Theory of moving striations in plasma of D-C discharge I. Basic equation and its general solution

As a base for the theory of moving striations a partial integro-differential equation (26) is derived from the equations of continuity (1), (2), the Laplace-Poisson equation (3) and relation (4) between the electric field and the temperature of the electrons. Apart from the processes necessary for the actual formation of striations according to [1] and for the amplification of the wave of stratification according to [2], the equation also includes the processes defining the Debye length of the electrons, the influence of the axial electric field and of its local deflections on the motion of current carriers and the direct influence of the deviations in concentration of the electrons on the rate of production of current carriers. In deriving the equation the main attention is paid to the physical sense of the mathematical operations applied. The general solution is found by the method of the two-sided Laplace transformation and is described by triple integral convolution (42).

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I.

(1), (2), - (3) (4) (26). , , [1], , [2], , , . . (42).

     

Das Verteilungsgesetz der Ferromagnetischen Bereiche vom Standpunkt des Aktivierungsfeldes aus Betrachtet

Zusammenfassung Unter der Voraussetzung, daß das Ahtivierungsfeld für die reversible Bewegung der Blochschen Wände dem Maxwellschen Verteilungsgesetz unterliegt, wird die Entstehung des Maximums der inneren Reibung im Wechselfeld theoretisch erläutert. Weiter wird die Lösung der Differenzialgleichung für die Bewegung einer Blochschen Wand bei gleichzeitiger Wirkung des Wechselfeldes und der Torsionsbeanspruchung gegeben. Die Messung bei einigen Torsionsfrequenzen ermöglicht die Bestimmung gewisser mikroskopischer Konstanten.

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Спектралъный метод о пределения изотонно го состава свинца. Частъ I

, . , . - . PbI4058 Å . , . 1000000. , , . - , .     

Mikrophy'sikalische Vorgänge,die die Entstehung der Schnellen Schichtungswellen in der Neonglimmentladung bedingen

Zusammenfassung Im nachstehenden Artikel werden mikrophysikalische Vorgänge behandelt, die das Auftreten schneller Schichtungswellen in Neonglimmentladungen veranlassen können. Es werden sowohl die qualitativen Abhängigkeiten, als auch die ziffernmäigen Werte der Parameter der Schichtungswellen mit den charakteristischen Gröenwerten der in diesem Entladungstypus vor sich gehenden Vorgänge verglichen. Auf Grund der vorgenommenen Vergleiche kann gesagt werden, da die Relaxationszeiten der schnellen Wellen durch die Diffusionslebensdauer der atomaren, bzw. molekularen Ionen gegeben sind.

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, . , . , , .

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Zum Schlu danken wir F. Kroupa und V. Krejí für die aufmerksame Lesung der Arbeit und wertvolle Hinweise.     

Der Einfluss von Fremdstoffgehalt auf einige Kenngrössen der Verfestigungskurven von Zinkeinkristallen

Zusammenfassung Es wurde der Einfluß von Fremdstoffgehalt: auf die kritische Schubspannung ₀, den Verfestigungskoeffizient _A im BereichA der Verfestigungskurve; die Längea _A des BereichsA, und die Schubspannung _A am Ende des BereichsA, von Zinkeinkristallen untersucht. Es konnte gezeigt werden, daß der Einfluß von Fremdstoffgehalt auf den Wert der kritischen Schubspannung vorwiegend indirekter Natur ist. Die Abnahme des Verfestigungskoeffizienten mit zunehmendem Fremdstoffgehalt kann an Hand erhöhter Leerstellenkonzentration erklärt werden. Das Auftreten des BereichsB wird im Zusammenhang mit der Entstehung von Frankschen Halbversetzungen erwogen.

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₀, _A , _A . , . . .

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Herrn P. Sirotek bin ich für den Umbau und die Instandsetzung des Polanyiaparates zu Dank verpflichtet. Mein Dank gehört ferner Herrn J. Voráek, für die präzise Durchführung der polarographischen Analysen, Frau I. Ejemová und M. Postránecká, für die Verrichtung der Orientierungsbestimmungen und Rechenarbeiten. Gleichzeitig möchte ich Frl. Svobodová meinen herzlichen Dank aussprechen — sie hat, auf Anregung des Lehrstuhls für mathematische Statistik an der mathematisch-physikalischen Fakultät der Karlsuniversität in Prag, mit großem Verständnis die statistische Auswertung der Meßergebnisse durchgeführt. Herrn Dr. F. Kroupa und Ing. B. esták bin ich für das Durchlesen des Manuskripts sowie wertvolle Hinweise zu Dank verpflichtet. Mein besonderer Dank für zahlreiche fruchtbare Diskussionen und Anregungen gilt Herrn P. Kratochvíl. Herrn Prof. Dr. A. Seeger danke ich ganz besonders für Kritik des Manuskripts und wertvolle Ratschläge.     

ВОЗМОЖНОСТЬ ИССЛЕДО ВАНИЯ ХОДА ИСКАЖЕНИЙ РЕШЕТКИ В КРИСТАЛЛИКАХ ПРИ ПО МОЩИ РЕНТГЕНОВСКИХ Л УЧЕЙ РАЗНОЙ ДЛИНЫ ВОЛНЫ

, . , (K , , ), - , -. -, 25 a 1956.     

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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Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

On the validity of an einstein relation in models of interface dynamics

We consider models of interface dynamics derived from Ising systems with Kac interactions and we prove the validity of the Einstein relation=, where is the proportionality coefficient in the motion by curvature, is the interface mobility, and is the surface tension.     

Domain configurations of the uniaxial infinite cylinder

Models for the possible domain configurations of a uniaxial infinite cylinder are put forward and their theory is developed. For materials having an easy plane and no hexagonal anisotropy either closed flux or helical magnetization configurations are proposed. For non-vanishing hexagonal anisotropy these models are somewhat modified to the partially closed flux configuration and the disc domain structure.

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Part of this paper was presented at the International Conference of Magnetism and Crystallography, Kyoto, Japan 1961.

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In conclusion I should like to thank Z. Frait and Z. roubek for valuable remarks.     

К ТЕОРИИ ГРАВИТАЦИОННОГО ИЗЛУЧЕНИЯ

. , , , . , . . . . , , . ; , .

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On the theory of gravitational radiation

The equations of motion of weakly radiating particles are investigated in a linear approximation in which the pseudo-Euclidian metric remains valid but energy changes caused by gravitational radiation are considered. The classical relativistic equations of motion with variable rest mass are applied. An elementary theory of the gravitational radiation of a rotator is formulated. The results are applied for particles in circular accelerators. It is found that a rotator with non-zero rest mass cannot exist for an unlimited period and that it cannot exceed the velocity of light. This explains why particles with non-zero rest mass cannot attain the velocity of light in circular accelerators; it is also shown that the gravitational radiation of particles in circular accelerators does not exist in practice.

     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Wavelength distribution of X-rays in the focus of a monochromator and an estimate of the influence of this distribution on precision measurements of lattice constants

Wavelength distribution in the focus of a Johansson type monochromator is computed assuming the tube focus emissivityG(), reflection curveR() and wavelength distribution of the incident radiationJ(-₀) are known. It is shown e.g. that the centre of gravity may be shifted in accordance with the position of the crystal on the focal circle which may considerably influence precision measurements of lattice parameters.

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, G(,) R() J(-₀) . , , , .

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The author is grateful to Z. Hemanová for carrying out all the computations very carefully.     

Diffusion parameters of thermal neutrons in diphenyl

The diffusion length, diffusion coefficient and mean life time of thermal neutrons in rigid, Czechoslovak made, diphenyl were measured by the impulse method at the temperature 20°C. The experimental results are discussed.

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, ( ) 20°C. .

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We thank J. Jadavan and the accelerator group for their co-operation.     

К В. Ч. НАГРЕВУ РАЗРЕЖЕННОЙ ПЛАЗМЫ

[2]. . , . , . . . .     

On the Effect of Increasing the Radiative-Transition Rate Near a Nanosize Point

A short review of theoretical and experimental studies concerning the photoexcited florescence and Raman scattering of light for a substance in a space containing small material bodies is presented. Calculations of the radiativetransition probability for atoms (molecules) in the vicinity of bodies with a size much smaller than the light wavelength are performed. The probabilities of the singlephoton and doublephoton transitions are shown to increase by factors of 9 and 81 in the vicinity of a nanosize sphere with dielectric constant ||\ 1. The probability of a radiative transition in the vicinity of the vertex of a conic needle bearing up against a plane (both with || 1) increases by factors of (/R _in)² and (/R _in)⁴ for singlephoton and doublephoton transitions, respectively (R _in is the curvature radius for the needle vertex). This theoretical result is suggested as an explanation of the effect of increasing the radiation process intensity in the experiments carried out in the studies cited below.     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

On the determination of the position of the energy level of surface recombination centres

A detailed analysis of the dependence of the surface recombination velocitys on the surface potential _s leads to the conclusion that the position of the surface recombination level with respect to the centre of the energy gapE _t -E _i does not coincide with the valueq _s *, while the surface recombination velocitys decreases to half its maximum value. The difference between the two quantities is negligible only when the width of the curves( _s ) between the points corresponding to the valuess=1/2s _max is greater than 8kT.

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s _s , E _t -E _{i s} , s . , s( _s ) , s=1/2s _max, 8kT.

     

КРУЧЕНИЕ СТЕРЖНЕЙ С С ЕЧЕНИЕМ ФОРМЫ ПРЯМОУГОЛЬНИКА С ВЫР ЕЗОМ

[1] , 1) . [2].

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Twisting of notched rectangularly-shaped bars

It was pointed out in paper [1] that special cases of this solution are the problems of the torsion of a notched and unnotched rectangularly-shaped bar. Here, some results obtained earlier are generalized and in one concrete case very good agreement is obtained with the results of Sapondjan [2].