194 research outputs found
Weyl's Lagrangian in teleparallel form
The main result of the paper is a new representation for the Weyl Lagrangian
(massless Dirac Lagrangian). As the dynamical variable we use the coframe, i.e.
an orthonormal tetrad of covector fields. We write down a simple Lagrangian -
wedge product of axial torsion with a lightlike element of the coframe - and
show that this gives the Weyl Lagrangian up to a nonlinear change of dynamical
variable. The advantage of our approach is that it does not require the use of
spinors, Pauli matrices or covariant differentiation. The only geometric
concepts we use are those of a metric, differential form, wedge product and
exterior derivative. Our result assigns a variational meaning to the tetrad
representation of the Weyl equation suggested by J. B. Griffiths and R. A.
Newing
Note on a Micropolar Gas-Kinetic Theory
The micropolar fluid mechanics and its transport coefficients are derived
from the linearized Boltzmann equation of rotating particles. In the dilute
limit, as expected, transport coefficients relating to microrotation are not
important, but the results are useful for the description of collisional
granular flow on an inclined slope.
(This paper will be published in Traffic and Granular Flow 2001 edited by
Y.Sugiyama and D. E. Wolf (Springer))Comment: 15 pages, 0 figure. To be published in Traffic and Granular Flow 2001
edited by Y.Sugiyama and D. E. Wolf (Springer
On the General Analytical Solution of the Kinematic Cosserat Equations
Based on a Lie symmetry analysis, we construct a closed form solution to the
kinematic part of the (partial differential) Cosserat equations describing the
mechanical behavior of elastic rods. The solution depends on two arbitrary
analytical vector functions and is analytical everywhere except a certain
domain of the independent variables in which one of the arbitrary vector
functions satisfies a simple explicitly given algebraic relation. As our main
theoretical result, in addition to the construction of the solution, we proof
its generality. Based on this observation, a hybrid semi-analytical solver for
highly viscous two-way coupled fluid-rod problems is developed which allows for
the interactive high-fidelity simulations of flagellated microswimmers as a
result of a substantial reduction of the numerical stiffness.Comment: 14 pages, 3 figure
Packing of elastic wires in spherical cavities
We investigate the morphologies and maximum packing density of thin wires
packed into spherical cavities. Using simulations and experiments, we find that
ordered as well as disordered structures emerge, depending on the amount of
internal torsion. We find that the highest packing densities are achieved in
low torsion packings for large systems, but in high torsion packings for small
systems. An analysis of both situations is given in terms of energetics and
comparison is made to analytical models of DNA packing in viral capsids.Comment: 4 page
Anisotropic elastic theory of preloaded granular media
A macroscopic elastic description of stresses in static, preloaded granular
media is derived systematically from the microscopic elasticity of individual
inter-grain contacts. The assumed preloaded state and friction at contacts
ensure that the network of inter-grain contacts is not altered by small
perturbations. The texture of this network, set by the preparation of the
system, is encoded in second and fourth order fabric tensors. A small
perturbation generates both normal and tangential inter-grain forces, the
latter causing grains to reorient. This reorientation response and the
incremental stress are expressed in terms of the macroscopic strain.Comment: 7 pages, 2 figures. Accepted version. [email protected]
[email protected]
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
Rotational elasticity and couplings to linear elasticity
It is the aim of the paper to present a new point of view on rotational
elasticity in a nonlinear setting using orthogonal matrices. The proposed
model, in the linear approximation, can be compared to the well known
equilibrium equations of static linear elasticity. An appropriate kinetic
energy is identified and we present a dynamical model of rotational elasticity.
The propagation of elastic waves in such a medium is studied and we find two
classes of waves, transversal rotational waves and longitudinal rotational
waves, both of which are solutions of the nonlinear partial differential
equations. For certain parameter choices, the transversal wave velocity can be
greater than the longitudinal wave velocity. Moreover, parameter ranges are
identified where the model describes an auxetic material. However, in all cases
the potential energy functional is positive definite. Finally, we couple the
rotational waves to linear elastic waves to study the behaviour of the coupled
system. We find wave like solutions to the coupled equations and can visualise
our results with the help of suitable figures.Comment: 19 pages, 2 figures, heavily revised and largely extended versio
ALA and ALA hexyl ester in free and liposomal formulations for the photosensitisation of tumour organ cultures
In spite of the wide range of tumours successfully treated with 5-aminolevulinic acid mediated photodynamic therapy, the fact that 5-aminolevulinic acid has low lipid solubility, limits its clinical application. More lipophilic 5-aminolevulinic acid prodrugs and the use of liposomal carriers are two approaches aimed at improving 5-aminolevulinic acid transmembrane access. In this study we used both 5-aminolevulinic acid and its hexyl ester in their free and encapsulated formulations to compare their corresponding endogenous synthesis of porphyrins. Employing murine tumour cultures, we found that neither the use of hexyl ester nor the entrappment of either 5-aminolevulinic acid or hexyl ester into liposomes increase the rate of tumour porphyrin synthesis. By light and electronic microscopy it was demonstrated that exposure of tumour explants to either free or liposomal 5-aminolevulinic acid and subsequent illumination induces the same type of subcellullar damage. Mitochondria, endoplasmic reticulum and plasma membrane are the structures mostly injured in the early steps of photodynamic treatment. In a later stage, cytoplasmic and nuclear disintegration are observed. By electronic microscopy the involvement of the endocytic pathway in the incorporation of liposomal 5-aminolevulinic acid into the cells was shown
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