Incremental Distance Transforms (IDT)

A new generic scheme for incremental implementations of distance transforms (DT) is presented: Incremental Distance Transforms (IDT). This scheme is applied on the cityblock, Chamfer, and three recent exact Euclidean DT (E2DT). A benchmark shows that for all five DT, the incremental implementation results in a significant speedup: 3.4×−10×. However, significant differences (i.e., up to 12.5×) among the DT remain present. The FEED transform, one of the recent E2DT, even showed to be faster than both city-block and Chamfer DT. So, through a very efficient incremental processing scheme for DT, a relief is found for E2DT’s computational burden

Is the Quantum Hall Effect influenced by the gravitational field?

Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field $\mathbf{g}(x)$ influences the QHE. In the realm of (1 + 2)-dimensional phenomenological macroscopic electrodynamics, the Ohm-Hall law is metric independent (`topological'). This suggests that it does not couple to $\mathbf{g}(x)$. We corroborate this result by a microscopic calculation of the Hall conductance in the presence of a post-Newtonian gravitational field.Comment: 4 page

Josephson squelch filter for quantum nanocircuits

We fabricated and tested a squelch circuit consisting of a copper powder filter with an embedded Josephson junction connected to ground. For small signals (squelch-ON), the small junction inductance attenuates strongly from DC to at least 1 GHz, while for higher frequencies dissipation in the copper powder increases the attenuation exponentially with frequency. For large signals (squelch-OFF) the circuit behaves as a regular metal powder filter. The measured ON/OFF ratio is larger than 50dB up to 50 MHz. This squelch can be applied in low temperature measurement and control circuitry for quantum nanostructures such as superconducting qubits and quantum dots.Comment: Corrected and completed references 6,7,8. Updated some minor details in figure

Multipole moments in Kaluza-Klein theories

This paper contains discussion of the problem of motion of extended i.e. non point test bodies in multidimensional space. Extended bodies are described in terms of so called multipole moments. Using approximated form of equations of motion for extended bodies deviation from geodesic motion is derived. Results are applied to special form of space-time.Comment: 11 pages, AMS-TeX, few misprints corrected, to appear in Classical and Quantum Gravit

Geometry of General Hypersurfaces in Spacetime: Junction Conditions

We study imbedded hypersurfaces in spacetime whose causal character is allowed to change from point to point. Inherited geometrical structures on these hypersurfaces are defined by two methods: first, the standard rigged connection induced by a rigging vector (a vector not tangent to the hypersurface anywhere); and a second, more physically adapted, where each observer in spacetime induces a new type of connection that we call the rigged metric connection. The generalisation of the Gauss and Codazzi equations are also given. With the above machinery, we attack the problem of matching two spacetimes across a general hypersurface. It is seen that the preliminary junction conditions allowing for the correct definition of Einstein's equations in the distributional sense reduce to the requirement that the first fundamental form of the hypersurface be continuous. The Bianchi identities are then proven to hold in the distributional sense. Next, we find the proper junction conditions which forbid the appearance of singular parts in the curvature. Finally, we derive the physical implications of the junction conditions: only six independent discontinuities of the Riemann tensor are allowed. These are six matter discontinuities at non-null points of the hypersurface. For null points, the existence of two arbitrary discontinuities of the Weyl tensor (together with four in the matter tensor) are also allowed.Comment: Latex, no figure

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or nonmetricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or nonmetricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (comprising torsion and nonmetricity). All this is compared to the recent results of Vandyck.Comment: 9 pages, REVTeX, no figures; minor changes, version to be published in Class. Quantum Gra

The constitutive tensor of linear elasticity: its decompositions, Cauchy relations, null Lagrangians, and wave propagation

In linear anisotropic elasticity, the elastic properties of a medium are described by the fourth rank elasticity tensor C. The decomposition of C into a partially symmetric tensor M and a partially antisymmetric tensors N is often used in the literature. An alternative, less well-known decomposition, into the completely symmetric part S of C plus the reminder A, turns out to be irreducible under the 3-dimensional general linear group. We show that the SA-decomposition is unique, irreducible, and preserves the symmetries of the elasticity tensor. The MN-decomposition fails to have these desirable properties and is such inferior from a physical point of view. Various applications of the SA-decomposition are discussed: the Cauchy relations (vanishing of A), the non-existence of elastic null Lagrangians, the decomposition of the elastic energy and of the acoustic wave propagation. The acoustic or Christoffel tensor is split in a Cauchy and a non-Cauchy part. The Cauchy part governs the longitudinal wave propagation. We provide explicit examples of the effectiveness of the SA-decomposition. A complete class of anisotropic media is proposed that allows pure polarizations in arbitrary directions, similarly as in an isotropic medium.Comment: 1 figur

Non-equilibrium dynamics of stochastic point processes with refractoriness

Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse, and the counting of particles by detector devices. Here we present an extension of renewal theory to describe ensembles of point processes with time varying input. This is made possible by a representation in terms of occupation numbers of two states: Active and refractory. The dynamics of these occupation numbers follows a distributed delay differential equation. In particular, our theory enables us to uncover the effect of refractoriness on the time-dependent rate of an ensemble of encoding point processes in response to modulation of the input. We present exact solutions that demonstrate generic features, such as stochastic transients and oscillations in the step response as well as resonances, phase jumps and frequency doubling in the transfer of periodic signals. We show that a large class of renewal processes can indeed be regarded as special cases of the model we analyze. Hence our approach represents a widely applicable framework to define and analyze non-stationary renewal processes.Comment: 8 pages, 4 figure