Sedimentation of homogeneous suspensions in finite vessels

The question of a possible container shape dependence of the sedimentation velocity in a homogeneous suspension is reexamined. To this end we develop a statistical theory of suspensions based on low-Reynolds-number hydrodynamics of spherical particles in a container. It is shown, to first order in the volume fraction, that in an arbitrary vessel the relative sedimentation velocity is shape independent, but that at the same time shape-dependent convection occurs. The theory forms a bridge between earlier calculations for special geometries by Beenakker and Mazur and a phenomenological theory recently proposed by Nozières.This paper is dedicated to N. G. van Kampen.     

On the theory of multiple scattering II. Critical scattering

The systematic theory of multiple scattering which we gave in a previous paper is further elaborated for critical scattering. It is shown that in each order the multiple-scattering intensity near the critical point is in essence a contraction of consecutive uncorrelated single-scattering intensities. The anomaly of the critical depolarization factor is calculated and is found to be in quantitative agreement with recent experimental results. Double scattering corrections to the Ornstein-Zernike plot are discussed.     

On the motion and brownian motion of n spheres in a viscous fluid

An extension of Faxén's theorem is given for the case that n spheres move with arbitrary velocities through a fluid in non-uniform steady flow. Explicit expressions for the friction and mutual friction tensors, valid to order R^?3, where R is a typical distance between spheres, are obtained together with this extension. These expressions contain 2-, 3- and 4-sphere contributions. Brownian motion of n spheres as a consequence of fluid fluctuations is discussed on the basis of the relationships derived.     

On the motion of a sphere with arbitrary slip in a viscous incompressible fluid

An expression for the force on a sphere moving with a time-dependent velocity through an incompressible fluid in nonstationary, nonhomogeneous flow is obtained for the case of arbitrary slip on the surface of the sphere.     

Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero

This paper provides evidence for the Birch and Swinnerton-Dyer conjecture for analytic rank  abelian varieties  that are optimal quotients of attached to newforms. We prove theorems about the ratio , develop tools for computing with , and gather data about certain arithmetic invariants of the nearly abelian varieties of level . Over half of these have analytic rank , and for these we compute upper and lower bounds on the conjectural order of  . We find that there are at least such for which the Birch and Swinnerton-Dyer conjecture implies that is divisible by an odd prime, and we prove for of these that the odd part of the conjectural order of really divides by constructing nontrivial elements of using visibility theory. We also give other evidence for the conjecture. The appendix, by Cremona and Mazur, fills in some gaps in the theoretical discussion in their paper on visibility of Shafarevich-Tate groups of elliptic curves.

     

The determination of chain statistical parameters by light scattering measurements.

The effects of volume exclusion on polymer chain conformations can be determined from the study of the angular dependence of radiation scattered by chain molecules. It is found that useful information can be obtained only when the variable x is large, where x is the product of the square of the magnitude of the scattering vector and of the mean square radius of gyration. Hence, solutions of macromolecules of very high molecular weight are needed for these investigations. The theoretical treatment of the scattering function is based on several assumptions. The validity of these assumptions is examined by computing, using a Monte-Carlo technique, various moments of intramolecular separations and comparing the results so obtained, in the limit of a chain of infinite length, with the analytical results. The computations seem to verify the validity of the theoretical model. The scattering behavior of solutions of recently synthesized polystyrene of Mw = 4.4 X 10(7) in cyclohexane at various temperatures and in benzene at 40 degrees was investigated. From the log-log plots of the scattering function vs. x, a statistical parameter was calculated, whose value depends on the magnitude of long-range correlations between any pair of chain elements. It is found that above the theta temperature this parameter is practically independent of temperature and that its numerical value was found to agree well with the value obtained from Monte-Carlo calculations. In the neighborhood of the theta temperature, this parameter decreases rapidly with decreasing temperature, indicating a first-order transition in chain conformation.     

To the question of electron angular distribution at Μ-meson decay

The paper describes the measurement of the angular distribution of electrons at the decay of-mesons in a longitudinal magnetic field. The results of measurement indicate that electrons are emitted with preference not only in the direction parallel to the spin orientation of -meson but also in the antiparallel direction in disagreement with the angular distribution predicted by theory.

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The authors thank N. V. Rabin for irradiating the nuclear emulsions, Prof. Dr. V. Petrílka and M. Suk for mediating relations with the Joint Institute of Nuclear Research in Dubna and Dr. J. Pernegr for valuable discussions and remarks. Thanks also go to H. Koutová and H. Slámová for carefully scanning the nuclear emulsions.     

Studies on the imidazole series

The reaction of 2-mercaptoimidazole and its 4(5)-aryl- and 4,5-diaryl-substituted derivatives with -halogenoketones has yielded a number of alkyl-, acyl-, and aryl-substituted imidazo[2,1-b]thiazoles.For part XLV, see [1].