Improved bounds for sampling contingency tables

We study the problem of sampling contingency tables (nonnegative integer matrices with specified row and column sums) uniformly at random. We give an algorithm which runs in polynomial time provided that the row sums r_i and the column sums c_j satisfy r_i = Ω(n^3/2m log m), and c_j = Ω(m^3/2n log n). This algorithm is based on a reduction to continuous sampling from a convex set. The same approach was taken by Dyer, Kannan, and Mount in previous work. However, the algorithm we present is simpler and has weaker requirements on the row and column sums. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 135–146, 2002     

EFFECT OF SEATING ON EXPOSURES TO WHOLE-BODY VIBRATION IN VEHICLES

The vibration isolation efficiency of seating has been evaluated in 100 work vehicles in 14 categories (cars, vans, lift trucks, lorries, tractors, buses, dumpers, excavators, helicopters, armoured vehicles, mobile cranes, grass rollers, mowers and milk floats). Seat isolation efficiency, expressed by the SEAT value, was determined for all seats (67 conventional seats and 33 suspension seats) from the vertical acceleration measured on the floors and on the seats of the vehicles.For most categories of vehicle, the average SEAT value was less than 100%, indicating that the average seat provided some attenuation of vibration. However, there were large variations in SEAT values between vehicles within categories. Two alternative vibration frequency weightings (W_b from BS 6841, 1987; W_k from ISO 2631, 1997) yielded SEAT values that differed by less than 6%. Overall, the SEAT values determined by two alternative methods (the ratio of r.m.s. values and the ratio of vibration dose values) differed by less than 4·5% when using weighting W_b, although larger differences may be expected in some situations. The median SEAT value for the suspension seats was 84·6%; the median SEAT value for the conventional seats was 86·9% (based on weighting W_b and the ratio of r.m.s. values).Predicted SEAT values were obtained assuming that each seat could be interchanged between vehicles without altering its transmissibility. The calculations suggest that 94% of the vehicles investigated might benefit from changing the current seat to a seat from one of the other vehicles investigated. Although the predictions are based on assumptions that will not always apply, it is concluded that the severity of whole-body vibration exposures in many work environments can be lessened by improvements to seating dynamics.     

A linearized vector radiative transfer model for atmospheric trace gas retrieval

We present a plane parallel radiative transfer model for polarized light, that provides the intensity vector as well as the derivatives of the four Stokes parameters with respect to atmospheric trace gas profiles. These derivatives are essential for retrieval of height resolved trace gas information from satellite measurements of backscattered sunlight. The model uses the Gauss-Seidel iteration technique for solving the radiative transfer equation. For the first time, the forward-adjoint radiative perturbation theory is applied for the linearization of a radiative transfer model including polarization. The accuracy of the model is better than 0.025% for all four Stokes parameters and better than 0.03% for the derivatives.     

Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flow

Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical–numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd.     

Elastic and Thermophysical Properties of Poly(Vinyl Chloride) and Chlorinated Polyethylene Blends

The results of experimental and theoretical investigations of elastic and thermophysical properties of poly(vinyl chloride) (PVC) and chlorinated polyethylene (CPE) blends are presented. Eight types of specimens with different ratios of weight contents of PVC and CPE (PVC/CPE = 100/0, 90/10, 80/20, 60/40, 40/60, 20/80, 10/90, and 0/100) were tested. The effect of blend composition on the elastic constants (tensile and shear modulus) is discussed. The data on the thermal conductivity, thermal diffusivity, and heat capacity of the blends investigated are also presented.     

A simple and realistic triton wave function

We propose a simple triton wave function that consists of a product of three correlation operators operating on a three-body spin-isospin state. This wave function is formally similar to that used in the recent variational theories of nuclear matter, the main difference being in the long-range behavior of the correlation operators. Variational calculations are carried out with the Reid potential, using this wave function in the so-called “symmetrized product” and “independent pair” forms. The triton energy and density distributions obtained with the symmetrized product wave function agree with those obtained in Faddeev and other variational calculations using harmonic oscillator states. The proposed wave function and calculational methods can be easily generalized to treat the four-nucleon α-particle.     

Investigations in the amplitude of sounded piano tones

The relationship between final hammer velocity and maximum amplitude of radiated piano sound was investigated. Piano tones with varying hammer velocities were produced by a computer-monitored acoustic piano containing optical sensors and solenoids, and the sounded tones were recorded and digitized for analysis. Maximum amplitudes over the duration of the sounded tones were linearly proportional to piano hammer velocities for a range of frequencies and hammer velocities. Changes in room acoustics did not alter the linear relationship. Measurements of maximum amplitudes of individual tones and combined tones (dyads) also indicated a linear relationship between the sum of the maximum amplitudes of the individual tones and the maximum amplitude of the dyads. These findings indicate that the principle of superposition holds for peak amplitudes of sounded piano tones. Findings are discussed with regard to production and perception of musical dynamics.     

The first total synthesis of (R)-convolutamydine A

The first total synthesis of (R)-convolutamydine A has been achieved by the organocatalytic addition of acetone to 4,6-dibromoisatin. The absolute configuration was determined by single crystal X-ray diffraction. DFT studies were used to model the transition states for the aldol reaction and equilibrium geometries of the post-aldol reaction intermediates. The DFT study revealed that the aldol bond forming reaction was considerably endothermic.     

What is Erased in the Quantum Erasure?

In this paper, we re-examine a series of gedanken welcher Weg (WW) experiments introduced by Scully, Englert and Walther that contain the essential ideas underlying the quantum eraser. For this purpose we use the Bohm model which gives a sharp picture of the behaviour of the atoms involved in these experiments. This model supports the thesis that interference disappears in such WW experiments, even though the centre of mass wave function remains coherent throughout the experiment. It also shows exactly what it means to say ‘that the interference can be restored by manipulating the WW detectors long after the atoms have passed’. It does not support Wheeler’s notion that ‘the past is undefined and undefinable without the observation (in the present)’.