Tracer of electrical conduit or pipes

Device matches ends of a buried conduit, transversing an inaccessible area, without cutting the current

Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.Comment: 7 pages, 4 figure

Corona-type theorems and division in some function algebras on planar domains

Let $A$ be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if $f,f_1,\dots,f_n\in A$ satisfy $|f|\leq \sum_{j=1}^n |f_j|$, does there exist $g_j\in A$ and a constant $N\in\N$ such that $f^N=\sum_{j=1}^n g_j f_j$? A prominent role in our proofs is played by a new space, C_{\dbar, 1}(K), which we call the algebra of \dbar-smooth functions. In the case $n=1$, a complete solution is given for the algebras $A^m(K)$ of functions holomorphic in $K^\circ$ and whose first $m$-derivatives extend continuously to \ov{K^\circ}. This necessitates the introduction of a special class of compacta, the so-called locally L-connected sets. We also present another constructive proof of the Nullstellensatz for $A(K)$, that is only based on elementary \dbar-calculus and Wolff's method.Comment: 23 pages, 6 figure

Ratemeter

An instantaneous reading tachometer in which reoccurring events to be measured in rate, trigger a threestate timing generator in which the first two states are of fixed duration and the third state is of variable duration is described. An electrical decay circuit is set to a reference level by the second state and the third state causes this reference level to decay until the reoccurrence of an event. This triggers a new first state which in turn triggers a sample and hold circuit to hold the decayed level. The decayed level is amplified and provided as an output indicative of the instantaneous rate of occurence of the last two successive events

Reduced Persistence Length and Fluctuation-Induced Interactions of Directed Semiflexible Polymers on Fluctuating surfaces

We consider directed semiflexible polymers embedded in a fluctuating surface which is governed by either surface tension or bending rigidity. The attractive interactions induced by the fluctuations of the surface reduce the rigidity of the polymers. In particular, it is shown that for arbitrarily stiff parallel polymers, there is a characteristic separation below which they prefer to bend rather than stay linear. The out-of plane fluctuations of the polymer, screen out the long-range fluctuation-induced forces, resulting in only a short-ranged effective attraction.Comment: REVTEX, one postscript figur

Strong-Coupling Theory for Counter-Ion Distributions

The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature. In this paper we derive, using field-theoretic methods, a theory which becomes exact in the opposite limit of strong coupling. Formally, it corresponds to a standard virial expansion. Long-range divergences, which render the virial expansion intractable for homogeneous bulk systems, are shown to be renormalizable for the case of inhomogeneous distribution functions by a systematic expansion in inverse powers of the coupling parameter. For a planar charged wall, our analytical results compare quantitatively with extensive Monte-Carlo simulations.Comment: 7 pages, 3 figures; to appear in Europhys. Let

Cubic interaction vertices for fermionic and bosonic arbitrary spin fields

Using the light-cone gauge approach to relativistic field dynamics, we study arbitrary spin fermionic and bosonic fields propagating in flat space of dimension greater than or equal to four. Generating functions of parity invariant cubic interaction vertices for totally symmetric and mixed-symmetry massive and massless fields are obtained. For the case of totally symmetric fields, we derive restrictions on the allowed values of spins and the number of derivatives. These restrictions provide a complete classification of parity invariant cubic interaction vertices for totally symmetric fermionic and bosonic fields. As an example of application of the light-cone formalism, we obtain simple expressions for the Yang-Mills and gravitational interactions of massive arbitrary spin fermionic fields. For some particular cases, using our light-cone cubic vertices, we discuss the corresponding manifestly Lorentz invariant and on-shell gauge invariant cubic vertices.Comment: 57 pages, LaTeX-2e. v2: Results and conclusions of version v1 unchanged. New results for cubic vertices of mixed-symmetry fields added. Appendix A fully rewritten. Typos corrected. References added. arXiv admin note: significant text overlap with arXiv:hep-th/051234