Patterns at the onset of electroconvection in freely suspended smectic films

We report the results of experiments on electrically driven convection that occurs in a thin, freely suspended film of smectic A liquid crystal when an electric field is applied in the plane of the film. Convection in a vortex pattern is found above a well-defined critical voltage. The film behaves as a two-dimensional isotropic liquid: neither its thickness nor the director field are modified by the flow. We present measurements of the critical voltage at the onset of convection in two experimental configurations—one which allows the injection of charges into the film from the electrodes, and one which does not. When injection is present, the critical voltage for the onset of flow increases monotonically with increasing frequency of applied field. With no injection, there is no instability at DC and the critical voltage diverges there. The nature of the flow pattern observed at onset changes with frequency. Below a certain frequency the film flows in vortices that extend over the width of the film; above this frequency the flow is confined to two lines of smaller vortices localized along the electrodes. We present a simple discussion of the mechanisms which drive the convection.     

Mesoscale strain measurement in deformed crystals: A comparison of X-ray microdiffraction with electron backscatter diffraction

Mapping of residual stresses at the mesoscale is increasingly practical thanks to technological developments in electron backscatter diffraction (EBSD) and X-ray microdiffraction using high brilliance synchrotron sources. An analysis is presented of a Cu single crystal deformed in compression to about 10% macroscopic strain. Local orientation measurements were made on sectioned and polished specimens using EBSD and X-ray microdiffraction. In broad strokes, the results are similar to each other with orientations being observed that are on the order of 5° misoriented from that of the original crystallite. At the fine scale it is apparent that the X-ray technique can distinguish features in the structure that are much finer in detail than those observed using EBSD even though the spatial resolution of EBSD is superior to that of X-ray diffraction by approximately two orders of magnitude. The results are explained by the sensitivity of the EBSD technique to the specimen surface condition. Dislocation dynamics simulations show that there is a relaxation of the dislocation structure near the free surface of the specimen that extends approximately 650 Å into the specimen. The high spatial resolution of the EBSD technique is detrimental in this respect as the information volume extends only 200 Å or so into the specimen. The X-rays probe a volume on the order of 2 µm in diameter, thus measuring the structure that is relatively unaffected by the near-surface relaxation.     

Use of Crustacean Shells for Uptake and Removal of Metal Ions in Solution

Abstract

The use of crustacean shells, in particular crab shells, for the removal of metal ions in solution is described. Research studies found in the literature on the ability of the shells, effect of particle size, pH, competitive studies in mixtures of metals, application to real samples such as acid mine drainage, and use of the shells in a column are presented. The major component of the shells that allows uptake to occur is chitin. Several mechanisms are proposed for uptake. There are conflicting accounts in the literature on such areas as the effect of pH, flow rate, and particle size.     

Optimal objective function approximation for separable convex quadratic programming

We present an optimal piecewise-linear approximation method for the objective function of separable convex quadratic programs. The method provides guidelines on how many grid points to use and how to position them for a piecewise-linear approximation if the error induced by the approximation is to be bounded a priori.Corresponding author.     

Evidence of high-frequency acoustic emissions from the white-beaked dolphin (Lagenorhynchus albirostris)

Recordings of the signals from a school of white-beaked dolphins show that the frequency of their acoustic emissions extends to at least 305 kHz. These signals were detected by a sector scanning sonar used as a passive listening device of high bearing and time resolution. The records contain three types of signal, one of high intensity, one of a variable high repetition rate, and another showing a time-varying effect. Acoustic signals radiated by dolphins have been recorded and studied over a long period of time by many investigators. The purpose of this letter is to report evidence that acoustic emissions from white-beaked dolphins have significant energy at frequencies around 305 kHz, about one octave higher than previously observed. The observations discussed here were made aboard the fisheries research vessel CLIONE in the Wellbank flat area of the southern North Sea on 13 June 1970 between 1040 and 1110 h. When the dolphin signals were observed, the transmitter of the sector-scanning sonar in use was turned off, and the system was utilized as a passive listening device of high bearing and time resolution.     

Possible new phase transitions in hexagonal RbxWO3

Two correlated phase transitions have been observed in hexagonal Rb_xWO₃ in the concentration range 0.16≤x≤0.33. One of these is a concentration-dependent transition which occurs near x=0.25, and precipitously affects the superconducting transition temperature. The other is a temperature-dependent transition which appears as anomalies in the resistivity, Hall coefficient, and Seebeck coefficient between 100K and 280K. The temperature at which the anomalies occur depends strongly on the x-value.     

Galerkin methods applied to some model equations for non-linear dispersive waves

The application of a dissipative Galerkin scheme to the numerical solution of the Korteweg de Vries (KdV) and Regularised Long Wave (RLW) equations, is investigated. The accuracy and stability of the proposed schemes is derived using a localised Fourier analysis. With cubic splines as basis functions, the errors in the numerical solutions of the KdV equation for different mesh-sizes and different amounts of dissipation is determined. It is shown that the Galerkin scheme for the RLW equation gives rise to much smaller errors (for a given mesh-size), and allows larger steps to be taken for the integrations in time (for a specified error tolerance). Also, the interaction of two solitons is compared for the KdV and RLW equations, and several differences in their behaviour are found.     

A radical diophantine equation

All solutions in positive integers x, yz of the diophantine equation $\text{x}{}^{\mathrm{<mtext>1</mtext><mtext>m</mtext>}}\text{+ y}{}^{\mathrm{<mtext>1</mtext><mtext>n</mtext>}}\text{= z}{}^{\mathrm{<mtext>1</mtext><mtext>r</mtext>}}$ are determined, where m, n, r are given positive integers. The proof makes use of a simple criterion for the irreducibility of the polynomial xⁿ ? a over the rationals, where a is a positive rational.     

Finite-size scaling study of a first-order temperature-driven symmetry-breaking structural phase transition

We present a study of finite-size effects in a model exhibiting a first-order temperature-driven symmetry-breaking structural phase transition in theL × cylindrical geometry in theL limit. Exact studies demonstrate the applicability of our scaling ansatz even in the one-dimensional limit, making this model ideal for studying finite-size effects. The scaling ansatz, similar to the previously developed ansatz for field-driven transitions, demonstrates that latent heat is crucial in driving these transitions. This ansatz is supported by a 2×2 phenomenological transfer matrix based upon the symmetries of the system; this produces an analytic free energy which has the scaling form. Order parameter probability distributions show that the high- and low-temperature phases coexist only in a small finite-size-affected regime near the bulk transition temperature; this regime vanishes exponentially fast asL diverges.