12,612 research outputs found
Particle-fluid interactions for flow measurements
Study has been made of the motion of single particle and of group of particles, emphasizing solid particles in gaseous fluid. Velocities of fluid and particle are compared for several conditions of physical interest. Mean velocity and velocity fluctuations are calculated for single particle, and some consideration is given to multiparticle systems
A nilpotent group without local functional equations for pro-isomorphic subgroups
The pro-isomorphic zeta function of a torsion-free finitely generated
nilpotent group G enumerates finite index subgroups H such that H and G have
isomorphic profinite completions. It admits an Euler product decomposition,
indexed by the rational primes. We manufacture the first example of a
torsion-free finitely generated nilpotent group G such that the local Euler
factors of its pro-isomorphic zeta function do not satisfy functional
equations. The group G has nilpotency class 4 and Hirsch length 25. It is
obtained, via the Malcev correspondence, from a Z-Lie lattice L with a suitable
algebraic automorphism group Aut(L).Comment: 16 page
On pro-isomorphic zeta functions of -groups of even Hirsch length
Pro-isomorphic zeta functions of finitely generated nilpotent groups form one
of the group-theoretic generalisations of the Riemann zeta functions. They are
Dirichlet generating functions enumerating finite-index subgroups whose
profinite completion is isomorphic to that of the ambient group. We study
pro-isomorphic zeta functions of -groups; these form the building blocks
of finitely generated class two nilpotent groups with centre of rank two, up to
commensurability. These groups were classified by Grunewald and Segal, and can
be indexed by primary polynomials whose companion matrices define commutator
relations. We provide a key step towards the elucidation of the pro-isomorphic
zeta functions of -groups of even Hirsch length by describing the
automorphism groups of the associated graded Lie rings. Utilizing this
description of the automorphism groups, we calculate the local pro-isomorphic
zeta functions of groups associated to the polynomials and . In both
cases, the local zeta functions are uniform in the prime~ and satisfy
functional equations.Comment: 29 page
The Pioneer Anomaly and a Machian Universe
We discuss astronomical and astrophysical evidence, which we relate to the
principle of zero-total energy of the Universe, that imply several relations
among the mass M, the radius R and the angular momentum L of a "large" sphere
representing a Machian Universe. By calculating the angular speed, we find a
peculiar centripetal acceleration for the Universe. This is an ubiquituous
property that relates one observer to any observable. It turns out that this is
exactly the anomalous acceleration observed on the Pioneers spaceships. We have
thus, shown that this anomaly is to be considered a property of the Machian
Universe. We discuss several possible arguments against our proposal.Comment: 6 pages including front page. Publishe
Turbulence measurements using the laser Doppler velocimeter
The photomultiplier signal representing the axial velocity of water within a glass pipe is examined. It is shown that with proper analysis of the photomultiplier signal, the turbulent information that can be obtained in liquid flows is equivalent to recent hot film studies. In shear flows the signal from the laser Doppler velocimeter contains additional information which may be related to the average shear
Scintillation reduction for combined Gaussian-vortex beam propagating through turbulent atmosphere
We numerically examine the spatial evolution of the structure of coherent and
partially coherent laser beams (PCBs), including the optical vortices,
propagating in turbulent atmospheres. The influence of beam fragmentation and
wandering relative to the axis of propagation (z-axis) on the value of the
scintillation index (SI) of the signal at the detector is analyzed. A method
for significantly reducing the SI, by averaging the signal at the detector over
a set of PCBs, is described. This novel method is to generate the PCBs by
combining two laser beams - Gaussian and vortex beams, with different
frequencies (the difference between these two frequencies being significantly
smaller than the frequencies themselves). In this case, the SI is effectively
suppressed without any high-frequency modulators.Comment: 13 pages, 8 figure
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