16,536 research outputs found
Field Theories on Null Manifolds
We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges
Evolution of Topological Defects During Inflation
Topological defects can be formed during inflation by phase transitions as
well as by quantum nucleation. We study the effect of the expansion of the
Universe on the internal structure of the defects. We look for stationary
solutions to the field equations, i.e. solutions that depend only on the proper
distance from the defect core. In the case of very thin defects, whose core
dimensions are much smaller than the de Sitter horizon, we find that the
solutions are well approximated by the flat space solutions. However, as the
flat space thickness parameter increases we notice a deviation from
this, an effect that becomes dramatic as approaches . Beyond this critical value we find no stationary solutions to the field
equations. We conclude that only defects that have flat space thicknesses less
than the critical value survive, while thicker defects are smeared out by the
expansion.Comment: 14 page
Measurement of retinal vessel widths from fundus images based on 2-D modeling
Changes in retinal vessel diameter are an important sign of diseases such as hypertension, arteriosclerosis and diabetes mellitus. Obtaining precise measurements of vascular widths is a critical and demanding process in automated retinal image analysis as the typical vessel is only a few pixels wide. This paper presents an algorithm to measure the vessel diameter to subpixel accuracy. The diameter measurement is based on a two-dimensional difference of Gaussian model, which is optimized to fit a two-dimensional intensity vessel segment. The performance of the method is evaluated against Brinchmann-Hansen's half height, Gregson's rectangular profile and Zhou's Gaussian model. Results from 100 sample profiles show that the presented algorithm is over 30% more precise than the compared techniques and is accurate to a third of a pixel
Approximation of corner polyhedra with families of intersection cuts
We study the problem of approximating the corner polyhedron using
intersection cuts derived from families of lattice-free sets in .
In particular, we look at the problem of characterizing families that
approximate the corner polyhedron up to a constant factor, which depends only
on and not the data or dimension of the corner polyhedron. The literature
already contains several results in this direction. In this paper, we use the
maximum number of facets of lattice-free sets in a family as a measure of its
complexity and precisely characterize the level of complexity of a family
required for constant factor approximations. As one of the main results, we
show that, for each natural number , a corner polyhedron with basic
integer variables and an arbitrary number of continuous non-basic variables is
approximated up to a constant factor by intersection cuts from lattice-free
sets with at most facets if and that no such approximation is
possible if . When the approximation factor is allowed to
depend on the denominator of the fractional vertex of the linear relaxation of
the corner polyhedron, we show that the threshold is versus .
The tools introduced for proving such results are of independent interest for
studying intersection cuts
Gravity of higher-dimensional global defects
Solutions of Einstein's equations are found for global defects in a
higher-dimensional spacetime with a nonzero cosmological constant Lambda. The
defect has a (p-1)-dimensional core (brane) and a `hedgehog' scalar field
configuration in the n extra dimensions. For Lambda = 0 and n > 2, the
solutions are characterized by a flat brane worldsheet and a solid angle
deficit in the extra dimensions. For Lambda > 0, one class of solutions
describes spherical branes in an inflating higher-dimensional universe.
Instantons obtained by a Euclidean continuation of such solutions describe
quantum nucleation of the entire inflating brane-world, or of a spherical brane
in an inflating higher-dimensional universe. For Lambda < 0, one class of
solutions exhibits an exponential warp factor. It is similar to spacetimes
previously discussed by Randall and Sundrum for n = 1 and by Gregory for n = 2.Comment: 18 pages, no figures, uses revte
Novel universality classes of coupled driven diffusive systems
Motivated by the phenomenologies of dynamic roughening of strings in random
media and magnetohydrodynamics, we examine the universal properties of driven
diffusive system with coupled fields. We demonstrate that cross-correlations
between the fields lead to amplitude-ratios and scaling exponents varying
continuosly with the strength of these cross-correlations. The implications of
these results for experimentally relevant systems are discussed.Comment: To appear in Phys. Rev. E (Rapid Comm.) (2003
Helioseismic analysis of the hydrogen partition function in the solar interior
The difference in the adiabatic gradient gamma_1 between inverted solar data
and solar models is analyzed. To obtain deeper insight into the issues of
plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted,
that is, the difference due to the change in the equation of state alone. Our
method uses reference models based on two equations of state currently used in
solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL
equation of state (developed at Livermore). Solar oscillation frequencies from
the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days
in operation are used. Our results confirm the existence of a subtle effect of
the excited states in hydrogen that was previously studied only theoretically
(Nayfonov & Dappen 1998). The effect stems from internal partition function of
hydrogen, as used in the MHD equation of state. Although it is a pure-hydrogen
effect, it takes place in somewhat deeper layers of the Sun, where more than
90% of hydrogen is ionized, and where the second ionization zone of helium is
located. Therefore, the effect will have to be taken into account in reliable
helioseismic determinations of the astrophysically relevant helium-abundance of
the solar convection zone.Comment: 30 pages, 4 figures, 1 table. Revised version submitted to Ap
Changes in the sensitivity of solar p-mode frequency shifts to activity over three solar cycles
Low-degree solar p-mode observations from the long-lived Birmingham Solar
Oscillations Network (BiSON) stretch back further than any other single
helioseismic data set. Results from BiSON have suggested that the response of
the mode frequency to solar activity levels may be different in different
cycles. In order to check whether such changes can also be seen at higher
degrees, we compare the response of medium-degree solar p-modes to activity
levels across three solar cycles using data from Big Bear Solar Observatory
(BBSO), Global Oscillation Network Group (GONG), Michelson Doppler Imager (MDI)
and Helioseismic and Magnetic Imager (HMI), by examining the shifts in the mode
frequencies and their sensitivity to solar activity levels. We compare these
shifts and sensitivities with those from radial modes from BiSON. We find that
the medium-degree data show small but significant systematic differences
between the cycles, with solar cycle 24 showing a frequency shift about 10 per
cent larger than cycle 23 for the same change in activity as determined by the
10.7 cm radio flux. This may support the idea that there have been changes in
the magnetic properties of the shallow subsurface layers of the Sun that have
the strongest influence on the frequency shifts.Comment: 6 pages, 3 figures, accepted by MNRAS 3rd July 201
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