3,641 research outputs found
Weighted Radon transforms for which the Chang approximate inversion formula is precise
We describe all weighted Radon transforms on the plane for which the Chang
approximate inversion formula is precise. Some subsequent results, including
the Cormack type inversion for these transforms, are also given
Aspects of the stochastic Burgers equation and their connection with turbulence
We present results for the 1 dimensional stochastically forced Burgers
equation when the spatial range of the forcing varies. As the range of forcing
moves from small scales to large scales, the system goes from a chaotic,
structureless state to a structured state dominated by shocks. This transition
takes place through an intermediate region where the system exhibits rich
multifractal behavior. This is mainly the region of interest to us. We only
mention in passing the hydrodynamic limit of forcing confined to large scales,
where much work has taken place since that of Polyakov.
In order to make the general framework clear, we give an introduction to
aspects of isotropic, homogeneous turbulence, a description of Kolmogorov
scaling, and, with the help of a simple model, an introduction to the language
of multifractality which is used to discuss intermittency corrections to
scaling.
We continue with a general discussion of the Burgers equation and forcing,
and some aspects of three dimensional turbulence where - because of the
mathematical analogy between equations derived from the Navier-Stokes and
Burgers equations - one can gain insight from the study of the simpler
stochastic Burgers equation. These aspects concern the connection of
dissipation rate intermittency exponents with those characterizing the
structure functions of the velocity field, and the dynamical behavior,
characterized by different time constants, of velocity structure functions. We
also show how the exponents characterizing the multifractal behavior of
velocity structure functions in the above mentioned transition region can
effectively be calculated in the case of the stochastic Burgers equation.Comment: 25 pages, 4 figure
Power corrections and perturbative coupling from lattice gauge thoeries
From the analysis of the perturbative expansion of the lattice regularized
gluon condensate, toghether with MC data, we present evidence of OPE-unexpected
dim-2 power corrections in the scaling behaviour of the Wilson loop. These can
be interpreted as an indication that in lattice gauge theories the running
coupling at large momentum contains contributions of order Q^2.Comment: 3 pages, 2 figures. Talk given at the Lattice97 conference,
Edinburgh, U
Homogeneous singularities inside collapsing wormholes
We analyze analytically and numerically the origin of the singularity in the
course of the collapse of a wormhole with the exotic scalar field Psi with
negative energy density, and with this field Psi together with the ordered
magnetic field H. We do this under the simplifying assumptions of the spherical
symmetry and that in the vicinity of the singularity the solution of the
Einstein equations depends only on one coordinate (the homogeneous
approximation). In the framework of these assumptions we found the principal
difference between the case of the collapse of the ordinary scalar field Phi
with the positive energy density together with an ordered magnetic field H and
the collapse of the exotic scalar field Psi together with the magnetic field H.
The later case is important for the possible astrophysical manifestation of the
wormholes.Comment: 10 pages, 5 figures each of which has a),b),c),and d) sub-figures. To
be published in "Physical review. D, Particles, fields, gravitation, and
cosmology
Constraints on Mass Spectrum of Fourth Generation Fermions and Higgs Bosons
We reanalyze constraints on the mass spectrum of the chiral fourth generation
fermions and the Higgs bosons for the standard model (SM4) and the two Higgs
doublet model (THDM). We find that the Higgs mass in the SM4 should be larger
than roughly the fourth generation up-type quark mass, while the light CP even
Higgs mass in the THDM can be smaller. Various mass spectra of the fourth
generation fermions and the Higgs bosons are allowed. The phenomenology of the
fourth generation models is still rich.Comment: 15 pages, 16 figures; some points clarified, references added, to
appear in Phys.Rev.
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