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Dynamical-systems approaches to spatiotemporal chaos have been developed primarily for single-phase flows, where the system state is defined by bulk velocity fields. Extending these ideas to two-phase flows remains challenging because the…
We investigate a system of geometric evolution equations describing a curvature and torsion driven motion of a family of 3D curves in the normal and binormal directions. We explore the direct Lagrangian approach for treating the geometric…
This article reviews several recently developed Lagrangian tools and shows how their combined use succeeds in obtaining a detailed description of purely advective transport events in general aperiodic flows. In particular, because of the…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
Origami is the archetype of a structural material with unusual mechanical properties that arise almost exclusively from the geometry of its constituent folds and forms the basis for mechanical metamaterials with an extreme deformation…
Brownian motion of free particles on curved surfaces is studied by means of the Langevin equation written in Riemann normal coordinates. In the diffusive regime we find the same physical behavior as the one described by the diffusion…
Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom we concentrate on are based on the orthogonal and affine…
Soft robots are made of compliant materials and perform tasks that are challenging for rigid robots. However, their continuum nature makes it difficult to develop model-based control strategies. This work presents a robust model-based…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
An arbitrary Lagrangian--Eulerian (ALE) finite element method for arbitrarily curved and deforming two-dimensional materials and interfaces is presented here. An ALE theory is developed by endowing the surface with a mesh whose in-plane…
Robotic manipulators often face challenges in handling objects of different sizes and materials, limiting their effectiveness in practical applications. This issue is particularly pronounced when manipulating meter-scale objects or those…
We consider several quadrilateral origami tilings, including the Miura-ori crease pattern, allowing for crease-reversal defects above the ground state which maintain local flat-foldability. Using exactly solvable models, we show that these…
Ring origami, consisting of closed-loop rods, is a class of shape-morphing structures that undergo shape transformation through folding enabled by snap-buckling instabilities, referred to as snap-folding instabilities. Previous studies have…
Ruled surfaces play an important role in various types of design, architecture, manufacturing, art, and sculpture. They can be created in a variety of ways, which is a topic that has been the subject of much discussion in mathematics and…
Origami structures enabled by folding and unfolding can create complex 3D shapes. However, even a small 3D shape can have large 2D unfoldings. The huge initial dimension of the 2D flattened structure makes fabrication difficult, and defeats…
We propose a novel computational framework for modeling and simulating origami structures. In this framework, bilinear solid-shell elements are employed to model the origami panels while crease folding is considered through the angle…
Inspired by the allure of additive fabrication, we pose the problem of origami design from a new perspective: how can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve…
We introduce the Study variety of conformal kinematics and investigate some of its properties. The Study variety is a projective variety of dimension ten and degree twelve in real projective space of dimension 15, and it generalizes the…
Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, we exploit kirigami…
Miura-Ori, a celebrated origami pattern that facilitates functionality in matter, has found multiple applications in the field of mechanical metamaterials. Modifications of Miura-Ori pattern can produce curved configurations during folding,…