Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform Grids

A numerical method based on cubic splines with nonuniform grid is given for singularly-perturbed nonlinear two-point boundary-value problems. The original nonlinear equation is linearized using quasilinearization. Difference schemes are derived for the linear case using a variable-mesh cubic spline and are used to solve each linear equation obtained via quasilinearization. Second-order uniform convergence is achieved. Numerical examples are given in support of the theoretical results.     

Quasi-hexagonal self-organization of nanoparticles upon the laser-controlled deposition of Ga atoms

A cooperative defect-deformation (DD) mechanism is developed for the nucleation of the quasi-monodisperse ensemble of nanoparticles in the low-temperature deposition of Ga atoms in the presence of laser radiation. A comparison with experiment is carried out, and a good agreement between the theoretical and experimental results has been obtained. In particular, in accordance with the DD model, it has been found that the arrangement of nanoparticles is characterized by a latent hexagonal order, and their shape is quasi-hexagonal. It has been shown that the characteristics of the deposited ensemble of nanoparticles can be controlled with the use of an anisotropic deformation.     

Technical Stability of Nonlinear Spatial Dynamic States of Continuous Systems in the Case of Their Interaction with a Flow of a Liquid

Nonlinear Oscillations -     

On the entropy of fusion

The asymptotic value of the melting entropy, i.e. ΔS_f = R ln 2 for vanishing relative change of volume on melting, can be derived from the vibrational entropy due to vibrating dislocations, which are introduced into a material on melting.     

Improved method for measurement of rhodanese activity using methanethiosulfonate as sulfur donor substrate and its application to human serum.

We have developed a sensitive method for the measurement of rhodanese activity in human serum which is based on the colorimetric method for the determination of thiocyanate produced from methanethiosulfonate and cyanide as substrates. Thiocyanate gives a red complex with ferric ion in an acidic condition. The present method is about 70-fold more sensitive than the conventional method using cyanide and thiosulfate as substrates and correlates well (r = 0.997) with the conventional method in bovine liver rhodanese. Within-run precision of the method is 0.91% for 420 units/l serum and the calibration curve is linear up to 1850 units/l. The normal value for human serum, determined by the present method on 31 healthy persons, was 20.9 +/- 20.0 units/l (mean +/- 2S.D.). Rhodanese activity was clearly elevated in some serum samples which were observed at abnormal values in some biochemical diagnostic tests and showed significant positive correlations with guanase activity (r = 0.728, p less than 0.01) and glutamic-oxalacetic transaminase activity (r = 0.625, p less than 0.01).     

A microeconomic simulation model of reproduction

Translated from Programmnoe Oborudovanie i Voprosy Prinyatiya Reshenii, pp. 152–184, 1989.     

Integration of the nonlinear Schroedinger equation with a self-consistent source

It is shown that the nonlinear Schroedinger equation with a self-consistent source admits investigation by the inverse scattering method for the Dirac operator. The conditions are found under which the solutions of the nonlinear Schroedinger equation with a self-consistent source describe the creation and annihilation of solitons.     

Modeling synchronization and suppression of spontaneous otoacoustic emissions using Van der Pol oscillators: effects of aspirin administration

Many of the aspects of the interaction of spontaneous otoacoustic emissions with external tones (suppression and synchronization) can be qualitatively simulated by the behavior of a single driven Van der Pol oscillator. Analytical and numerical investigations of a model of spontaneous otoacoustic emissions based on such an oscillator (with appropriate parametric changes in the nonlinear and negative damping components) lead to predictions of the nature of the changes in suppression and synchronization (frequency-locking) tuning curves when the levels of spontaneous otoacoustic emissions are modified. Observations of the suppression and synchronization of spontaneous otoacoustic emissions by external tones of different frequencies and levels were obtained while the levels of spontaneous emissions were altered by aspirin administration. Modeling an emission as a single Van der Pol oscillator qualitatively accounts for: (1) the reduction of the level of an external tone required to suppress the emission by a decibel amount equivalent to the level reduction induced by aspirin administration; (2) the broadening of the frequency-locking tuning curve of an emission whose level is reduced; and (3) the pulling of the emission frequency by an external tone. It does not account for: (1) the observed asymmetry in the slopes of the external-tone suppression curves (more gradual for frequencies of the suppressor tone higher, rather than lower, than that of the emission); and (2) the frequency pushing of the emission by an external tone.