Related papers: Topological rigidity in twisted, elastic ribbons
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…
Entangled states are ubiquitous amongst fibrous materials, whether naturally occurring (keratin, collagen, DNA) or synthetic (nanotube assemblies, elastane). A key mechanical characteristic of these systems is their ability to reorganise in…
We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions…
In this paper the new model of plastic deformation is constructed. For classification of plastic statuses the theory of knot is used.
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum…
A growing or compressed thin elastic sheet adhered to a rigid substrate can exhibit a buckling instability, forming an inward hump. Our study shows that the strip morphology depends on the delicate balance between the compression energy and…
Disclinations are ubiquitous lattice defects existing in almost all crystalline materials. In two-dimensional nanomaterials, disclinations lead to the warping and deformation of the hosting material, yielding non-Euclidean geometries.…
We study the non-rigidity of Euclidean $t$-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean $t$-designs. We show that certain tight…
Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat…
Topological insulators are crystalline materials that have revolutionized our ability to control wave transport. They provide us with unidirectional channels that are immune to obstacles, defects or local disorder, and can even survive some…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
We present a general theory for the equilibrium structure of cylindrical tubules and helical ribbons of chiral lipid membranes. This theory is based on a continuum elastic free energy that permits variations in the direction of molecular…
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
Symmetry plays an important role in the topological band theory to remedy the eigenstates' gauge obstruction at the cost of a symmetry anomaly and zero-energy boundary modes. One can also make use of the symmetry to enumerate the…
The concepts of topology have a profound impact on physics research spanning the fields of condensed matter, photonics and acoustics and predicting topological states that provide unprecedented versatility in routing and control of waves of…
Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable vibrational properties, that originate in the geometry of their unit cell. At the heart of such unusual…
This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…
We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a ``figure-8'' twist. Using vibrated granular chains, which permit controlled preparation and direct observation of such a…
In this work are consider several topics in the Topological Membrane (TM) approach to string theory. The string dynamics is generated from the bulk physics, namely from the 3D Topologically Massive Gauge Theory (TMGT) and Topologically…