Similarity of the concentration field of gas-phase turbulent jets

This work is an experimental investigation of the turbulent concentration field formed when the nozzle gas from a round, momentum-driven, free turbulent jet mixes with gas entrained from a quiescent reservoir. The measurements, which were made with a non-intrusive laser-Rayleigh scattering diagnostic at Reynolds numbers of 5000, 16000, and 40000, cover the axial range from 20 to 90 jet exit diameters and resolve the full range of temporal and spatial concentration scales. Reynolds-number-independent and Reynolds-number-dependent similarities are investigated. The mean and r.m.s. values of the concentration are found to be consistent with jet similarity laws. Concentration fluctuation power spectra are found to be self-similar along rays emanating from the virtual origin of the jet. The probability density function for the concentration is also found to be self-similar along rays. Near the centreline of the jet, the scaled probability density function of jet fluid concentration is found to be nearly independent of the Reynolds number

Evaluation of routines for numerical solution of the matrix equation AX + XA sup T + B = 0

Evaluation of routines for numerical solution of matrix equation for time-invariant linear system

Some Economic Implications of a Federal Ireland. ESRI Memorandum Series No. 97 1974

Economists are frequently accused of building elaborate structures out of the most unlikely set of hypotheses. One cannot help suspecting that this charge will be levelled against this paper which makes no attempt to assess the political probability of any agreement on a Federal relationship between Northern Ireland and the Republic. In defense it can be argued that the object of this paper is to examine some of the economic issues that would arise under a federal arrangement while recognising that economic factors are unlikely to be the sole, or dominant, influences in the future political position of Northern Ireland. It would not, of course, be possible to explore every aspect of the economic consequences of a Federal Ireland even under the assumption that the structure of the economy of Northern Ireland and the Republic remains as it is today. Rather we shall have to be content to examine some of the major problems that would face any proposed federation. Thus, to some extent, the bias of this paper will be pessimistic since it will not concentrate on any credit side of the balance sheet. However it must be stated that most of the benefits, if they exist, flow from the assumed dynamic effects of federation; which effects seem to owe more to wishful thinking than an analysis of the present structure of both economies

Two qubits can be entangled in two distinct temperature regions

We have found that for a wide range of two-qubit Hamiltonians the canonical-ensemble thermal state is entangled in two distinct temperature regions. In most cases the ground state is entangled; however we have also found an example where the ground state is separable and there are still two regions. This demonstrates that the qualitative behavior of entanglement with temperature can be much more complicated than might otherwise have been expected; it is not simply determined by the entanglement of the ground state, even for the simple case of two qubits. Furthermore, we prove a finite bound on the number of possible entangled regions for two qubits, thus showing that arbitrarily many transitions from entanglement to separability are not possible. We also provide an elementary proof that the spectrum of the thermal state at a lower temperature majorizes that at a higher temperature, for any Hamiltonian, and use this result to show that only one entangled region is possible for the special case of Hamiltonians without magnetic fields.Comment: 6 pages, 4 figures, many new result

Seasonality and Unemployment in Ireland. Quarterly Economic Commentary, October 1975

It is widely known that many statistical series exhibit a distinct seasonal pattern. That is, they tend to rise or fall according to the time of the year even when the underlying levels of the series are constant. Such seasonal movements are often a reflection of variations in the climate-ice-cream sales peak in the summer and coal-sales peak in the winter-or of traditional holiday periods. Obviously we would wish to remove the seasonal variation in order to examine the underlying trend of any given economic' series. If we do not correct data for seasonality it becomes quite difficult to distinguish between movements which reflect the normal seasonal pattern and other underlying movements

Quantum Computation as Geometry

Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms, or to prove limitations on the power of quantum computers.Comment: 13 Pages, 1 Figur