528 research outputs found
Comments on the tethered galaxy problem
In a recent paper Davis et al. make the counter intuitive assertion that a
galaxy held `tethered' at a fixed distance from our own could emit blueshifted
light. Moreover, this effect may be derived from the simplest
Friedmann-Robertson-Walker spacetimes and the (0.3,0.7) case which is believed
to be a good late time model of our own universe.
In this paper we recover the previous authors' results in a more transparent
form. We show how their results rely on a choice of cosmological distance scale
and revise the calculations in terms of observable quantities which are
coordinate independent. By this method we see that, although such a tethering
would reduce the redshift of a receding object, it would not do so sufficiently
to cause the proposed blueshift. The effect is also demonstrated to be much
smaller than conjectured below the largest intergalactic scales. We also
discuss some important issues, raised by this scenario, relating to the
interpretation of redshift and distance in relativistic cosmology.Comment: 6 pages, 3 figures, submitted to Am.J.Phy
Research Progress Report: Fox-Pheasant Relationships in South Dakota, 1965
A 5-year cooperative study designed to obtain information regarding effects of foxes on pheasant populations in eastern South Dakota was initiated in 1964. Specific objectives were to determine (1) population fluctuations of foxes and pheasants, (2) fox food habits and reproductive characteristics and (3) effectiveness and cost of fox reduction to increase pheasant abundance. Studies were conducted on four pairs of 100-square-mile areas. Fox populations were reduced on one member of each pair beginning in January 1965, and individual foxes were removed on a complaint basis on the other. Each pair of areas is referred to as a unit. When summer pheasant data on the fox-reduction and check areas are considered, significant differences are noted in adult pheasants per mile, broods per mile, and brood size from 1964 to 1965. Changes in adult pheasants per mile in Unit 2 showed the decline in the fox-reduction area was significantly (0. 01) less than in the check area. However, in Units 1 and 4 the declines in the check areas were significantly (0. 01) less than those in the fox-reduction areas. The difference in decline in broods per mile in the fox-reduction compared to the check area from 1964 to 1965 was negligible in Unit 1. In Unit 2 the fox-reduction area showed a slight increase compared to a decrease in the check area. This difference is significant (0. 01). In Unit 4 a smaller decline occurred in the fox-reduction area than in the check area. The difference in Unit 4 is significant (0. 05). The proportion of hens with broods showed an increase from 1964 to 1965 in the fox-reduction areas of Units 1, 2, and 4 and a lesser increase or a decrease in the corresponding check areas. A significant (0. 01) increase in brood size occurred from 1964 to 1965 in the fox-reduction compared to the check area of Unit 1. A non-significant increase occurred in the check area compared to the fox-reduction area in Unit 2. The adult pheasant-per-mile averages during the spring of 1965 showed more birds in the fox-reduction area than in the check area of Unit 1, and the reverse in Unit 2. Neither difference is significant. Units 3 and 4 showed significantly (0. 01) more adults per mile in the fox reduction than in the check areas during this same period. Fox data revealed that counting tracks in snow along transects is the best of three methods for determining fox activity in an area. Such counts in reduction and check areas within each unit showed that fox activity was sufficiently comparable in each pair of areas prior to fox reduction. Methods used to reduce fox populations also reduced to some extent other predators, including nest robbers. Grasses, mice, pheasants, rabbits, and insects, in descending order, respectively, were the most frequently occurring items found in stomachs of foxes taken in the study areas from January to June 1965. Grasses were found in stomachs that also contained mice and insects. Pheasants were the item composing the greatest volume, followed by rabbits and mice. Prairie deer mice made up the majority of small mammal remains. (See more in Text
Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
The "metric" structure of nonrelativistic spacetimes consists of a one-form
(the absolute clock) whose kernel is endowed with a positive-definite metric.
Contrarily to the relativistic case, the metric structure and the torsion do
not determine a unique Galilean (i.e. compatible) connection. This subtlety is
intimately related to the fact that the timelike part of the torsion is
proportional to the exterior derivative of the absolute clock. When the latter
is not closed, torsionfreeness and metric-compatibility are thus mutually
exclusive. We will explore generalisations of Galilean connections along the
two corresponding alternative roads in a series of papers. In the present one,
we focus on compatible connections and investigate the equivalence problem
(i.e. the search for the necessary data allowing to uniquely determine
connections) in the torsionfree and torsional cases. More precisely, we
characterise the affine structure of the spaces of such connections and display
the associated model vector spaces. In contrast with the relativistic case, the
metric structure does not single out a privileged origin for the space of
metric-compatible connections. In our construction, the role of the Levi-Civita
connection is played by a whole class of privileged origins, the so-called
torsional Newton-Cartan (TNC) geometries recently investigated in the
literature. Finally, we discuss a generalisation of Newtonian connections to
the torsional case.Comment: 79 pages, 7 figures; v2: added material on affine structure of
connection space, former Section 4 postponed to 3rd paper of the serie
Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
We investigate properties of a quasi-local mass in a higher-dimensional
spacetime having symmetries corresponding to the isomertries of an
-dimensional maximally symmetric space in Einstein-Gauss-Bonnet gravity
in the presence of a cosmological constant. We assume that the Gauss-Bonnet
coupling constant is non-negative. The quasi-local mass was recently defined by
one of the authors as a counterpart of the Misner-Sharp quasi-local mass in
general relativity. The quasi-local mass is found to be a quasi-local conserved
charge associated with a locally conserved current constructed from the
generalized Kodama vector and exhibits the unified first law corresponding to
the energy-balance law. In the asymptotically flat case, it converges to the
Arnowitt-Deser-Misner mass at spacelike infinity, while it does to the
Deser-Tekin and Padilla mass at infinity in the case of asymptotically AdS.
Under the dominant energy condition, we show the monotonicity of the
quasi-local mass for any , while the positivity on an untrapped hypersurface
with a regular center is shown for and for with an additional
condition, where is the constant sectional curvature of each spatial
section of equipotential surfaces. Under a special relation between coupling
constants, positivity of the quasi-local mass is shown for any without
assumptions above. We also classify all the vacuum solutions by utilizing the
generalized Kodama vector. Lastly, several conjectures on further
generalization of the quasi-local mass in Lovelock gravity are proposed.Comment: 13 pages, no figures, 1 table; v4, new results added in the
asymptotically AdS case, accepted for publication in Physical Review
Probing single molecule orientations in model lipid membranes with near-field scanning optical microscopy
This is the published version, also available here: http://dx.doi.org/10.1063/1.481367.Single molecule near-field fluorescence measurements are utilized to characterize the molecular level structure in LangmuirâBlodgett monolayers of L-α-dipalmitoylphosphatidylcholine (DPPC).Monolayers incorporating 3Ă10â4 molâ% of the fluorescent lipid analog N-(6-tetramethylrhodaminethiocarbamoyl)-1,2-dihexadecanoyl-sn- glycero-3-phosphoethanolamine, triethylammonium salt (TRITCâDHPE) are transferred onto a freshly cleaved mica surface at low (Ï=8âmN/m) and high (Ï=30âmN/m)surfacepressures. The near-field fluorescence images exhibit shapes in the single molecule images that are indicative of the lipid analog probe orientation within the films. Modeling the fluorescence patterns yields the single molecule tilt angle distribution in the monolayers which indicates that the majority of the molecules are aligned with their absorption dipole moment pointed approximately normal to the membrane plane. Histograms of the data indicate that the average orientation of the absorption dipole moment is 2.2° (Ï=4.8°) in monolayers transferred at Ï=8âmN/m and 2.4° (Ï=5.0°) for monolayers transferred at Ï=30âmN/m. There is no statistical difference in the mean tilt angle or distribution for the two monolayer conditions studied. The insensitivity of tilt angle to filmsurfacepressure may arise from small chromophore doped domains of trapped liquid-expanded lipid phase remaining at high surfacepressure. There is no evidence in the near-field fluorescence images for probe molecules oriented with their dipole moment aligned parallel with the membrane plane. We do, however, find a small but significant population of probe molecules (âŒ13%) with tilt angles greater than 16°. Comparison of the simultaneously collected near-field fluorescence and force images suggests that these large angle orientations are not the result of significant defects in the films. Instead, this small population may represent a secondary insertion geometry for the probe molecule into the lipidmonolayer
Maxwell Fields and Shear-Free Null Geodesic Congruences
We study and report on the class of vacuum Maxwell fields in Minkowski space
that possess a non-degenerate, diverging, principle null vector field (null
eigenvector field of the Maxwell tensor) that is tangent to a shear-free null
geodesics congruence. These congruences can be either surface forming (the
tangent vectors proportional to gradients) or not, i.e., the twisting
congruences. In the non-twisting case, the associated Maxwell fields are
precisely the Lienard-Wiechert fields, i.e., those Maxwell fields arising from
an electric monopole moving on an arbitrary worldline. The null geodesic
congruence is given by the generators of the light-cones with apex on the
world-line. The twisting case is much richer, more interesting and far more
complicated. In a twisting subcase, where our main interests lie, it can be
given the following strange interpretation. If we allow the real Minkowski
space to be complexified so that the real Minkowski coordinates x^a take
complex values, i.e., x^a => z^a=x^a+iy^a with complex metric g=eta_abdz^adz^b,
the real vacuum Maxwell equations can be extended into the complex and
rewritten as curlW =iWdot, divW with W =E+iB. This subcase of Maxwell fields
can then be extended into the complex so as to have as source, a complex
analytic world-line, i.e., to now become complex Lienard-Wiechart fields. When
viewed as real fields on the real Minkowski space, z^a=x^a, they possess a real
principle null vector that is shear-free but twisting and diverging. The twist
is a measure of how far the complex world-line is from the real 'slice'. Most
Maxwell fields in this subcase are asymptotically flat with a time-varying set
of electric and magnetic moments, all depending on the complex displacements
and the complex velocities.Comment: 3
Linear Einstein equations and Kerr-Schild maps
We prove that given a solution of the Einstein equations for the
matter field , an autoparallel null vector field and a solution
of the linearized Einstein equation on the
given background, the Kerr-Schild metric ( arbitrary constant) is an exact solution of the Einstein equation for the
energy-momentum tensor . The mixed form of the Einstein equation for
Kerr-Schild metrics with autoparallel null congruence is also linear. Some more
technical conditions hold when the null congruence is not autoparallel. These
results generalize previous theorems for vacuum due to Xanthopoulos and for
flat seed space-time due to G\"{u}rses and G\"{u}rsey.Comment: 9 pages, accepted by Class. Quant. Gra
Lagrangian and Hamiltonian for the Bondi-Sachs metrics
We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the
Einstein vacuum equations in a closed form. Following the Dirac approach to
constrained systems we investigate the related Hamiltonian formulation.Comment: 8 page
Non-Abelian pp-waves in D=4 supergravity theories
The non-Abelian plane waves, first found in flat spacetime by Coleman and
subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are
shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity
theories coupled to scalar and vector multiplets, including the theory of SU(2)
Yang-Mills coupled to an axion \sigma and dilaton \phi recently obtained as the
reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this
latter case they provide the most general supersymmetric solution. Passing to
the Riemannian formulation of this theory we show that the most general
supersymmetric solution may be constructed starting from a self-dual Yang-Mills
connection on a self-dual metric and solving a Poisson equation for e^\phi. We
also present the generalization of these solutions to non-Abelian AdS pp-waves
which allow a negative cosmological constant and preserve 1/4 of supersymmetry.Comment: Latex, 1+12 page
3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations
The equivalence problem for second order ODEs given modulo point
transformations is solved in full analogy with the equivalence problem of
nondegenerate 3-dimensional CR structures. This approach enables an analog of
the Feffereman metrics to be defined. The conformal class of these (split
signature) metrics is well defined by each point equivalence class of second
order ODEs. Its conformal curvature is interpreted in terms of the basic point
invariants of the corresponding class of ODEs
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