42,148 research outputs found
Necessity of Acceleration-Induced Nonlocality
The purpose of this paper is to explain clearly why nonlocality must be an
essential part of the theory of relativity. In the standard local version of
this theory, Lorentz invariance is extended to accelerated observers by
assuming that they are pointwise inertial. This locality postulate is exact
when dealing with phenomena involving classical point particles and rays of
radiation, but breaks down for electromagnetic fields, as field properties in
general cannot be measured instantaneously. The problem is corrected in
nonlocal relativity by supplementing the locality postulate with a certain
average over the past world line of the observer.Comment: 12 pages; v2: improved version accepted for publication in Ann. Phys.
(Berlin
Mach's Principle
We briefly review the history of Mach's principle and discuss its
significance in the light of modern physics.Comment: 20 pages; v2: improved version published as the second chapter of The
Measurement of Gravitomagnetism: A Challenging Enterprise, edited by L. Iorio
(Nova Science, New York, 2007), pp. 13-2
Explicit Fermi Coordinates and Tidal Dynamics in de Sitter and Goedel Spacetimes
Fermi coordinates are directly constructed in de Sitter and Goedel spacetimes
and the corresponding exact coordinate transformations are given explicitly.
The quasi-inertial Fermi coordinates are then employed to discuss the dynamics
of a free test particle in these spacetimes and the results are compared to the
corresponding generalized Jacobi equations that contain only the lowest-order
tidal terms. The domain of validity of the generalized Jacobi equation is thus
examined in these cases. Furthermore, the difficulty of constructing explicit
Fermi coordinates in black-hole spacetimes is demonstrated.Comment: 23 pages, 3 figures; v2: expanded version (27 pages, 3 figures
Distribution of parallel vortices studied by spin-polarized neutron reflectivity and magnetization
We present the studies of non-uniformly distributed vortices in Nb/Al
multilayers at applied field near parallel to film surface by using
spin-polarized neutron reflectivity (SPNR) and DC magnetization measurements.
We have observed peaks above the lower critical field, Hc1, in the M-H curves
from the multilayers.
Previous works with a model calculation of minimizing Gibbs free energy have
suggested that the peaks could be ascribed to vortex line transitions for
spatial commensuration in a thin film superconductor. In order to directly
determine the distribution of vortices, we performed SPNR measurements on the
multilayer and found that the distribution and density of vortices are
different at ascending and descending fields. At ascending 2000 Oe which is
just below the first peak in the M-H curve, SPNR shows that vortices are mostly
localized near a middle line of the film meanwhile the vortices are distributed
in broader region at the descending 2000 Oe. That is related to the observation
of more vortices trapped at the descending field. As the applied field is
sightly tilted (< 3.5degree), we observe another peak at a smaller field. The
peak position is consistent with the parallel lower critical field (Hc1||). We
discuss that the vortices run along the applied field below Hc1|| and rotate
parallel to the surface at Hc1||.Comment: 17 pages, 9 figure
Heterostructure unipolar spin transistors
We extend the analogy between charge-based bipolar semiconductor electronics
and spin-based unipolar electronics by considering unipolar spin transistors
with different equilibrium spin splittings in the emitter, base, and collector.
The current of base majority spin electrons to the collector limits the
performance of ``homojunction'' unipolar spin transistors, in which the
emitter, base, and collector all are made from the same magnetic material. This
current is very similar in origin to the current of base majority carriers to
the emitter in homojunction bipolar junction transistors. The current in
bipolar junction transistors can be reduced or nearly eliminated through the
use of a wide band gap emitter. We find that the choice of a collector material
with a larger equilibrium spin splitting than the base will similarly improve
the device performance of a unipolar spin transistor. We also find that a
graded variation in the base spin splitting introduces an effective drift field
that accelerates minority carriers through the base towards the collector.Comment: 9 pages, 2 figure
Nonlocality of Accelerated Systems
The conceptual basis for the nonlocality of accelerated systems is presented.
The nonlocal theory of accelerated observers and its consequences are briefly
described. Nonlocal field equations are developed for the case of the
electrodynamics of linearly accelerated systems.Comment: LaTeX file, no figures, 9 pages, to appear in: "Black Holes,
Gravitational Waves and Cosmology" (World Scientific, Singapore, 2003
Extension of weakly and strongly F-regular rings by flat maps
Let (R,m) -> (S,n) be a flat local homomorphism of excellent local rings. We
investigate the conditions under which the weak or strong F-regularity of R
passes to S. We show that is suffices that the closed fiber S/mS be Gorenstein
and either F-finite (if R and S have a common test element), or F-rational
(otherwise)
Test ideals and flat base change problems in tight closure theory
Test ideals are an important concept in tight closure theory and their
behavior via flat base change can be very difficult to understand. Our paper
presents results regarding this behavior under flat maps with reasonably nice
(but far from smooth) fibers. This involves analyzing, in depth, a special type
of ideal of test elements, called the CS test ideal. Besides providing new
results, the paper also contains extensions of a theorem by G. Lyubeznik and K.
E. Smith on the completely stable test ideal and of theorems by F. Enescu and,
independently, M. Hashimoto on the behavior of F-rationality under flat base
change.Comment: 18 pages, to appear in Trans. Amer. Math. So
The Structure of F-Pure Rings
For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write
R^{1/q} = R^{a_q} \oplus M_q, where M_q has no free direct summands over R. We
investigate the structure of F-finite, F-pure rings R by studying how the
numbers a_q grow with respect to q. This growth is quantified by the splitting
dimension and the splitting ratios of R which we study in detail. We also prove
the existence of a special prime ideal P(R) of R, called the splitting prime,
that has the property that R/P(R) is strongly F-regular. We show that this
ideal captures significant information with regard to the F-purity of R.Comment: 15 page
Prospects in the orbital and rotational dynamics of the Moon with the advent of sub-centimeter lunar laser ranging
Lunar Laser Ranging (LLR) measurements are crucial for advanced exploration
of the laws of fundamental gravitational physics and geophysics. Current LLR
technology allows us to measure distances to the Moon with a precision
approaching 1 millimeter. As NASA pursues the vision of taking humans back to
the Moon, new, more precise laser ranging applications will be demanded,
including continuous tracking from more sites on Earth, placing new CCR arrays
on the Moon, and possibly installing other devices such as transponders, etc.
Successful achievement of this goal strongly demands further significant
improvement of the theoretical model of the orbital and rotational dynamics of
the Earth-Moon system. This model should inevitably be based on the theory of
general relativity, fully incorporate the relevant geophysical processes, lunar
librations, tides, and should rely upon the most recent standards and
recommendations of the IAU for data analysis. This paper discusses methods and
problems in developing such a mathematical model. The model will take into
account all the classical and relativistic effects in the orbital and
rotational motion of the Moon and Earth at the sub-centimeter level. The new
model will allow us to navigate a spacecraft precisely to a location on the
Moon. It will also greatly improve our understanding of the structure of the
lunar interior and the nature of the physical interaction at the core-mantle
interface layer. The new theory and upcoming millimeter LLR will give us the
means to perform one of the most precise fundamental tests of general
relativity in the solar system.Comment: 26 pages, submitted to Proc. of ASTROCON-IV conference (Princeton
Univ., NJ, 2007
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