arXiv subjects

Efi Efrati

Publications and source records attributed to Efi Efrati.

At least 19 recordsLinked to original sources

arXiv2026

Recovering long-range cumulative response to geometric frustration in quasi-1d systems, mediated by constitutive softness

Cumulative geometric frustration can drive self-limited assembly and morphology selection through size-dependent energetic costs. However, the slenderness of quasi-one-dimensional systems generally suppresses the formation of long-range longitudinal gradients. We show that the suppression of longitudinal gradients can be overcome by tuning the ratio between the longitudinal and transverse (shear) moduli. We demonstrate the recovery of cumulative frustration across distinct quasi-one-dimensional systems, each frustrated through a different mechanism, by the introduction of a soft response mode.

physics.class-ph↗

arXiv2025

Path integral approach for predicting the diffusive statistics of geometric phases in chaotic Hamiltonian systems

From the integer quantum Hall effect, to swimming at low Reynolds number, geometric phases arise in the description of many different physical systems. In many of these systems the temporal evolution prescribed by the geometric phase can be directly measured by an external observer. By definition, geometric phases rely on the history of the system's internal dynamics, and so their measurement is directly related to temporal correlations in the system. They, thus, provide a sensitive tool for studying chaotic Hamiltonian systems. In this work we present a toy model consisting of an autonomous, low-dimensional, chaotic Hamiltonian system designed to have a simple planar internal state space, and a single geometric phase. The diffusive phase dynamics in the highly chaotic regime is thus governed by the loop statistics of planar random walks. We show that the naïve loop statistics result in ballistic behavior of the phase, and recover the diffusive behavior by considering a bounded shape space, or a quadratic confining potential.

nlin.CD↗

arXiv2023

Rounded notch method of femoral endarterectomy offers mechanical advantages in finite element models

Objective: Use of a vascular punch to produce circular heel and toe arteriotomies for femoral endarterectomy with patch angioplasty is a novel technique. This study investigated the plausibility of this approach and the mechanical advantages of the technique using finite element models. Methods: The patient underwent a standard femoral endarterectomy. Prior to patch angioplasty, a 4.2 mm coronary vascular punch was used to created proximal and distal circular arteriotomies. The idealized artery was modeled as a 9 mm cylinder with a central slit. The vertices of the slit were modeled as: a sharp V consistent with traditional linear arteriotomy, circular punched hole, and beveled punched hole. The artery was pressurized to achieve displacement consistent with the size of a common femoral artery prior to patch angioplasty. Maximum von Mises stress, area-averaged stress, and stress concentration factors were evaluated for all three models. Results: Maximum von Mises stress was 0.098 MPa with 5 mm of displacement and increased to 0.26 MPa with 10 mm of displacement. Maximum stress in the uniform circular model was 0.019 MPa and 0.018 with a beveled notch. Average stress was lowest in the circular punch model at 0.006 MP and highest in the linear V notch arteriotomy at 0.010 MPa. Stress concentration factor was significantly lower in both circular models compared with the V notch. Conclusions: Femoral endarterectomy modified with the creation of circular arteriotomies is a safe and effective surgical technique. Finite element modeling revealed reduced maximum von Mises stress and average stress at the vertices of a circular or beveled punch arteriotomy compared with a linear, V shaped arteriotomy. Reduced vertex stress may promote lower risk of restenosis.

physics.med-ph↗

arXiv2023

Compatible director fields in $\mathbb{R}^3$

The geometry and interactions between the constituents of a liquid crystal, which are responsible for inducing the partial order in the fluid, may locally favor an attempted phase that could not be realized in $\mathbb{R}^3$. While states that are incompatible with the geometry of $\mathbb{R}^3$ were identified more than 50 years ago, the collection of compatible states remained poorly understood and not well characterized. Recently, the compatibility conditions for three-dimensional director fields were derived using the method of moving frames. These compatibility conditions take the form of six differential relations in five scalar fields locally characterizing the director field. In this work, we rederive these equations using a more transparent approach employing vector calculus. We then use these equations to characterize a wide collection of compatible phases.

cond-mat.soft↗

arXiv2022

Bridging cumulative and non-cumulative geometric frustration response via a frustrated $N$-state spin system

The resolution of geometric frustration in systems with continuous degrees of freedom often involves a cooperative inhomogeneous response and super-extensive energy scaling. In contrast, the frustration in frustrated Ising-like spin systems is resolved uniformly. In this work we bridge between these two extremes by studying a frustrated model composed of N-state spins, and varying N. The expected cooperative response, observed for large N, is strongly attenuated as N is reduced, in a non-trivial way. Moderate N values show unique topological-like phases not observed before in frustrated models.

cond-mat.soft↗

arXiv2022

Cumulative geometric frustration and superextensive energy scaling in a nonlinear classical XY-spin model

Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either non-cumulative, which implies an extensive energy growth, or cumulative which implies super-extensive energy scaling and highly cooperative ground state configurations which may depend on the dimensions of the system. Cumulative geometric frustration was identified in a variety of continuous systems including liquid crystals, filament bundles and molecular crystals. However, a spin-lattice model which clearly demonstrates cumulative geometric frustration was lacking. In this work we describe a non-linear variation of the XY-spin model on a triangular lattice that displays cumulative geometric frustration. The model is studied numerically and analyzed in three distinct parameter regimes, which are associated with different energy minimizing configurations. We show that, despite the difference in the ground state structure in the different regimes, in all cases the super-extensive power-law growth of the frustration energy for small domains grows with the same universal exponent that is predicted from the structure of the underlying compatibility condition.

cond-mat.soft↗

arXiv2021

Cumulative geometric frustration in physical assemblies

Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large morphological variations and other exotic response properties. While these unique characteristics can be shown to be a direct outcome of the geometric frustration, some geometrically frustrated systems do not exhibit any of the above phenomena. In this work we exploit the intrinsic approach to provide a framework for directly addressing the frustration in physical assemblies. The framework highlights the role of the compatibility conditions associated with the intrinsic fields describing the physical assembly. We show that the structure of the compatibility conditions determines the behavior of small assemblies, and in particular predicts their super-extensive energy growth exponent. We illustrate the use of this framework to several well known frustrated assemblies.

cond-mat.soft↗

arXiv2021

Moving frames and compatibility conditions for three-dimensional director fields

The geometry and topology of the region in which a director field is embedded impose limitations on the kind of supported orientational order. These limitations manifest as compatibility conditions that relate the quantities describing the director field to the geometry of the embedding space. For example, in two dimensions (2D) the splay and bend fields suffice to determine a director uniquely (up to rigid motions) and must comply with one relation linear in the Gaussian curvature of the embedding manifold. In 3D there are additional local fields describing the director, i.e. fields available to a local observer residing within the material, and a number of distinct ways to yield geometric frustration. So far it was unknown how many such local fields are required to uniquely describe a 3D director field, nor what are the compatibility relations they must satisfy. In this work, we address these questions directly. We employ the method of moving frames to show that a director field is fully determined by five local fields. These fields are shown to be related to each other and to the curvature of the embedding space through six differential relations. As an application of our method, we characterize all uniform distortion director fields, i.e., directors for which all the local characterizing fields are constant in space, in manifolds of constant curvature. The classification of such phases has been recently provided for directors in Euclidean space, where the textures correspond to foliations of space by parallel congruent helices. For non-vanishing curvature, we show that the pure twist phase is the only solution in positively curved space, while in the hyperbolic space uniform distortion fields correspond to foliations of space by (non-necessarily parallel) congruent helices. Further analysis is expected to allow to also construct of new non-uniform director fields.

cond-mat.soft↗

arXiv2021

Explicit, time-reversible and symplectic integrator for Hamiltonians in isotropic uniformly curved geometries

The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the kinetic term to construct an explicit time-reversible symplectic scheme of second order. We use iterative applications of the method to construct a fourth order scheme and demonstrate its efficiency.

math.NA↗

arXiv2021

Construction of exact minimal parking garages: nonlinear helical motifs in optimally packed lamellar structures

Minimal surfaces arise as energy minimizers for fluid membranes and are thus found in a variety of biological systems. The tight lamellar structures of the endoplasmic reticulum and plant thylakoids are composed of such minimal surfaces in which right and left handed helical motifs are embedded in stoichiometry suggesting global pitch balance. So far, the analytical treatment of helical motifs in minimal surfaces was limited to the small-slope approximation where motifs are represented by the graph of harmonic functions. However, in most biologically and physically relevant regimes the inter-motif separation is comparable with its pitch, and thus this approximation fails. Here, we present a recipe for constructing exact minimal surfaces with an arbitrary distribution of helical motifs, showing that any harmonic graph can be deformed into a minimal surface by exploiting lateral displacements only. We analyze in detail pairs of motifs of the similar and of opposite handedness and also an infinite chain of identical motifs with similar or alternating handedness. Last, we study the second variation of the area functional for collections of helical motifs with asymptotic helicoidal structure and show that in this subclass of minimal surfaces stability requires that the collection of motifs is pitch balanced.

math.DG↗

arXiv2019

Regular Regimes of the Three Body Harmonic System

The symmetric harmonic three-mass system with finite rest lengths, despite its apparent simplicity, displays a wide array of interesting dynamics for different energy values. At low energy the system shows regular behavior that produces a deformation-induced rotation with a constant averaged angular velocity. As the energy is increased this behavior makes way to a chaotic regime with rotational behavior statistically resembling Lévy walks and random walks. At high enough energies, where the rest lengths become negligible, the chaotic signature vanishes and the system returns to regularity, with a single dominant frequency. The transition to and from chaos, as well as the anomalous power law statistics measured for the angular displacement of the harmonic three mass system are largely governed by the structure of regular solutions of this mixed Hamiltonian system. Thus a deeper understating of the system's irregular behavior requires mapping out its regular solutions. In this work we provide a comprehensive analysis of the system's regular regimes of motion, using perturbative methods to derive analytical expressions of the system as almost-integrable in its low- and high-energy extremes. The compatibility of this description with the full system is shown numerically. In the low-energy regime, the Birkhoff normal form method is utilized to circumvent the low-order 1:1 resonance of the system, and the conditions for Kolmogorov-Arnold-Moser theory are shown to hold. The integrable approximations provide the back-bone structure around which the behavior of the full non-linear system is organized, and provide a pathway to understanding the origin of the power-law statistics measured in the system.

nlin.CD↗

arXiv2019

Curved geometries from planar director fields - Solving the two-dimensional inverse problem

Thin nematic elastomers, composite hydrogels and plant tissues are among many systems that display uniform anisotropic deformation upon external actuation. In these materials, the spatial orientation variation of a local director field induces intricate global shape changes. Despite extensive recent efforts, to date, there is no general solution to the inverse design problem: how to design a director field that deforms exactly into a desired surface geometry upon actuation, or whether such a field exists. In this work, we phrase this inverse problem as a hyperbolic system of differential equations. We prove that the inverse problem is locally integrable, provide an algorithm for its integration, and derive bounds on global solutions. We classify the set of director fields that deform into a given surface, thus paving the way to finding optimized fields.

cond-mat.soft↗

arXiv2018

The metric description of viscoelasticity and instabilities in viscoelastic solids

Many manmade and naturally occurring materials form viscoelastic solids. The increasing use of biologically inspired elastomeric material and the extreme mechanical response these elastomers offer drive the need for a better, more intuitive and quantitative understanding of the mechanical response of such continua. This is in particular important in determining the stability of viscoelastic structure over time where in lieu of robust rules we often must resort to simulations. In this work we put forward a metric description of viscoelasticity in which the continua is characterized by temporally evolving reference lengths quantified by a rest reference metric. This rest reference metric serves as a state variable describing the result of the viscoelastic flow in the system, and allows us to provide robust claims regarding stability of incompressible isotropic viscoelastic media. We demonstrate these claims for a simple bistable systems of three standard-linear-solid spring dashpot assemblies where the predicted rules can be verified by explicit calculations, and also show quantitative agreement with recent experiments in viscoelastic silicone rubber shells that display delayed stability loss.

cond-mat.soft↗

arXiv2017

Delayed instabilities in viscoelastic solids through a metric description

While determining the stability of an unconstrained elastic structure is a straightforward task, this is not the case for viscoelastic structures. Seemingly elastically stable conformations of viscoelastic structures may gradually creep until stability is lost, and conversely, creeping does not necessarily imply that a structure will eventually become unstable. Understanding instabilities in viscoelastic structures requires a more intuitive description of viscoelasticity to allow analytical results and quantitative predictions. In this work we put forward a metric description of viscoelasticity in which the continua is characterized by temporally evolving reference lengths with respect to which elastic strains are measured. Formulating the three dimensional theory using metric tensors we are able to predict which structures will exhibit delayed instability due to viscoelastic flow. We also quantitatively describe the viscoelastic relaxation in free standing structures including cases where the relaxation leads to no apparent motion. We demonstrate these results and the power of the metric approach by elucidating the subtle mechanism of delayed instability in elastomer shells showing quantitative agreement with experimental measurements.

cond-mat.soft↗

arXiv2017

Rotational random walk of the harmonic three body system

When Robert Brown first observed colloidal pollen grains in water he inaccurately concluded that their motion arose "neither from currents in the fluid, nor from its gradual evaporation, but belonged to the particle itself". In this work we study the dynamics of a classical molecule consisting of three masses and three harmonic springs in free space that does display a rotational random walk "belonging to the particle itself". The geometric nonlinearities arising from the non-zero rest lengths of the springs connecting the masses break the integrability of the harmonic system and lead to chaotic dynamics in many regimes of phase space. The non-trivial connection of the system's shape space allows it, much like falling cats, to rotate with zero angular momentum and manifest its chaotic dynamics as an orientational random walk. In the transition to chaos the system displays random orientation reversals and provides a simple realization of Lévy walks.

nlin.CD↗

arXiv2017

Geometric frustration and compatibility conditions for two dimensional director fields

The uniform director field obtained for the nematic ground state of the hard-rod model of liquid crystals in two dimensions reflects the high symmetry of the constituents of the liquid; It is a manifestation of the constituents' local tendency to avoid splaying and bending with respect to one another. In contrast, bent-core (or banana shaped) liquid-crystal-forming-molecules locally favor a state of zero splay and constant bend. However, such a structure cannot be realized in the plane and the resulting liquid-crystalline phase is frustrated and must exhibit some compromise of these two mutually contradicting local intrinsic tendencies. The generation of geometric frustration from the intrinsic geometry of the constituents of a material is not only natural and ubiquitous but also leads to a striking variety of morphologies of ground states and exotic response properties. In this work we establish the necessary and sufficient conditions for two scalar functions, $s$ and $b$ to describe the splay and bend of a director field in the plane. We generalize these compatibility conditions for geometries with non-vanishing constant Gaussian curvature, and provide a reconstruction formula for the director field depending only on the splay and bend fields and their derivatives. Last, we discuss optimal compromises for simple incompatible cases where the locally preferred values of the splay and bend cannot be globally achieved.

cond-mat.soft↗

arXiv2016

Non-affine bending mode of thin cylindrical tubes

We discuss the response of thin cylindrical tubes to small indentations. The stretching-free embedding of these surfaces is completely determined by the embedding of one edge curve, thus reducing their bending response to an effectively one dimensional problem. We obtain that in general thin cylindrical tubes will bend non-uniformly in response to an indentation normal to their surface. As a consequence, their local bending stiffness, as measured by indenting at various locations along their axis, is predicted to peak at the center and decrease by a universal factor of 4 at either end of the tube. This characteristic spatial profile of the bending stiffness variation allows a direct determination of the bending modulus of very thin tubes that are shorter than their pinch persistence length, $l_{p}\propto R^{3/2}/t^{1/2}$, where $R$ is the tube diameter and $t$ its wall thickness. We compare our results with experiments performed on rolled-up stainless steel sheets.

cond-mat.soft↗

arXiv2014

Confined disclinations: exterior vs material constraints in developable thin elastic sheets

We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical and experimental methods. Such sheets occur in packaging, surgery and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle $δ$ of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope $ε$ and thin wedges. In this regime the single parameter $δ/ε^2$ determines the shape. We discuss the singular limit in which the cone becomes a plane. We discuss the unexpected slow convergence to the semicircular buckling seen experimentally.

cond-mat.soft↗