arXiv subjects

Itamar Procaccia

Publications and source records attributed to Itamar Procaccia.

At least 181 records · Page 10Linked to original sources

arXiv2007

Dynamic Failure in Amorphous Solids via a Cavitation Instability

The understanding of dynamic failure in amorphous materials via the propagation of free boundaries like cracks and voids must go beyond elasticity theory, since plasticity intervenes in a crucial and poorly understood manner near the moving free boundary. In this Letter we focus on failure via a cavitation instability in a radially-symmetric stressed material, set up the free boundary dynamics taking both elasticity and visco-plasticity into account, using the recently proposed athermal Shear Transformation Zone theory. We demonstrate the existence (in amorphous systems) of fast cavitation modes accompanied by extensive plastic deformations and discuss the revealed physics.

cond-mat.mtrl-sci↗

arXiv2007

Comparison of Theory and Direct Numerical Simulations of Drag Reduction by Rodlike Polymers in Turbulent Channel Flows

Numerical simulations of turbulent channel flows, with or without additives, are limited in the extent of the Reynolds number \Re and Deborah number \De. The comparison of such simulations to theories of drag reduction, which are usually derived for asymptotically high \Re and \De, calls for some care. In this paper we present a study of drag reduction by rodlike polymers in a turbulent channel flow using direct numerical simulation and illustrate how these numerical results should be related to the recently developed theory.

nlin.CD↗

arXiv2007

Mechanical Properties of Glass Forming Systems

We address the interesting temperature range of a glass forming system where the mechanical properties are intermediate between those of a liquid and a solid. We employ an efficient Monte-Carlo method to calculate the elastic moduli, and show that in this range of temperatures the moduli are finite for short times and vanish for long times, where `short' and `long' depend on the temperature. By invoking some exact results from statistical mechanics we offer an alternative method to compute shear moduli using Molecular Dynamics simulations, and compare those to the Monte-Carlo method. The final conclusion is that these systems are not "viscous fluids" in the usual sense, as their actual time-dependence concatenates solid-like materials with varying local shear moduli.

cond-mat.stat-mech↗

arXiv2007

Energy Conservation and Second-Order Statistics in Stably Stratified Turbulent Boundary Layers

We address the dynamical and statistical description of stably stratified turbulent boundary layers with the important example of the atmospheric boundary layer with a stable temperature stratification in mind. Traditional approaches to this problem, based on the profiles of mean quantities, velocity second-order correlations, and dimensional estimates of the turbulent thermal flux run into a well known difficulty, predicting the suppression of turbulence at a small critical value of the Richardson number, in contradiction with observations. Phenomenological attempts to overcome this problem suffer from various theoretical inconsistencies. Here we present an approach taking into full account all the second-order statistics, which allows us to respect the conservation of total mechanical energy. The analysis culminates in an analytic solution of the profiles of all mean quantities and all second-order correlations removing the unphysical predictions of previous theories. We propose that the approach taken here is sufficient to describe the lower parts of the atmospheric boundary layer, as long as the Richardson number does not exceed an order of unity. For much higher Richardson numbers the physics may change qualitatively, requiring careful consideration of the potential Kelvin-Helmoholtz waves and their interaction with the vortical turbulence.

nlin.CD↗

arXiv2007

On the Self-Affine Roughness of a Crack Front in Heterogeneous Media

The long-ranged elastic model, which is believed to describe the evolution of a self-affine rough crack-front, is analyzed to linear and non-linear orders. It is shown that the nonlinear terms, while important in changing the front dynamics, are not changing the scaling exponent which characterizes the roughness of the front. The scaling exponent thus predicted by the model is much smaller than the one observed experimentally. The inevitable conclusion is that the gap between the results of experiments and the model that is supposed to describe them is too large, and some new physics has to be invoked for another model.

cond-mat.dis-nn↗

arXiv2007

Elasticity with Arbitrarily Shaped Inhomogeneity

A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding medium. In this paper we present a new, semi-analytic method for finding the stress tensor for an infinite plate with such an inhomogeneity. The solution involves two conformal maps, one from the inside and the second from the outside of the unit circle to the inside, and respectively outside, of the inhomogeneity. The method provides a solution by matching the conformal maps on the boundary between the inhomogeneity and the surrounding material. This matching converges well only for relatively mild distortions of the unit circle due to reasons which will be discussed in the article. We provide a comparison of the present result to known previous results.

cond-mat.mtrl-sci↗

arXiv2007

Colloquium: Theory of Drag Reduction by Polymers in Wall Bounded Turbulence

The flow of fluids in channels, pipes or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases many-folds when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered in the mid-twentieth century that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this colloquium review we first summarize the phenomenology of drag reduction by polymers, stressing both its universal and non-universal aspects, and then proceed to review a recent theory that provides a quantitative explanation of all the known phenomenology. We treat both flexible and rod-like polymers, explaining the existence of universal properties like the Maximum Drag Reduction (MDR) asymptote, as well as non-universal cross-over phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally we also discuss other agents for drag reduction with a stress on the important example of bubbles.

nlin.CD↗

arXiv2007

Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation II: Analysis of Simulated Amorphous Silicon

In the preceding paper, we developed an athermal shear-transformation-zone (STZ) theory of amorphous plasticity. Here we use this theory in an analysis of numerical simulations of plasticity in amorphous silicon by Demkowicz and Argon (DA). In addition to bulk mechanical properties, those authors observed internal features of their deforming system that challenge our theory in important ways. We propose a quasithermodynamic interpretation of their observations in which the effective disorder temperature, generated by mechanical deformation well below the glass temperature, governs the behavior of other state variables that fall in and out of equilibrium with it. Our analysis points to a limitation of either the step-strain procedure used by DA in their simulations, or the STZ theory in its ability to describe rapid transients in stress-strain curves, or perhaps to both. Once we allow for this limitation, we are able to bring our theoretical predictions into accurate agreement with the simulations.

cond-mat.mtrl-sci↗

arXiv2006

Free-Boundary Dynamics in Elasto-plastic Amorphous Solids: The Circular Hole Problem

We develop an athermal shear-transformation-zone (STZ) theory of plastic deformation in spatially inhomogeneous, amorphous solids. Our ultimate goal is to describe the dynamics of the boundaries of voids or cracks in such systems when they are subjected to remote, time-dependent tractions. The theory is illustrated here for the case of a circular hole in an infinite two-dimensional plate, a highly symmetric situation that allows us to solve much of the problem analytically. In spite of its special symmetry, this example contains many general features of systems in which stress is concentrated near free boundaries and deforms them irreversibly. We depart from conventional treatments of such problems in two ways. First, the STZ analysis allows us to keep track of spatially heterogeneous, internal state variables such as the effective disorder temperature, which determines plastic response to subsequent loading. Second, we subject the system to stress pulses of finite duration, and therefore are able to observe elasto-plastic response during both loading and unloading. We compute the final deformations and residual stresses produced by these stress pulses. Looking toward more general applications of these results, we examine the possibility of constructing a boundary-layer theory that might be useful in less symmetric situations.

cond-mat.mtrl-sci↗

arXiv2006

Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results

In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and nonlinear fields coincide. The argument depended on an assumption of continuity of the solutions as a function of a parameter. The aim of this paper is to provide a rigorous proof for the validity of the assumption. In addition we clarify here when the swap of a nonlinear model by a linear one will not work.

nlin.CD↗

arXiv2006

Direct Identification of the Glass Transition: Growing Length Scale and the Onset of Plasticity

Understanding the mechanical properties of glasses remains elusive since the glass transition itself is not fully understood, even in well studied examples of glass formers in two dimensions. In this context we demonstrate here: (i) a direct evidence for a diverging length scale at the glass transition (ii) an identification of the glass transition with the disappearance of fluid-like regions and (iii) the appearance in the glass state of fluid-like regions when mechanical strain is applied. These fluid-like regions are associated with the onset of plasticity in the amorphous solid. The relaxation times which diverge upon the approach to the glass transition are related quantitatively.

cond-mat.stat-mech↗

arXiv2006

Athermal Shear-Transformation-Zone Theory of Amorphous Plastic Deformation I: Basic Principles

We develop an athermal version of the shear-transformation-zone (STZ) theory of amorphous plasticity in materials where thermal activation of irreversible molecular rearrangements is negligible or nonexistent. In many respects, this theory has broader applicability and yet is simpler than its thermal predecessors. For example, it needs no special effort to assure consistency with the laws of thermodynamics, and the interpretation of yielding as an exchange of dynamic stability between jammed and flowing states is clearer than before. The athermal theory presented here incorporates an explicit distribution of STZ transition thresholds. Although this theory contains no conventional thermal fluctuations, the concept of an effective temperature is essential for understanding how the STZ density is related to the state of disorder of the system.

cond-mat.mtrl-sci↗

arXiv2006

Oscillatory Instability in Two-Dimensional Dynamic Fracture

The stability of a rapid dynamic crack in a two dimensional infinite strip is studied in the framework of Linear Elasticity Fracture Mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack becomes unstable by a finite wavelength oscillatory mode at a velocity $v_c$, $0.8c_R<v_c<0.85c_R$, where $c_R$ is the Rayleigh wave speed. The relevance of this theoretical calculation to the oscillatory instability reported in the companion experimental Letter is discussed.

cond-mat.mtrl-sci↗

arXiv2006

Statistical Mechanics of the Glass Transition

The statistical mechanics of simple glass forming systems in 2 dimensions is worked out. The glass disorder is encoded via a Voronoi tessellation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, $T_g$ and $T_k$, the first associated with jamming and the second associated with the appearance of a quasi-crystal at very low temperatures.

cond-mat.stat-mech↗

arXiv2006

Reynolds number dependence of drag reduction by rod-like polymers

We present experimental and theoretical results addressing the Reynolds number (Re) dependence of drag reduction by sufficiently large concentrations of rod-like polymers in turbulent wall-bounded flows. It is shown that when Re is small the drag is {\em enhanced}. On the other hand when Re increases the drag is reduced and eventually the Maximal Drag Reduction (MDR) asymptote is attained. The theory is shown to be in excellent agreement with experiments, rationalizing and explaining all the universal and the non-universal aspects of drag reduction by rod-like polymers.

nlin.CD↗

arXiv2006

Analytic Model of the Universal Structure of Turbulent Boundary Layers

Turbulent boundary layers exhibit a universal structure which nevertheless is rather complex, being composed of a viscous sub-layer, a buffer zone, and a turbulent log-law region. In this letter we present a simple analytic model of turbulent boundary layers which culminates in explicit formulae for the profiles of the mean velocity, the kinetic energy and the Reynolds stress as a function of the distance from the wall. The resulting profiles are in close quantitative agreement with measurements over the entire structure of the boundary layer, without any need of re-fitting in the different zones.

nlin.CD↗

arXiv2006

Dissipative Visco-plastic Deformation in Dynamic Fracture: Tip Blunting and Velocity Selection

Dynamic fracture in a wide class of materials reveals "fracture energy" $Γ$ much larger than the expected nominal surface energy due to the formation of two fresh surfaces. Moreover, the fracture energy depends on the crack velocity, $Γ=Γ(v)$. We show that a simple dynamical theory of visco-plasticity coupled to asymptotic pure linear-elasticity provides a possible explanation to the above phenomena. The theory predicts tip blunting characterized by a dynamically determined crack tip radius of curvature. In addition, we demonstrate velocity selection for cracks in fixed-grip strip geometry accompanied by the identification of $Γ$ and its velocity dependence.

cond-mat.mtrl-sci↗

arXiv2006

On the Anomalous Scaling Exponents in Nonlinear Models of Turbulence

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence. We achieve this by constructing, for any given nonlinear model, a linear model of passive advection of an auxiliary field whose anomalous scaling exponents are the same as the scaling exponents of the nonlinear problem. The statistics of the auxiliary linear model are dominated by `Statistically Preserved Structures' which are associated with exact conservation laws. The latter can be used for example to determine the value of the anomalous scaling exponent of the second order structure function. The approach is equally applicable to shell models and to the Navier-Stokes equations.

nlin.CD↗