15,923 research outputs found
Transforming planar graph drawings while maintaining height
There are numerous styles of planar graph drawings, notably straight-line
drawings, poly-line drawings, orthogonal graph drawings and visibility
representations. In this note, we show that many of these drawings can be
transformed from one style to another without changing the height of the
drawing. We then give some applications of these transformations
A New Way to Make Waves
I describe a new algorithm for solving nonlinear wave equations. In this
approach, evolution takes place on characteristic hypersurfaces. The algorithm
is directly applicable to electromagnetic, Yang-Mills and gravitational fields
and other systems described by second differential order hyperbolic equations.
The basic ideas should also be applicable to hydrodynamics. It is an especially
accurate and efficient way for simulating waves in regions where the
characteristics are well behaved. A prime application of the algorithm is to
Cauchy-characteristic matching, in which this new approach is matched to a
standard Cauchy evolution to obtain a global solution. In a model problem of a
nonlinear wave, this proves to be more accurate and efficient than any other
present method of assigning Cauchy outer boundary conditions. The approach was
developed to compute the gravitational wave signal produced by collisions of
two black holes. An application to colliding black holes is presented.Comment: In Proceeding of CIMENICS 2000, The Vth International Congress on
Numerical Methods in Engineering and Applied Science (Puerto La Cruz,
Venezuela, March 2000
Rational Maps, Monopoles and Skyrmions
We discuss the similarities between BPS monopoles and Skyrmions, and point to
an underlying connection in terms of rational maps between Riemann spheres.
This involves the introduction of a new ansatz for Skyrme fields. We use this
to construct good approximations to several known Skyrmions, including all the
minimal energy configurations up to baryon number nine, and some new solutions
such as a baryon number seventeen Skyrme field with the truncated icosahedron
structure of a buckyball.
The new approach is also used to understand the low-lying vibrational modes
of Skyrmions, which are required for quantization. Along the way we discover an
interesting Morse function on the space of rational maps which may be of use in
understanding the Sen forms on the monopole moduli spaces.Comment: 35pp including four figures, typos corrected, appearing in Nuclear
Physics
Disconnected Skeleton: Shape at its Absolute Scale
We present a new skeletal representation along with a matching framework to
address the deformable shape recognition problem. The disconnectedness arises
as a result of excessive regularization that we use to describe a shape at an
attainably coarse scale. Our motivation is to rely on the stable properties of
the shape instead of inaccurately measured secondary details. The new
representation does not suffer from the common instability problems of
traditional connected skeletons, and the matching process gives quite
successful results on a diverse database of 2D shapes. An important difference
of our approach from the conventional use of the skeleton is that we replace
the local coordinate frame with a global Euclidean frame supported by
additional mechanisms to handle articulations and local boundary deformations.
As a result, we can produce descriptions that are sensitive to any combination
of changes in scale, position, orientation and articulation, as well as
invariant ones.Comment: The work excluding {\S}V and {\S}VI has first appeared in 2005 ICCV:
Aslan, C., Tari, S.: An Axis-Based Representation for Recognition. In
ICCV(2005) 1339- 1346.; Aslan, C., : Disconnected Skeletons for Shape
Recognition. Masters thesis, Department of Computer Engineering, Middle East
Technical University, May 200
Stationary problems for equation of the KdV type and dynamical -matrices.
We study a quite general family of dynamical -matrices for an auxiliary
loop algebra related to restricted flows for equations of
the KdV type. This underlying -matrix structure allows to reconstruct Lax
representations and to find variables of separation for a wide set of the
integrable natural Hamiltonian systems. As an example, we discuss the
Henon-Heiles system and a quartic system of two degrees of freedom in detail.Comment: 25pp, LaTe
Discrete spherical means of directional derivatives and Veronese maps
We describe and study geometric properties of discrete circular and spherical
means of directional derivatives of functions, as well as discrete
approximations of higher order differential operators. For an arbitrary
dimension we present a general construction for obtaining discrete spherical
means of directional derivatives. The construction is based on using the
Minkowski's existence theorem and Veronese maps. Approximating the directional
derivatives by appropriate finite differences allows one to obtain finite
difference operators with good rotation invariance properties. In particular,
we use discrete circular and spherical means to derive discrete approximations
of various linear and nonlinear first- and second-order differential operators,
including discrete Laplacians. A practical potential of our approach is
demonstrated by considering applications to nonlinear filtering of digital
images and surface curvature estimation
Horizon-absorption effects in coalescing black-hole binaries: An effective-one-body study of the non-spinning case
We study the horizon absorption of gravitational waves in coalescing,
circularized, nonspinning black hole binaries. The horizon absorbed fluxes of a
binary with a large mass ratio (q=1000) obtained by numerical perturbative
simulations are compared with an analytical, effective-one-body (EOB) resummed
expression recently proposed. The perturbative method employs an analytical,
linear in the mass ratio, effective-one-body (EOB) resummed radiation reaction,
and the Regge-Wheeler-Zerilli (RWZ) formalism for wave extraction.
Hyperboloidal (transmitting) layers are employed for the numerical solution of
the RWZ equations to accurately compute horizon fluxes up to the late plunge
phase. The horizon fluxes from perturbative simulations and the EOB-resummed
expression agree at the level of a few percent down to the late plunge. An
upgrade of the EOB model for nonspinning binaries that includes horizon
absorption of angular momentum as an additional term in the resummed radiation
reaction is then discussed. The effect of this term on the waveform phasing for
binaries with mass ratios spanning 1 to 1000 is investigated. We confirm that
for comparable and intermediate-mass-ratio binaries horizon absorbtion is
practically negligible for detection with advanced LIGO and the Einstein
Telescope (faithfulness greater than or equal to 0.997)
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