48 research outputs found
A variational formulation of relativistic hydrodynamics
We combine Taub's and Ray's variational approaches to relativistic
hydrodynamics of perfect fluids into another simple formulation.Comment: 3 pages; published versio
Perfect magnetohydrodynamics as a field theory
We propose the generally covariant action for the theory of a self-coupled
complex scalar field and electromagnetism which by virtue of constraints is
equivalent, in the regime of long wavelengths, to perfect magnetohydrodynamics
(MHD). We recover from it the Euler equation with Lorentz force, and the
thermodynamic relations for a prefect fluid. The equation of state of the
latter is related to the scalar field's self potential. We introduce 1+3
notation to elucidate the relation between MHD and field variables. In our
approach the requirement that the scalar field be single valued leads to the
quantization of a certain circulation in steps of ; this feature leads,
in the classical limit, to the conservation of that circulation. The
circulation is identical to that in Oron's generalization of Kelvin's
circulation theorem to perfect MHD; we here characterize the new conserved
helicity associated with it. We also demonstrate the existence for MHD of two
Bernoulli-like theorems for each spacetime symmetry of the flow and geometry;
one of these is pertinent to suitably defined potential flow. We exhibit the
conserved quantities explicitly in the case that two symmetries are
simultaneously present, and give examples. Also in this case we exhibit a new
conserved MHD circulation distinct from Oron's, and provide an example.Comment: RevTeX, 16 pages, no figures; clarifications added and typos
corrected; version to be published in Phys. Rev.
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
Human factors and missed solutions to Enigma design weaknesses
The German World War II Enigma suffered from design weaknesses that facilitated its large-scale decryption by the British throughout the war. The author shows that the main technical weaknesses (self-coding and reciprocal coding) could have been avoided using simple contemporary technology, and therefore the true cause of the weaknesses is not technological but must be sought elsewhere. Specifically, human factors issues resulted in the persistent failure to seek out more effective designs. Similar limitations seem to beset the literature on the period, which misunderstands the Enigma weaknesses and therefore inhibits broader thinking about design or realising the critical role of human factors engineering in cryptography
Thermal conductivity through the nineteenth century
As a material property and as a metaphor, thermal conductivity occupies an
important position in physical, biological and geological sciences. Yet, its
precise measurement is dependent on using electricity as a proxy because
flowing heat cannot directly be measured.Comment: Submitted to Physics Today. 4,500 words, 4 figure
Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars
We develop the formalism required to study the nonlinear interaction of modes
in rotating Newtonian stars in the weakly nonlinear regime. The formalism
simplifies and extends previous treatments. At linear order, we elucidate and
extend slightly a formalism due to Schutz, show how to decompose a general
motion of a rotating star into a sum over modes, and obtain uncoupled equations
of motion for the mode amplitudes under the influence of an external force.
Nonlinear effects are added perturbatively via three-mode couplings. We
describe a new, efficient way to compute the coupling coefficients, to zeroth
order in the stellar rotation rate, using spin-weighted spherical harmonics.
We apply this formalism to derive some properties of the coupling
coefficients relevant to the nonlinear interactions of unstable r-modes in
neutron stars, postponing numerical integrations of the coupled equations of
motion to a later paper. From an astrophysical viewpoint, the most interesting
result of this paper is that many couplings of r-modes to other rotational
modes (modes with zero frequencies in the non-rotating limit) are small: either
they vanish altogether because of various selection rules, or they vanish to
lowest order in the angular velocity. In zero-buoyancy stars, the coupling of
three r-modes is forbidden entirely and the coupling of two r-modes to one
hybrid rotational mode vanishes to zeroth order in rotation frequency. In
incompressible stars, the coupling of any three rotational modes vanishes to
zeroth order in rotation frequency.Comment: 62 pages, no figures. Corrected error in computation of coupling
coefficients, added new selection rule and an appendix on energy and angular
momentum of mode