7,174 research outputs found
Nematic Structure of Space-Time and its Topological Defects in 5D Kaluza-Klein Theory
We show, that classical Kaluza-Klein theory possesses hidden nematic
dynamics. It appears as a consequence of 1+4-decomposition procedure, involving
4D observers 1-form \lambda. After extracting of boundary terms the, so called,
"effective matter" part of 5D geometrical action becomes proportional to square
of anholonomicity 3-form \lambda\wedge d\lambda. It can be interpreted as twist
nematic elastic energy, responsible for elastic reaction of 5D space-time on
presence of anholonomic 4D submanifold, defined by \lambda. We derive both 5D
covariant and 1+4 forms of 5D nematic equilibrium equations, consider simple
examples and discuss some 4D physical aspects of generic 5D nematic topological
defects.Comment: Latex-2e, 14 pages, 1 Fig., submitted to GR
Lipschitz regularity for inner-variational equations
We obtain Lipschitz regularity results for a fairly general class of
nonlinear first-order PDEs. These equations arise from the inner variation of
certain energy integrals. Even in the simplest model case of the Dirichlet
energy the inner-stationary solutions need not be differentiable everywhere;
the Lipschitz continuity is the best possible. But the proofs, even in the
Dirichlet case, turn out to relay on topological arguments. The appeal to the
inner-stationary solutions in this context is motivated by the classical
problems of existence and regularity of the energy-minimal deformations in the
theory of harmonic mappings and certain mathematical models of nonlinear
elasticity; specifically, neo-Hookian type problems.Comment: No figure
Gauge fields in graphene
The physics of graphene is acting as a bridge between quantum field theory
and condensed matter physics due to the special quality of the graphene
quasiparticles behaving as massless two dimensional Dirac fermions. Moreover,
the particular structure of the 2D crystal lattice sets the arena to study and
unify concepts from elasticity, topology and cosmology. In this paper we
analyze these connections combining a pedagogical, intuitive approach with a
more rigorous formalism when required.Comment: Update of the manuscript published on-line in Physics Reports. 43
pages, 18 figure
Localization, Stability, and Resolution of Topological Derivative Based Imaging Functionals in Elasticity
The focus of this work is on rigorous mathematical analysis of the
topological derivative based detection algorithms for the localization of an
elastic inclusion of vanishing characteristic size. A filtered quadratic misfit
is considered and the performance of the topological derivative imaging
functional resulting therefrom is analyzed. Our analysis reveals that the
imaging functional may not attain its maximum at the location of the inclusion.
Moreover, the resolution of the image is below the diffraction limit. Both
phenomena are due to the coupling of pressure and shear waves propagating with
different wave speeds and polarization directions. A novel imaging functional
based on the weighted Helmholtz decomposition of the topological derivative is,
therefore, introduced. It is thereby substantiated that the maximum of the
imaging functional is attained at the location of the inclusion and the
resolution is enhanced and it proves to be the diffraction limit. Finally, we
investigate the stability of the proposed imaging functionals with respect to
measurement and medium noises.Comment: 38 pages. A new subsection 6.4 is added where we consider the case of
random Lam\'e coefficients. We thought this would corrupt the statistical
stability of the imaging functional but our calculus shows that this is not
the case as long as the random fluctuation is weak so that Born approximation
is vali
Novel effects of strains in graphene and other two dimensional materials
The analysis of the electronic properties of strained or lattice deformed
graphene combines ideas from classical condensed matter physics, soft matter,
and geometrical aspects of quantum field theory (QFT) in curved spaces. Recent
theoretical and experimental work shows the influence of strains in many
properties of graphene not considered before, such as electronic transport,
spin-orbit coupling, the formation of Moir\'e patterns, optics, ... There is
also significant evidence of anharmonic effects, which can modify the
structural properties of graphene. These phenomena are not restricted to
graphene, and they are being intensively studied in other two dimensional
materials, such as the metallic dichalcogenides. We review here recent
developments related to the role of strains in the structural and electronic
properties of graphene and other two dimensional compounds.Comment: 75 pages, 15 figures, review articl
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