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Sep 18, 2013
09/13

by
Victor L'vov; Itamar Procaccia

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This is a paper written for the wider physics community, not necessarily experts in turbulence.

Source: http://arxiv.org/abs/chao-dyn/9606015v1

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Sep 21, 2013
09/13

by
Edan Lerner; Itamar Procaccia

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Strongly correlated amorphous solids are a class of glass-formers whose inter-particle potential admits an approximate inverse power-law form in a relevant range of inter-particle distances. We study the steady-state plastic flow of such systems, firstly in the athermal, quasi-static limit, and secondly at finite temperatures and strain rates. In all cases we demonstrate the usefulness of scaling concepts to reduce the data to universal scaling functions where the scaling exponents are...

Source: http://arxiv.org/abs/0905.3319v1

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Sep 21, 2013
09/13

by
Victor L'vov; Itamar Procaccia

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The lectures presented by one of us (IP) at the Les Houches summer school dealt with the scaling properties of high Reynolds number turbulence in fluid flows. The results presented are available in the literature and there is no real need to reproduce them here. Quite on the contrary, some of the basic tools of the field and theoretical techniques are not available in a pedagogical format, and it seems worthwhile to present them here for the benefit of the interested student. We begin with a...

Source: http://arxiv.org/abs/chao-dyn/9502010v1

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Sep 20, 2013
09/13

by
Luca Biferale; Itamar Procaccia

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We discuss the problem of anisotropy and intermittency in statistical theory of high Reynolds-number turbulence (and turbulent transport). We present a detailed description of the new tools that allow effective data analysis and systematic theoretical studies such as to separate isotropic from anisotropic aspects of turbulent statistical fluctuations. Employing the invariance of the equations of fluid mechanics to all rotations, we show how to decompose the (tensorial) statistical objects in...

Source: http://arxiv.org/abs/nlin/0404014v1

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Sep 21, 2013
09/13

by
Smarajit Karmakar; Itamar Procaccia

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Over the last decade computer simulations have had an increasing role in shedding light on difficult statistical physical phenomena and in particular on the ubiquitous problem of the glass transition. Here in a wide variety of materials the viscosity of a super-cooled liquid increases by many orders of magnitude upon decreasing the temperature over a modest range. A natural concern in these computer simulation is the very small size of the simulated systems compared to experimental ones,...

Source: http://arxiv.org/abs/1204.6634v2

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Sep 19, 2013
09/13

by
Yossi Cohen; Itamar Procaccia

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The stress field at the tip of a crack of a thin plate of elastic material that is broken due to a mode III shear tearing has a universal form with a non-universal amplitude, known as the stress intensity factor, which depends on the crack length and the boundary conditions. We present in this paper exact analytic results for this stress intensity factor, thus enriching the small number of exact results that can be obtained within Linear Elastic Fracture Mechanics (LEFM).

Source: http://arxiv.org/abs/1010.2924v3

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Jul 20, 2013
07/13

by
Eran Bouchbinder; Itamar Procaccia

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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

Source: http://arxiv.org/abs/cond-mat/0609224v1

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Sep 17, 2013
09/13

by
Anders Levermann; Itamar Procaccia

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We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth patterns are compared to those obtained by the best algorithms of direct numerical solutions. The fractal dimension of the patterns is discussed.

Source: http://arxiv.org/abs/cond-mat/0305521v1

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Sep 23, 2013
09/13

by
Smarajit Karmakar; Itamar Procaccia

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The dramatic slowing down associated with the glass transition cannot be fully understood without an associated static length that is expected to increase rapidly as the temperature is reduced. The search for such a length was long and arduous, without a universally accepted candidate at hand. Recently a natural such length $\xi_s$ was proposed, stemming from a cross-over between plastic and elastic mechanical responses of the material. In this Letter we show that supercooled liquids in which...

Source: http://arxiv.org/abs/1105.4053v1

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Sep 19, 2013
09/13

by
Anders Levermann; Itamar Procaccia

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Experiments in quasi 2-dimensional geometry (Hele Shaw cells) in which a fluid is injected into a visco-elastic medium (foam, clay or associating-polymers) show patterns akin to fracture in brittle materials, very different from standard Laplacian growth patterns of viscous fingering. An analytic theory is lacking since a pre-requisite to describing the fracture of elastic material is the solution of the bi-Laplace rather than the Laplace equation. In this Letter we close this gap, offering a...

Source: http://arxiv.org/abs/cond-mat/0208403v1

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Sep 18, 2013
09/13

by
Itamar Procaccia; Jacques Zylberg

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We employ a recently developed model that allows the study of two-dimensional brittle crack propagation under fixed grip boundary conditions. The crack development highlights the importance of voids which appear ahead of the crack as observed in experiments on the nano-scale. The appearance of these voids is responsible for roughening the crack path on small scales, in agreement with theoretical expectations. With increasing speed of propagation one observes the branching instabilities that...

Source: http://arxiv.org/abs/1211.4528v1

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Sep 22, 2013
09/13

by
Benny Davidovich; Itamar Procaccia

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Diffusion Limited Aggregation (DLA) is a model of fractal growth that was introduced in 1981 and had since attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. Despite tremendous efforts there is no theory to compute the fractal dimension of DLA from first principles. In this Letter we offer such a theory for fractal growth patterns in two dimensions, including DLA as a particular case. In this theory the fractal dimension of...

Source: http://arxiv.org/abs/cond-mat/0003044v1

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Sep 18, 2013
09/13

by
Roberto Benzi; Itamar Procaccia

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Direct Numerical Simulations established that the FENE-P model of viscoelastic flows exhibits the phenomenon of turbulent drag reduction which is caused in experiments by dilute polymeric additives. To gain analytic understanding of the phenomenon we introduce in this Letter a simple 1-dimensional model of the FENE-P equations. We demonstrate drag reduction in the simple model, and explain analytically the main observations which include (i) reduction of velocity gradients for fixed throughput...

Source: http://arxiv.org/abs/cond-mat/0210523v1

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Sep 20, 2013
09/13

by
Victor L'vov; Itamar Procaccia

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The scaling properties of correlation functions of non-scalar fields (constructed from velocity derivatives) in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. It is explained that these exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. This set has never been measured in either numerical or laboratory experiments. These exponents are important for the general theory of turbulence, but also for...

Source: http://arxiv.org/abs/chao-dyn/9603001v1

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Sep 18, 2013
09/13

by
Eran Bouchbinder; Itamar Procaccia

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In spite of the apparent similarity of micro-branching instabilities in different brittle materials, we propose that the physics determining the typical length- and time-scales characterizing the post-instability patterns differ greatly from material to material. We offer a scaling theory connecting the pattern characteristics to material properties (like molecular weight) in brittle plastics like PMMA, and stress the fundamental differences with patterns in glass which are crucially influenced...

Source: http://arxiv.org/abs/cond-mat/0504438v1

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Sep 19, 2013
09/13

by
Benny Davidovich; Itamar Procaccia

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We employ the recently introduced conformal iterative construction of Diffusion Limited Aggregates (DLA) to study the multifractal properties of the harmonic measure. The support of the harmonic measure is obtained from a dynamical process which is complementary to the iterative cluster growth. We use this method to establish the existence of a series of random scaling functions that yield, via the thermodynamic formalism of multifractals, the generalized dimensions D(q) of DLA for q >= 1....

Source: http://arxiv.org/abs/chao-dyn/9812026v1

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Sep 20, 2013
09/13

by
Yossi Cohen; Itamar Procaccia

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Motivated by recent experiments, we present a study of the dynamics of cracks in thin sheets. While the equations of elasticity for thin plates are well known, there remains the question of path selection for a propagating crack. We invoke a generalization of the principle of local symmetry to provide a criterion for path selection and demonstrate qualitative agreement with the experimental findings. The nature of the singularity at the crack tip is studied with and without the interference of...

Source: http://arxiv.org/abs/1002.4207v4

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Sep 20, 2013
09/13

by
Victor L'vov; Itamar Procaccia

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Elements of the analytic structure of anomalous scaling and intermittency in fully developed hydrodynamic turbulence are described. We focus here on the structure functions of velocity differences that satisfy inertial range scaling laws $S_n(R)\sim R^{\zeta_n}$, and the correlation of energy dissipation $K_{\epsilon\epsilon}(R) \sim R^{-\mu}$. The goal is to understand the exponents $\zeta_n$ and $\mu$ from first principles. In paper II of this series it was shown that the existence of an...

Source: http://arxiv.org/abs/chao-dyn/9507007v2

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Sep 21, 2013
09/13

by
Itamar Procaccia; Ido Regev

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Tetrahedral liquids such as water and silica-melt show unusual thermodynamic behavior such as a density maximum and an increase in specific-heat when cooled to low temperatures. There is a debate in the literature whether these phenomena stem from a phase transition into a low-density and high-density liquid phases, which occur in the supercooled regime. Here we consider a model of tetrahedral liquids for which we construct a volume-constrained statistical mechanical theory which quantifies the...

Source: http://arxiv.org/abs/1108.1225v2

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Sep 23, 2013
09/13

by
Yossi Cohen; Itamar Procaccia

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This Letter is motivated by some recent experiments on pan-cake shaped nano-samples of metallic glass that indicate a decline in the measured shear modulus upon decreasing the sample radius. Similar measurements on crystalline samples of the same dimensions showed a much more modest change. In this Letter we offer a theory of this phenomenon; we argue that such results are generically expected for any amorphous solid, with the main effect being related to the increased contribution of surfaces...

Source: http://arxiv.org/abs/1212.4690v1

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Jul 20, 2013
07/13

by
Edan Lerner; Itamar Procaccia

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We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) which are long lived but each of which relaxes as a simple function of time. Without the clusters the relaxation of the background is simply determined by one typical length which we deduce from an elementary statistical mechanical...

Source: http://arxiv.org/abs/0804.1205v1

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Sep 22, 2013
09/13

by
Edan Lerner; Itamar Procaccia

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A number of current theories of plasticity in amorphous solids assume at their basis that plastic deformations are spatially localized. We present in this paper a series of numerical experiments to test the degree of locality of plastic deformation. These experiments increase in terms of the stringency of the removal of elastic contributions to the observed elasto-plastic deformations. It is concluded that for all our simulational protocols the plastic deformations are not localized, and their...

Source: http://arxiv.org/abs/0901.3477v2

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Sep 23, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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In this paper we derive here, on the basis of the NS eqs. a set of fusion rules for correlations of velocity differences when all the separation are in the inertial interval. Using this we consider the standard hierarchy of equations relating the $n$-th order correlations (originating from the viscous term in the NS eq.) to $n+1$'th order (originating from the nonlinear term) and demonstrate that for fully unfused correlations the viscous term is negligible. Consequently the hierarchic chain is...

Source: http://arxiv.org/abs/chao-dyn/9607006v1

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Sep 18, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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The main difficulty of statistical theories of fluid turbulence is the lack of an obvious small parameter. In this paper we show that the formerly established fusion rules can be employed to develop a theory in which Kolmogorov's statistics of 1941 acts as the zero order, or background statistics, and the anomalous corrections to the K41 scaling exponents $\zeta_n$ of the $n$th order structure functions can be computed analytically. The crux of the method consists of renormalizing a 4-point...

Source: http://arxiv.org/abs/nlin/0005025v2

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Sep 20, 2013
09/13

by
Jean-Pierre Eckmann; Itamar Procaccia

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The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with...

Source: http://arxiv.org/abs/0802.4346v1

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Sep 22, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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We propose a scheme for the calculation from the NS equations of the scaling exponents $\zeta_n$ of the $n$th order correlators in fully developed hydrodynamic turbulence. The scheme is nonperturbative and constructed to respect the fundamental rescaling symmetry of the Euler equation. It constitutes an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of $\zeta_n$. As a consequence $\zeta_n$ are determined by solvability conditions and not...

Source: http://arxiv.org/abs/chao-dyn/9707015v1

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Sep 23, 2013
09/13

by
Itamar Procaccia; K. R. Sreenivasan

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We present a personal view of the state of the art in turbulence research. We summarize first the main achievements in the recent past, and then point ahead to the main challenges that remain for experimental and theoretical efforts.

Source: http://arxiv.org/abs/0710.5446v1

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Sep 18, 2013
09/13

by
Victor S. L'vov; Itamar Procaccia

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It is shown that the idea that scaling behavior in turbulence is limited by one outer length $L$ and one inner length $\eta$ is untenable. Every n'th order correlation function of velocity differences $\bbox{\cal F}_n(\B.R_1,\B.R_2,\dots)$ exhibits its own cross-over length $\eta_{n}$ to dissipative behavior as a function of, say, $R_1$. This length depends on $n$ {and on the remaining separations} $R_2,R_3,\dots$. One result of this Letter is that when all these separations are of the same...

Source: http://arxiv.org/abs/chao-dyn/9606018v1

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Sep 18, 2013
09/13

by
Omri Gat; Itamar Procaccia; Reuven Zeitak

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We present a numerical method which is used to calculate anomalous scaling exponents of structure functions in the Kraichnan passive scalar advection model (R. H. Kraichnan, Phys. Fluids {\bf11}, 945 (1968)). This Monte-Carlo method, which is applicable in any space dimension, is based on the Lagrangian path interpretation of passive scalar dynamics, and uses the recently discovered equivalence between scaling exponents of structure functions and relaxation rates in the stochastic shape...

Source: http://arxiv.org/abs/cond-mat/9803190v1

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Sep 18, 2013
09/13

by
Victor L'vov; Evgenii Podivilov; Itamar Procaccia

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It is shown that the description of anomalous scaling in turbulent systems requires the simultaneous use of two normalization scales. This phenomenon stems from the existence of two independent (infinite) sets of anomalous scaling exponents that appear in leading order, one set due to infrared anomalies, and the other due to ultraviolet anomalies. To expose this clearly we introduce here a set of local fields whose correlation functions depend simultaneously on the the two sets of exponents....

Source: http://arxiv.org/abs/chao-dyn/9601001v1

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Sep 19, 2013
09/13

by
Yoram Cohen; Anna Pomyalov; Itamar Procaccia

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We analyze numerically the time-dependent linear operators that govern the dynamics of Eulerian correlation functions of a decaying passive scalar advected by a stationary, forced 2-dimensional Navier-Stokes turbulence. We show how to naturally discuss the dynamics in terms of effective compact operators that display Eulerian Statistically Preserved Structures which determine the anomalous scaling of the correlation functions. In passing we point out a bonus of the present approach, in...

Source: http://arxiv.org/abs/nlin/0303006v1

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Sep 18, 2013
09/13

by
Felipe Barra; Mauricio Herrera; Itamar Procaccia

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An exact integro-differential equation for the conformal map from the unit circle to the boundary of an evolving cavity in a stressed 2-dimensional solid is derived. This equation provides an accurate description of the dynamics of precursors to fracture when surface diffusion is important. The solution predicts the creation of sharp grooves that eventually lead to material failure via rapid fracture. Solutions of the new equation are demonstrated for the dynamics of an elliptical cavity and...

Source: http://arxiv.org/abs/cond-mat/0212100v2

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Sep 21, 2013
09/13

by
Edan Lerner; Itamar Procaccia; Jacques Zylberg

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In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of up-scaled quasi-species that allow the construction of a theory with a finite number of 'states'. Once constructed, the theory identifies a typical scale $\xi$ that increases rapidly with lowering the temperature and which determines the...

Source: http://arxiv.org/abs/0902.1888v1

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Sep 19, 2013
09/13

by
Oleg Kupervasser; Zeev Olami; Itamar Procaccia

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The roughening of expanding flame fronts by the accretion of cusp-like singularities is a fascinating example of the interplay between instability, noise and nonlinear dynamics that is reminiscent of self-fractalization in Laplacian growth patterns. The nonlinear integro-differential equation that describes the dynamics of expanding flame fronts is amenable to analytic investigations using pole decomposition. This powerful technique allows the development of a satisfactory understanding of the...

Source: http://arxiv.org/abs/nlin/0302019v2

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Sep 18, 2013
09/13

by
Daniel Segel; Victor L'vov; Itamar Procaccia

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In turbulent flows the $n$'th order structure functions $S_n(R)$ scale like $R^{\zeta_n}$ when $R$ is in the "inertial range". Extended Self-Similarity refers to the substantial increase in the range of power law behaviour of $S_n(R)$ when they are plotted as a function of $S_2(R)$ or $S_3(R)$. In this Letter we demonstrate this phenomenon analytically in the context of the ``multiscaling" turbulent advection of a passive scalar. This model gives rise to a series of differential...

Source: http://arxiv.org/abs/chao-dyn/9601002v1

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Sep 21, 2013
09/13

by
Eran Bouchbinder; Itamar Procaccia; Shani Sela

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Structure functions of rough fracture surfaces in isotropic materials exhibit complicated scaling properties due to the broken isotropy in the fracture plane generated by a preferred propagation direction. Decomposing the structure functions into the even order irreducible representations of the SO(2) symmetry group (indexed by $m=0,2,4...$) results in a lucid and quickly convergent description. The scaling exponent of the isotropic sector ($m=0$) dominates at small length scales. One can...

Source: http://arxiv.org/abs/cond-mat/0508549v2

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Sep 22, 2013
09/13

by
Felipe Barra; Anders Levermann; Itamar Procaccia

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The method of iterated conformal maps is developed for quasi-static fracture of brittle materials, for all modes of fracture. Previous theory, that was relevant for mode III only, is extended here to mode I and II. The latter require solution of the bi-Laplace rather than the Laplace equation. For all cases we can consider quenched randomness in the brittle material itself, as well as randomness in the succession of fracture events. While mode III calls for the advance (in time) of one analytic...

Source: http://arxiv.org/abs/cond-mat/0205132v1

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Sep 22, 2013
09/13

by
Smarajit Karmakar; Edan Lerner; Itamar Procaccia

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We derive expressions for the lowest nonlinear elastic constants of amorphous solids in athermal conditions (up to third order), in terms of the interaction potential between the constituent particles. The effect of these constants cannot be disregarded when amorphous solids undergo instabilities like plastic flow or fracture in the athermal limit; in such situations the elastic response increases enormously, bringing the system much beyond the linear regime. We demonstrate that the existing...

Source: http://arxiv.org/abs/1004.2198v1

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Sep 21, 2013
09/13

by
H. G. E. Hentschel; Itamar Procaccia

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We address the relaxation dynamics in hydrogen-bonded super-cooled liquids near the glass transition, measured via Broad-Band Dielectric Spectroscopy (BDS). We propose a theory based on decomposing the relaxation of the macroscopic dipole moment into contributions from hydrogen bonded clusters of $s$ molecules, with $s_{min}\le s \le s_{max}$. The existence of $s_{max}$ is due to dynamical arrest and its value may depend on the cooling protocol and on the aging time. The existence of $s_{max}$...

Source: http://arxiv.org/abs/0709.4404v1

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Sep 20, 2013
09/13

by
Eran Bouchbinder; Joachim Mathiesen; Itamar Procaccia

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We propose a theoretical model for branching instabilities in 2-dimensional fracture, offering predictions for when crack branching occurs, how multiple cracks develop, and what is the geometry of multiple branches. The model is based on equations of motion for crack tips which depend only on the time dependent stress intensity factors. The latter are obtained by invoking an approximate relation between static and dynamic stress intensity factors, together with an essentially exact calculation...

Source: http://arxiv.org/abs/cond-mat/0410448v1

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Sep 18, 2013
09/13

by
Benny Davidovitch; Anders Levermann; Itamar Procaccia

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Diffusion Limited Aggregation (DLA) is a model of fractal growth that had attained a paradigmatic status due to its simplicity and its underlying role for a variety of pattern forming processes. We present a convergent calculation of the fractal dimension D of DLA based on a renormalization scheme for the first Laurent coefficient of the conformal map from the unit circle to the expanding boundary of the fractal cluster. The theory is applicable from very small (2-3 particles) to asymptotically...

Source: http://arxiv.org/abs/cond-mat/0008053v1

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Sep 18, 2013
09/13

by
Victor L'vov; Evgenii Podivilov; Itamar Procaccia

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It is shown that the generalization of the Navier-Stokes equations to a theory with $N$ ``internal state" copies of the velocity fields is a step in a wrong direction: the $N\to\infty$ limit has no physical sense and produces wrong results, whereas the treatment of the first order terms in $1/N$ is even more complicated than the initial problem of description of turbulence in the frame of the Navier-Stokes equation.

Source: http://arxiv.org/abs/chao-dyn/9601003v1

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Sep 18, 2013
09/13

by
Edan Lerner; Itamar Procaccia; Ido Regev

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The Shintani-Tanaka model is a glass-forming system whose constituents interact via anisotropic potential depending on the angle of a unit vector carried by each particle. The decay of time-correlation functions of the unit vectors exhibits the characteristics of generic relaxation functions during glass transitions. In particular it exhibits a 'stretched exponential' form, with the stretching index beta depending strongly on the temperature. We construct a quantitative theory of this...

Source: http://arxiv.org/abs/0806.3685v1

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Sep 21, 2013
09/13

by
Smarajit Karmakar; Edan Lerner; Itamar Procaccia

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The art of making structural, polymeric and metallic glasses is rapidly developing with many applications. A limitation to their use is their mechanical stability: under increasing external strain all amorphous solids respond elastically to small strains but have a finite yield stress which cannot be exceeded without effecting a plastic response which typically leads to mechanical failure. Understanding this is crucial for assessing the risk of failure of glassy materials under mechanical...

Source: http://arxiv.org/abs/1008.3967v1

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Sep 19, 2013
09/13

by
Smarajit Karmakar; Edan Lerner; Itamar Procaccia

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Amorphous solids that underwent a strain in one direction such that they responded in a plastic manner `remember' that direction also when relaxed back to a state with zero mean stress. We address the question `what is the order parameter that is responsible for this memory?' and is therefore the reason for the different subsequent responses of the material to strains in different directions. We identify such an order parameter which is readily measurable, we discuss its trajectory along the...

Source: http://arxiv.org/abs/0910.4281v2

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Jul 20, 2013
07/13

by
Yoram Cohen; Thomas Gilbert; Itamar Procaccia

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It was conjectured recently that Statiscally Preserved Structures underlie the statistical physics of turbulent transport processes. We analyze here in detail the time-dependent (non compact) linear operator that governs the dynamics of correlation functions in the case of shell models of passive scalar advection. The problem is generic in the sense that the driving velocity field is neither Gaussian nor $\delta$-correlated in time. We show how to naturally discuss the dynamics in terms of an...

Source: http://arxiv.org/abs/nlin/0107016v1

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Jul 20, 2013
07/13

by
Eran Bouchbinder; Anna Pomyalov; Itamar Procaccia

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Dynamic fracture in a wide class of materials reveals "fracture energy" $\Gamma$ 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, $\Gamma=\Gamma(v)$. 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...

Source: http://arxiv.org/abs/cond-mat/0604050v2

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Sep 20, 2013
09/13

by
Laurent Boué; Victor L'vov; Itamar Procaccia

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Kelvin waves propagating on quantum vortices play a crucial role in the phenomenology of energy dissipation of superfluid turbulence. Previous theoretical studies have consistently focused on the zero-temperature limit of the statistical physics of Kelvin-wave turbulence. In this letter, we go beyond this athermal limit by introducing a small but finite temperature in the form of non-zero mutual friction dissipative force; A situation regularly encountered in actual experiments of superfluid...

Source: http://arxiv.org/abs/1205.0461v3

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6.0

Jun 30, 2018
06/18

by
Itamar Procaccia; Corrado Rainone; Murari Singh

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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...

Topics: Disordered Systems and Neural Networks, Condensed Matter

Source: http://arxiv.org/abs/1704.05285

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59

Sep 18, 2013
09/13

by
Felipe Barra; Benny Davidovitch; Itamar Procaccia

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The method of iterated conformal maps for the study of Diffusion Limited Aggregates (DLA) is generalized to the study of Laplacian Growth Patterns and related processes. We emphasize the fundamental difference between these processes: DLA is grown serially with constant size particles, while Laplacian patterns are grown by advancing each boundary point in parallel, proportionally to the gradient of the Laplacian field. We introduce a 2-parameter family of growth patterns that interpolates...

Source: http://arxiv.org/abs/cond-mat/0105608v1