32 research outputs found
Transformation Properties of the Lagrangian and Eulerian Strain Tensors
A coordinate independent derivation of the Eulerian and Lagrangian strain
tensors of finite deformation theory is given based on the parallel propagator,
the world function, and the displacement vector field as a three-point tensor.
The derivation explicitly shows that the Eulerian and Lagrangian strain tensors
are two-point tensors, each a function of both the spatial and material
coordinates. The Eulerian strain is a two-point tensor that transforms as a
second rank tensor under transformation of spatial coordinates and transforms
as a scalar under transformation of the material coordinates. The Lagrangian
strain is a two-point tensor that transforms as scalar under transformation of
spatial coordinates and transforms as a second rank tensor under transformation
of the material coordinates. These transformation properties are needed when
transforming the strain tensors from one frame of reference to another moving
frame.Comment: 35 pages double-space, 3 figure
Clock Synchronization and Navigation in the Vicinity of the Earth
Clock synchronization is the backbone of applications such as high-accuracy
satellite navigation, geolocation, space-based interferometry, and
cryptographic communication systems. The high accuracy of synchronization
needed over satellite-to-ground and satellite-to-satellite distances requires
the use of general relativistic concepts. The role of geometrical optics and
antenna phase center approximations are discussed in high accuracy work. The
clock synchronization problem is explored from a general relativistic point of
view, with emphasis on the local measurement process and the use of the tetrad
formalism as the correct model of relativistic measurements. The treatment
makes use of J. L. Synge's world function of space-time as a basic coordinate
independent geometric concept. A metric is used for space-time in the vicinity
of the Earth, where coordinate time is proper time on the geoid. The problem of
satellite clock syntonization is analyzed by numerically integrating the
geodesic equations of motion for low-Earth orbit (LEO), geosynchronous orbit
(GEO), and highly elliptical orbit (HEO) satellites. Proper time minus
coordinate time is computed for satellites in these orbital regimes. The
frequency shift as a function of time is computed for a signal observed on the
Earth's geoid from a LEO, GEO, and HEO satellite. Finally, the problem of
geolocation in curved space-time is briefly explored using the world function
formalism.Comment: 49 pages, 19 figures. To be published in "Progress in General
Relativity and Quantum Cosmology Research", Nova Science Publishers, Inc.,
Hauppauge, New York, December 2004. Paper was replaced due to font problems
in the figure
Stress in Rotating Disks and Cylinders
The solution of the classic problem of stress in a rotating elastic disk or
cylinder, as solved in standard texts on elasticity theory, has two features:
dynamical equations are used that are valid only in an inertial frame of
reference, and quadratic terms are dropped in displacement gradient in the
definition of the strain. I show that, in an inertial frame of reference where
the dynamical equations are valid, it is incorrect to drop the quadratic terms
because they are as large as the linear terms that are kept. I provide an
alternate formulation of the problem by transforming the dynamical equations to
a corotating frame of reference of the disk/cylinder, where dropping the
quadratic terms in displacement gradient is justified. The analysis shows that
the classic textbook derivation of stress and strain must be interpreted as
being carried out in the corotating frame of the medium.Comment: 13 pages. This is a detailed derivation of stress in rotating disks
and cylinder
Quantum Positioning System
A quantum positioning system (QPS) is proposed that can provide a user with
all four of his space-time coordinates. The user must carry a corner cube
reflector, a good clock, and have a two-way classical channel of communication
with the origin of the reference frame. Four pairs of entangled photons
(biphotons) are sent through four interferometers: three interferometers are
used to determine the user's spatial position, and an additional interferometer
is used to synchronize the user's clock to coordinate time in the reference
frame. The spatial positioning part of the QPS is similar to a classical
time-of-arrival (TOA) system, however, a classical TOA system (such as GPS)
must have synchronized clocks that keep coordinate time and therefore the
clocks must have long-term stability, whereas in the QPS only a photon
coincidence counter is needed and the clocks need only have short-term
stability. Several scenarios are considered for a QPS: one is a terrestrial
system and another is a space-based-system composed of low-Earth orbit (LEO)
satellites. Calculations indicate that for a space-based system, neglecting
atmospheric effects, a position accuracy below the 1 cm-level is possible for
much of the region near the Earth. The QPS may be used as a primary system to
define a global 4-dimensional reference frame.Comment: 20 pages, 10 figure
Fermi Coordinates of an Observer Moving in a Circle in Minkowski Space: Apparent Behavior of Clocks
Coordinate transformations are derived from global Minkowski coordinates to
the Fermi coordinates of an observer moving in a circle in Minkowski
space-time. The metric for the Fermi coordinates is calculated directly from
the tensor transformation rule. The behavior of ideal clocks is examined from
the observer's reference frame using the Fermi coordinates. A complicated
relation exists between Fermi coordinate time and proper time on stationary
clocks (in the Fermi frame) and between proper time on satellite clocks that
orbit the observer. An orbital Sagnac-like effect exists for portable clocks
that orbit the Fermi coordinate origin. The coordinate speed of light is
isotropic but varies with Fermi coordinate position and time. The magnitudes of
these kinematic effects are computed for parameters that are relevant to the
Global Positioning System (GPS) and are found to be small; however, for future
high-accuracy time transfer systems, these effects may be of significant
magnitude
Interaction of Diatomic Molecules with Photon Angular Momentum
The interaction of a diatomic molecule with photons carrying well-defined
angular momentum and parity is investigated to determine whether photon
absorption can induce molecular rotational transitions between states having
angular momentum . A transformation from laboratory coordinates to
coordinates with origin at the center-of-mass of the nuclei is used to obtain
the interaction between the photons and the molecule's center-of-mass,
electronic, and rotational degrees of freedom. For molecules making transitions
between rotational levels, there is a small parameter, , where
is the photon wave vector and is the size of the molecule, which enters
into the and photon absorption probabilities. For electric photons
having arbitrary angular momentum , the probability of absorbing an
photon divided by the probability of absorbing an photon, scales
as . The probability of absorbing an photon, divided
by the probability of absorbing and photon scales according to the same
factor.Comment: 9 pages, no figure
Transfer of Spatial Reference Frame Using Singlet States and Classical Communication
A simple protocol is described for transferring spatial direction from Alice
to Bob (two spatially separated observers) up to inversion. The two observers
are assumed to share quantum singlet states and classical communication. The
protocol assumes that Alice and Bob have complete free will (measurement
independence) and is based on maximizing the Shannon mutual information between
Alice and Bob's measurement outcomes. Repeated use of this protocol for each
spatial axis of Alice allows transfer of a complete 3-dimensional reference
frame, up to inversion of each of the axes. The technological complexity of
this protocol is similar to that needed for BB84 quantum key distribution, and
hence is much simpler to implement than recently proposed schemes for
transmission of reference frames. A second protocol based on a Bayesian
formalism is also presented.Comment: 6 pages, 3 figure
Force on an Asymmetric Capacitor
When a high voltage (~30 kV) is applied to a capacitor whose electrodes have
different physical dimensions, the capacitor experiences a net force toward the
smaller electrode (Biefeld-Brown effect). We have verified this effect by
building four capacitors of different shapes. The effect may have applications
to vehicle propulsion and dielectric pumps. We review the history of this
effect briefly through the history of patents by Thomas Townsend Brown. At
present, the physical basis for the Biefeld-Brown effect is not understood. The
order of magnitude of the net force on the asymmetric capacitor is estimated
assuming two different mechanisms of charge conduction between its electrodes:
ballistic ionic wind and ionic drift. The calculations indicate that ionic wind
is at least three orders of magnitude too small to explain the magnitude of the
observed force on the capacitor. The ionic drift transport assumption leads to
the correct order of magnitude for the force, however, it is difficult to see
how ionic drift enters into the theory. Finally, we present a detailed
thermodynamic treatment of the net force on an asymmetric capacitor. In the
future, to understand this effect, a detailed theoretical model must be
constructed that takes into account plasma effects: ionization of gas (or air)
in the high electric field region, charge transport, and resulting dynamic
forces on the electrodes. The next series of experiments should determine
whether the effect occurs in vacuum, and a careful study should be carried out
to determine the dependence of the observed force on gas pressure, gas species
and applied voltage.Comment: 25 pages, new version has corrections of typos and wording, and
additional references added. This version is to be published as an Army
Research Laboratory Technical Report (in press, March 2003
Tradeoff between Efficiency and Melting for a High-Performance Electromagnetic Rail Gun
We estimate the temperature distribution in the rails of an electromagnetic
rail gun (EMG) due to the confinement of the current in a narrow surface layer
resulting from the skin effect. In order to obtain analytic results, we assume
a simple geometry for the rails, an electromagnetic skin effect boundary edge
that propagates with the accelerating armature, and a current carrying channel
controlled by magnetic field diffusion into the rails. We compute the
temperature distribution in the rails at the time that the armature leaves the
rails. For the range of exit velocities, from 1500 m/s to 5000 m/s, we find the
highest temperatures are near the gun breech. After a single gun firing, the
temperature reaches the melting temperature of the metal rails in a layer of
finite thickness near the surface of the rails, for rails made of copper or
tantalum. We plot the thickness of the melt layer as a function of position
along the rails. In all cases, the thickness of the melt layer increases with
gun velocity, making damage to the gun rails more likely at higher velocity. We
also calculate the efficiency of the EMG as a function of gun velocity and find
that the efficiency increases with increasing velocity, but only if the length
of the gun is sufficiently long. The thickness of the melted layer also
decreases with increasing rail length. Therefore, there is a tradeoff: for
rails of sufficient length, the gun efficiency increases with increasing
velocity but the melted layer thickness in the rails also increases.Comment: 10 pages, 13 figure
Phase Sensitivity of a Mach-Zehnder Quantum Sensor
We investigate the dependence of the fidelity of a Mach-Zehnder quantum
interferometer on the prior information about the phase, for Fock state input
and for maximally entangled (N00N) state input. For no prior information, the
fidelity for Fock state input is greater than for N00N state input. In the
limit of a narrow distribution describing the prior information, we find that
both Fock and N00N state inputs lead to nearly equal fidelity.Comment: 4 pages, 4 figure