21,726 research outputs found
Morphing of Triangular Meshes in Shape Space
We present a novel approach to morph between two isometric poses of the same
non-rigid object given as triangular meshes. We model the morphs as linear
interpolations in a suitable shape space . For triangulated 3D
polygons, we prove that interpolating linearly in this shape space corresponds
to the most isometric morph in . We then extend this shape space
to arbitrary triangulations in 3D using a heuristic approach and show the
practical use of the approach using experiments. Furthermore, we discuss a
modified shape space that is useful for isometric skeleton morphing. All of the
newly presented approaches solve the morphing problem without the need to solve
a minimization problem.Comment: Improved experimental result
Computing A Glimpse of Randomness
A Chaitin Omega number is the halting probability of a universal Chaitin
(self-delimiting Turing) machine. Every Omega number is both computably
enumerable (the limit of a computable, increasing, converging sequence of
rationals) and random (its binary expansion is an algorithmic random sequence).
In particular, every Omega number is strongly non-computable. The aim of this
paper is to describe a procedure, which combines Java programming and
mathematical proofs, for computing the exact values of the first 64 bits of a
Chaitin Omega:
0000001000000100000110001000011010001111110010111011101000010000. Full
description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted
Stability of Magnetized Disks and Implications for Planet Formation
This paper considers gravitational perturbations in geometrically thin disks
with rotation curves dominated by a central object, but with substantial
contributions from magnetic pressure and tension. The treatment is general, but
the application is to the circumstellar disks that arise during the
gravitational collapse phase of star formation. We find the dispersion relation
for spiral density waves in these generalized disks and derive the stability
criterion for axisymmetric disturbances (the analog of the Toomre
parameter ) for any radial distribution of the mass-to-flux ratio
. The magnetic effects work in two opposing directions: on one hand,
magnetic tension and pressure stabilize the disk against gravitational collapse
and fragmentation; on the other hand, they also lower the rotation rate making
the disk more unstable. For disks around young stars the first effect generally
dominates, so that magnetic fields allow disks to be stable for higher surface
densities and larger total masses. These results indicate that magnetic fields
act to suppress the formation of giant planets through gravitational
instability. Finally, even if gravitational instability can form a secondary
body, it must lose an enormous amount of magnetic flux in order to become a
planet; this latter requirement represents an additional constraint for planet
formation via gravitational instability and places a lower limit on the
electrical resistivity.Comment: accepted in Ap
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