Related papers: Tight composites knots and chirality
The effects of entanglement in solutions and melts of unknotted ring polymers have been addressed by several theoretical and numerical studies. The system properties have been typically profiled as a function of ring contour length at fixed…
We analyze correlation functions in a toy model of a random geometry interacting with matter. We show that in general the connected correlator will contain a long-range scaling part which is in some sense a remnant of the disconnected part.…
We consider chiral loop corrections to the effective couplings which describe the strong interactions of two heavy mesons of even or odd parities and a light pseudoscalar meson, within a framework which combines heavy quark effective theory…
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…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invariants are notoriously difficult to find and often involve…
This article surveys the use of configuration space integrals in the study of the topology of knot and link spaces. The main focus is the exposition of how these integrals produce finite type invariants of classical knots and links. More…
New expansionary and rotational quadratic forms are constructed for $E^n$-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric…
We use numerical simulations to study tangentially active flexible ring polymers with different knot topologies. Simple, unknotted active rings display a transition from an extended phase to a collapsed one upon increasing the degree of…
We consider a multilayered metamaterial composed of anisotropic layers with in-plane anisotropy axes periodically rotated with respect to each other. Due to the breaking of inversion symmetry, the structure develops an effective chirality.…
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight knot, and its length is a knot invariant measuring…
A selection of open problems in the theory of composites is presented. Particular attention is drawn to the question of whether two-dimensional, two-phase, composites with general geometries have the same set of possible effective tensors…
Strong coupling phenomena, such as the like charged macroions attraction, opposite charged macroions repulsion, charge renormalization or charge inversion, are known to be mediated by multivalent counterions. Most theories treat the…
We show how the double cohomology of the String and Felder BRST charges naturally leads to the ring structure of $c<1$ strings. The chiral ring is a ring of polynomials in two variables modulo an equivalence relation of the form $x^p \simeq…
For over a century, the structure of materials has been described by a combination of rotations, rotation-inversions and translational symmetries. By recognizing the reversal of static structural rotations between clockwise and…
Chirality refers to a geometric phenomenon in which objects are not superimposable on their mirror image. Structures made of nano-scale chiral elements can display chiroptical effects, such as dichroism for left- and right- handed…
Recent progress in holographic correspondence uncovered remarkable relations between key characteristics of the theories on both sides of duality and certain integrable models. In this note we revisit the problem of the role of certain…
Chirality is a manifestation of the asymmetry inherent in nature. It has been defined as the symmetry breaking of the parity of static objects, and the definition was extended to dynamic motion such that true and false chiralities were…
In this work, we relate the geometry of chaotic attractors of typical analytic unimodal maps to the behavior of the critical orbit. Our main result is an explicit formula relating the combinatorics of the critical orbit with the exponents…
We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.