104 research outputs found
Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids
Transformation elasticity, by analogy with transformation acoustics and
optics, converts material domains without altering wave properties, thereby
enabling cloaking and related effects. By noting the similarity between
transformation elasticity and the theory of incremental motion superimposed on
finite pre-strain it is shown that the constitutive parameters of
transformation elasticity correspond to the density and moduli of
small-on-large theory. The formal equivalence indicates that transformation
elasticity can be achieved by selecting a particular finite (hyperelastic)
strain energy function, which for isotropic elasticity is semilinear strain
energy. The associated elastic transformation is restricted by the requirement
of statically equilibrated pre-stress. This constraint can be cast as \tr
{\mathbf F} = constant, where is the deformation gradient,
subject to symmetry constraints, and its consequences are explored both
analytically and through numerical examples of cloaking of anti-plane and
in-plane wave motion.Comment: 20 pages, 5 figure
New Mechanics of Spinal Injury
The prediction and prevention of spinal injury is an important aspect of
preventive health science. The spine, or vertebral column, represents a chain
of 26 movable vertebral bodies, joint together by transversal viscoelastic
intervertebral discs and longitudinal elastic tendons. This paper proposes a
new locally-coupled loading-rate hypothesis}, which states that the main cause
of both soft- and hard-tissue spinal injury is a localized Euclidean jolt, or
SE(3)-jolt, an impulsive loading that strikes a localized spine in several
coupled degrees-of-freedom simultaneously. To show this, based on the
previously defined covariant force law, we formulate the coupled Newton-Euler
dynamics of the local spinal motions and derive from it the corresponding
coupled SE(3)-jolt dynamics. The SE(3)-jolt is the main cause of two basic
forms of spinal injury: (i) hard-tissue injury of local translational
dislocations; and (ii) soft-tissue injury of local rotational disclinations.
Both the spinal dislocations and disclinations, as caused by the SE(3)-jolt,
are described using the Cosserat multipolar viscoelastic continuum model.
Keywords: localized spinal injury, coupled loading-rate hypothesis, coupled
Newton-Euler dynamics, Euclidean jolt dynamics, spinal dislocations and
disclinationsComment: 14 pages, 1 figure, Late
New Mechanics of Traumatic Brain Injury
The prediction and prevention of traumatic brain injury is a very important
aspect of preventive medical science. This paper proposes a new coupled
loading-rate hypothesis for the traumatic brain injury (TBI), which states that
the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an
impulsive loading that strikes the head in several coupled degrees-of-freedom
simultaneously. To show this, based on the previously defined covariant force
law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions
within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt
dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid
discontinuous deformations: translational dislocations and rotational
disclinations. Brain's dislocations and disclinations, caused by the
SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum
brain model.
Keywords: Traumatic brain injuries, coupled loading-rate hypothesis,
Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and
disclinationsComment: 18 pages, 1 figure, Late
Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
In 1922, Cartan introduced in differential geometry, besides the Riemannian
curvature, the new concept of torsion. He visualized a homogeneous and
isotropic distribution of torsion in three dimensions (3d) by the "helical
staircase", which he constructed by starting from a 3d Euclidean space and by
defining a new connection via helical motions. We describe this geometric
procedure in detail and define the corresponding connection and the torsion.
The interdisciplinary nature of this subject is already evident from Cartan's
discussion, since he argued - but never proved - that the helical staircase
should correspond to a continuum with constant pressure and constant internal
torque. We discuss where in physics the helical staircase is realized: (i) In
the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d
theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's
case of constant pressure and constant intrinsic torque - and b) in 3d Poincare
gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the
gauge field theory of dislocations of Lazar et al., as we prove for the first
time by arranging a suitable distribution of screw dislocations. Our main
emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure
The impact of Stieltjes' work on continued fractions and orthogonal polynomials
Stieltjes' work on continued fractions and the orthogonal polynomials related
to continued fraction expansions is summarized and an attempt is made to
describe the influence of Stieltjes' ideas and work in research done after his
death, with an emphasis on the theory of orthogonal polynomials
Religiosity and corporate financial reporting: evidence from a European country
Using a sample of Portuguese privately-held firms, I examine the association between religiosity and
financial reporting quality. The results suggest that firms headquartered in Portuguese areas with strong
religious adherence and in the core area of the Portuguese religious cult (the district where the Fátima
Sanctuary is located) generally experience lower incidence of earnings management. I provide further
evidence that the results are robust to alternative measures of religiosity, and that are not driven by firms
headquartered in rural areas. I also conclude that religious social norms, together with other forms of
external financial monitoring, represent a mechanism for reducing costly agency conflicts. While the
religious practice declined in the last decades in Portugal, I provide evidence that, even in a such context,
religiosity is associated with reduced acceptance of unethical business practices, in particular, with reduced
acceptance of aggressive accounting practices.I thank participants of the Second Paris Financial Management Conference (PFMC, 2014) and the 3RD
Workshop on Business Ethics (EIASM, 2015) for their helpful insights.info:eu-repo/semantics/publishedVersio
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