63,871 research outputs found
Indirect Image Registration with Large Diffeomorphic Deformations
The paper adapts the large deformation diffeomorphic metric mapping framework
for image registration to the indirect setting where a template is registered
against a target that is given through indirect noisy observations. The
registration uses diffeomorphisms that transform the template through a (group)
action. These diffeomorphisms are generated by solving a flow equation that is
defined by a velocity field with certain regularity. The theoretical analysis
includes a proof that indirect image registration has solutions (existence)
that are stable and that converge as the data error tends so zero, so it
becomes a well-defined regularization method. The paper concludes with examples
of indirect image registration in 2D tomography with very sparse and/or highly
noisy data.Comment: 43 pages, 4 figures, 1 table; revise
Ground states in complex bodies
A unified framework for analyzing the existence of ground states in wide
classes of elastic complex bodies is presented here. The approach makes use of
classical semicontinuity results, Sobolev mappinngs and Cartesian currents.
Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev
maps and Cartesian currents describe the inner substructure of the material
elements. Balance equations for irregular minimizers are derived. A
contribution to the debate about the role of the balance of configurational
actions follows. After describing a list of possible applications of the
general results collected here, a concrete discussion of the existence of
ground states in thermodynamically stable quasicrystals is presented at the
end.Comment: 30 pages, in print on ESAIM-COC
Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients
In the present paper, a two-dimensional solid consisting of a linear elastic isotropic material, for which the
deformation energy depends on the second gradient of the displacement, is considered. The strain energy is demonstrated
to depend on 6 constitutive parameters: the 2 Lam´e constants (λ and μ) and 4 more parameters (instead of 5 as it is in
the 3D-case). Analytical solutions for classical problems such as heavy sheet, bending and flexure are provided. The idea is
very simple: The solutions of the corresponding problem of first gradient classical case are imposed, and the corresponding
forces, double forces and wedge forces are found. On the basis of such solutions, a method is outlined, which is able to
identify the six constitutive parameters. Ideal (or Gedanken) experiments are designed in order to write equations having
as unknowns the six constants and as known terms the values of suitable experimental measurements
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