相关论文: Self-shrinking Platonic solids
Self-similar curves are a recurring motif in nature. The tension-free stationary states of conformally invariant energies describe the simplest curves of this form. Planar logarithmic spirals, for example, are associated with conformal…
We proof here the existence of a topological thick and thin decomposition of any closed definable thick isolated singularity germ in the spirit of the recently discovered metric thick and thin decomposition of complex normal surface…
The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is…
We discuss the phenomenon of spontaneous self-compactification in a model colloidal system, proposed in a recent work on DNA-mediated self-assembly. We focus on the effect of thermal fluctuations on the stability of membrane-like…
Extensions of the $Stirling$ numbers of the second kind and $Dobinski$ -like formulas are proposed in a series of exercises for graduates. Some of these new formulas recently discovered by me are to be found in the source paper $ [1]$.…
The paper considers the uniqueness question of factorization of a knotted handlebody in the $3$-sphere along decomposing $2$-spheres. We obtain a uniqueness result for factorization along decomposing $2$-spheres meeting the handlebody at…
Nineteen classical superintegrable systems in two-dimensional non-Euclidean spaces are shown to possess hidden symmetries leading to their linearization. They are the two Perlick systems [A. Ballesteros, A. Enciso, F.J. Herranz and O.…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
We consider a method of construction of self-similar dendrites on a plane and establish main topological and metric properties of resulting class of dendrites.
We study d-wave Fermi surface deformations (dFSD), the so-called Pomeranchuk instability, on bilayer and infinite-layer square lattices. Since the order parameter of the dFSD has Ising symmetry, there are two stacking patterns along the c…
We develop the basic tools for classifying edge-to-edge tilings of the sphere by congruent pentagons. Then we prove that, for the edge combination $a^2b^2c$, such tilings are three two-parameter families of pentagonal subdivisions of the…
We investigate the integer solutions of Diophantine equations related to perfect numbers. These solutions generalize the example, found by Descartes in 1638, of an odd, ``spoof'' perfect factorization $3^2\cdot 7^2\cdot 11^2\cdot 13^2\cdot…
Recent simulations have studied the formation of patterns in a binary mixture of immiscible surfactants absorbed onto the surface of a spherical nanoparticle. The resulting patterns (Janus, spots and stripes) were in good agreement with…
We study numerically the hydrodynamics of a self-propelled particle system, consisting of spherical squirmers sedimented on a flat surface. We observe the emergence of dynamic structures, due to the interplay of particle-particle and…
Self-assembled dendronized CdS nanoparticles have been attracting considerable attention because of their photoluminescence properties depending on annealing treatments. In this study, their annealing-induced self-assembled structure was…
We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…
The proposed algorithm by Philippe D'Arco et al. 2013 J. Phys.: Condens. Matter 25 355401 was not well compared with other possible solutions for symmetry independent configuration (SIC) generation. In this comment, three well known…
Self-assembling peptides (SAPs) have shown to offer great promise in therapeutics and have the ability to undergo self-assembly and form ordered nanostructures. However SAP gels are often associated with inherent weak and transient…
We investigate a class of "shape allophiles" that fit together like puzzle pieces as a method to access and stabilize desired structures by controlling directional entropic forces. Squares are cut into rectangular halves, which are shaped…
Using Traizet's regeneration method, we prove that for each positive integer n there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space of genus 2n-1 and 4 ends in the quotient by the maximal…