Symmetry-breaking transitions in equilibrium shapes of coherent precipitates: Effect of elastic anisotropy and inhomogeneity

We examine the symmetry-breaking transitions in equilibrium shapes of coherent precipitates in two-dimensional (2-D) systems under a plane-strain condition with the principal misfit strain components ε* _xx and ε* _yy . For systems with cubic elastic moduli, we first show all the shape transitions associated with different values of t=ε* _yy /ε* _xx . We also characterize each of these transitions, by studying its dependence on elastic anisotropy and inhomogeneity. For systems with dilatational misfit (t=1) and those with pure shear misfit (t=−1), the transition is from an equiaxed shape to an elongated shape, resulting in a break in rotational symmetry. For systems with nondilatational misfit (−1<t<1; t ≠ 0), the transition involves a break in mirror symmetries normal to the x- and y-axes. The transition is continuous in all cases, except when 0<t<1. For systems which allow an invariant line (−1≤t<0), the critical size increases with an increase in the particle stiffness. However, for systems which do not allow an invariant line (0<t≤1), the critical size first decreases, reaches a minimum, and then starts increasing with increasing particle stiffness; moreover, the transition is also forbidden when the particle stiffness is greater than a critical value.     

Investigation of the action of flame retardants in cellulose. I. Investigation of the flame retardant action of 2,2′-oxybis(5,5-dimethyl-1,3,2-dioxaphosphorinane-2,2′-disulfide) in cellulose

Pyrolysis experiments were performed in high vacuum and under reduced air pressure (100 Pa). The volatile products of pure cellulose and cellulose containing various amounts of flame retardant 2,2′-oxybis (5,5-dimethyl-1,3,2-dioxaphosphorinane-2,2′-disulfide), i.e., Sandoflam 5060 of Sandoz AG, were studied by means of gas chromatography in combination with mass spectroscopy. The volatile products were characterized with infrared spectroscopy. The studied revealed that the incorporation of the flame retardant enhanced the water release and shifted the onset of this reaction to lower temperature. On the basis of these findings an explanation for the mechanism of flame retardancy in generated cellulose fibers modified with this particular flame retardant is attempted. From experiments with different residual air pressure the influence of oxygen on the primary processes of the pyrolytic degradation of cellulose is being discussed.     

Bounds on the number of samples needed for neural learning.

The relationship between the number of hidden nodes in a neural network, the complexity of a multiclass discrimination problem, and the number of samples needed for effect learning are discussed. Bounds for the number of samples needed for effect learning are given. It is shown that Omega(min (d,n) M) boundary samples are required for successful classification of M clusters of samples using a two-hidden-layer neural network with d-dimensional inputs and n nodes in the first hidden layer.     

Continuous phase quadrature phase shift keyed signaling techniquewith coding

A continuous phase quadrature phase shift keyed (CPQPSK) modulation technique is presented. This method utilizes a conventional QPSK modulator and a phase trajectory converter to approximate M=4, h=1/4 continuous phase signal and allows low cost, low complexity, and high rate (>1 Gbit/s) CPM modem implementation for bandwidth efficient transmission through nonlinear satellite channels. Using a communications analysis computer program it has been found that CPQPSK has 99 percent out-of-band power of 0.8R (MSK has 99 percent out-of-band power of 1.2 R where R is defined as bit rate), continuous phase trajectories, and nearly constant envelope amplitude. Simulation of realistic hardware designs indicate that the CPQPSK will require an Eb/No of 14 dB to achieve a bit error rate (BER) of 10^-6. Forward error correcting techniques using block codes with an overhead of 10 percent indicate that the Eb/No requirements can be reduced to 11.2 dB for 10^-6 BER     

General formalism for the study of nonlinear pulse propagation in optical fibres

A general formalism for the study of nonlinear pulse propagation in optical fibres is presented. It is then applied to study the time evolution of a Gaussian laser pulse in a fibre with cubic and fifth-order nonlinearity in the index of refraction. The results are presented and discussed.     

Synthesis and characterisation of copolyesters from poly(ethylene terephthalate) and poly(hexamethylene terephthalate)

Copolyesters containing poly(ethylene terephthalate) and poly(hexamethylene terephthalate) (PHT) were prepared by a melt condensation reaction. The copolymers were characterised by infrared spectroscopy and intrinsic viscosity measurements. The density of the copolyesters decreased with increasing percentage of PHT segments in the backbone. Glass transition temperatures (T_g). melting points (T_m) and crystallisation temperatures (T_c) were determined by differential scanning calorimetry. An increase in the percentage of PHT resulted in decrease in T_g, T_m and T_c. The as-prepared copolyesters were crystalline in nature and no exotherm indicative of cold crystallisation was observed. The relative thermal stability of the polymers was evaluated by dynamic thermogravimetry in a nitrogen atmosphere. An increase in percentage of PHT resulted in a decrease in initial decomposition temperature. The rate of crystallisation of the copolymers was studied by small angle light scattering. An increase in percentage of PHT resulted in an increase in the rate of crystallisation.     

Control of free-radical emulsion polymerization of methyl methacrylate by oxygen injection. II. Experimental study

Oxygen injection has been proposed and experimentally demonstrated as an effective control measure for limiting the rate of heat release and altering the rate of polymerization in emulsion processes. A detailed mathematical model has been previously developed to describe the system behavior with and without oxygen injection. A simple lab scale apparatus was constructed and run extensively. Only trace quantities of oxygen are needed to inhibit the reaction completely. The facile response makes this method attractive for fast temperature control. However, because of the rapid penetration of dissolved oxygen into the polymer particles, growing radical chains are terminated prematurely, lowering product molecular weights. To minimize this detrimental effect, pulsed oxygen control is used and extensive experimental work was performed to determine the effects of controller set points on molecular weight. Moderate oxygen flows and moderate set point temperatures are found to give the optimal response without significant lowering of the final molecular weight. Injected quantities agree well with the order-of-magnitude sparging calculations needed to completely stop initiation. However, complete agreement between model simulations and experimental results was not reached due to an unmeasured loss of monomer from the reactor. Chain transfer to monomer is found to be important in modeling the polymer molecular weight. It has, however, a negligible effect on the reaction rate.