On the added mass of sphere in a circular cylinder considering real fluid effects

An experimental method combined with boundary layer theory is given for evaluating the added mass of a sphere moving along the axis of a circular cylinder filled with water or oil. The real fluid effects are separated from ideal fluid effects.

The experimental method consists essentially of a magnetic steel sphere propelled from rest by an electromagnetic coil in which the current is accurately controlled so that it only supplies force for a short time interval which is within the laminar flow regime of the fluid. The motion of the sphere as a function of time is recorded on single frame photographs using a short-arc multiple flash lamp with accurately controlled time intervals between flashes.

A concept of the effect of boundary layer displacement on the fluid flow around a sphere is introduced to evaluate the real fluid effects on the added mass. Surprisingly accurate agreement between experiment and theory is achieved.

Aspects of the washout of salmonid eggs. 1. Observations on the physical characteristics of real and artificial eggs, their rate of fall in a water column and their pattern of settlement in an experimental channel

When salmonid redds are disrupted by spates, the displaced eggs will drift downstream. The mean distance of travel, the types of locations in which the eggs resettle and the depth of reburial of displaced eggs are not known. Investigation of these topics under field conditions presents considerable practical problems, though the use of artificial eggs might help to overcome some of them. Attempts to assess the similarities and/or differences in performance between real and artificial eggs are essential before artificial eggs can validly be used to simulate real eggs. The present report first compares the two types of egg in terms of their measurable physical characteristics (e.g. dimensions and density). The rate at which eggs fall in still water will relate to the rate at which they are likely to resettle in flowing water in the field. As the rate of fall will be influenced by a number of additional factors (e.g. shape and surface texture) which are not easily measured directly, the rates of fall of the two types of egg have been compared directly under controlled conditions. Finally, comparisons of the pattern of settlement of the two types of egg in flowing water in an experimental channel have been made. Although the work was primarily aimed at testing the value of artificial eggs as a simulation of real eggs, several side issues more directly concerned with the properties of real eggs and the likely distance of drift in natural streams have also been explored. This is the first of three reports made on this topic by the author in 1984.

On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

The effect of intensive line fishing on the virgin biomass of a tropical deepwater snapper, the crimson jobfish (Pristipomoides filamentosus)

An intensive commercial hook-and-line fishing operation targeted the demersal fisheries resources at Saya de Malha Bank in the Southwest Indian Ocean. Fishing was conducted with 12 dories that were equipped with echo sounders and electric fishing reels and supported by a refrigerated mothership. Over a 13-day period in the 55–130 m depth range, a total of 74.3 metric tons (t) of fish were caught, of which the crimson jobfish (Pristipomoides filamentosus) represented 80%. Catch rates decreased with time and could not be attributed to changes in location, climatic conditions, fishing depth, fishing method, or bait type. The initial virgin biomass of P. filamentosus available to a line fishery at the North Western promontory of Saya de Malha Bank was estimated at 72.6 t through application of the Leslie model to daily catch and effort data. Biomass densities of 2364 kg/km2 and 1206 kg/km were obtained by applying the initial biomass estimates to the surface area and to the length of the dropoff that was fished. The potential sustainable yield prior to exploitation was estimated at 567 kg/km2 per year. The quantity of P. filamentosus caught by the mother-ship-dory fishing operation represented 82% of the initial biomass available to a hook-and-line fishery, equivalent to more that three times the estimated maximum sustainable yield. The results of the study are important to fisheries managers because they demonstrate that intensive line fishing operations have the potential to rapidly deplete demersal fisheries resources.

On the domain decomposition and transmission line modelling finite element method for time-domain induction motor analysis

This paper demonstrates how a finite element model which exploits domain decomposition is applied to the analysis of three-phase induction motors. It is shown that a significant gain in cpu time results when compared with standard finite element analysis. Aspects of the application of the method which are particular to induction motors are considered: the means of improving the convergence of the nonlinear finite element equations; the choice of symmetrical sub-domains; the modelling of relative movement; and the inclusion of periodic boundary conditions. © 1999 IEEE.

Optimization on the orthogonal group for independent component analysis

This paper derives a new algorithm that performs independent component analysis (ICA) by optimizing the contrast function of the RADICAL algorithm. The core idea of the proposed optimization method is to combine the global search of a good initial condition with a gradient-descent algorithm. This new ICA algorithm performs faster than the RADICAL algorithm (based on Jacobi rotations) while still preserving, and even enhancing, the strong robustness properties that result from its contrast. © Springer-Verlag Berlin Heidelberg 2007.

Effect of Solvent Molecular Size on the Self-Assembly of Amphiphilic Diblock Copolymer in Selective Solvent

Real-space self-consistent field theory (SCFT) is employed to study the effect of solvent molecular size on the self-assembly of amphiphilic diblock copolymer in selective solvent. The phase diagrams in wide ranges of interaction parameters and solvent molecular size were obtained in present study. The results indicate that the solvent molecular size is a key factor that determines the self-assembly of amphiphilic diblock copolymer. The self-assembled morphology changes from circle-like micelle to line-like micelle, then to loop-like micelle by decreasing the solvent molecular size in a wide range of solvent selectivity. We analyze and discuss this change in terms of the solvent solubility and the entropy contribution.