Existence theory for spatially competitive network facility location models

Models for locating a firm's production facilities while simultaneously determining production levels at these facilities and shipping patterns so as to maximize the firm's profits are presented. In these models, existing firms, are assumed to act in accordance with an appropriate model of spatial equilibrium. A proof of existence of a solution to the combined location-equilibrium problem is provided.     

Weyl gauging and spontaneously broken Lorentz symmetry: Some alternative models

Some new effective actions are suggested for theories in which the affine connection is not completely specified by the metric. The new actions lead to models in which the metric, torsion, and Weyl vector fields all propagate. The dimensionally reduced versions do not contain third derivatives of the gauge potentials in the field equation. Some simple models which exhibit simultaneous breaking of Weyl andD-dimensional Lorentz symmetry are investigated. It is shown that it is possible for this effect to occur in any model in which the field action contains the Einstein-Hilbert term. This is due to the fact that the contortion occurs in this object as part of an indefinite quadratic form.     

VERIFICATION OF SMOM AND QMOM POPULATION BALANCE MODELING IN CFD CODE USING ANALYTICAL SOLUTIONS FOR BATCH PARTICULATE PROCESSES

For many processes of industrial significance, due to the strong coupling between particle interactions and fluid dynamics, the population balance must be solved as part of a computational fluid dynamics （CFD） simulation. In this work, a CFD based population balance model is tested using a batch crystallization reactor. In this CFD model, the population balance is solved by the standard method of moments （SMOM） and the quadrature method of moments （QMOM）. The results of these simulations are compared to analytical solutions for the population balance in a batch tank where 1） nucleation, 2） growth, 3） aggregation, and 4） breakage are taking place separately. The results of these comparisons show that the first 6 moments of the population balance are accurately predicted for nucleation, growth, aggregation and breakage at all times.     

Shear and extensional flow of polyacrylamide solutions

As part of an EEC Science Stimulation programme on extensional viscosity two major conferences were organised on the subject. The second of these was devoted to the results obtained on a standard fluid, M 1. The data obtained in shear flow was remarkably consistent from laboratory to laboratory. Extensional flow results presented quite a different picture. Using a series of nonequilibrium techniques such as the spinline rheometer, opposing jet, falling drop and converging flow, extensional viscosity results were obtained which differed by as much as two to three orders of magnitude. Nevertheless, it was apparent that consistancy did exist between similar techniques. It is in the context of this information that the measurements described below have been made.The shear and extensional flow properties of partially ionised polyacrylamide in solution at concentrations ranging from 5 ppm were measured. The method of solution preparation was found to have a profound effect on the behaviour of the solutions in shear flow. The influence of salt concentration and pH was investigated and is discussed in the context of molecular shape in solution.Extensional flow measurements, using the spinline rheometer, show that the solutions are strongly strain thickening even at concentrations as low as 5 ppm. These results are considered in the light of polymer entanglement and association in the strong flow field.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs

Robert E. Jamison characterized chordal graphs by the edge set of every k-cycle being the symmetric difference of k−2 triangles. Strongly chordal (and chordal bipartite) graphs can be similarly characterized in terms of the distribution of triangles (respectively, quadrilaterals). These results motivate a definition of ‘strongly chordal bipartite graphs’, forming a class intermediate between bipartite interval graphs and chordal bipartite graphs.     

A computational study of some rheological influences on the “splashing experiment”

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N₁ and N₂, especially N₁, the extensional viscosity, and the dynamic moduli G′ and G″. In this paper, we shall confine attention to ‘constant-viscosity’ Boger fluids, and, accordingly, we shall limit attention to N₁, η_E, G′ and G″.We shall concentrate on the “splashing” problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high η_E can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model.     

Iterated Point–Line Configurations Grow Doubly-Exponentially

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (Comput. Geom. 27:257–267, 2004) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi–Trotter Theorem and an analysis of the “minimum degree” of the growing configuration.