The ɛ-expansion for the Hierarchical Model

In this paper, the Hierarchical Model is studied near a non-trivial fixed point of its renormalization group. Our analysis is an extension of work of Bleher and Sinai. We prove the validity of the -expansion for . We then show that the renormalization transformations around have an unstable manifold which is completely characterized by the tangent map and can be brought to normal form. We then establish relations between this result and the critical behaviour of the model in the thermodynamic limit.     

The simplified Fermi accelerator in classical and quantum mechanics

We review the simplified classical Fermi acceleration mechanism and construct a quantum counterpart by imposing time-dependent boundary conditions on solutions of the free Schrödinger equation at the unit interval. We find similiar dynamical features in the sense that limiting KAM curves, respectively purely singular quasienergy spectrum, exist(s) for sufficiently smooth wall oscillations (typically ofC ² type). In addition, we investigate quantum analogs to local approximations of the Fermi map both in its quasiperiodic and irregular phase space regions. In particular, we find pure point q.e. spectrum in the former case and conjecture that random boundary conditions are necessary to model a quantum analog to the chaotic regime of the classical accelerator.     

Generalized voter models

We examine a one-dimensional class of interacting particle systems which generalize some voter models. This class includes a particular case in the class of models of catalytic surfaces introduced by Swindle and Grannan. We show that this class has the clustering property of ordinary finite-range voter models, at least when one is concerned with translation-invariant measures on the state space.Research supported by P.M.S. 9157461.     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field

We study the resonant magnetopolaron effects in parabolic quantum wells in a tilted magnetic field. The renormalization of the first excited level, which is resonant with the ground state level plus one longitudinal-optical phonon is calculated at the resonance using an improved resonance approximation to be E= where is the polaron coupling constant. The exponent and the factor are calculated in dependence on the tilt angle of the magnetic field and the confinement energy.     

The motion of 90° wedge domains in BaTiO3 in an alternating electric field

The paper deals with the motion of 90° wedge domains in BaTiO₃ in an alternating field of 50 c/s. The critical field, the positional hysteresis loops with double asymmetry, the production of wedges with polarization perpendicular to the field and 180° substructure in the wedges were studied. The differences between the behaviour of the wedges and the individual 90° walls are pointed out which are caused by differences in the energy balance of these formations and by different interactions with 180° processes. The upper limit of contribution of the wedge motion to the initial permittivity is estimated. The results are discussed from the phenomenological point of view.

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90° BaTiO₃

90° BaTiO₃ , 50 Hz. , , , , , , 180° . 90° , 180° . , . .

     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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. .

     

The influence of oscillations on ionization in a discharge path

The paper solves the problem of gas ionization in a discharge path in a very dilute gas, where the free path of the electrons is much larger than the dimensions of the path and the transit time of the electrons between the electrodes is of the order of the period of the applied h-f voltage. It was found that for a certain ratio of the transit time of the electrons between the electrodes in the discharge path to the period of the h-f oscillation, resonance occurs when the wattless current component is zero. The electron density rises in the path and thus also the gas ionization.

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In conclusion, the author would like to thank F. Benda for preparing the equipment, M. Kivánek for preparing the equipment and some of the measurements, and A. Hrdá for the measurements and for working out the case with equally large a-c and d-c voltages within the framework of her thesis.     

О СУЩЕСТВОВАНИИ ОТРИ ЦАТЕЛЬНОГО ЯВЛЕНИЯ БАРКГАУЗЕНА

. . , . , . , . coo , 13. 5. 1954 . - .     

On the yellow colouring of lithium fluoride crystals

The paper deals with the causes of the yellow colouring of LiF crystals. In accordance with some other writers the authors arrived at the conclusion that colouring is caused by impurities. Selective absorption in the infra-red region at 2·8 is independent of this colouring. Analytical data were supplemented by crystal growing experiments in which defined admixtures of heavy metals, such as Co, Mn, Fe, Cr, Ni, Pt, Cu, were added to the melt. It is shown that, of the admixtures used, the most intense colouring is produced by manganese. Experiments on the effect of Cu and Pt were not entirely conclusive. In vacuum colour-producing impurities evaporate quite easily from the melt until their concentration drops below the critical limit required for colouring; in air this happens only if the charge is left in the melted state for a longer period (in our case a 1 kg charge was kept at 100°C above melting point for 36 hours). Results are improved if a dried gas, for instance nitrogen, is bubbled through the meit. A colourless crystal can be obtained in this manner even without using a vacuum; the starting material, however, must be sufficiently pure. A new method was worked out for preparing the salt by direct precipitation of LiCl and HF. Heavy metals are removed from the lithium component by means of cupral and dithizone. The construction of the apparatus used for the crystal growing experients in vacuum differs from that described in the appropriate literature.

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LiF

LiF. , . 2,8 . . , , , Mn, Fe, Cr, Ni, Pt, Cu. , . , . Pt . , , , ( : 1 kg-36 100° ). , , , . , , . LiCl HF. . , .

     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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Деформация усика С ли нейной дислокацией

, , . : .

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The deformation of a whisker with edge dislocation

An approximate solution is given of the deformation of a plate caused by an edge dislocation lying in the central plane. The results are used to discuss the bending of a whisker as a result of an edge dislocation; in the calculations the whisker is approximated as an infinite band.

     

Основные соотношени я длн построения механических селект оров нейтронов

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The temperature dependence of the refractive index of germanium

The temperature dependence of the refractive index of germanium in a wave-length region of 1·8–5·5 and temperature region of 100–530 °K is given for three samples of single crystal germanium having different concentrations of impurities. The temperature dependence of the refractive index is non-linear. Our results are compared with those of other authors. An attempt is also made to theoretically interpret the observed dependence.

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1,8–5,5 100–530° K . . . , .

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In conclusion the author thanks Dr. Trousil from the Institute of Technical Physics, Czechoslovak Academy of Sciences, Prague, for supplying the germanium, Mr. Tma for preparing and polishing the prisms, Dr. Tauc from the same institute for enabling most of the measurements to be carried out in his laboratory, and Mrs. ilhavá for help in the measurements.     

Сцинтилляционный сп ектрометр с сложение м импулъсов от двух кри сталлов

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The propagation of excitation energy in perturbed crystals

The process of the propagation of excitation energy in perturbed dielectric crystals with a weak bond between the atoms having zero permanent dipole moment is studied. It is shown that on certain assumptions this process of propagation can be regarded as the motion of a Frenkel exciton in the electrostatic field of the defect. Frenkel's exciton can be characterized in this case as a neutral polarizable particle having induced dipole moment equal to the change in the induced dipole moment of the crystal during the excitation of one of its atoms.

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, . , . .

     

Elastic stress around linear dislocation in anisotropic medium

Relations are derived for the elastic stress field around a linear dislocation in an infinite medium with general anisotropy. The strongly deformed material around the core of the dislocation is cut out in the shape of an elliptic cylinder. The conditions of a free surface are used on the boundary thus formed. The calculation of the field around a crack in a crystal, the model of which was proposed by Fujita in [9], is given as an example.

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. , , , . , [9] .

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The author thanks Dr. F. Kroupa for valuable discussions and all-round help in solving the problem and Z. Hemanová for performing the numerical calculations.     

Nonstationary Markov chains and convergence of the annealing algorithm

We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t ₀) ast+, with a computable constantC andt ₀ the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t^–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly.     

ЭЛЕКТРОПРОВОД НОСТЬ И ТЕРМОЗЛЕКТРОДВИЖУ ЩАЯ СИЛА СЕРОГО ОЛОВА

, , , . .     

ВЛИЯНИЕ СТАРЕНИЯ НА Э ЛЕКТРИЧЕСКИЕ СВОЙСТ ВА ПОЛУПРОВОДНИКОВОЙ С ИСТЕМЫ Bi2Te3-Bi2Se3

, Bi₂Te₃-Bi₂Se₃. , , , . .

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Influence of ageing on change in electrical properties of semiconducting systems of Bi₂Te₃-Bi₂Se₃

The paper describes the effect of ageing observed on a semiconducting system Bi₂Te₃ — Bi₂Se₃. It is shown that the change in electrical conductivity and thermoelectric force, which takes place during ageing, is caused by the change in concentration of the free electrons. The influence of this process on the efficiency of equipment employing the Peltier effect is analyzed.