8,904 research outputs found
Measurement of extremely low fluid permeabilities of rocks significant to studies of the origin of life Final report
Permeater for measuring low fluid permeabilities of rocks used to study origin of lif
Stability of Relative Equilibria of Point Vortices on a Sphere and Symplectic Integrators
This paper analyzes the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are provided for the (integrable) case N = 3. Stability of relative equilibria is analyzed by the energy-momentum method. Explicit criteria for stability of different configurations with generic and non-generic momenta are obtained. In each case, a group of transformations is specied, such that motion in the original (unreduced) phase space is stable modulo this group. Finally, we outline the construction of a symplectic-momentum integrator for vortex dynamics on a sphere
The geometry and analysis of the averaged Euler equations and a new diffeomorphism group
We present a geometric analysis of the incompressible averaged Euler
equations for an ideal inviscid fluid. We show that solutions of these
equations are geodesics on the volume-preserving diffeomorphism group of a new
weak right invariant pseudo metric. We prove that for precompact open subsets
of , this system of PDEs with Dirichlet boundary conditions are
well-posed for initial data in the Hilbert space , . We then use
a nonlinear Trotter product formula to prove that solutions of the averaged
Euler equations are a regular limit of solutions to the averaged Navier-Stokes
equations in the limit of zero viscosity. This system of PDEs is also the model
for second-grade non-Newtonian fluids
Gauge Theory for Finite-Dimensional Dynamical Systems
Gauge theory is a well-established concept in quantum physics,
electrodynamics, and cosmology. This theory has recently proliferated into new
areas, such as mechanics and astrodynamics. In this paper, we discuss a few
applications of gauge theory in finite-dimensional dynamical systems with
implications to numerical integration of differential equations. We distinguish
between rescriptive and descriptive gauge symmetry. Rescriptive gauge symmetry
is, in essence, re-scaling of the independent variable, while descriptive gauge
symmetry is a Yang-Mills-like transformation of the velocity vector field,
adapted to finite-dimensional systems. We show that a simple gauge
transformation of multiple harmonic oscillators driven by chaotic processes can
render an apparently "disordered" flow into a regular dynamical process, and
that there exists a remarkable connection between gauge transformations and
reduction theory of ordinary differential equations. Throughout the discussion,
we demonstrate the main ideas by considering examples from diverse engineering
and scientific fields, including quantum mechanics, chemistry, rigid-body
dynamics and information theory
Resonant Geometric Phases for Soliton Equations
The goal of the present paper is to introduce a multidimensional generalization of asymptotic reduction given in a paper by Alber and Marsden [1992], to use this to obtain a new class of solutions that we call resonant solitons, and to study the corresponding geometric phases. The term "resonant solitons" is used because those solutions correspond to a spectrum with multiple points, and they also represent a dividing solution between two different types of solitons. In this sense, these new solutions are degenerate and, as such, will be considered as singular points in the moduli space of solitons
Cocycles, compatibility, and Poisson brackets for complex fluids
Motivated by Poisson structures for complex fluids containing cocycles, such
as the Poisson structure for spin glasses given by Holm and Kupershmidt in
1988, we investigate a general construction of Poisson brackets with cocycles.
Connections with the construction of compatible brackets found in the theory
of integrable systems are also briefly discussed
Differential rotation of Kepler-71 via transit photometry mapping of faculae and starspots
Knowledge of dynamo evolution in solar-type stars is limited by the difficulty of using active region monitoring to measure stellar differential rotation, a key probe of stellar dynamo physics. This paper addresses the problem by presenting the first ever measurement of stellar differential rotation for a main-sequence solar-type star using starspots and faculae to provide complementary information. Our analysis uses modelling of light curves of multiple exoplanet transits for the young solar-type star Kepler-71, utilizing archival data from the Kepler mission. We estimate the physical characteristics of starspots and faculae on Kepler-71 from the characteristic amplitude variations they produce in the transit light curves and measure differential rotation from derived longitudes. Despite the higher contrast of faculae than those in the Sun, the bright features on Kepler-71 have similar properties such as increasing contrast towards the limb and larger sizes than sunspots. Adopting a solar-type differential rotation profile (faster rotation at the equator than the poles), the results from both starspot and facula analysis indicate a rotational shear less than about 0.005 rad d-1, or a relative differential rotation less than 2 per cent, and hence almost rigid rotation. This rotational shear contrasts with the strong rotational shear of zero-age main-sequence stars and the modest but significant shear of the modern-day Sun. Various explanations for the likely rigid rotation are considered
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