Related papers: A Roche Model for Uniformly Rotating Rings
The circle method has been successfully used over the last century to study rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to a range of results…
A thin shell finite element approach based on Loop's subdivision surfaces is proposed, capable of dealing with large deformations and anisotropic growth. To this end, the Kirchhoff-Love theory of thin shells is derived and extended to allow…
Electromagnetic (EM) wave scattering by many parallel infinite cylinders is studied asymptotically as a tends to 0, where a is the radius of the cylinders. It is assumed that the centres of the cylinders are distributed so that their…
As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility.…
In this paper, we present an asymptotic model describing localised flexural vibrations along a structured ring containing point masses or spring-mass resonators in an elastic plate. The values for the required masses and stiffnesses of…
This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We numerically analyse the rotation of a neutrally buoyant spheroid in a shear flow at small shear Reynolds number. Using direct numerical stability analysis of the coupled nonlinear particle-flow problem we compute the linear stability of…
We develop an effective model to describe the dynamics of a system of particle moving in circular configurations around a central mass, by considering the continuum limit of the angular distribution, to obtain the stable configurations for…
Existence and uniqueness of rotating fluid bodies in equilibrium is still poorly understood in General Relativity (GR). Apart from the limiting case of infinitely thin disks, the only known global results in the stationary rotating case…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
This paper gives an analysis of the movement of n vortices on the sphere. When the vortices have equal circulation, there is a polygonal solution that rotates uniformly around its center. The main result concerns the global existence of…
We use perturbation theory and the relativistic Cowling approximation to numerically compute characteristic oscillation modes of rapidly rotating relativistic stars which consist of a perfect fluid obeying a polytropic equation of state. We…
We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…
A solution to the Einstein field equations that represents a rigidly rotating dust accompanied by a thin matter shell of the same type is found.
A thin liquid film falling on a uniformly heated horizontal plate spreads into fingering ripples that can display a complex dynamics ranging from continuous waves, nonlinear spatially localized periodic wave patterns (i.e. rivulet…
We analyse the motion of a sphere that rolls without slipping on a conical surface having its axis in the direction of the constant gravitational field of the Earth. This nonholonomic system admits a solution in terms of quadratures. We…
We investigate by means of a number of different dynamical Monte Carlo simulation methods the self-assembly of equilibrium polymers in dilute, semidilute and concentrated solutions under good-solvent conditions. In our simulations, both…
Wrinkling instabilities of thin elastic sheets can be used to generate periodic structures over a wide range of length scales. Viscosity of the thin elastic sheet or its surrounding medium has been shown to be responsible for dynamic…
An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…