Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Electro-optic pulse response of ferroelectric liquid crystals

The electro-optic response of ferroelectric smectic C* liquid crystals has been studied. Anomalous switching behaviour of such materials which possess a negative dielectric anisotropy has been reported. These materials show a minimum in response time at a sufficiently high field. We present results showing the dependency of this minimum upon spontaneous polarisation and the effect of AC bias. Calculations based upon the equation of motion of the director around the cone are presented which describe this effect and its dependence on the relative magnitudes of the spontaneous polarization and dielectric anisotropy of the material. Good agreement with the experimental results is found.     

High Concentration Arsenic Diffusion in Crystalline Silicon: An Asymptotic Analysis

For fairly high concentrations, the effective arsenic diffusioncoefficient is known to grow linearly with the concentration.In this paper, we consider the strongly enhanced diffusion ofarsenic by asymptotic methods, and extend the results of a previouspaper (King & Please, 1987) in three ways: we characterizean additional (low-concentration) region; we consider the influenceof the initial data; and we consider the case of constant surfaceconcentration.     

Chaos-controlling technique for suppressing self-modulation in backward-wave tubes

A method for suppressing self-modulation in backward-wave tubes is proposed. Additional delay is introduced into the feedback circuit, owing to which the output signal amplitude affects the electron beam current that enters into the interaction space. Numerical simulations demonstrate that the operating current in the single-frequency oscillation mode may be increased roughly twofold.     

1,1,3-Trimethyl-3-phenylindan as a Luminescent Additive to a Plastic Scintillator Based on Poly(methyl Methacrylate)

The luminescence and scintillation properties of poly(methyl methacrylate) containing 1,1,3-trimethyl-3-phenylindan were studied.     

Synthesis of New Plant Growth Regulators,Isomeric 1-(Dimethyloctyl)- and 1-Alkylpiperidinium and -morpholinium Halides by Telomerization of Isoprene with Secondary Amines

The known plant growth regulator, Al'den [1-(3,7-dimethyloctyl)-1-allylpiperidinium bromide], and also 1-(3,7-dimethyloctyl)-1-methylpiperidinium iodide were synthesized by treatment with allyl bromide and methyl iodide, respectively, of exhaustively hydrogenated 1-nerylpiperidine which was obtained by anionic telomerization of isoprene with piperidine. Various quaternary ammonium salts having a terpene sub- stituent with unnatural dimethyloctane skeleton, which effectively stimulate florification of Aster Chinensis L., were prepared by the action of alkyl halides on telomerization products derived from isoprene and piperidine or morpholine in the presence of palladium complexes.