159 research outputs found
Theory of weakly damped free-surface flows: a new formulation based on potential flow solutions
Several theories for weakly damped free-surface flows have been formulated.
In this paper we use the linear approximation to the Navier-Stokes equations to
derive a new set of equations for potential flow which include dissipation due
to viscosity. A viscous correction is added not only to the irrotational
pressure (Bernoulli's equation), but also to the kinematic boundary condition.
The nonlinear Schr\"odinger (NLS) equation that one can derive from the new set
of equations to describe the modulations of weakly nonlinear, weakly damped
deep-water gravity waves turns out to be the classical damped version of the
NLS equation that has been used by many authors without rigorous justification
A constructive approach to the soliton solutions of integrable quadrilateral lattice equations
Scalar multidimensionally consistent quadrilateral lattice equations are
studied. We explore a confluence between the superposition principle for
solutions related by the Backlund transformation, and the method of solving a
Riccati map by exploiting two kn own particular solutions. This leads to an
expression for the N-soliton-type solutions of a generic equation within this
class. As a particular instance we give an explicit N-soliton solution for the
primary model, which is Adler's lattice equation (or Q4).Comment: 22 page
Strong coupling in massive gravity by direct calculation
We consider four-dimensional massive gravity with the Fierz-Pauli mass term.
The analysis of the scalar sector has revealed recently that this theory
becomes strongly coupled above the energy scale \Lambda = (M_{Pl}^2 m^4)^{1/5}
where m is the mass of the graviton. We confirm this scale by explicit
calculations of the four-graviton scattering amplitude and of the loop
correction to the interaction between conserved sources.Comment: 9 pages, 3 figures, some clarifications adde
On brane-induced gravity in warped backgrounds
We study whether modification of gravity at large distances is possible in
warped backgrounds with two branes and a brane-induced term localized on one of
the branes. We find that there are three large regions in the parameter space
where the theory is weakly coupled up to high energies. In one of these regions
gravity on the brane is four-dimensional at arbitrarily large distances, and
the induced Einstein term results merely in the renormalization of the 4d
Planck mass. In the other two regions the behavior of gravity changes at
ultra-large distances; however, radion becomes a ghost. In parts of these
regions, both branes have positive tensions, so the only reason for the
appearance of the ghost field is the brane-induced term. In between these three
regions, there are domains in the parameter space where gravity is strongly
coupled at phenomenologically unacceptable low energy scale.Comment: 12 pages, 2 fig, JHEP3 style required, typos correcte
Magnetized Particle Capture Cross Section for Braneworld Black Hole
Capture cross section of magnetized particle (with nonzero magnetic moment)
by braneworld black hole in uniform magnetic field is considered. The magnetic
moment of particle was chosen as it was done by \citet{rs99} and for the
simplicity particle with zero electric charge is chosen. It is shown that the
spin of particle as well as the brane parameter are to sustain the stability of
particles circularly orbiting around the black hole in braneworld i.e. spin of
particles and brane parameter try to prevent the capture by black hole.Comment: 7 pages, 4 figures, Accepted for publication in Astrophysics & Space
Scienc
Curvature line parametrized surfaces and orthogonal coordinate systems. Discretization with Dupin cyclides
Cyclidic nets are introduced as discrete analogs of curvature line
parametrized surfaces and orthogonal coordinate systems. A 2-dimensional
cyclidic net is a piecewise smooth -surface built from surface patches of
Dupin cyclides, each patch being bounded by curvature lines of the supporting
cyclide. An explicit description of cyclidic nets is given and their relation
to the established discretizations of curvature line parametrized surfaces as
circular, conical and principal contact element nets is explained. We introduce
3-dimensional cyclidic nets as discrete analogs of triply-orthogonal coordinate
systems and investigate them in detail. Our considerations are based on the Lie
geometric description of Dupin cyclides. Explicit formulas are derived and
implemented in a computer program.Comment: 39 pages, 30 figures; Theorem 2.7 has been reformulated, as a
normalization factor in formula (2.4) was missing. The corresponding
formulations have been adjusted and a few typos have been correcte
The apparent Coulomb reacceleration of neutrons in electrodissociation of the deuteron
We demonstrate that the final state - interaction in the reaction of
electrodissociation of the deuteron at large in a static external field
leads to the apparent reacceleration of neutrons. The shift of the neutron
velocity from the velocity of the deuteron beam is related to the
quantum-mechanical forward-backward asymmetry of the missing momentum
distribution in the scattering.Comment: LATEX, 9 pages, 1 figure available from the authors on request,
Juelich preprint KFA-IKP(TH)-1994-3
Strong Coupling vs. 4-D Locality in Induced Gravity
We re-examine the problem of strong coupling in a regularized version of DGP
(or ``brane-induced'') gravity. We find that the regularization of ref.
hep-th/0304148 differs from DGP in that it does not exhibit strong coupling or
ghosts up to cubic order in the interactions. We suggest that the nonlocal
nature of the theory, when written in terms of the 4-D metric, is a plausible
reason for this phenomenon. Finally, we briefly discuss the possible behavior
of the model at higher-order in perturbation theory.Comment: 19 pages, accepted for publication in PR
Classical and Quantum Consistency of the DGP Model
We study the Dvali-Gabadadze-Porrati model by the method of the boundary
effective action. The truncation of this action to the bending mode \pi
consistently describes physics in a wide range of regimes both at the classical
and at the quantum level. The Vainshtein effect, which restores agreement with
precise tests of general relativity, follows straightforwardly. We give a
simple and general proof of stability, i.e. absence of ghosts in the
fluctuations, valid for most of the relevant cases, like for instance the
spherical source in asymptotically flat space. However we confirm that around
certain interesting self-accelerating cosmological solutions there is a ghost.
We consider the issue of quantum corrections. Around flat space \pi becomes
strongly coupled below a macroscopic length of 1000 km, thus impairing the
predictivity of the model. Indeed the tower of higher dimensional operators
which is expected by a generic UV completion of the model limits predictivity
at even larger length scales. We outline a non-generic but consistent choice of
counterterms for which this disaster does not happen and for which the model
remains calculable and successful in all the astrophysical situations of
interest. By this choice, the extrinsic curvature K_{\mu\nu} acts roughly like
a dilaton field controlling the strength of the interaction and the cut-off
scale at each space-time point. At the surface of Earth the cutoff is \sim 1 cm
but it is unlikely that the associated quantum effects be observable in table
top experiments.Comment: 26 pages, 1 eps figur
Cosmic Strings in a Braneworld Theory with Metastable Gravitons
If the graviton possesses an arbitrarily small (but nonvanishing) mass,
perturbation theory implies that cosmic strings have a nonzero Newtonian
potential. Nevertheless in Einstein gravity, where the graviton is strictly
massless, the Newtonian potential of a cosmic string vanishes. This discrepancy
is an example of the van Dam--Veltman--Zakharov (VDVZ) discontinuity. We
present a solution for the metric around a cosmic string in a braneworld theory
with a graviton metastable on the brane. This theory possesses those features
that yield a VDVZ discontinuity in massive gravity, but nevertheless is
generally covariant and classically self-consistent. Although the cosmic string
in this theory supports a nontrivial Newtonian potential far from the source,
one can recover the Einstein solution in a region near the cosmic string. That
latter region grows as the graviton's effective linewidth vanishes (analogous
to a vanishing graviton mass), suggesting the lack of a VDVZ discontinuity in
this theory. Moreover, the presence of scale dependent structure in the metric
may have consequences for the search for cosmic strings through gravitational
lensing techniques.Comment: 18 pages, 2 figures, revtex. Improved discussion of interpolating
solution. To be published in Phys. Rev.
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