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