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.     

An optical method and neural network for surface roughness measurement

The measurement of surface roughness using stylus equipment has several disadvantages. A non-contact optical method is needed for measuring the surface roughness of engineering metals with improved accuracy. One candidate for an optical method is the use of a laser source, where the laser light intensity reflected from the surface represents the surface roughness of the illuminated area. A relation can be developed between the reflected laser beam intensity and the surface roughness of the metal. The present study examines the measurement of the surface roughness of the stainless steel samples using a He-Ne laser beam. In the measurement a Gaussian curve parameter of a Gaussian function approximating the peak of the reflected intensity is measured with a fast response photodetector. In order to achieve this, an experimental setup is designed and built. In the experimental apparatus, fiber-optic cables are used to collect the reflected beam from the surface. The output of the fiber-optic system is fed to a back-propagation neural network to classify the resulting surface profile and predict the surface roughness value. The results obtained from the present study are then compared with the stylus measurement results. It is found that the resolution of the surface texture improves considerably in the case of optical method and the neural network developed for this purpose can classify the surface texture according to the control charts developed mathematically.     

Production of neutrinos at HERA

For theep collider at HERA, we study processes with neutrinos in the final state. Furthermore, we discuss the production ofW andZ bosons. Because of the very small lifetimes of theW andZ, we consider the production of their leptonic decay products rather than the bosons themselves. All the results are based on exact calculations of the matrix element at the tree level. Total cross sections and various kinematical distributions are presented.     

Fibre stability in anisotropic matrix at small strains

As acknowledged in almost all monographs on the fracture of composite materials, one of the major fracture mechanism in unidirectional fibrous composites under uniaxial compression along the reinforcing elements is the stability loss of the material structure (the structural instability). According to this mechanism, theoretical investigations of the fracture along the fibres are reduced to those of the stability loss in the material structure, and the value of external critical forces is accepted as the value of failure forces. At present, numerous theoretical investigations have been carried out in this field with the use of the three-dimensional linearized theory of stability in the framework of the piecewise-homogeneous body model. However, in all the investigations it is assumed that the matrix and the fibre material are isotropic. It is evident that in many cases it is necessary to take into account the anisotropy of the matrix material when investigating the stability loss of fibres. In view of the above, in the framework of the piecewise-homogeneous body model using the three-dimensional linearized theory of stability, the present paper considers the stability loss of the fibre in the anisotropic (transversally isotropic) matrix. The effect of the properties of the matrix material on the critical values of the external loading is examined.Submitted to the 10th International Conference of Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 603–611. September–October, 1997.     

Mechanisms of ion-beam-enhanced diffusion in amorphous silicon

We have investigated ion-beam-enhanced diffusion of Au in undoped and B doped amorphous Si. The diffusion coefficients depend linearly on ion flux and exibit an Arrhenius-like temperature dependence with an activation energy of 0.37 eV in the temperature range 200–350° C. Moreover the diffusivity is enhanced by a factor of 5 by B-doping at a concentration of 1×10²⁰ atoms/cm³. A similar enhancement is observed in thermal diffusion of Au which has an activation energy of 1.5 eV. On the basis of these results a model for the ion-beam-enhanced diffusion of Au is proposed where the high density of defects present in amorphous Si act as traps for the fast moving interstitial Au atoms. The effectiveness of this trapping process can be changed by the high concentration of mobile defects generated by the beam and also by a change in the charge state of the traps induced by the presence of B.     

Glass-forming liquids,anomalous liquids,and polyamorphism in liquids and biopolymers

Summary Glass formation in nature and materials science is reviewed and the recent recognition of polymorphism within the glassy state, polyamorphism, is discussed. The process by which the glassy state originates during the continuous cooling or viscous slowdown process, is examined and the three canonical characteristics of relaxing liquids are correlated through the fragility. The conversion of strong liquids to fragile liquids by pressure-induced coordination number increases is discussed, and then it is shown that for the same type of system it is possible to have the same conversion accomplished via a first-order transition within the liquid state. The systems in which this can happen are of the same type which exhibit polyamorphism, and the whole phenomenology can be accounted for by a recent simple modification of the van der Waals model for tetrahedrally bonded liquids. The concept of complex amorphous systems which can lose a significant number of degrees of freedom through weak first-order transitions is then used to discuss the relation between native and denatured hydrated proteins, since the latter have much in common with plasticized chain polymer systems. Finally, we close the circle by taking a short-time-scale phenomenon given much attention by protein physicists,viz., the onset of an anomaly in the Debye-Waller factor with increasing temperature, and showing that for a wide variety of liquids, including computer-simulated strong and fragile ionic liquids, this phenomenon is closely correlated with the experimental glass transition temperature. This implies that the latter owes its origin to the onset of strong anharmonicity in certain components of the vibrational density of states (evidently related to the boson peak) which then permits the system to gain access to its configurational degrees of freedom. The more anharmonic these vibrational components, the closer to the Kauzmann temperature will commence the exploration of configuration space and, for a given configurational microstate degeneracy, the more fragile the liquid will be. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.