489 research outputs found
Scalar field in a minimally coupled brane world: no-hair and other no-go theorems
In the brane-world framework, we consider static, spherically symmetric
configurations of a scalar field with the Lagrangian (\d\phi)^2/2 - V(\phi),
confined on the brane. We use the 4D Einstein equations on the brane obtained
by Shiromizu et al., containing the usual stress tensor T\mN, the tensor
\Pi\mN, quadratic in T\mN, and E\mN describing interaction with the bulk.
For models under study, the tensor \Pi\mN has zero divergence, so we can
consider a "minimally coupled" brane with E\mN = 0, whose 4D gravity is
decoupled from the bulk geometry. Assuming E\mN =0, we try to extend to brane
worlds some theorems valid for scalar fields in general relativity (GR). Thus,
the list of possible global causal structures in all models under consideration
is shown to be the same as is known for vacuum with a term in GR:
Minkowski, Schwarzschild, (A)dS and Schwarzschild-(A)dS. A no-hair theorem,
saying that, given a potential , asymptotically flat black holes
cannot have nontrivial external scalar fields, is proved under certain
restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g,
traversable wormholes supported by a scalar field, but only at the expense of
enormous matter densities in the strong field region.Comment: 8 pages, Latex2e. Numerical estimates and a few references adde
A symplectic realization of the Volterra lattice
We examine the multiple Hamiltonian structure and construct a symplectic
realization of the Volterra model. We rediscover the hierarchy of invariants,
Poisson brackets and master symmetries via the use of a recursion operator. The
rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page
Efficient numerical diagonalization of hermitian 3x3 matrices
A very common problem in science is the numerical diagonalization of
symmetric or hermitian 3x3 matrices. Since standard "black box" packages may be
too inefficient if the number of matrices is large, we study several
alternatives. We consider optimized implementations of the Jacobi, QL, and
Cuppen algorithms and compare them with an analytical method relying on
Cardano's formula for the eigenvalues and on vector cross products for the
eigenvectors. Jacobi is the most accurate, but also the slowest method, while
QL and Cuppen are good general purpose algorithms. The analytical algorithm
outperforms the others by more than a factor of 2, but becomes inaccurate or
may even fail completely if the matrix entries differ greatly in magnitude.
This can mostly be circumvented by using a hybrid method, which falls back to
QL if conditions are such that the analytical calculation might become too
inaccurate. For all algorithms, we give an overview of the underlying
mathematical ideas, and present detailed benchmark results. C and Fortran
implementations of our code are available for download from
http://www.mpi-hd.mpg.de/~globes/3x3/ .Comment: 13 pages, no figures, new hybrid algorithm added, matches published
version, typo in Eq. (39) corrected; software library available at
http://www.mpi-hd.mpg.de/~globes/3x3
Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion
It is well known that the long-range nature of the Coulomb interaction makes
the definition of asymptotic ``in'' and ``out'' states of charged particles
problematic in quantum field theory. In particular, the notion of a simple
particle pole in the vacuum charged particle propagator is untenable and should
be replaced by a more complicated branch cut structure describing an electron
interacting with a possibly infinite number of soft photons. Previous work
suggests a Dirac propagator raised to a fractional power dependent upon the
fine structure constant, however the exponent has not been calculated in a
unique gauge invariant manner. It has even been suggested that the fractal
``anomalous dimension'' can be removed by a gauge transformation. Here, a gauge
invariant non-perturbative calculation will be discussed yielding an
unambiguous fractional exponent. The closely analogous case of soft graviton
exponents is also briefly explored.Comment: Updated with a corrected sign error, longer discussion of fractal
dimension, and more reference
Coordinate Representation of the Two-Spinon wavefunction and Spinon Interaction
By deriving and studying the coordinate representation for the two-spinon
wavefunction, we show that spinon excitations in the Haldane-Shastry model
interact. The interaction is given by a short-range attraction and causes a
resonant enhancement in the two-spinon wavefunction at short separations
between the spinons. We express the spin susceptibility for a finite lattice in
terms of the resonant enhancement, given by the two-spinon wavefunction at zero
separation. In the thermodynamic limit, the spinon attraction turns into the
square-root divergence in the dynamical spin susceptibility.Comment: 19 pages, 5 .eps figure
Exotic Statistics for Ordinary Particles in Quantum Gravity
Objects exhibiting statistics other than the familiar Bose and Fermi ones are
natural in theories with topologically nontrivial objects including geons,
strings, and black holes. It is argued here from several viewpoints that the
statistics of ordinary particles with which we are already familiar are likely
to be modified due to quantum gravity effects. In particular, such
modifications are argued to be present in loop quantum gravity and in any
theory which represents spacetime in a fundamentally piecewise-linear fashion.
The appearance of unusual statistics may be a generic feature (such as the
deformed position-momentum uncertainty relations and the appearance of a
fundamental length scale) which are to be expected in any theory of quantum
gravity, and which could be testable.Comment: Awarded an honourable mention in the 2008 Gravity Research Foundation
Essay Competitio
Settlements of Neighboring Buildings During Piling Works
Two case histories of heavy damaging the neighbouring buildings in Sankt-Petersburg during construction the bored piles are presented. The analysis of causes of the damages has shown that ground inflow into the housing tubes due to low strength properties of water saturated liquid-plastic loams is the main cause of additional settlements of existing houses during construction the bored piles of large diameter close to them
Submesoscale physicochemical dynamics directly shape bacterioplankton community structure in space and time
Submesoscale eddies and fronts are important components of oceanic mixing and energy fluxes. These phenomena occur in the surface ocean for a period of several days, on scales between a few hundred meters and few tens of kilometers. Remote sensing and modeling suggest that eddies and fronts may influence marine ecosystem dynamics, but their limited temporal and spatial scales make them challenging for observation and in situ sampling. Here, the study of a submesoscale filament in summerly Arctic waters (depth 0–400 m) revealed enhanced mixing of Polar and Atlantic water masses, resulting in a ca. 4 km wide and ca. 50 km long filament with distinct physical and biogeochemical characteristics. Compared to the surrounding waters, the filament was characterized by a distinct phytoplankton bloom, associated with depleted inorganic nutrients, elevated chlorophyll a concentrations, as well as twofold higher phyto- and bacterioplankton cell abundances. High-throughput 16S rRNA gene sequencing of bacterioplankton communities revealed enrichment of typical phytoplankton bloom-associated taxonomic groups (e.g., Flavobacteriales) inside the filament. Furthermore, linked to the strong water subduction, the vertical export of organic matter to 400 m depth inside the filament was twofold higher compared to the surrounding waters. Altogether, our results show that physical submesoscale mixing can shape distinct biogeochemical conditions and microbial communities within a few kilometers of the ocean. Hence, the role of submesoscale features in polar waters for surface ocean biodiversity and biogeochemical processes need further investigation, especially with regard to the fate of sea ice in the warming Arctic Ocean
Multitemporal generalization of the Tangherlini solution
The n-time generalization of the Tangherlini solution [1] is considered. The
equations of geodesics for the metric are integrated. For it is shown
that the naked singularity is absent only for two sets of parameters,
corresponding to the trivial extensions of the Tangherlini solution. The motion
of a relativistic particle in the multitemporal background is considered. This
motion is governed by the gravitational mass tensor. Some generalizations of
the solution, including the multitemporal analogue of the Myers-Perry charged
black hole solution, are obtained.Comment: 14 pages. RGA-CSVR-005/9
Correlation effects during liquid infiltration into hydrophobic nanoporous mediums
Correlation effects arising during liquid infiltration into hydrophobic
porous medium are considered. On the basis of these effects a mechanism of
energy absorption at filling porous medium by nonwetting liquid is suggested.
In accordance with this mechanism, the absorption of mechanical energy is a
result expenditure of energy for the formation of menisci in the pores on the
shell of the infinite cluster and expenditure of energy for the formation of
liquid-porous medium interface in the pores belonging to the infinite cluster
of filled pores. It was found that in dependences on the porosity and,
consequently, in dependences on the number of filled pores neighbors, the
thermal effect of filling can be either positive or negative and the cycle of
infiltration-defiltration can be closed with full outflow of liquid. It can
occur under certain relation between percolation properties of porous medium
and the energy characteristics of the liquid-porous medium interface and the
liquid-gas interface. It is shown that a consecutive account of these
correlation effects and percolation properties of the pores space during
infiltration allow to describe all experimental data under discussion
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