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We consider the thermal undulation, or shape fluctuation, of an almost planar fluid membrane surrounded by the same near-critical binary fluid mixtures on both sides. A weak preferential attraction is assumed between the membrane and one…
The motion of flexible fibers through structured fluidic environments is ubiquitous in nature and industrial applications. Most often, their dynamics results from the complex interplay between internal elastic stresses, contact forces and…
In this paper we extend the recent theory of shear-localization in 2-dimensional amorphous solids to 3-D. In 2-D the fundamental instability of shear-localization is related to the appearance of a line of displacement quadrupoles, that…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a…
One of the enticing features common to most of the two-dimensional electronic systems that are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in…
We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of…
The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness…
We devise a new time-stepping algorithm for two-dimensional nonlinear unsteady surface and interfacial waves. The algorithm uses Cauchy's integral formula, which only requires information on the interface, to solve Laplace equation by using…
In this paper we study an inverse problem in convex geometry, inspired by a problem in materials science. Firstly, we consider the question of whether a Laguerre tessellation (a partition by convex polytopes) can be recovered from only the…
In recent years, there has been extensive research on planar metasurfaces capable of arbitrarily controlling scattered fields. However, rigorous studies on conformal metasurfaces, such as those that are cylindrical, have been few in number…
The scaling behavior of fully flexible elastic tethered surfaces has been debated for decades. Some theories predict that self-avoiding surfaces would crumple in the absence of bending rigidity, while most simulations suggested that they…
The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…
Cracks in brittle materials produce two types of generic surface structures: facets at low velocities and micro-branches at higher ones. Here we observe a transition from faceting to micro-branching in polyacrylamide gels that is…
The steady, asymmetric and two-dimensional flow of viscous, incompressible, and Newtonian fluid through a rectangular channel with splitter plate parallel to walls is investigated numerically. In the past, the position of the splitter plate…
We experimentally study linear and nonlinear waves on the surface of a fluid covered by an elastic sheet where both tension and flexural waves take place. An optical method is used to obtain the full space-time wave field, and the…
Using the gauge theoretic approach for Lie applicable surfaces, we characterise certain subclasses of surfaces in terms of polynomial conserved quantities. These include isothermic and Guichard surfaces of conformal geometry and…
Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…