Related papers: Theory of tectonics in the sphere
We derive a F\"{o}ppl-von K\'{a}rm\'{a}n-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we…
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 analyse the massless wave equation on a class of two dimensional manifolds consisting of an arbitrary number of topological cylinders connected to one or more topological spheres. Such manifolds are endowed with a degenerate…
While hard-sphere models form the foundation of theoretical condensed matter physics, real systems often exhibit some degree of softness. We present a theoretical and numerical study of a class of nearly hard-sphere systems, generalized…
A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedgeshaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. By using methods of the theory…
Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like space-time models allow the existence of privileged coordinate systems where the…
In this paper, we introduce an alternative representation of the electromagnetic field scattered from a homogeneous sphere coated with a homogeneous layer of uniform thickness. Specifically, we expand the scattered field using a set of…
We propose an exact solution for a stratosphere dynamical core formulated in geopotential/pressure coordinates with a time-evolving lower boundary supplied by the troposphere. Rather than constraining the stratospheric circulation via…
We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly…
A model for terrestrial planets, inclusive of viscous fluid behavior and featuring finite normal stress differences, is developed. This work offers new insights for the interpretation of planetary survey data. Evolution equations for…
We study elasticity-driven morphological transitions of soft spherical core shell structures in which the core can be treated as an isotropic elastic continuum and the surface or shell as a tensionless liquid layer, whose elastic response…
We formulate a method for computing Stokes flow past a highly deformed sphere with arbitrarily defined surface velocity. The fundamental ingredient is an explicit extrapolation operator extending a velocity field from the surface of a…
Phonons in solid materials can be understood as the Goldstone bosons of the spontaneously broken spacetime symmetries. As such their low energy dynamics are greatly constrained and can be captured by standard effective field theory (EFT)…
Abyssal hills, arguably the most extensive coherent pattern in Earth's surface topography, record the spacing of normal faults formed at mid-ocean ridges. At fast-spreading ridges, high-resolution bathymetry shows a pronounced spectral peak…
We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of N hard spheres of diameter $\epsilon$ in two space dimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N $\epsilon$ =…
The Lorenz--Mie formulation of electromagnetic scattering by a homogeneous, isotropic, dielectric-magnetic sphere was extended to incorporate topologically insulating surface states characterized by a surface admittance $\gamma$.…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…
We consider the $N$-vortex problem on the sphere assuming that all vortices have equal strength. We develop a theoretical framework to analyse solutions of the equations of motion with prescribed symmetries. Our construction relies on the…
A simple derivation of the classical solutions of a nonlinear model describing a harmonic oscillator on the sphere and the hyperbolic plane is presented in polar coordinates. These solutions are then related to those in cartesian…
This paper investigates the pseudo-spin based edge states for flexural waves in a honeycomb perforated phononic plate, which behaves an elastic analogue of the quantum spin Hall effect. We utilize finite element method to analyse the…