2,591 research outputs found
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
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 . 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
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