Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Structural instability during rolling of tungsten in terms of nonlinear thermodynamics

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–55, March, 1991.     

Analysis of atmospheric particular matter and water using atomic emission spectrometry with inductively-coupled plasma and two-jet plasmatron

Summary A method for the atomic emission spectrometric analysis of air and water with inductively coupled and two-jet direct current plasmas has been developed. The method has been applied to the determination of impurity contents with good accuracy and sensitivity.     

On an abstract integro-differential equation with periodic coefficient. II

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 54, pp. 57–68, 1990.     

Topological and ergodic properties of closed 1-forms with incommensurable periods

V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 2, pp. 1–12, April–June, 1991.     

Structural and optical characterization of the propolis films

We have performed structural and optical characterizations of the propolis (an organic entity of biological nature) films grown on various non-organic substrates. The films were grown from a propolis melt or a propolis alcohol solution. The crystal structure has been observed in the films precipitated from the solution onto substrates such as an amorphous glass and sapphire or semiconductor indium monoselenide. For any growth method, the propolis film is a semiconductor with the bandgap of 3.07 eV at 300 K that is confirmed by a maximum in photoluminescence spectra at 2.86 eV. We argue that propolis films might be used in various optoelectronic device applications.     

An experiment with arithmetic precision in linear algebra computations

Several techniques for experimental determination of floating point precision in practical computations are examined, and applied to linear algebra algorithms. These techniques are simple enough to be directly applicable to existing production codes, requiring a very limited amount of software on many machines, and yet they yield interesting information on the numerical precision of a computation. Our choice of linear algebra algorithms includes a direct solver (namely the MA32 program from the Harwell Library) and several variants of preconditioned conjugate gradients (the methods DIAG, INV, MINV and POL of Reference 1). The results may be of interest as method selection criteria, and thus complement Mflop performance data available from several sources.