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Full-Text Articles in Physics
Indentation Of Ultrathin Elastic Films And The Emergence Of Asymptotic Isometry, Dominic Vella, Jianghui Huang, Narayanan Menon, Thomas P. Russell, Benny Davidovitch
Indentation Of Ultrathin Elastic Films And The Emergence Of Asymptotic Isometry, Dominic Vella, Jianghui Huang, Narayanan Menon, Thomas P. Russell, Benny Davidovitch
Benny Davidovitch
We study the indentation of a thin elastic film floating at the surface of a liquid. We focus on the onset of radial wrinkles at a threshold indentation depth and the evolution of the wrinkle pattern as indentation progresses far beyond this threshold. Comparison between experiments on thin polymer films and theoretical calculations shows that the system very quickly reaches the far from threshold regime, in which wrinkles lead to the relaxation of azimuthal compression. Furthermore, when the indentation depth is sufficiently large that the wrinkles cover most of the film, we recognize a novel mechanical response in which the …
A Comparative Analysis Of Numerical Approaches To The Mechanics Of Elastic Sheets, Michael Taylor, Benny Davidovitch, Zhanlong Qiu, Katia Bertoldi
A Comparative Analysis Of Numerical Approaches To The Mechanics Of Elastic Sheets, Michael Taylor, Benny Davidovitch, Zhanlong Qiu, Katia Bertoldi
Benny Davidovitch
No abstract provided.
A Sheet On Deformable Sphere: "Wrinklogami" Patterns Suppress Curvature-Induced Delamination, Evan Hohlfeld, Benny Davidovitch
A Sheet On Deformable Sphere: "Wrinklogami" Patterns Suppress Curvature-Induced Delamination, Evan Hohlfeld, Benny Davidovitch
Benny Davidovitch
No abstract provided.
Mechanics Of Large Folds In Thin Interfacial Films, Vincent Demery, Benny Davidovitch, Christian D. Santangelo
Mechanics Of Large Folds In Thin Interfacial Films, Vincent Demery, Benny Davidovitch, Christian D. Santangelo
Benny Davidovitch
A thin film at a liquid interface responds to uniaxial confinement by wrinkling and then by folding; its shape and energy have been computed exactly before self contact. Here, we address the mechanics of large folds, i.e. folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers and capillary rafts, we discuss how to incorporate film weight, selfadhesion …
Roadmap To The Morphological Instabilities Of A Stretched Twisted Ribbon, Julien Chopin, Vincent Demery, Benny Davidovitch
Roadmap To The Morphological Instabilities Of A Stretched Twisted Ribbon, Julien Chopin, Vincent Demery, Benny Davidovitch
Benny Davidovitch
We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive theoretical framework through which we construct a 4D phase diagram of this basic system, spanned by the exerted twist and tension as well as the thickness and length of the ribbon. Different types of instabilities appear in various "corners" of this 4D parameter space, and are addressed through distinct types of asymptotic methods. Our theory employs three instruments, whose concerted implementation is necessary to …
Convergent Calculation Of The Asymptotic Dimension Of Diffusion Limited Aggregates: Scaling And Renormalization Of Small Clusters, Benny Davidovitch, Anders Levermann, Itamar Procaccia
Convergent Calculation Of The Asymptotic Dimension Of Diffusion Limited Aggregates: Scaling And Renormalization Of Small Clusters, Benny Davidovitch, Anders Levermann, Itamar Procaccia
Benny Davidovitch
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 large (n⃗ ∞) clusters. The computed dimension is D=1.713±0.003.
Far From Threshold Buckling Analysis Of Thin Films, B Davidovitch, R Schroll, D. Vella, M. Adda-Bedia, E. Cerda
Far From Threshold Buckling Analysis Of Thin Films, B Davidovitch, R Schroll, D. Vella, M. Adda-Bedia, E. Cerda
Benny Davidovitch
Thin films buckle easily and form wrinkled states in regions of well defined size. The extent of a wrinkled region is typically assumed to reflect the zone of in-plane compressive stresses prior to buckling, but recent experiments on ultrathin sheets have shown that wrinkling patterns are signif- icantly longer and follow different scaling laws than those predicted by standard buckling theory. Here we focus on a simple setup to show the striking differences between near-threshold buckling and the analysis of wrinkle patterns in very thin films, which are typically far from threshold.
Reaction- Limited Sintering In Nearly Saturated Environments, Benny Davidovitch, Deniz Ertas, Thomas C. Halsey
Reaction- Limited Sintering In Nearly Saturated Environments, Benny Davidovitch, Deniz Ertas, Thomas C. Halsey
Benny Davidovitch
We study the shape and growth rate of necks between sintered spheres with dissolutionprecipitation dynamics in the reaction-limited regime. We determine the critical shape that separates those initial neck shapes that can sinter from those that necessarily dissolve, as well as the asymptotic evolving shape of sinters far from the critical shape. We compare our results with past results for the asymptotic neck shape in closely related but more complicated models of surface dynamics; in particular we confirm a scaling conjecture, originally due to Kuczinsky. Finally, we consider the relevance of this problem to the diagenesis of sedimentary rocks and …
The Average Shape Of Transport-Limited Aggregates, Benny Davidovitch, Jachyuk Choi, Martin Z. Bazant
The Average Shape Of Transport-Limited Aggregates, Benny Davidovitch, Jachyuk Choi, Martin Z. Bazant
Benny Davidovitch
We study the relation between stochastic and continuous transport-limited growth models, which generalize conformal-mapping formulations of diffusion-limited aggregation (DLA) and viscous fingering, respectively. We derive a nonlinear integro-differential equation for the asymptotic shape (average conformal map) of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation, where the interface moves at its local expected velocity. Our equation accurately describes advection-diffusion-limited aggregation (ADLA), and, due to nonlinear averaging over fluctuations, the average ADLA cluster is similar, but not identical, to an exact solution of the mean-field dynamics. Similar results should apply to all models in our class, thus explaining the …
Spreading Of Thin Films Assisted By Thermal Fluctuations, Benny Davidovitch, Esteban Moro, Howard A. Stone
Spreading Of Thin Films Assisted By Thermal Fluctuations, Benny Davidovitch, Esteban Moro, Howard A. Stone
Benny Davidovitch
We study the spreading of viscous drops on a solid substrate, taking into account the effects of thermal fluctuations in the fluid momentum. A nonlinear stochastic lubrication equation is derived, and studied using numerical simulations and scaling analysis. We show that asymptoically spreading drops admit self-similar shapes, whose average radii can increase at rates much faster than these predicted by Tanner's law. We discuss the physical realizablility of our results for thin molecular and complex fluid films, and predict that such phenomenon can in principal be observed in various flow geometries.
Dynamics Of Conformal Maps For A Class Of Non-Laplacian Growth Phenomena, Martin Z. Bazant, Jaehyuk Choi, Benny Davidovitch
Dynamics Of Conformal Maps For A Class Of Non-Laplacian Growth Phenomena, Martin Z. Bazant, Jaehyuk Choi, Benny Davidovitch
Benny Davidovitch
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro- migration. Both continuous and stochastic dynamics are described by generalizing conformal- mapping techniques for viscous fingering and diffusion-limited aggregation, respectively. A gen- eral notion of time in stochastic growth is also introduced. The theory is applied to simulations of advection-diffusion-limited aggregation in a background potential flow. A universal crossover in mor- phology is observed from diffusion-limited to advection-limited fractal patterns with an associated crossover in the growth rate, controlled by a time-dependent effective Peclet number. …
Ripening Of Porous Media, Benny Davidovitch, Deniz Ertas, Thomas C. Halsey
Ripening Of Porous Media, Benny Davidovitch, Deniz Ertas, Thomas C. Halsey
Benny Davidovitch
We address the surface tension-driven dynamics of porous media in nearly saturated pore-space solutions. We linearize this dynamics in the reaction-limited regime near its fixed points – surfaces of constant mean curvature (CMC surfaces). We prove that the only stable interface for this dynamics is the plane, and estimate the time scale for a CMC surface to become unstable. We also discuss the differences between open and closed system dynamics, pointing out the unlikelihood that CMC surfaces are ever realized in these systems on any time scale.
Iterated Conformal Dynamics And Laplacian Growth, Felipe Barra, Benny Davidovitch, Itamar Procaccia
Iterated Conformal Dynamics And Laplacian Growth, Felipe Barra, Benny Davidovitch, Itamar Procaccia
Benny Davidovitch
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, proportional to the gradient of the Laplacian field. We introduce a two-parameter family of growth patterns that interpolates between DLA and a discrete version of Laplacian growth. The ultraviolet putative finite-time singularities are regularized here by a minimal tip size, equivalently for all the models in …
Thermodynamic Formalism Of The Harmonic Measure Of Diffusion Limited Aggregates: Phase Transition And Converged, Mogens H. Jensen, Anders Levermann, Joachim Mathiesen, Benny Davidovitch, Itamar Procaccia
Thermodynamic Formalism Of The Harmonic Measure Of Diffusion Limited Aggregates: Phase Transition And Converged, Mogens H. Jensen, Anders Levermann, Joachim Mathiesen, Benny Davidovitch, Itamar Procaccia
Benny Davidovitch
No abstract provided.
Laplacian Growth And Diffusion Limited Aggregation: Different Universality Classes, Felipe Barra, Benny Davidovitch, Anders Leverman, Itamar Procaccia
Laplacian Growth And Diffusion Limited Aggregation: Different Universality Classes, Felipe Barra, Benny Davidovitch, Anders Leverman, Itamar Procaccia
Benny Davidovitch
It had been conjectured that diffusion limited aggregates and Laplacian growth patterns (with small surface tension) are in the same universality class. Using iterated conformal maps we construct a oneparameter family of fractal growth patterns with a continuously varying fractal dimension. This family can be used to bound the dimension of Laplacian growth patterns from below. The bound value is higher than the dimension of diffusion limited aggregates, showing that the two problems belong to two different universality classes.