Converting environmental wastes into valuable resources

This concept employs a viable energy saving method that uses a solvent to separate oil from particle matter; it can be used in metal forming industries to deoil sludges, oxides, and particle matter that is presently committed to landfill. If oily particles are used in their oily state, severe consequences to environmental control systems such as explosions or filter blinding, occur in the air handling equipment. This is due to the presence of hydrocarbons in the stack gasses resulting from the oily particles. After deoiling, the particles can be recycled and the separated oil can be used as a fuel. The process does not produce a waste of it's own and does not harm air or water. It demonstrates the dual benefits of it being commercially viable and in the national interest of conserving resources

Maps and navigation methods

Different maps and scales are discussed with particular emphasis on their use in aviation. The author makes the observation that current navigation methods are slow and dangerous and should be replaced by scientific methods of navigation based on loxodromy and the use of the compass

Non-relativistic conformal symmetries and Newton-Cartan structures

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational "dynamical exponent", $z$. The Schr\"odinger-Virasoro algebra of Henkel et al. corresponds to $z=2$. Viewed as projective Newton-Cartan symmetries, they yield, for timelike geodesics, the usual Schr\"odinger Lie algebra, for which z=2. For lightlike geodesics, they yield, in turn, the Conformal Galilean Algebra (CGA) and Lukierski, Stichel and Zakrzewski [alias "\alt" of Henkel], with $z=1$. Physical systems realizing these symmetries include, e.g., classical systems of massive, and massless non-relativistic particles, and also hydrodynamics, as well as Galilean electromagnetism.Comment: LaTeX, 47 pages. Bibliographical improvements. To appear in J. Phys.

Space-Time Noncommutativity from Particle Mechanics

We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space-time noncommutativity. We show that there is an algebraic map from this gauge back to the standard `commuting' gauge. Therefore the Poisson algebra, and the resulting quantum theory, are identical in the two gauges. The only difference is in the interpretation of space-time coordinates. The procedure is repeated for the case of a coupling with a constant electromagnetic field, where the reparametrization symmetry is preserved. For more arbitrary interactions, we show that standard dynamical system can be rendered noncommutative in space and time by a simple change of variables.Comment: 13 p

Chiral fermions as classical massless spinning particles

Semiclassical chiral fermion models with Berry term are studied in a symplectic framework. In the free case, the system can be obtained from Souriau's model for a relativistic massless spinning particle by "enslaving" the spin. The Berry term is identified with the classical spin two-form of the latter model. The Souriau model carries a natural Poincar\'e symmetry that we highlight, but spin enslavement breaks the boost symmetry. However the relation between the models allows us to derive a Poincare symmetry of unconventional form for chiral fermions. Then we couple our system to an external electromagnetic field. For gyromagnetic ratio $g=0$ we get curious superluminal Hall-type motions; for $g=2$ and in a pure constant magnetic field in particular, we find instead spiraling motions.Comment: Substantially revised and extended version. 31 pages, 5 figures. Details clarified and references added. To be published in PR

Anyons with anomalous gyromagnetic ratio & the Hall effect

Letting the mass depend on the spin-field coupling as $M^2=m^2-(eg/2c^2)F_{\alpha\beta}S^{\alpha\beta}$, we propose a new set of relativistic planar equations of motion for spinning anyons. Our model can accommodate any gyromagnetic ratio $g$ and provides us with a novel version of the Bargmann-Michel-Telegdi equations in 2+1 dimensions. The system becomes singular when the field takes a critical value, and, for $g\neq2$, the only allowed motions are those which satisfy the Hall law. For each $g\neq2,0$ a secondary Hall effect arises also for another critical value of the field. The non-relativistic limit of our equations yields new models which generalize our previous ``exotic'' model, associated with the two-fold central extension of the planar Galilei group.Comment: The affiliation of the first author's Institution is presented in detail. LaTeX, 12 pages no figures. To appear in Phys. Lett.

Representations of the conformal Lie algebra in the space of tensor densities on the sphere

Let ${\mathcal F}_\lambda(\mathbb{S}^n)$ be the space of tensor densities on $\mathbb{S}^n$ of degree $\lambda$. We consider this space as an induced module of the nonunitary spherical series of the group $\mathrm{SO}_0(n+1,1)$ and classify $(\mathrm{so}(n+1,1),\mathrm{SO}(n+1))$-sim$unitary submodules of${\mathcal F}_\lambda(\mathbb{S}^n)$as a function of$\lambda$.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP