Some remarks on the two-body-problem in geometrodynamics

The interest in the two body problem in geometrodynamics and its present status are discussed. Special consideration is given to time-symmetric initial data. An equation relating the “bare mass energy,” the potential energy and the “vibrational energy” at the initial moment is proposed. The significance of coordinate conditions in dynamical equations is discussed next. Conditions implying maximal slicings of spacetime and harmonic coordinates in those slices are considered in detail, as they seem to be well suited for numerical calculations and for interpretation of the results of such calculations.     

A model of solidification under microgravity conditions

The influence of the microgravity environment on solidification processes is discussed. A simple model of the solidification of a binary-alloy is presented with the chemical diffusion influenced by the gravitational field. Using the results of Mullins and Sekerka, we employ the linear theory of hydrodynamic stability to investigate the interfacial instability driving the pattern-forming processes in solidification. As a result, we estimate the characteristic size of the elements of the emerging pattern. We show that, in spite of good agreement of our result with the size of cellulae observed in experiments, the model cannot explain the changes in the patterns occurring in space environment. In conclusion we shortly discuss the possibility of adding realism to our simple model by including the effect of convection.     

Deposition of copper films by unbalanced d.c. magnetron sputtering

The electrical resistivity of as deposited polycrystalline copper thin films as a function of varying the process parameters has been investigated. Trying to minimize the resistivity of the copper thin films is important in the semiconductor industry, due to the fact that low resistivity copper can be employed to great advantage for new metallization schemes in advanced ultralarge scale integrated circuits. This paper presents the optimum choice of parameters that are necessary to achieve low resistivities of the thin films in reproducible experiments. All the depositions were performed using an unbalanced d.c. planar magnetron sputtering source (consisting of a circular copper target (98% purity, 0.01% Fe, 0.005% Ni, 0.005% Si) with a diameter of 100mm fitted with two electromagnets). The copper thin films were deposited onto glass substrates with argon being used as the sputtering gas. The resistivity was studied as a function of the pressure of the sputtering gas, the substrate bias, the substrate to target distance, the magnetron power, and the substrate temperature. It was found that depositions producing thin films with a resistivity of that approaching the bulk material (1.7×10^–8m) were obtained if the sputtering gas pressure was below 0.2 Pa. The effect of the substrate bias was insignificant at these pressures. The crystallographic structure of the copper thin films, determined by X-ray diffraction, is also reported.The authors would like to thank Dr. Soukup for his support during this research. We would also like to express our gratitude to Mr. A. Rajský for improving the design of the sputtering device. This work was partially financed by a grant from the Grant Agency of the Czech Republic No. 202/93/0508.     

Forbidden Gap Argument for Phase Transitions Proved by Means of Chessboard Estimates

Chessboard estimates are one of the standard tools for proving phase coexistence in spin systems of physical interest. In this note we show that the method not only produces a point in the phase diagram where more than one Gibbs states coexist, but that it can also be used to rule out the existence of shift-ergodic states that differ significantly from those proved to exist. For models depending on a parameter (say, the temperature), this shows that the values of the conjugate thermodynamic quantity (the energy) inside the ``transitional gap'' are forbidden in all shift-ergodic Gibbs states. We point out several models where our result provides useful additional information concerning the set of possible thermodynamic equilibria.     

Multi-velocity and multi-temperature model of the mixture of polyatomic gases issuing from kinetic theory

In this paper, we consider Euler-like balance laws for mixture components that involve macroscopic velocities and temperatures for each different species. These laws are not conservation laws due to mutual interaction between species. In particular, source terms that describe the rate of change of momentum and energy of the constituents appear. These source terms are computed with the help of kinetic theory for mixtures of polyatomic gases. Moreover, if we restrict the attention to processes which occur in the neighborhood of the average velocity and temperature of the mixture, the phenomenological coefficients of extended thermodynamics can be determined from the computed source terms.     

On the efficiency of small-angle Čerenkov second harmonic generation in optical waveguides

It is well known that in the non-depleted pump approximation, the efficiency of a second harmonic generation (SHG) of a guided mode in a non-linear optical waveguide increases quadratically with the interaction length (P ₂ L ²), and linearly (P ₂ L) in the erenkov regime. The efficiency of the erenkov SHG in the waveguide with a non-linear substrate and linear guiding layer is known to be strongly peaked at a particular pump wavelength and a particular waveguide thickness, with the erenkov angle approaching zero. The known theory predicts an infinite efficiency value at the peak, however. In this contribution, a simple integral expression for the SHG efficiency in the erenkov regime is derived. For large erenkov angles and interaction lengths it yields the expected P ₂ L dependence, while in the limit of small erenkov angles the dependence is found to have the form of P L ^3/2, possessing also a finite value at the efficiency peak. The condition determining the accurate position of the efficiency peak in the waveguide thickness–pump wavelength plane is given, too.     

Role of dispersed phase in the creep of ferritic steels

The effect of carbide particles of M4C₃ and M₂₃C₆ on the creep properties of low-alloy and modified chromium steels is investigated.Presented at the 4th International Symposium on Plasticity of Metals and Alloys, Srní, Czechoslovakia, September 7–11, 1987.     

Dynamics of intense Langmuir waves in current-carrying plasmas

Basic equations including ponderomotive effects of Langmuir waves in a current-carrying plasma are presented. In such a system, dynamics of an initially monochromatic plasma wave is investigated both analytically and numerically. Various regimes of developed modified decay and modulational instabilities of the wave are modelled by using a macroparticle numerical code. In this way the cooperative nature of both ponderomotive and drift effects supporting plasma heating is demonstrated. The underlying physical processes are discussed and relation to the solar flare theory is suggested.Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.It is pleasure to acknowledge the staff members of the Computational Centre at Ondejov for their kind support in performing the numerical computations.     

On the Validity of Entropy Production Principles for Linear Electrical Circuits

We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’ parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.