213 research outputs found
Multipole moments in Kaluza-Klein theories
This paper contains discussion of the problem of motion of extended i.e. non
point test bodies in multidimensional space. Extended bodies are described in
terms of so called multipole moments. Using approximated form of equations of
motion for extended bodies deviation from geodesic motion is derived. Results
are applied to special form of space-time.Comment: 11 pages, AMS-TeX, few misprints corrected, to appear in Classical
and Quantum Gravit
General relativistic spinning fluids with a modified projection tensor
An energy-momentum tensor for general relativistic spinning fluids compatible
with Tulczyjew-type supplementary condition is derived from the variation of a
general Lagrangian with unspecified explicit form. This tensor is the sum of a
term containing the Belinfante-Rosenfeld tensor and a modified perfect-fluid
energy-momentum tensor in which the four-velocity is replaced by a unit
four-vector in the direction of fluid momentum. The equations of motion are
obtained and it is shown that they admit a Friedmann-Robertson-Walker
space-time as a solution.Comment: Submitted to General Relativity and Gravitatio
Ultrafast transient lens spectroscopy of various C-40 carotenoids: lycopene, beta-carotene, (3R,3'R)- zeaxanthin, (3R,3'R,6'R)-lutein, echinenone, canthaxanthin, and astaxanthin
A Generalization of the Goldberg-Sachs Theorem and its Consequences
The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds
endowed with torsion-free connection compatible with the metric, the treatment
includes all signatures as well as complex manifolds. It is shown that when the
Weyl tensor is algebraically special severe geometric restrictions are imposed.
In particular it is demonstrated that the simple self-dual eigenbivectors of
the Weyl tensor generate integrable isotropic planes. Another result obtained
here is that if the self-dual part of the Weyl tensor vanishes in a Ricci-flat
manifold of (2,2) signature the manifold must be Calabi-Yau or symplectic and
admits a solution for the source-free Einstein-Maxwell equations.Comment: 14 pages. This version matches the published on
Earthquake-Resistant Fiber Reinforced Concrete Coupling Beams Without Diagonal Bars
Results from large-scale tests on fibre-reinforced concrete coupling beams subjected to large displacement reversals are reported. The main goal of using fibre reinforcement was to eliminate the need for diagonal bars and reduce the amount of confinement reinforcement required for adequate seismic performance. Experimental results indicate that the use of 30 mm long, 0.38 mm diameter hooked steel fibres with a 2300 MPa minimum tensile strength and in a volume fraction of 1.5% allows elimination of diagonal bars in coupling beams with span-todepth ratios greater than or equal to 2.2. Further, no special confinement reinforcement is required except at the ends of the coupling beams. The fibre-reinforced concrete coupling beam design was implemented in a high-rise building in the city of Seattle, WA, USA. A brief description of the coupling beam design used for this building, and construction process followed in the field, is provided
On a class of invariant coframe operators with application to gravity
Let a differential 4D-manifold with a smooth coframe field be given. Consider
the operators on it that are linear in the second order derivatives or
quadratic in the first order derivatives of the coframe, both with coefficients
that depend on the coframe variables. The paper exhibits the class of operators
that are invariant under a general change of coordinates, and, also, invariant
under the global SO(1,3)-transformation of the coframe. A general class of
field equations is constructed. We display two subclasses in it. The subclass
of field equations that are derivable from action principles by free variations
and the subclass of field equations for which spherical-symmetric solutions,
Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the
resulting metric is computed. Invoking the Geodesic Postulate, we find all the
equations that are experimentally (by the 3 classical tests) indistinguishable
from Einstein field equations. This family includes, of course, also Einstein
equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool
employed in the paper is an invariant formulation reminiscent of Cartan's
structural equations. The article sheds light on the possibilities and
limitations of the coframe gravity. It may also serve as a general procedure to
derive covariant field equations
Eutectic Colony Formation: A Stability Analysis
Experiments have widely shown that a steady-state lamellar eutectic
solidification front is destabilized on a scale much larger than the lamellar
spacing by the rejection of a dilute ternary impurity and forms two-phase cells
commonly referred to as `eutectic colonies'. We extend the stability analysis
of Datye and Langer for a binary eutectic to include the effect of a ternary
impurity. We find that the expressions for the critical onset velocity and
morphological instability wavelength are analogous to those for the classic
Mullins-Sekerka instability of a monophase planar interface, albeit with an
effective surface tension that depends on the geometry of the lamellar
interface and, non-trivially, on interlamellar diffusion. A qualitatively new
aspect of this instability is the occurence of oscillatory modes due to the
interplay between the destabilizing effect of the ternary impurity and the
dynamical feedback of the local change in lamellar spacing on the front motion.
In a transient regime, these modes lead to the formation of large scale
oscillatory microstructures for which there is recent experimental evidence in
a transparent organic system. Moreover, it is shown that the eutectic front
dynamics on a scale larger than the lamellar spacing can be formulated as an
effective monophase interface free boundary problem with a modified
Gibbs-Thomson condition that is coupled to a slow evolution equation for the
lamellar spacing. This formulation provides additional physical insights into
the nature of the instability and a simple means to calculate an approximate
stability spectrum. Finally, we investigate the influence of the ternary
impurity on a short wavelength oscillatory instability that is already present
at off-eutectic compositions in binary eutectics.Comment: 26 pages RevTex, 14 figures (28 EPS files); some minor changes;
references adde
Dynamics of a faceted nematic-smectic B front in thin-sample directional solidification
We present an experimental study of the directional-solidification patterns
of a nematic - smectic B front. The chosen system is C_4H_9-(C_6H_{10})_2CN (in
short, CCH4) in 12 \mu m-thick samples, and in the planar configuration
(director parallel to the plane of the sample). The nematic - smectic B
interface presents a facet in one direction -- the direction parallel to the
smectic layers -- and is otherwise rough, and devoid of forbidden directions.
We measure the Mullins-Sekerka instability threshold and establish the
morphology diagram of the system as a function of the solidification rate V and
the angle theta_{0} between the facet and the isotherms. We focus on the
phenomena occurring immediately above the instability threshold when theta_{0}
is neither very small nor close to 90^{o}. Under these conditions we observe
drifting shallow cells and a new type of solitary wave, called "faceton", which
consists essentially of an isolated macroscopic facet traveling laterally at
such a velocity that its growth rate with respect to the liquid is small.
Facetons may propagate either in a stationary, or an oscillatory way. The
detailed study of their dynamics casts light on the microscopic growth
mechanisms of the facets in this system.Comment: 12 pages, 19 figures, submitted to Phys. Rev.
Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid
A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff
fluid in general relativity is performed using the 1+3 covariant approach that
enables the dynamics of the fluid to be determined without assuming any
particular form for the space-time metric. The spin contributions to the field
equations produce a bounce that averts an initial singularity, provided that
the spin density exceeds the rate of shear. At later times, when the spin
contribution can be neglected, a Weyssenhoff fluid reduces to a standard
cosmological fluid in general relativity. Numerical solutions for the time
evolution of the generalised scale factor in spatially-curved models are
presented, some of which exhibit eternal oscillatory behaviour without any
singularities. In spatially-flat models, analytical solutions for particular
values of the equation-of-state parameter are derived. Although the scale
factor of a Weyssenhoff fluid generically has a positive temporal curvature
near a bounce, it requires unreasonable fine tuning of the equation-of-state
parameter to produce a sufficiently extended period of inflation to fit the
current observational data.Comment: 34 pages, 18 figure
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