Related papers: A Roche Model for Uniformly Rotating Rings
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…
The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over the random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for…
In this paper, we discuss the problem of determination of light radiation pressure force upon an anisotropic surface. The optical parameters of such a surface are considered to have major and minor axes, so the model is called an…
We consider a column of a rotating stationary surface in Euclidean space. We obtain a value $l_0>0$ in such way that if the length $l$ of column satisfies $l>l_0$, then the surface is instable. This extends, in some sense, previous results…
In the first part of this work a summary is provided of some recent experiments and theoretical results which are relevant in the research of systems of polymer rings in nontrivial topological conformations. Next, some advances in modeling…
The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is…
Surfaces sputtered by ion beam bombardment have been known to exhibit patterns whose behavior is modeled with stochastic partial differential equations. However, we apply a new approach by the use of the famous Lorentz equations to simulate…
Quantum field model of unstable particles with random mass is suggested to describe the finite-width effects in decay rate. Within the framework of this model we derive the convolution formula for a width of the channels with unstable…
In this paper, we discuss the normality of the toric rings of stable set polytopes, and the set of generators and Gr\"obner bases of toric ideals of stable set polytopes by using the results on that of edge polytopes of finite nonsimple…
By using the blob theory and computer simulations, we investigate the properties of a linear polymer performing a stationary rotational motion around a long impenetrable rod. In particular, in the simulations the rotation is induced by a…
We study distribution of orbits sampled at polynomial times for uniquely ergodic topological dynamical systems $(X, T)$. First, we prove that if there exists an increasing sequence $(q_n)$ for which the rigidity condition \[…
Simple mathematical models have been unable to predict the conditions leading to instabilities in a tuneable ring laser. Here, we propose a nonlinear iterative map model for tuneable ring lasers. Solving a reduced nonlinear Schr\"odinger…
We derive an effective equation of motion for the orientational dynamics of a neutrally buoyant spheroid suspended in a simple shear flow, valid for arbitrary particle aspect ratios and to linear order in the shear Reynolds number. We show…
Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…
Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly…
The properties common to the Lorenz and Chen attractors, as well as their fundamental differences, have been studied for many years in a vast number of works and remain a topic far from a rigorous and complete description. In this paper we…
We investigate CMC-surfaces with periodic metric in a dressing orbit of the cylinder. It is shown, that such surfaces are always of finite type. Using the periodicity conditions for the extended frame of a CMC-surface, we develop an…
We develop a new closed-form model for the dynamics of an elastic and isotropic sphere and use it to derive new closed-form resonant frequencies.
This paper develops a novel numerical method for obtaining structures of rapidly rotating stars based on a self-consistent field scheme. The solution is obtained iteratively. Both rapidly rotating barotropic and baroclinic equilibrium…