47,474 research outputs found
Dynamics and Topological Aspects of a Reconstructed Two-Dimensional Foam Time Series Using Potts Model on a Pinned Lattice
We discuss a method to reconstruct an approximate two-dimensional foam
structure from an incomplete image using the extended Potts mode with a pinned
lattice we introduced in a previous paper. The initial information consists of
the positions of the vertices only. We locate the centers of the bubbles using
the Euclidean distance-map construction and assign at each vertex position a
continuous pinning field with a potential falling off as . We nucleate a
bubble at each center using the extended Potts model and let the structure
evolve under the constraint of scaled target areas until the bubbles contact
each other. The target area constraint and pinning centers prevent further
coarsening. We then turn the area constraint off and let the edges relax to a
minimum energy configuration. The result is a reconstructed structure very
close to the simulation. We repeated this procedure for various stages of the
coarsening of the same simulated foam and investigated the simulation and
reconstruction dynamics, topology and area distribution, finding that they
agree to good accuracy.Comment: 31 pages, 20 Postscript figures Accepted in the Journal of
Computational Physic
On reconstructing n-point configurations from the distribution of distances or areas
One way to characterize configurations of points up to congruence is by
considering the distribution of all mutual distances between points. This paper
deals with the question if point configurations are uniquely determined by this
distribution. After giving some counterexamples, we prove that this is the case
for the vast majority of configurations. In the second part of the paper, the
distribution of areas of sub-triangles is used for characterizing point
configurations. Again it turns out that most configurations are reconstructible
from the distribution of areas, though there are counterexamples.Comment: 21 pages, late
Reconstruction of potential energy profiles from multiple rupture time distributions
We explore the mathematical and numerical aspects of reconstructing a
potential energy profile of a molecular bond from its rupture time
distribution. While reliable reconstruction of gross attributes, such as the
height and the width of an energy barrier, can be easily extracted from a
single first passage time (FPT) distribution, the reconstruction of finer
structure is ill-conditioned. More careful analysis shows the existence of
optimal bond potential amplitudes (represented by an effective Peclet number)
and initial bond configurations that yield the most efficient numerical
reconstruction of simple potentials. Furthermore, we show that reconstruction
of more complex potentials containing multiple minima can be achieved by
simultaneously using two or more measured FPT distributions, obtained under
different physical conditions. For example, by changing the effective potential
energy surface by known amounts, additional measured FPT distributions improve
the reconstruction. We demonstrate the possibility of reconstructing potentials
with multiple minima, motivate heuristic rules-of-thumb for optimizing the
reconstruction, and discuss further applications and extensions.Comment: 20 pages, 9 figure
3D particle tracking velocimetry using dynamic discrete tomography
Particle tracking velocimetry in 3D is becoming an increasingly important
imaging tool in the study of fluid dynamics, combustion as well as plasmas. We
introduce a dynamic discrete tomography algorithm for reconstructing particle
trajectories from projections. The algorithm is efficient for data from two
projection directions and exact in the sense that it finds a solution
consistent with the experimental data. Non-uniqueness of solutions can be
detected and solutions can be tracked individually
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