1,176 research outputs found
Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy
Spatial non-locality of space-fractional viscoelastic equations of motion is
studied. Relaxation effects are accounted for by replacing second-order time
derivatives by lower-order fractional derivatives and their generalizations. It
is shown that space-fractional equations of motion of an order strictly less
than 2 allow for a new kind anisotropy, associated with angular dependence of
non-local interactions between stress and strain at different material points.
Constitutive equations of such viscoelastic media are determined. Explicit
fundamental solutions of the Cauchy problem are constructed for some cases
isotropic and anisotropic non-locality
On Tensorial Concomitants and the Non-Existence of a Gravitational Stress-Energy Tensor
The question of the existence of gravitational stress-energy in general
relativity has exercised investigators in the field since the inception of the
theory. Folklore has it that no adequate definition of a localized
gravitational stress-energetic quantity can be given. Most arguments to that
effect invoke one version or another of the Principle of Equivalence. I argue
that not only are such arguments of necessity vague and hand-waving but, worse,
are beside the point and do not address the heart of the issue. Based on a
novel analysis of what it may mean for one tensor to depend in the proper way
on another, I prove that, under certain natural conditions, there can be no
tensor whose interpretation could be that it represents gravitational
stress-energy in general relativity. It follows that gravitational energy, such
as it is in general relativity, is necessarily non-local. Along the way, I
prove a result of some interest in own right about the structure of the
associated jet bundles of the bundle of Lorentz metrics over spacetime.Comment: 20 pages (including 2 1/2 pages biblio
Transformation Optics, Generalized Cloaking and Superlenses
In this paper, transformation optics is presented together with a
generalization of invisibility cloaking: instead of an empty region of space,
an inhomogeneous structure is transformed via Pendry's map in order to give, to
any object hidden in the central hole of the cloak, a completely arbitrary
appearance. Other illusion devices based on superlenses considered from the
point of view of transformation optics are also discussed.Comment: 7 pages (two columns), 9 figures, to appear in IEEE Trans. Mag.,
invited paper in Compumag 2009 (Florianopolis, Brasil), corresponding slides
available on http://www.fresnel.fr/perso/nicolet
Two constructions with parabolic geometries
This is an expanded version of a series of lectures delivered at the 25th
Winter School ``Geometry and Physics'' in Srni.
After a short introduction to Cartan geometries and parabolic geometries, we
give a detailed description of the equivalence between parabolic geometries and
underlying geometric structures.
The second part of the paper is devoted to constructions which relate
parabolic geometries of different type. First we discuss the construction of
correspondence spaces and twistor spaces, which is related to nested parabolic
subgroups in the same semisimple Lie group. An example related to twistor
theory for Grassmannian structures and the geometry of second order ODE's is
discussed in detail.
In the last part, we discuss analogs of the Fefferman construction, which
relate geometries corresponding different semisimple Lie groups
Mesoscopic theory for fluctuating active nematics
Peer reviewedPublisher PD
Orientation-dependent handedness and chiral design
Chirality occupies a central role in fields ranging from biological
self-assembly to the design of optical metamaterials. The definition of
chirality, as given by Lord Kelvin, associates chirality with the lack of
mirror symmetry: the inability to superpose an object on its mirror image.
While this definition has guided the classification of chiral objects for over
a century, the quantification of handed phenomena based on this definition has
proven elusive, if not impossible, as manifest in the paradox of chiral
connectedness. In this work, we put forward a quantification scheme in which
the handedness of an object depends on the direction in which it is viewed.
While consistent with familiar chiral notions, such as the right-hand rule,
this framework allows objects to be simultaneously right and left handed. We
demonstrate this orientation dependence in three different systems - a
biomimetic elastic bilayer, a chiral propeller, and optical metamaterial - and
find quantitative agreement with chirality pseudotensors whose form we
explicitly compute. The use of this approach resolves the existing paradoxes
and naturally enables the design of handed metamaterials from symmetry
principles
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