Linear stability of radially-heated circular Couette flow with simulated radial gravity

The stability of circular Couette flow between vertical concentric cylinders in the presence of a radial temperature gradient is considered with an effective “radial gravity.” In addition to terrestrial buoyancy − ρg e _z we include the term − ρg _m f(r)e _r where g _m f(r) is the effective gravitational acceleration directed radially inward across the gap. Physically, this body force arises in experiments using ferrofluid in the annular gap of a Taylor–Couette cell whose inner cylinder surrounds a vertical stack of equally spaced disk magnets. The radial dependence f(r) of this force is proportional to the modified Bessel function K ₁(κr), where 2π/κ is the spatial period of the magnetic stack and r is the radial coordinate. Linear stability calculations made to compare with conditions reported by Ali and Weidman (J. Fluid Mech., 220, 1990) show strong destabilization effects, measured by the onset Rayleigh number R, when the inner wall is warmer, and strong stabilization effects when the outer wall is warmer, with increasing values of the dimensionless radial gravity γ = g _m /g. Further calculations presented for the geometry and fluid properties of a terrestrial laboratory experiment reveal a hitherto unappreciated structure of the stability problem for differentially-heated cylinders: multiple wavenumber minima exist in the marginal stability curves. Transitions in global minima among these curves give rise to a competition between differing instabilities of the same spiral mode number, but widely separated axial wavenumbers.     

A Heuristic Tree-search Method of Selecting Face Schedules at a Colliery

In the course of work on developing a planning system covering several levels of operations the problem has arisen of selecting the best schedule of coal faces and methods of work on them over an 18-month period at a colliery. A colliery has a number of faces which can come into operation at any time and in any order. The time at which faces are replaced depends on the time taken to work these out which, in turn, depends on the method of work used. A number of methods can be used on each face producing different results, and using different amounts of resources.Since the method would be used as a routine for a large number of collieries, an empirical near-optimum approach has been used which uses a mixture of heuristics, integer programming and search through a decision-tree.A computer program has been used successfully and is now being introduced for routine use.     

Some Difficulties Experienced by First Year Undergraduates— an Attempt to Remedy their Lack of Sixth Form Mathematics

Students come to universities with only O‐level Mathematics to read subjects such as Biology and Economics. These subjects now need a greater knowledge of mathematics. A Research Project at Lancaster is trying to meet their difficulties. A course is being run for 120 such students.

An account is given of experience with a variety of audio and visual aids designed for use with classes where no teacher is available and for individual learning.

The syllabus for the course is given in broad outline with reasons for choices.

Particular difficulties experienced by the students are outlined; also the clashes of interest which occur.

In an Appendix a mathematical model is suggested to relate the average rate of progress of a class to the rate of feeding in of information.     

Linear stability of radially-heated circular Couette flow with simulated radial gravity

The stability of circular Couette flow between vertical concentric cylinders in the presence of a radial temperature gradient is considered with an effective “radial gravity.” In addition to terrestrial buoyancy − ρg e _z we include the term − ρg _m f(r)e _r where g _m f(r) is the effective gravitational acceleration directed radially inward across the gap. Physically, this body force arises in experiments using ferrofluid in the annular gap of a Taylor–Couette cell whose inner cylinder surrounds a vertical stack of equally spaced disk magnets. The radial dependence f(r) of this force is proportional to the modified Bessel function K ₁(κr), where 2π/κ is the spatial period of the magnetic stack and r is the radial coordinate. Linear stability calculations made to compare with conditions reported by Ali and Weidman (J. Fluid Mech., 220, 1990) show strong destabilization effects, measured by the onset Rayleigh number R, when the inner wall is warmer, and strong stabilization effects when the outer wall is warmer, with increasing values of the dimensionless radial gravity γ = g _m /g. Further calculations presented for the geometry and fluid properties of a terrestrial laboratory experiment reveal a hitherto unappreciated structure of the stability problem for differentially-heated cylinders: multiple wavenumber minima exist in the marginal stability curves. Transitions in global minima among these curves give rise to a competition between differing instabilities of the same spiral mode number, but widely separated axial wavenumbers.     

The measurement of quality in auditorium acoustics by subjective scaling methods—A review of developments in theory and practice

A review is given of subjective measurement methods in auditorium acoustics. Particular emphasis is laid on research in what may be termed the field of psychometric room acoustics. In the past, traditional psychophysical methods have proved useful for the more limited purpose of determining the effects of physical changes on subjective attributes, but more recent developments in psychometric theory now permit aesthetic characteristics, such as quality, to be evaluated on valid subjective measurement scales. At present there is contention concerning the best approach to adopt in applying such subjective scales to the evaluation of auditoria. Two schools of thought have emerged: one favouring preference comparisons, the other semantic differential ratings. The advantages and disadvantages of both methods are discussed in relation to recent projects. It is suggested that the advantages of these two approaches could be combined to derive a reliable subjective measure for evaluating auditoria in the field.