Related papers: Closed, Two Dimensional Surface Dynamics
We obtain compact orientable embedded surfaces with constant mean curvature $0<H<\frac{1}{2}$ and arbitrary genus in $\mathbb{S}^2\times\mathbb{R}$. These surfaces have dihedral symmetry and desingularize a pair of spheres with mean…
In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation…
Slow dynamics in an amorphous quasi-two-dimensional complex plasma, comprised of microparticles of two different sizes, was studied experimentally. The motion of individual particles was observed using video microscopy, and the self-part of…
Let $\Sigma$ be a smooth closed hypersurface with non-negative Ricci curvature, isometrically immersed in a space form. It has been proved in \cite{P}, \cite{CZ}, and \cite{C2} that there are some $L^2$ inequalities on $\Sigma$ which…
We discuss the equilibrium conditions for a body made of two homogeneous components separated by oblate spheroidal surfaces and in relative motion. While exact solutions are not permitted for rigid rotation (unless a specific ambient…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
The affine motion of two-dimensional (2d) incompressible fluids surrounded by vacuum can be reduced to a completely integrable and globally solvable Hamiltonian system of ordinary differential equations for the deformation gradient in ${\rm…
This article is the second of a three-part series that derives a self-consistent theoretical framework of the electromechanics of arbitrarily curved lipid membranes. Existing continuum theories commonly treat lipid membranes as strictly…
We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using…
The equilibrium properties of block copolymer micelles confined in polymer thin films are investigated using self-consistent field theory. The theory is based on a model system consisting of AB diblock copolymers and A homopolymers. Two…
We use molecular dynamics computer simulations to study the equilibrium properties of the surface of amorphous silica. Two types of geometries are investigated: i) clusters with different diameters (13.5\AA, 19\AA, and 26.5\AA) and ii) a…
The analytic solution for the two-streams discrete ordinates equations is carried out on the spatial domain in one-dimensional spherical geometry. The solution satisfies all the physical and the geometric conditions, namely: the natural…
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
The bending energy of any freely deformable closed surface is quadratic in its curvature. In the absence of constraints, it will be minimized when the surface adopts the form of a round sphere. If the surface is confined within a…
We introduce two sets of continuum equations to describe granular flow on a free surface and study their properties. The equations derived from a microscopic picture that includes jumps and a mobility threshold, account for ripple and…
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…
We establish short-time existence of a smooth solution to the surface diffusion equation with an elastic term and without an additional curvature regularization in three space dimensions. We also prove the asymptotic stability of strictly…
This article aims to derive equations of motion for dynamical systems with angular momentum on Finsler geometries. To this end, we apply Souriau's Principle of General Covariance, which is a geometrical framework to derive diffeomorphism…
In this paper we consider the equiform motion of a helix in Euclidean space $\mathbf{E}^7$. We study and analyze the corresponding kinematic three dimensional surface under the hypothesis that its scalar curvature $\mathbf{K}$ is constant.…
Confinement can be used to systematically tame turbulent dynamics occurring in active fluids. Although periodic channels are the simplest geometries to study confinement numerically, the corresponding experimental realizations require…