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 D∗D^*-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 $D^*$-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 $D^*$-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 $x^2$ and $x^3$. In both cases, the local zeta functions are uniform in the prime~$p$ 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