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.     

Fluorides of ruthenium and chromium: Theoretical studies

The electronic and structural characteristics of CrF₅, CrF₄, RuF₅ and RuF₄ were studied. Ab initio (SCF-CI) calculations were performed with different structures and spin states for each complex. The favored conformation always corresponds to the highest multiplicity: doublet for CrF₅ in D_3h, triplet for CrF₄ in T_d, quadruplet for RuF₅ in C_4v and quintuplet for RuF₄ in D_4h symmetry.     

Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

Characterization of supercommuting matrices

For a given n-by-n matrix A, we consider the set of matrices which commute with A and all of whose principal submatrices commute with the corresponding principal submatrices of A. The properties of this set are examined, with particular attention to its dimension.     

Contextual quantum process theory

A logically complete interpretation of quantum mechanics is given in terms of a theory of quantum processes.Research performed during stays at Utrecht State University, at the Institute for the History and Foundations of Science and at the Department of Philosophy.     

Two-dimensional Numerical Simulation of the Beam-Plasma-Discharge

A two-dimensional self consistent model of the Beam-Plasma-Discharge (BPD) has been developed to calculate the discharge ignition of a bandlike electron beam in a discharge chamber. The discharge was considered in Argon with an initial concentration of 10¹⁴ cm^?3. The model allows calculation of the time evolution of perpendicular profiles of electron density, temperature and the potential.     

The combined effects of evaporation and quench steps on asymmetric membrane formation by phase inversion

An analysis of the effects of combined evaporation and quench periods on the formation of asymmetric membranes by the phase inversion technique is presented. The model for the evaporation period assumes binary diffusion and includes composition dependence in the mutual diffusion coefficient and free convection mass transfer in the gas phase. The quench period model includes the use of 4 composition-dependent diffusion coefficients and incorporates a modified from of the interface jump mass balance which enables efficient numerical analysis of composition gradients in the film at the beginning of the quench period. Results for the effects of evaporation-period variable, including: evaporation time, initial cast film thickness, casting surface dimension, and vapor-phase composition, clearly indicate that significant effects of the evaporation period on membrane structure formation and its reproducibility occur within 20 seconds.     

Investigations of potassium-cerium phosphates rich in P2O5

In the ternary system Ce₂O₃-K₂O-P₂O₅, the partial system Ce(PO₃)₃-KPO₃-P₂O₅ was examined by means of differential thermal analysis and powder X-ray diffraction. The phase compositions of the products obtained on various thermal treatments were investigated. The phase diagram of the system Ce(PO₃)₃-KPO₃-P₂O₅ is suggested.

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Zusammenfassung Mittels DTA und Röntgendiffraktion wurde im ternären System Ce₂O₃-K₂O-P₂O₅ das Teilsystem Ce(PO₃)₃-KPO₃-P₂O₅ untersucht. Die Phasenzusammensetzungen der durch verschiedene Erhitzungsvorgänge erhaltenen Produkte wurden untersucht und ein Phasendiagramm für das System Ce(PO₃)₃-KPO₃-P₂O₅ erstellt.

     

Short-range order in miscible polymer blends: A monte carlo study

Local ordering in miscible binary polymer blends with strong attractive interactions between the two types of chains was investigated by computer simulation of allowable conformations on an incompressible cubic lattice. A tendency toward maximum ordering (in which chains pack in alternate parallel rows) is shown by the calculation of pair correlations and in “snapshots” of the mixtures. A specific directional interaction is not necessarily required for ordering. A comparison of these results with those recently obtained using mean-field theory is presented. The heat capacity of mixing was also calculated and found to be positive, with a value close to that reported experimentally.