analysis is possible. We consider perturbations of the boundary, i.e. compression or (volume preserving) shear-strain, and we compute the response of glassy states to such perturbations: pressure and shear-stress. We find that both quantities overshoot before the glass state becomes unstable at a spinodal point where it melts into a liquid (or yields). We also estimate the yield stress of the glass. Finally, we study the stability of the glass basins towards breaking into sub-basins, corresponding to a Gardner transition. We find that close to the dynamical transition, glasses undergo a Gardner transition after an infinitesimal perturbation.

cond-mat.soft↗