11,724 research outputs found
A covariant formalism of spin precession with respect to a reference congruence
We derive an effectively three-dimensional relativistic spin precession
formalism. The formalism is applicable to any spacetime where an arbitrary
timelike reference congruence of worldlines is specified. We employ what we
call a stopped spin vector which is the spin vector that we would get if we
momentarily make a pure boost of the spin vector to stop it relative to the
congruence. Starting from the Fermi transport equation for the standard spin
vector we derive a corresponding transport equation for the stopped spin
vector. Employing a spacetime transport equation for a vector along a
worldline, corresponding to spatial parallel transport with respect to the
congruence, we can write down a precession formula for a gyroscope relative to
the local spatial geometry defined by the congruence. This general approach has
already been pursued by Jantzen et. al. (see e.g. Jantzen, Carini and Bini,
Ann. Phys. 215 (1997) 1), but the algebraic form of our respective expressions
differ. We are also applying the formalism to a novel type of spatial parallel
transport introduced in Jonsson (Class. Quantum Grav. 23 (2006) 1), as well as
verifying the validity of the intuitive approach of a forthcoming paper
(Jonsson, Am. Journ. Phys. 75 (2007) 463) where gyroscope precession is
explained entirely as a double Thomas type of effect. We also present the
resulting formalism in explicit three-dimensional form (using the boldface
vector notation), and give examples of applications.Comment: 27 pages, 8 figure
Degree growth of meromorphic surface maps
We study the degree growth of iterates of meromorphic selfmaps of compact
Kahler surfaces. Using cohomology classes on the Riemann-Zariski space we show
that the degrees grow similarly to those of mappings that are algebraically
stable on some birational model.Comment: 17 pages, final version, to appear in Duke Math Journa
Singular semipositive metrics in non-Archimedean geometry
Let X be a smooth projective Berkovich space over a complete discrete
valuation field K of residue characteristic zero, endowed with an ample line
bundle L. We introduce a general notion of (possibly singular) semipositive (or
plurisubharmonic) metrics on L, and prove the analogue of the following two
basic results in the complex case: the set of semipositive metrics is compact
modulo constants, and each semipositive metric is a decreasing limit of smooth
semipositive ones. In particular, for continuous metrics our definition agrees
with the one by S.-W. Zhang. The proofs use multiplier ideals and the
construction of suitable models of X over the valuation ring of K, using
toroidal techniques.Comment: 49 pages, 1 figure. Accepted in the Journal of Algebraic Geometr
Generalizing Optical Geometry
We show that by employing the standard projected curvature as a measure of
spatial curvature, we can make a certain generalization of optical geometry
(Abramowicz and Lasota 1997, Class. Quantum Grav. 14 (1997) A23). This
generalization applies to any spacetime that admits a hypersurface orthogonal
shearfree congruence of worldlines. This is a somewhat larger class of
spacetimes than the conformally static spacetimes assumed in standard optical
geometry. In the generalized optical geometry, which in the generic case is
time dependent, photons move with unit speed along spatial geodesics and the
sideways force experienced by a particle following a spatially straight line is
independent of the velocity. Also gyroscopes moving along spatial geodesics do
not precess (relative to the forward direction). Gyroscopes that follow a
curved spatial trajectory precess according to a very simple law of
three-rotation. We also present an inertial force formalism in coordinate
representation for this generalization. Furthermore, we show that by employing
a new sense of spatial curvature (Jonsson, Class. Quantum Grav. 23 (2006) 1)
closely connected to Fermat's principle, we can make a more extensive
generalization of optical geometry that applies to arbitrary spacetimes. In
general this optical geometry will be time dependent, but still geodesic
photons move with unit speed and follow lines that are spatially straight in
the new sense. Also, the sideways experienced (comoving) force on a test
particle following a line that is straight in the new sense will be independent
of the velocity.Comment: 19 pages, 1 figure. A more general analysis is presented than in the
former version. See also the companion papers arXiv:0708.2493,
arXiv:0708.2533 and arXiv:0708.253
Inertial forces and the foundations of optical geometry
Assuming a general timelike congruence of worldlines as a reference frame, we
derive a covariant general formalism of inertial forces in General Relativity.
Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota,
Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of
spacetime and investigate how these affect the inertial force formalism. While
many ways of describing spatial curvature of a trajectory has been discussed in
papers prior to this, one particular prescription (which differs from the
standard projected curvature when the reference is shearing) appears novel. For
the particular case of a hypersurface-forming congruence, using a suitable
rescaling of spacetime, we show that a geodesic photon is always following a
line that is spatially straight with respect to the new curvature measure. This
fact is intimately connected to Fermat's principle, and allows for a certain
generalization of the optical geometry as will be further pursued in a
companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For
the particular case when the shear-tensor vanishes, we present the inertial
force equation in three-dimensional form (using the bold face vector notation),
and note how similar it is to its Newtonian counterpart. From the spatial
curvature measures that we introduce, we derive corresponding covariant
differentiations of a vector defined along a spacetime trajectory. This allows
us to connect the formalism of this paper to that of Jantzen et. al. (see e.g.
Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure
Non-equilibrium dynamics in an interacting nanoparticle system
Non-equilibrium dynamics in an interacting Fe-C nanoparticle sample,
exhibiting a low temperature spin glass like phase, has been studied by low
frequency ac-susceptibility and magnetic relaxation experiments. The
non-equilibrium behavior shows characteristic spin glass features, but some
qualitative differences exist. The nature of these differences is discussed.Comment: 7 pages, 11 figure
A streamwise-constant model of turbulent pipe flow
A streamwise-constant model is presented to investigate the basic mechanisms
responsible for the change in mean flow occuring during pipe flow transition.
Using a single forced momentum balance equation, we show that the shape of the
velocity profile is robust to changes in the forcing profile and that both
linear non-normal and nonlinear effects are required to capture the change in
mean flow associated with transition to turbulence. The particularly simple
form of the model allows for the study of the momentum transfer directly by
inspection of the equations. The distribution of the high- and low-speed
streaks over the cross-section of the pipe produced by our model is remarkably
similar to one observed in the velocity field near the trailing edge of the
puff structures present in pipe flow transition. Under stochastic forcing, the
model exhibits a quasi-periodic self-sustaining cycle characterized by the
creation and subsequent decay of "streamwise-constant puffs", so-called due to
the good agreement between the temporal evolution of their velocity field and
the projection of the velocity field associated with three-dimensional puffs in
a frame of reference moving at the bulk velocity. We establish that the flow
dynamics are relatively insensitive to the regeneration mechanisms invoked to
produce near-wall streamwise vortices and that using small, unstructured
background disturbances to regenerate the streamwise vortices is sufficient to
capture the formation of the high- and low-speed streaks and their segregation
leading to the blunting of the velocity profile characteristic of turbulent
pipe flow
A nonlinear Schr\"odinger equation for water waves on finite depth with constant vorticity
A nonlinear Schr\"odinger equation for the envelope of two dimensional
surface water waves on finite depth with non zero constant vorticity is
derived, and the influence of this constant vorticity on the well known
stability properties of weakly nonlinear wave packets is studied. It is
demonstrated that vorticity modifies significantly the modulational instability
properties of weakly nonlinear plane waves, namely the growth rate and
bandwidth. At third order we have shown the importance of the coupling between
the mean flow induced by the modulation and the vorticity. Furthermore, it is
shown that these plane wave solutions may be linearly stable to modulational
instability for an opposite shear current independently of the dimensionless
parameter kh, where k and h are the carrier wavenumber and depth respectively
Lensing magnification of supernovae in the GOODS-fields
Gravitational lensing of high-redshift supernovae is potentially an important
source of uncertainty when deriving cosmological parameters from the measured
brightness of Type Ia supernovae, especially in deep surveys with scarce
statistics. Photometric and spectroscopic measurements of foreground galaxies
along the lines-of-sight of 33 supernovae discovered with the Hubble Space
Telescope, both core-collapse and Type Ia, are used to model the magnification
probability distributions of the sources. Modelling galaxy halos with SIS or
NFW-profiles and using M/L scaling laws provided by the Faber-Jackson and
Tully-Fisher relations, we find clear evidence for supernovae with lensing
(de)magnification. However, the magnification distribution of the Type Ia
supernovae used to determine cosmological distances matches very well the
expectations for an unbiased sample, i.e.their mean magnification factor is
consistent with unity. Our results show that the lensing distortions of the
supernova brightness can be well understood for the GOODS sample and that
correcting for this effect has a negligible impact on the derived cosmological
parameters.Comment: 22 pages, 9 figures, accepted for publication by Ap
Reconsidering Res Judicata: A Comparative Perspective
We aimed to prospectively investigate the paternal antigen-induced cytokine secretion by peripheral blood mononuclear cells (PBMCs) in response to hormone treatment in women undergoing in vitro fertilisation (IVF) and to examine the predictive value of the cytokine secretion profile in the outcome of IVF treatment, in a pilot study. Twenty-five women were included and IVF treatment was successful for six and unsuccessful for 19 women. Blood samples were collected before IVF treatment, on four occasions during IVF and four weeks after embryo transfer. The numbers of Th1-, Th2- and Th17-associated cytokine-secreting cells and cytokine levels in cell supernatants were analysed by enzyme-linked immunospot-forming (ELISpot), enzyme-linked immune-sorbent (ELISA) or Luminex assay. None of the cytokines (IFN-Îł, IL-4, IL-5, IL-10, IL-12, IL-13, IL-17, TNF and GM-CSF) had any predictive value regarding IVF outcome. The majority of the cytokines reached their peak levels at ovum pick-up, suggesting an enhancing influence of the hormonal stimulation. Pregnancy was associated with a high number of IL-4-, IL-5- and IL-13-secreting cells four weeks after ET. In conclusion, the results do not support our hypothesis of a more pronounced peripheral Th1 and Th17 deviation towards paternal antigens in infertile women with an unsuccessful IVF outcome, although this is based on a small number of observations. A larger study is required to confirm this conclusion. Higher numbers of Th2-associated cytokine-secreting cells in pregnant women four weeks after ET do corroborate the hypothesis of a Th2 deviation during pregnancy
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