11 research outputs found
Geodesics of Random Riemannian Metrics
We analyze the disordered Riemannian geometry resulting from random
perturbations of the Euclidean metric. We focus on geodesics, the paths traced
out by a particle traveling in this quenched random environment. By taking the
point of the view of the particle, we show that the law of its observed
environment is absolutely continuous with respect to the law of the random
metric, and we provide an explicit form for its Radon-Nikodym derivative. We
use this result to prove a "local Markov property" along an unbounded geodesic,
demonstrating that it eventually encounters any type of geometric phenomenon.
We also develop in this paper some general results on conditional Gaussian
measures. Our Main Theorem states that a geodesic chosen with random initial
conditions (chosen independently of the metric) is almost surely not
minimizing. To demonstrate this, we show that a minimizing geodesic is
guaranteed to eventually pass over a certain "bump surface," which locally has
constant positive curvature. By using Jacobi fields, we show that this is
sufficient to destabilize the minimizing property.Comment: 55 pages. Supplementary material at arXiv:1206.494
A Statistical Mechanical Problem in Schwarzschild Spacetime
We use Fermi coordinates to calculate the canonical partition function for an
ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the
validity of the results we prove theorems for limiting cases. We recover the
Newtonian gas law subject only to tidal forces in the Newtonian limit.
Additionally we recover the special relativistic gas law as the radius of the
orbit increases to infinity. We also discuss how the method can be extended to
the non ideal gas case.Comment: Corrected an equation misprint, added four references, and brief
comments on the system's center of mass and the thermodynamic limi
The Dipole Coupling of Atoms and Light in Gravitational Fields
The dipole coupling term between a system of N particles with total charge
zero and the electromagnetic field is derived in the presence of a weak
gravitational field. It is shown that the form of the coupling remains the same
as in flat space-time if it is written with respect to the proper time of the
observer and to the measurable field components. Some remarks concerning the
connection between the minimal and the dipole coupling are given.Comment: 10 pages, LaTe
Extended Fermi coordinates
We extend the notion of Fermi coordinates to a generalized definition in
which the highest orders are described by arbitrary functions. From this
definition rises a formalism that naturally gives coordinate transformation
formulae. Some examples are developped in which the extended Fermi coordinates
simplify the metric components.Comment: 16 pages, 1 figur
Comparison of costs for solar electric sources with diesel generators in remote locations
This paper looks specifically at three alternative sources for generating power in remote regions of the world. These include diesel electric, photovoltaic and solar thermal electric devices. Fuel cost, and more specifically, transportation costs of that fuel, dramatically change which device will be most cost effective over a ten year period under specific conditions. In areas where fuel is readily available, diesel still appears to be the best alternative financially. Even today, however, solar thermal generators appear to make sense in a number of realistic scenarios, especially those involving LDCs. Photovoltaics do not yet seem to be competitive, but technical advances may in fact change this in the future. Cultural factors must also be taken into account when choosing a device. These comparisons are all represented graphically and numerically in the body of this paper