arXiv subjects

Efi Efrati

Publications and source records attributed to Efi Efrati.

24 records · Page 2Linked to original sources

arXiv2014

Orientation-dependent handedness and chiral design

Chirality occupies a central role in fields ranging from biological self-assembly to the design of optical metamaterials. The definition of chirality, as given by Lord Kelvin, associates chirality with the lack of mirror symmetry: the inability to superpose an object on its mirror image. While this definition has guided the classification of chiral objects for over a century, the quantification of handed phenomena based on this definition has proven elusive, if not impossible, as manifest in the paradox of chiral connectedness. In this work, we put forward a quantification scheme in which the handedness of an object depends on the direction in which it is viewed. While consistent with familiar chiral notions, such as the right-hand rule, this framework allows objects to be simultaneously right and left handed. We demonstrate this orientation dependence in three different systems - a biomimetic elastic bilayer, a chiral propeller, and optical metamaterial - and find quantitative agreement with chirality pseudotensors whose form we explicitly compute. The use of this approach resolves the existing paradoxes and naturally enables the design of handed metamaterials from symmetry principles.

cond-mat.soft↗

arXiv2013

Furrows in the wake of propagating d-cones

We investigate the formation dynamics of plastic creases in thin elasto-plastic sheets. In contrast to the commonly accepted description of crumpled thin sheets, which asserts that creases form only by elastic interaction between two d-cones, the creases we study in this letter are created by plastic deformations left in the wake of a single propagating d-cone. Upon application of load, a d-cone initially remains stationary and responds by deforming globally. However, above a critical load, the d-cone undergoes a sharpening transition that focuses the stresses at its tip, allowing it to propagate along the sheet, leaving a furrow-like scar in its wake. Our results show that the dynamics of plastic defect creation are important for predicting the final geometry and statistics of a defect network in a crumpled thin sheet.

cond-mat.soft↗

arXiv2013

Real Space Renormalization in Statistical Mechanics

This paper discusses methods for the construction of approximate real space renormalization transformations in statistical mechanics. In particular, it compares two methods of transformation: the "potential-moving" approach most used in the period 1975-1980 and the "rewiring method" as it has been developed in the last five years. These methods both employ a parameter, called χ, that measures the complexity of the localized stochastic variable forming the basis of the analysis. Both methods are here exemplified by calculations in terms of fixed points for the smallest possible values of χ. These calculations describe three models for two-dimensional systems: The Ising model solved by Onsager, the tricritical point of that model, and the three-state Potts model. The older method, often described as lower bound renormalization theory, provides a heuristic method giving reasonably accurate results for critical indices at the lowest degree of complexity, i.e. χ=2. In contrast, the rewiring method, employing "singular value decomposition", does not perform as well for low χvalues but offers an error that apparently decreases slowly toward zero as χis increased. It appears likely that no such improvement occurs in the older approach. A detailed comparison of the two methods is performed, with a particular eye to describing the reasons why they are so different. For example, the old method quite naturally employed fixed points for its analysis; these are hard to use in the newer approach. A discussion is given of why the fixed point approach proves to be hard in this context. In the new approach the calculated the thermal critical indices are satisfactory for the smallest values of χbut hardly improve as χis increased, while the magnetic critical indices do not agree well with the known theoretical values.

cond-mat.stat-mech↗

arXiv2009

Buckling transition and boundary layer in non-Euclidean plates

Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending of the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, amongst all configurations with zero stretching content (isometric immersions of the mid-surface). For small but finite plate thickness we show the formation of a boundary layer, whose size scales with the square root of the plate thickness, and whose shape is determined by a balance between stretching and bending energies.

cond-mat.soft↗

arXiv2008

Elastic theory of unconstrained non-Euclidean plates

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for large displacements. We propose the concept of non-Euclidean plates to approximate many naturally formed thin elastic structures. We derive a thin plate theory, which is a generalization of existing linear plate theories, valid for large displacements but small strains, and arbitrary intrinsic geometry. We study a particular example of a hemispherical plate. We show the occurrence of a spontaneous buckling transition from a stretching dominated configuration to bending dominated configurations, under variation of the plate thickness.

cond-mat.soft↗

arXiv2004

Hydrodynamic singularities and clustering in a freely cooling inelastic gas

We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a well-developed nonlinear regime. We simplify the problem by dealing with a one-dimensional coarse-grained flow. We observe that at a late stage of the instability the shear stress becomes negligibly small, and the gas flows solely by inertia. As a result the flow formally develops a finite time singularity, as the velocity gradient and the gas density diverge at some location. We argue that flow by inertia represents a generic intermediate asymptotic of unstable free cooling of dilute inelastic gases.

cond-mat.stat-mech↗