Investigation of the dependence of inferred interfacial tension on rotation rate in a spinning drop tensiometer

The spinning drop tensiometer is widely used to study the interfacial properties of many systems. However, there have also been several reported limitations with the spinning drop tensiometer. In this paper, it is shown that there is a relationship between the measured interfacial tension and the rotation rate of the drop. A detailed investigation of this relationship is presented.     

Finite Element Methods for a Model for Full Waveform Acoustic Logging

A model is defined to simulate the propagation of waves in aradially symmetric, isotropic, composite system consisting ofa fluid-filled well bore ^f through a fluid-saturated poroussolid ^p. Biot's equations of motion are chosen to describe thepropagation of waves in ^p, while the standard equation of motionfor compressible inviscid fluids is used for ^f, with appropriateboundary conditions at the contact surface between ^f and ^p.Also, absorbing boundary conditions for the artificial boundariesof ^p are derived for the model, their effect being to make themtransparent for waves arriving normally First, results on the existence and uniqueness of the solutionof the differential problem are given and then a discrete-time,explicit finite element procedure is defined and analysed, withfinite element spaces suited for radially symmetric problemsbeing used for the spatial discretisation.     

TheN 7/5 law for charged bosons

Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfiesE ₀–AN ^7/5. We prove that 7/5 is the correct power by proving thatE ₀–BN ^7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed thatE ₀–CN^1/4. This 1/4 law is also validated here by showing thatE ₀–DN^1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.Work partially supported by U.S. National Science Foundation grant DMS 8600748Work partially supported by U.S. National Science Foundation grant PHY85-15288-A01Work supported by Alfred Sloan Foundation dissertation fellowship     

Existence of Néel order in some spin-1/2 Heisenberg antiferromagnets

The methods of Dyson, Lieb, and Simon are extended to prove the existence of Néel order in the ground state of the 3D spin-1/2 Heisenberg antiferromagnet on the cubic lattice. We also consider the spin-1/2 antiferromagnet on the cubic lattice with the coupling in one of the three lattice directions taken to ber times its value in the other two lattice directions. We prove the existence of Néel order for 0.16r1. For the 2D spin-1/2 model we give a series of inequalities which involve the two-point function only at short distances and each of which would by itself imply Néel order.