A survey of British rheological research

Summary This paper summarises a report, published by the National Engineering Laboratory, of a survey of rheological research in Britain during 1966. The report gives details of 783 research projects being carried out in 411 establishments.     

Applying forces to elastic network models of large biomolecules using a haptic feedback device

Elastic network models of biomolecules have proved to be relatively good at predicting global conformational changes particularly in large systems. Software that facilitates rapid and intuitive exploration of conformational change in elastic network models of large biomolecules in response to externally applied forces would therefore be of considerable use, particularly if the forces mimic those that arise in the interaction with a functional ligand. We have developed software that enables a user to apply forces to individual atoms of an elastic network model of a biomolecule through a haptic feedback device or a mouse. With a haptic feedback device the user feels the response to the applied force whilst seeing the biomolecule deform on the screen. Prior to the interactive session normal mode analysis is performed, or pre-calculated normal mode eigenvalues and eigenvectors are loaded. For large molecules this allows the memory and number of calculations to be reduced by employing the idea of the important subspace, a relatively small space of the first M lowest frequency normal mode eigenvectors within which a large proportion of the total fluctuation occurs. Using this approach it was possible to study GroEL on a standard PC as even though only 2.3% of the total number of eigenvectors could be used, they accounted for 50% of the total fluctuation. User testing has shown that the haptic version allows for much more rapid and intuitive exploration of the molecule than the mouse version.     

"A" cation polarity control in ACuTe2O7 (A = Sr2+, Ba2+, or Pb2+)

The synthesis and characterization of ACuTe(2)O(7) (A = Sr(2+), Ba(2+), or Pb(2+)) have been carried out. Interestingly, SrCuTe(2)O(7) and PbCuTe(2)O(7) are centrosymmetric and isostructural, whereas BaCuTe(2)O(7) is noncentrosymmetric and polar. All of the materials contain [CuTe(2)O(7)](2-) layers stacked along the b-axis direction that are separated by the "A" cations. The layers are composed of corner-shared CuO(5), TeO(6), and TeO(4) polyhedra. The influence of the "A" cation on the polarity is described by bond valence concepts, including the bond strain index and global instability index. Infrared, UV-vis, thermogravimetric, differential thermal analysis, and magnetic measurements were performed on all three materials. For BaCuTe(2)O(7), second-harmonic generation (SHG), piezoelectric, and polarization measurements were performed. A moderate SHG efficiency of approximately 70 × α-SiO(2) was measured. In addition, we determined that BaCuTe(2)O(7) is not ferroelectric; that is, the macroscopic polarization is not reversible. For BaCuTe(2)O(7), a pyroelectric coefficient of -9.5 μC/m(2)·K at 90 °C and a piezoelectric charge coefficient of 49 pm/V were determined. Crystal data are the following: SrCuTe(2)O(7), orthorhombic, space group Pbcm (No. 57), a = 7.1464(7) ?, b = 15.0609(15) ?, c = 5.4380(5) ?, V = 585.30(10) ?(3), and Z = 4; PbCuTe(2)O(7), orthorhombic, space group Pbcm (No. 57), a = 7.2033(5) ?, b = 15.0468(10) ?, c = 5.4691(4) ?, V = 592.78(7) ?(3), and Z = 4.     

Proton magnetic relaxation in ethylene oxide,tetrahydrofuran, and triethylene diamine as clathrate deuterates

Proton spin-lattice relaxation times (T ₁) have been measured for triethylene diamine, ethylene oxide, and tetrahydrofuran as clathrate deuterates. The results are interpreted in terms of anisotropic rotation of the guest molecules. Triethylene diamine is thought to be undergoing rotation about its C ₃ axis with a correlation time given by τ_c/s = 4·87 × 10^-14 exp (1680 K/T) at temperatures between 120 K and the decomposition point (308 K). Between 77 K and 120 K, T ₁ is dominated by conformational distortions of the guest molecule. Ethylene oxide and tetrahydrofuran rotate about at least two axes in the deuterate at rates sufficient to produce some motional narrowing. At high temperatures the relaxation is caused in both cases by rotation about an axis perpendicular to the C ₂ axis, and at lower temperatures by rotation about the C ₂ axis itself. The correlation times are for ethylene oxide τ_c/s = 6·76 × 10^-14 exp (450 K/T), T < 160 K; and for tetrahydrofuran τ_c/s = 4·79 × 10^-14 exp (470 K/T), T < 140 K.

The free induction decay shapes indicate that, in each case, low frequency motion is occurring about all axes throughout the temperature range studied (77 K to the decomposition temperature in each case). From the lack of an observable signal from the clathrate deuterates of hexamethylene tetramine and dioxan, it is deduced that there is no reorientational motion of these guests at frequencies greater than their rigid-lattice linewidths.     

A note on the circle containment problem

We extend a result due to Bárányet al. and prove the following theorem: given any setS ofn points in the plane, there are pointsx andy inS, such that every circle that containsx andy contains at least [5/84(n – 2)] other points ofS.     

Progress in stacked piezocomposite ultrasonic transducers for low frequency applications

A stacked ultrasonic transducer comprises multiple individual layers connected mechanically in series and electrically in parallel to reduce the fundamental thickness mode resonance to a frequency corresponding to the transit time of the complete stack and the electrical impedance to a value which corresponds to that of the layers of the stack in parallel. In turn, this allows lower frequency resonant operation than would be possible with a single layer, and facilitates electrical impedance matching to typical transmission circuitry. On transmission, an ideal stack of uniform layers will have an output amplitude larger than that of the equivalent single layer by a factor equal to the . However, using conventional signal amplification circuitry on reception, the output voltage amplitude will be smaller than that of the equivalent single layer by a similar factor. In the past, stacks have commonly been assembled from layers of conventional piezoceramic material but more recently there have been reports of stacks of 1–3 piezocomposites and it is this type that is considered here. The work described in this paper is motivated by the need to operate at frequencies lower than are possible using conventional piezocomposite fabrication technology. Progress in comparison of experimental and simulated results is outlined and the highlights of a theoretical design study are presented. These show that although the general behaviour of a stacked structure is easily predicted, a rigorous theoretical analysis is essential to understand the detail of even a limited range of possible designs.     

A general local-mode theory for high energy polyatomic overtone spectra and application to dichloromethane

A new model is developed to describe the overtone spectra of polyatomic molecules containing XH_n moieties. The infrared absorption is described as corresponding to excitation of localized modes of vibration rather than a set of symmetry allowed combinations of anharmonic normal modes. The possibility of assigning new bands in the more complex regions of the overtone spectra which involve combinations of both stretching and bending modes is examined and illustrated using the overtone spectrum of ammonia. The overtone spectrum of dichloromethane is recorded in the range λ = 9260 Å to λ = 5300 Å, and the CH overtone bands at 8850 Å, 7223 Å, and 6165 Å corresponding to the Δv_CH = 4, 5, and 6 overtones are identified. Specific features of these bands are discussed in detail in relation to the model. The common features and simplicity of the Δv_CH = 4 overtone bands of a series of halomethanes and ethanes are also interpreted in terms of the model.     

Large Deviations for Quicksort

LetQ_nbe the random number of comparisons made by quicksort in sortingndistinct keys when we assume that alln! possible orderings are equally likely. Known results concerning moments forQ_ndo not show how rare it is forQ_nto make large deviations from its mean. Here we give a good approximation to the probability of such a large deviation and find that this probability is quite small. As well as the basic quicksort, we consider the variant in which the partitioning key is chosen as the median of (2t+1) keys.     

A systems feedback representation of piezoelectric transducer operational impedance

An analysis of thickness-mode piezoelectric transducer impedance under a variety of mechanical load conditions is presented. A wideband, systems model is used to describe this impedance, which is representative of the electrical input impedance in the transmitting mode and the electrical output impedance for the receiving mode.For a fixed input voltage, the total current flowing through the transducer is considered as the vector sum of two current quantities. Firstly, an input current arising directly from the applied voltage source and secondly, a feedback current, which is generated by secondary piezoelectric action. By treating the problem in this manner, an extremely valuable insight into the nature of the electrical characteristics is provided. Complex variations in the impedance behaviour are readily explained and the physical processes that contribute to such deviations are clearly isolated.