arXiv subjects

Itamar Procaccia

Publications and source records attributed to Itamar Procaccia.

At least 73 records · Page 4Linked to original sources

arXiv2018

Magneto-mechanical Coupling in Thermal Amorphous Solids

Standard approaches to magneto-mechanical interactions in thermal magnetic crystalline solids involve Landau functionals in which the lattice anisotropy and the resulting magnetization easy axes are taken explicitly into account. In glassy systems one needs to develop a theory in which the amorphous structure precludes the existence of an easy axis, and in which the constituent particles are free to respond to their local amorphous surroundings and the resulting forces. We present a theory of all the mixed responses of an amorphous solids to mechanical strains and magnetic fields. Atomistic models are proposed in which we test the predictions of magnetostriction for both bulk and nano-film amorphous samples. The application to nano-films with emergent self-affine free interfaces requires a careful definition of the film 'width' and its change due to the magnetostriction effect.

cond-mat.soft↗

arXiv2018

Training, Memory and Universal Scaling in Amorphous Frictional Granular Matter

We report a joint experimental and theoretical investigation of cyclic training of amorphous frictional granular assemblies, with special attention to memory formation and retention. Measures of dissipation and compactification are introduced, culminating with a proposed scaling law for the reducing dissipation and increasing memory. This scaling law is expected to be universal, insensitive to the details of the elastic and frictional interactions between the granules.

cond-mat.soft↗

arXiv2017

How Generic are the Robust Theoretical Aspects of Jamming in Hard Sphere Models?

In very recent work the mean field theory of the jamming transition in infinite dimensional hard spheres models was presented. Surprisingly, this theory predicts quantitatively numerically determined characteristics of jamming in two and three dimensions. This is a rare and unusual finding. Here we argue that this agreement in non-generic: only for hard sphere models it happens that sufficiently close to jamming the effective interactions are in agreement with mean-field theory, justifying the truncation of many body interactions (which is the exact protocol in infinite dimensions). Any softening of the bare hard sphere interactions results in effective interactions that are not mean-field all the way to jamming, making the discussed phenomenon non generic.

cond-mat.soft↗

arXiv2017

Reply to Comment on `What Determines the Static Force Chains in Stressed Granular Media?'

The formalism proposed in Phys. Rev. Lett. 116, 078001 (2016) for determination of the normal and tangential inter-particle forces in frictional disks from visual data was criticized in a comment to that paper. However the theory developed in the original publication is aimed at finding the forces when provided with accurate measurements while the comment addresses a different problem, being the statistics of forces in a configuration with uncertainty of the relevant parameters. We address this difference in perspectives and point out that even with experimental errors one can improve the results using an iterative procedure proposed in Phys. Rev. E. Rapid Communication, 93, 060601(R) (2016).

cond-mat.soft↗

arXiv2017

Mechanical Failure in Amorphous Solids: Scale Free Spinodal Criticality

The mechanical failure of amorphous media is a ubiquitous phenomenon from material engineering to geology. It has been noticed for a long time that the phenomenon is "scale-free", indicating some type of criticality. In spite of attempts to invoke "Self-Organized Criticality", the physical origin of this criticality, and also its universal nature, being quite insensitive to the nature of microscopic interactions, remained elusive. Recently we proposed that the precise nature of this critical behavior is manifested by a spinodal point of a thermodynamic phase transition. Moreover, 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. Demonstrating this requires the introduction of an "order parameter" that is suitable for distinguishing between disordered amorphous systems, and an associated correlation function, suitable for picking up the growing correlation length. The theory, the order parameter, and the correlation functions used are universal in nature and can be applied to any amorphous solid that undergoes mechanical yield. Critical exponents for the correlation length divergence and the system size dependence are estimated. The phenomenon is seen at its sharpest in athermal systems, as is explained below; in this paper we extend the discussion also to thermal systems, showing that at sufficiently high temperatures the spinodal phenomenon is destroyed by thermal fluctuations.

cond-mat.dis-nn↗

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↗

arXiv2017

Breakdown of Nonlinear Elasticity in Stress-Controlled Thermal Amorphous Solids

In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample to sample fluctuations that grow without bound with the system size. More relevant however for experiments are the conditions of stress control. In the present Communication we show that also under stress control the shear modulus exists but higher order moduli show unbounded sample to sample fluctuation. The unavoidable consequence is that the characterization of stress-strain curves in experiments should be done with a stress-dependent shear modulus rather than with nonlinear expansions.

cond-mat.soft↗

arXiv2016

The sandpile revisited: Computer assisted determination of constitutive relations and the breaking of scaling

We revisit the problem of the stress distribution in a frictional sandpile under gravity, equipped with a new numerical model of granular assemblies with both normal and tangential (frictional) inter-granular forces. Numerical simulations allow a determination of the spatial dependence of all the components of the stress field as a function of systems size, the coefficient of static friction and the frictional interaction with the bottom surface. Our study clearly demonstrates that interaction with the bottom surface plays a crucial role in the formation of a pressure dip under the apex of a granular pile. Basic to the theory of sandpiles are assumptions about the form of scaling solutions and constitutive relations for cohesive-less hard grains for which no typical scale is available. We find that these constitutive relations must be modified; moreover for smaller friction coefficients and smaller piles these scaling assumptions break down in the bulk of the sandpile due to the presence of length scales that must be carefully identified. After identifying the crucial scale we provide a predictive theory to when scaling solutions are expected to break down. At the bottom of the pile the scaling assumption always breaks, due to the different interactions with the bottom surface. The consequences for measurable quantities like the pressure distribution and shear stress at the bottom of the pile are discussed. For example one can have a transition from no dip in the base-pressure to a dip at the center of the pile as a function of the system size.

cond-mat.dis-nn↗

arXiv2016

Emergent Inter-particle Interactions in Thermal Amorphous Solids

Amorphous media at finite temperatures, be them liquids, colloids or glasses, are made of interacting particles that move chaotically due to thermal energy, colliding and scattering continuously off each other. When the average configuration in these systems relaxes only at long times, one can introduce {\em effective interactions} that keep the {\em mean positions} in mechanical equilibrium. We introduce a new framework to determine these effective force-laws that define an effective Hessian that can be employed to discuss stability properties and density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these feel zero forces when not in contact and infinite forces when they touch. The present approach recaptures the effective interactions which for sufficiently dense spheres at temperature $T$ depends on the gap $h$ between spheres as $T/h$ [C. Brito and M. Wyart, Europhys. Lett. 76 149 (2006)]. In systems at lower densities or with longer microscopic interaction (say like Lennard-Jones), the emergent force laws will include ternary, quaternary and generally higher order many-body terms, even if the microscopic interactions are strictly binary.

cond-mat.soft↗

arXiv2016

Determining the Inter-Particle Force-Laws in Amorphous Solids from a Visual Image

We consider the problem of how to determine the force laws in an amorphous system of interacting particles. Given the positions of the centers of mass of the constituent particles we propose a new algorithm to determine the inter-particle force-laws. Having $n$ different types of constituents we determine the coefficients in the Laurent polynomials for the $n(n+1)/2$ possibly different force-laws. A visual providing the particle positions in addition to a measurement of the pressure is all that is required. The algorithm proposed includes a part that can correct for experimental errors in the positions of the particles. Such a correction of unavoidable measurement errors is expected to benefit many experiments in the field.

cond-mat.soft↗

arXiv2016

Scaling Theory of the Mechanical Properties of Amorphous Nano-Films

Numerical Simulations are employed to create amorphous nano-films of a chosen thickness on a crystalline substrate which induces strain on the film. The films are grown by a vapor deposition technique which was recently developed to create very stable glassy films. Using the exact relations between the Hessian matrix and the shear and bulk moduli we explore the mechanical properties of the nano-films as a function of the density of the substrate and the film thickness. The existence of the substrate dominates the mechanical properties of the combined substrate-film system. Scaling concepts are then employed to achieve data collapse in a wide range of densities and film thicknesses.

cond-mat.soft↗

arXiv2016

Microalloying and the mechanical properties of amorphous solids

The mechanical properties of amorphous solids like metallic glasses can be dramatically changed by adding small concentrations (as low as 0.1\%) of foreign elements. The glass-forming-ability, the ductility, the yield stress and the elastic moduli can all be greatly effected. This paper presents theoretical considerations with the aim of explaining the magnitude of these changes in light of the small concentrations involved. The theory is built around the experimental evidence that the microalloying elements organize around them a neighborhood that differs from both the crystalline and the glassy phases of the material in the absence of the additional elements. These regions act as {\em isotropic} defects that in unstressed systems dress the shear moduli. When strained, these defects interact with the incipient plastic responses which are quadrupolar in nature. It will be shown that this interaction interferes with the creation of system-spanning shear bands and increases the yield strain. We offer experimentally testable estimates of the lengths of nano-shear bands in the presence of the additional elements.

cond-mat.mtrl-sci↗

arXiv2016

Statistics of Plastic Events in Post-Yield Strain-Controlled Amorphous Solids

Amorphous solids yield in strain-controlled protocols at a critical value of the strain. For larger strains the stress and energy display a generic complex serrated signal with elastic segments punctuated by sharp energy and stress plastic drops having a wide range of magnitudes. Here we provide a theory of the scaling properties of such serrated signals taking into account the system-size dependence. We show that the statistics are not homogeneous - they separate sharply to a regime of `small' and `large' drops, each endowed with its own scaling properties. A scaling theory is first derived solely by data analysis, showing a somewhat complex picture. But after considering the physical interpretation one discovers that the scaling behavior and the scaling exponents are in fact very simple and universal.

cond-mat.soft↗

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

What determines static force chains in stressed granular media?

The determination of the normal and transverse (frictional) inter-particle forces within a granular medium is a long standing, taunting, and yet unresolved problem. We present a new formalism which employs the knowledge of the external forces and the orientations of contacts between particles (of any given sizes), to compute all the inter-particle forces. Having solved this problem we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.

cond-mat.soft↗

arXiv2016

Elasticity in Amorphous Solids: Nonlinear or Piece-Wise Linear?

Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean stress that remains constant with increasing strain. It is therefore very tempting to fit a nonlinear expansion of the stress in powers of the strain. We argue here that at low temperatures the meaning of such an expansion needs to be reconsidered. We point out the enormous difference between quenched and annealed averages of the stress vs. strain curves, and propose that a useful description of the mechanical response is given by a stress (or strain) dependent shear modulus for which a theoretical evaluation exists. The elastic response is piece-wise linear rather than nonlinear.

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↗

arXiv2015

Counter-flow Induced Decoupling in Super-Fluid Turbulence

In mechanically driven superfluid turbulence the mean velocities of the normal- and superfluid components are known to coincide: $\mathbf U_{\text{n}} =\mathbf U_{\text{s}}$. Numerous laboratory, numerical and analytical studies showed that under these conditions the mutual friction between the normal- and superfluid velocity components couples also their fluctuations: $\mathbf u'_{\text{n}}(\mathbf r,t) \approx \mathbf u'_{\text{s}}(\mathbf r,t)$ almost at all scales. In this paper we show that this is not the case in thermally driven superfluid turbulence; here the counterflow velocity $\mathbf U_{\text{ns}}\equiv \mathbf U_{\text{n}} -\mathbf U_{\text{s}}\ne 0$. We suggest a simple analytic model for the cross correlation function $\left\langle \mathbf u'_{\text{n}}(\mathbf r,t) \cdot \mathbf u'_{\text{s}}(\mathbf r',t)\right \rangle$ and its dependence on $U_{\text{ns}}$. We demonstrate that $\mathbf u'_{\text{n}}(\mathbf r,t)$ and $ \mathbf u'_{\text{s}}(\mathbf r,t)$ are decoupled almost in the entire range of separations $|\mathbf r-\mathbf r'|$ between the energy containing scale and intervortex distance.

cond-mat.other↗