Related papers: Tight composites knots and chirality
The injection of a long flexible rod into a two-dimensional domain yields a complex pattern commonly studied through elasticity theory, packing analysis, and fractal geometries. "Loop" is a one-vertex entity that is naturally formed in this…
We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the way we introduce a new class of combinatorial matroids and associated linear…
During the early developmental process of organisms, the formation of the left-right laterality requires a subtle mechanism, as it is associated with other principal body axes. Any inherent chiral feature in an egg cell can in principal…
We study rigidity properties of linearly ordered sets (chains) under automorphisms, order-embeddings, epimorphisms, and endomorphisms. We focus on two main cases, dense subchains of the real numbers, and uncountable dense chains of higher…
Relationships between a chaotic behavior and closely related properties of topological transitivity, sensitivity to initial conditions, density of closed orbits of homeomorphism groups and their countable products are investigated. We…
We develop a theory of chirality and racemization on isotopy classes of finite loops, formulated intrinsically within the loop isotopy groupoid understood in the categorical sense. Motivated by earlier work on quasigroups…
The standard model ascribes distinct properties to different chiralities of fermions. We show how to incorporate this aspect in an extended spacetime-property framework involving two different attributes using a generalized metric which…
Chirality is a fundamental feature in all domains of nature, ranging from particle physics over electromagnetism to chemistry and biology. Chiral objects lack a mirror plane and inversion symmetry and therefore cannot be spatially aligned…
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear…
Plasticity refers to thermodynamically irreversible deformation associated with a change of configuration of materials. Friction is a phenomenological law that describes the forces resisting sliding between two solids or across an embedded…
We show that the Ginsparg-Wilson (GW) relation can play an important role to define chiral structures in {\it finite} noncommutative geometries. Employing GW relation, we can prove the index theorem and construct topological invariants even…
Fundamental studies of the interaction of chiral light with chiral matter are important for the development of techniques that allow handedness-selective optical detection of chiral organic molecules. One approach to achieve this goal is…
We consider in this paper the general properties of laminates designed to be isotropic in extension and in bending and with a coupling between the in- and out-of plane responses. In particular, we analyze the mathematical properties of the…
In continuum mechanics, the non-centrosymmetric micropolar theory is usually used to capture the chirality inherent in materials. However when reduced to a two dimensional (2D) isotropic problem, the resulting model becomes non-chiral.…
The density matrix of composite spin system is discussed in relation to the adjoint representation of unitary group U(n). The entanglement structure is introduced as an additional ingredient to the description of the linear space carrying…
Chirality has been a property of central importance in chemistry and biology for more than a century, and is now taking on increasing relevance in condensed matter physics. Recently, electrons were found to become spin polarized after…
We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nano-channels and under periodic compression. We…
Widely known for their uses in displays and electro-optics, liquid crystals are more than just technological marvels. They vividly reveal the topology and structure of various solitonic and singular field configurations, often markedly…
The present paper is a comment regarding the robustness of the chirality in presence of the space-reflection asymmetry, which leads to pairs of interleaved positive- and negative-parity bands. The recent results reported in Ref.…
Due to their microstructure, quasi brittle materials present rough cracks. Under sliding of the crack lips, this roughness involves in one hand induced opening and in the other hand some apparent plasticity which is due to the interlocking…