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Dive into the research topics where Corrado Rainone is active.

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Featured researches published by Corrado Rainone.


Physical Review Letters | 2015

Following the evolution of hard sphere glasses in infinite dimensions under external perturbations: compression and shear strain.

Corrado Rainone; Pierfrancesco Urbani; Hajime Yoshino; Francesco Zamponi

We consider the adiabatic evolution of glassy states under external perturbations. The formalism we use is very general. Here we use it for 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.


Physical Review E | 2015

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

Patrick Charbonneau; Yuliang Jin; Giorgio Parisi; Corrado Rainone; B. Seoane; Francesco Zamponi

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.


Physical Review Letters | 2016

Mechanical Yield in Amorphous Solids: A First-Order Phase Transition.

Prabhat K. Jaiswal; Itamar Procaccia; Corrado Rainone; Murari Singh

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 elastoplastic steady state. A long-standing riddle in the materials community is what the difference is 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.


Journal of Statistical Mechanics: Theory and Experiment | 2016

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

Corrado Rainone; Pierfrancesco Urbani

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.


Proceedings of the National Academy of Sciences of the United States of America | 2017

Shear bands as manifestation of a criticality in yielding amorphous solids

Giorgio Parisi; Itamar Procaccia; Corrado Rainone; Murari Singh

Significance The art of making structural, polymeric, and metallic glasses is rapidly developing with many applications. A limitation is that, under increasing external strain, all amorphous solids have a yield stress, which when exceeded, results in a plastic response leading to mechanical failure. Understanding this is crucial for assessing the risk of failure of glassy materials under loads. The universality of the mechanical yield requires a theory that is general enough to transcend the microscopic details of different glasses, which all show similar stress–strain curves with a yield point. We provide a general theory that is thermodynamic in nature, showing that the mechanical yield is a spinodal criticality in an appropriately constructed free energy landscape. Amorphous solids increase their stress as a function of an applied strain until a mechanical yield point whereupon the stress cannot increase anymore, afterward 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 that is associated with the system-spanning instabilities (also known as shear bands), which are typical to the mechanical yield. The theory, the order parameter used, and the correlation functions that exhibit the divergent correlation length are universal in nature and can be applied to any amorphous solids that undergo mechanical yield.


Proceedings of the National Academy of Sciences of the United States of America | 2015

Calorimetric glass transition in a mean-field theory approach

Manuel Sebastian Mariani; Giorgio Parisi; Corrado Rainone

Significance Understanding the properties of glasses is one of the major open challenges of theoretical physics. Making analytical predictions is usually very difficult for the known glassy models. Moreover, in experiments and numerical simulations thermalization of glasses cannot be achieved without sophisticated procedures, such as the vapor deposition technique. In this work we study a glassy model that is simple enough to be analytically solved and that can be thermalized in the glassy phase with a simple numerical method, opening the door to an intensive comparison between replica theory predictions and numerical outcomes. 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 thermalizing the system in the supercooled liquid phase, where the thermalization time may be extremely large. We consider here a hard-sphere mean-field model that is solvable in any number of spatial dimensions; moreover, we easily obtain thermalized configurations even in the glass phase. We study the 3D version of this model and we perform Monte Carlo simulations that mimic heating and cooling experiments performed on ultrastable glasses. The numerical findings are in good agreement with the analytical results and qualitatively capture the features of ultrastable glasses observed in experiments.


Physical Review E | 2016

Emergent interparticle interactions in thermal amorphous solids

Oleg Gendelman; Edan Lerner; Yoav G. Pollack; Itamar Procaccia; Corrado Rainone; Birte Riechers

Amorphous media at finite temperatures, be them liquids, colloids, or glasses, are made of interacting particles that move chaotically due to thermal energy, continuously colliding and scattering off each other. When the average configuration in these systems relaxes only at long times, one can introduce effective interactions that keep the mean positions in mechanical equilibrium. We introduce a framework to determine the effective force laws that define an effective Hessian that can be employed to discuss stability properties and the density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these experience zero forces when not in contact and infinite forces when they touch. Close to jamming we recapture the effective interactions that at temperature T depend on the gap h between spheres as T/h [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006)EULEEJ0295-507510.1209/epl/i2006-10238-x]. For hard spheres at lower densities or for systems whose binary bare interactions are longer ranged (at any density), the emergent force laws include ternary, quaternary, and generally higher-order many-body terms, leading to a temperature-dependent effective Hessian.


Archive | 2017

The Replica Symmetric Ansatz

Corrado Rainone

In this chapter we perform the computation of the Franz-Parisi potential for the hard sphere (HS) model in the MF limit. As we anticipated, the perturbations we focus on will be adiabatic compression/decompression and quasi-static shear strain, and we compute the response of glassy states to these perturbations.


Archive | 2017

The Full Replica Symmetry Breaking Ansatz

Corrado Rainone

In the preceding chapter, we have computed the FP potential assuming the simplest possible replica symmetric ansatz for the slave replicas sampling the bottom of the followed glassy state.


Archive | 2017

The State Following Construction

Corrado Rainone

In the preceding chapter we have detailed how glasses are endowed with well defined and time-independent physical properties: they have a specific heat, a compressibility, a Debye-Waller factor, a shear modulus, etc.: our aim is to compute analytically those quantities from a first-principles theory.

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Itamar Procaccia

Weizmann Institute of Science

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Murari Singh

Jawaharlal Nehru University

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Giorgio Parisi

Sapienza University of Rome

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Yoav G. Pollack

Weizmann Institute of Science

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Francesco Zamponi

École Normale Supérieure

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Edan Lerner

University of Amsterdam

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Birte Riechers

Weizmann Institute of Science

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Carmel A. B. Z. Shor

Weizmann Institute of Science

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Oleg Gendelman

Technion – Israel Institute of Technology

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Pierfrancesco Urbani

Centre national de la recherche scientifique

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