相关论文: Helical close packings of ideal ropes

We use numerical simulations to show how a fully flexible filament binding to a deformable cylindrical surface may acquire a macroscopic persistence length and a helical conformation. This is a result of the nontrivial elastic response to…

One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range…

This paper develops the foundations of Hom-heaps, Hom-trusses, and Hom-braces as natural Hom-type analogues of their classical counterparts. We establish the correspondence between Hom-heaps and Hom-groups, showing that the retract of a…

We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops…

Chirality is known to play a central role in the properties of many physical systems across a wide range of spatial and temporal scales. Chemical and optical properties of materials are only two of the many examples where transformation…

In this paper, we consider the problem of how to establish algebraic structures on nearness approximation spaces. Essentially, our approach is to define the nearness ring, nearness ideal and nearness ring of all weak cosets by considering…

We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…

We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…

Ropelength and embedding thickness are related measures of geometric complexity of classical knots and links in Euclidean space. In their recent work, Freedman and Krushkal posed a question regarding lower bounds for embedding thickness of…

Tangles of loops which approximate an aspect of the Kerr-Newman black hole metrics at large scales compared to the Planck length are constructed. The physical aspect the tangles approximate is discussed. This construction may be useful in…

We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation, measured along their inter-center vector. This directional distance is derived from the Elliptic Contact…

The presence of ordered structures such as helices in collapsed states of polymer chains is still an open question challenging physics and biology. In this work, we present a potential model for polymer chains with monomers that are not…

We examine the metrics that arise when a finite set of points is embedded in the real line, in such a way that the distance between each pair of points is at least 1. These metrics are closely related to some other known metrics in the…

This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…

Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packings are known. The packing of 2D crosses does…

A systematic study of closed classical orbits of the hydrogen atom in crossed electric and magnetic fields is presented. We develop a local bifurcation theory for closed orbits which is analogous to the well-known bifurcation theory for…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

The toric ring together with the toric ideal arising from a nested configuration is studied, with particular attention given to the algebraic study of normality of the toric ring as well as the Gr\"obner bases of the toric ideal. One of the…

We investigate theoretically the properties of an ideal trapped gas in a time-dependent harmonic potential. Using a scaling formalism, we are able to present simple analytical results for two important classes of experiments: free expansion…

We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection…