Characteristics analysis of metal-clad and absorptive dielectric waveguides by a simple and accurate perturbation method

We present a simple and accurate method for characteristic analysis of metal-clad dielectric waveguides and absorptive waveguides. The real partN of the complex modal indexN=N + iN is obtained by solving the corresponding real eigenvalue equation, and the imaginary partN is given by (n/), where= + i is the complex dielectric constant of the absorptive layer, and N/ is obtained by numerical differentiation. The method is straightforward, and the cumbersome solution of complex transcendental equations is completely eliminated. Results for simple structures are in good agreement with those obtained by exact analysis.     

МЕТОД ДЛЯ ВЫЧИСЛЕНИЯ КОЛЕБАНИЙ НАРУШЕННО Й АТОМНОЙ ЦЕПОЧКИ

- . - , .     

Explicit determination of a potential withn bound states by means of the solution of the inverse problem

A potential havingn bound states is obtained for a Jost functionf(k), given as the ratio of two polynomials of the ordern in the impulsek, by solving the Gelfand-Levitan equation. The special case when the parameters have such values that no bound state need be considered, is studied separately. In the cases studied the linear integral Gelfand-Levitan equation is transformed ton linear inhomogeneous algebraic equations forn unknown quantities, by means of which one can determine the potential and the solution of the Schrödinger equation. Forn=1 the results agree with those previously known.

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f(k), n- k, - , . , , . - , . n=1 .

     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

Химическая сенсиБил изация фотографичес кой эмульсии

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Chemical sensiblilisation of photographic emulsion

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, 7. V. 1953 .     

РАДИАЦИОННЫЙ ЗАХВАТ МЕДЛЕННЫХ НЕЙТРОНОВ ЯДРАМИ АТОМОВ

- S³³, Cl³⁶, K⁴⁰, ⁴¹, V⁵², n⁵⁶ Hg²⁰⁰. 100–1200 keV .

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Radiative capture of slow neutrons on atomic nuclei

The energies and absolute intensities of gamma radiation from the radiative capture of thermal neutrons on S³³, Cl³⁶, K⁴⁰, Ca⁴¹, V⁵², Mn⁵⁶ and Hg²⁰⁰ nuclei were measured by means of a one-crystal scintillation spectrometer. The transitions measured in the energy interval 100–1200 keV are mostly transitions between the lowest excited states of the nuclei studied.

     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

On the relation between the thickness dependence of optical absorption and the surface layers of barium titanate single crystals

Single crystals of BaTiO₃, prepared by crystallization in the system BaCl₂-BaO-BaTiO₃-show a dependence of the optical absorption coefficient on the sample thickness. The observed thickness dependence of the absorption coefficient can be explained by the existence of a surface layer with optical properties differing from those of the inner part of the crystal. By means of an etching method a direct determination of the thickness of the surface layer of crystals in the thickness range of 0.075 to 0.178 mm was carried out. The value found is (6.0±0.2)×10^-4 cm.

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iO₃, 1₂-BaO-BaTiO₃ . . 0,075 0,178 mm. (6,0±0,2). 10^-4 cm.

     

The distribution of neutron density in the vicinity of a partly inserted black rod in two-group approximation

The neutron density in the vicinity of a black cylindrical rod partly inserted in a bare reactor is calculated and illustrated by a numerical example. The starting point is a two-group diffusion theory approximation. While the dependence of the effect of the rod on the insertion depth can be calculated simply by means of perturbation theory, the question of the neutron density estimate in the vicinity of the rod is considerably more difficult and in some considerations the estimate of the neutron density caused by the presence of the rod is indispensable. The method makes it possible to determine the reactivity value of the rod in dependence on the insertion depth and especially the neutron density deformation in the vicinity of the rod.

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()

. , . , , . , . [1] . .

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In conclusion the author thanks J. Svato for help in carrying out the numerical calculations.     

Струи паров материал ов электродов нри кратковременном электрическом разря де с Большой силой тока

. . , .

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The vapour jets of electrode material of a short-time high-intensity electric discharge

The velocity of vapours from electrodes and the values of the electric gradient of the channel were measured. An explanation is given of the dependence of the discharge rate of the vapours on the electrode material and the thermal origin of the jets is confirmed. The validity of the results is shown for the case of a different experimental arrangement, or the formation of other types of discharges on electrodes.

     

ВЛИЯНИЕ ПЕРЕХОДНЫХ Э ФФЕКТОВ НА ИЗМЕРЕНИЕ КРИВЫХ НАМАГНИЧЕННОСТИ КОМ МУТАЦИОННЫМ БАЛЛИСТИЧЕСКИМ МЕТО ДОМ

The paper gives an analysis of the conditions in the primary circuit of equipment for measuring the magnetization curves of ferromagnets by the ballistic method. It investigates the influence of transitional current states caused by sudden changes in the circuit parameters (commutation, switching off and on of circuit), on the magnetic state of the ferromagnet. In this connection it points out the disadvantages of using the commutational ballistic method compared with the summation ballistic method for measuring the magnetization curves of ferromagnets with rectangular hysteresis loop and very short magnetization reversal time.

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РАДИАЦИОННЫЕ ПОПРАВКИ К ПОЛЯРИЗАЦИИ ЭЛЕКТРОНА ПРИ БЕТА-РАСПАДЕ СВОБОДНОГО НЕЙТРОНА

/M1 ( — ,M — ) (= 1/137) - . 0,2% –v/c, , .

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Radiative corrections to the electron polarization in the beta decay of a free neutron

An expression for the electromagnetic radiative corrections of the order (=1/137) to the longitudinal polarization degree of the electron in the beta decay of a free neutron is derived in the approximation /M1 ( is the neutron-proton mass difference,M — mass of the neutron). The corrections are not larger than 0·2% and it seems that they cannot explain the deviation of the experimental value for the electron polarization from the value –v/c (measured in the beta decay of nuclei).

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Studium der Stationären und Laufenden Schichtung in der Entladung in Neon Mit Hilfe eines Lokalen Hochfrequenzfeldes

Zusammenfassung Es wurde ein Verfahren zur Erregung von stationären Schichten, der Schichtungswelle und der laufenden Schichten in der Gleichstromentladung ausgearbeitet, das auf der Einwirkung eines Hochfrequenzfeldes auf einen kurzen Abschnitt der positiven Säule beruht. Dieses Verfahren wurde zum Studium aller drei angeführten Schichtungsarten in Neon benützt, insbesondere jedoch zum Studium des Zusammenhanges zwischen den laufenden und den stationären Schichten.Bei stationären Schichten wurden zweifache Strukturen festgestellt und es wurde deren Abhängigkeit vom Entladungsstrom und von der Größe des erregenden Hochfrequenzfeldes verfolgt.Bei der Schichtungswelle wurde die Stelle deren Entstehung ermittelt und es wurde nachgewiesen, daß das Hochfrequenzfeld diese Welle lokal an der Stelle dessen Einwirkung auf die positive Säule hervorruft.Bei den laufenden Schichten wurde deren Resonanzfrequenz in Abhängigkeit vom Entladungsstrom und die Abhängigkeit der Wellenlänge der Schichten von der Frequenz untersucht.Es wurde festgestellt, daß der extrapolierte Wert der Wellenlänge für die Nullfrequenz erheblich niedriger ist als die Länge der stationären Schichten. Weiter wurde eine Übereinstimmung der Frequenz der laufenden Schichten in der Schichtungswelle mit der Resonanzfrequenz der künstlich hervorgerufenen laufenden Schichten festgestellt.

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, , . , . . , . . , . , .

     

Новый тип рентгеновс кого спектрографа

. 1', . . .     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

Spatial period of moving striations as function of electric field strength in glow discharge

During a systematic investigation of the parameters of a moving stratification in a glow discharge in helium and neon it was found that the spatial period of the striations is a simple, unique function of the d-c (constant) component of the longitudinal electric field strengthE. It was found that this dependence is hyperbolic and that the simple relation (1) or (2) thus holds. In the relation has the significance of a potential fall between the corresponding points of two neighbouring striations and in the measured range of pressures, currents and diameters of discharge tubes it depends only on the sort of gas and type of striations.

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, , E. , , , (1) (2). (1) (2). , .

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The principal results of this work were reported at the 1st conference on electronics in Prague on April 26, 1960.     

On the Hamiltonian interpolation of near-to-the identity symplectic mappings with application to symplectic integration algorithms

We reconsider the problem of the Hamiltonian interpolation of symplectic mappings. Following Moser's scheme, we prove that for any mapping , analytic and -close to the identity, there exists an analytic autonomous Hamiltonian system, H such that its time-one mapping _H differs from by a quantity exponentially small in 1/. This result is applied, in particular, to the problem of numerical integration of Hamiltonian systems by symplectic algorithms; it turns out that, when using an analytic symplectic algorithm of orders to integrate a Hamiltonian systemK, one actually follows exactly, namely within the computer roundoff error, the trajectories of the interpolating Hamiltonian H, or equivalently of the rescaled Hamiltonian K=^-1H, which differs fromK, but turns out to be ⁵ close to it. Special attention is devoted to numerical integration for scattering problems.     

О взаимодействии экс итонов с колебаниями кристаллической реш етки

, - . : - . - .     

Das Anhaften von Exzitonen an Störstellen des Kristallgitters

Zusammenfassung Es wird der Proze des Anhaftens von Exzitonen an Vakanzen und F-Zentren in den Ionenkristallen studiert. Die Bewegung der Exzitonen im Felde der Vakanz und des F-Zentrums wird in adiabatischer Annäherung untersucht. Mit Hilfe der klassischen Methoden werden die Wirkungsquerschnitte des Anhaftens des Exzitons an den Vakanzen und F-Zentren bestimmt und diskutiert.

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F- . F- . F- .

     

НИЗКОЧАСТОТНЫЕ КОЛЕ БАНИЯ ПРЯМОУГОЛЬНЫХ ПЛАСТИНОК ADP

- — . , - NH₄H₂PO₄,- ADP. ; - .