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.     

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

The bicovariant differential calculus on the κ-Poincaré group and on the κ-Minkowski space

The bicovariant differential calculus on the four-dimensional-Poincaré group and the corresponding Lie-algebra like structure are described. The differential calculus on then-dimensional-Minkowski space covariant under the action of the-Poincaré group is constructed.Presented at the 4^th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Supported by KBN grant 2 P 302 217 06 p 02Supported by KBN grant 2 P 302 867 06     

Химическая сенсиБил изация фотографичес кой эмульсии

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Chemical sensiblilisation of photographic emulsion

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, 7. V. 1953 .     

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.     

Generalized Transvectants-Rankin–Cohen Brackets

We introduce o(p+1q+1)-invariant bilinear differential operators on the space of tensor densities on Rⁿ generalizing the well-known bilinear sl₂-invariant differential operators in the one-dimensional case, called Transvectants or Rankin–Cohen brackets. We also consider already known linear o(p+1q+1)-invariant differential operators given by powers of the Laplacian.     

The quantum efficiency of the internal photo-electric effect in indium antimonide

A method is described for measuring the relative quantum efficiency of the internal photo-electric effect in semi-conductors by simultaneously measuring the photo-magnetoelectric and photo-conductive effect. The results of measurements on indium antimonide are given. The quantum efficiency begins to increase if the energy of the photon exceeds 0·47 eVat room temperature. The quantum efficiency as a function of the energy of the photon is analysed on the basis of the conception of impact ionization and it is shown that a study of the structure of this curve can supply information on the, band structure of a semi-conductor in the region of high energies of electrons and holes.

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. . , 0,47 eV . , .

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The authors thank M. Závtová and M. Vantuchová for efficient help with the measurements, K. mirous and V. Vrchovská for preparing the material, E. Antoník for critical remarks and M. Matyá and A. Müller for determining the constants of the material.     

МЕТОД ДЛЯ ВЫЧИСЛЕНИЯ КОЛЕБАНИЙ НАРУШЕННО Й АТОМНОЙ ЦЕПОЧКИ

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Honeycomb domain structure

A theory is given of a new structure produced when demagnetizing uniaxial single crystals (e.g. magnetoplumbite) in a field normal to thec axis. The experimental results fully support the theory on the assumption that domain structures produced under normal conditions are metastable. Methods are given by which stable structures can be prepared from such metastable ones. On the basis of these results opinions are expressed as to the nucleation of plate and honeycomb structures, produced either by reducing the field from saturation or by cooling below the Curie point.

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, (, ) , c. , , , , , . , . , .

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In conclusion the authors would like to thank C. Novák from the Institute of Technical Physics, Czechoslovak Academy of Sciences, for checking the calculation of the harmonic analysis and Z. Málek and J. Eousek for carefully reading the paper and for valuable remarks.     

A contribution to the theory of X-ray monochromators

The characteristic function is introduced, describing completely the monochromating effect of monochromating units. Expressions for this function are presented for monochromating units frequently used. An example of computation for Johansson's unit shows the conditions in a special case. The curves indicating the shift of the wavelength centroid of monochromated radiation for crystals of different perfection allow conclusions to be drawn about the influence of the alignment of the crystal on precision measurements of lattice constants. The experiments verify the suggested model. The computations for a given experimental arrangement permit a simple determination of the effective breadth of the reflection curve, if a distance of two suitably chosen diffraction lines of a polycrystalline specimen is measured. Finally, it was found experimentally that a small elastic bending does not essentially alter the reflection curve of highly elastic and imperfect crystals unless macroscopic distortions are present.

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

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The author is deeply grateful to Prof. A. Kochanovská for her encouraging interest and wishes to express his thanks to Z. Hemanová for her careful computations.     

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.     

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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The energy of periodic surface structures in ferromagnetism

The periodic domain structures on unfavourably oriented surface layers of ferromagnetic materials were studied both experimentally and theoretically. The connection between the surface structure and the crystallographic orientation of the crystals was confirmed. All the terms contributing to the total energy of the surface layer were calculated. A general solution of the potential problem is given for arbitrary periodic distribution of the charges.

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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 .

     

Complex Hyperspherical Equations, Nodal-Partitioning, and First-Excited-State Theorems in ℝ n

Three problems related to the spherical quantum billiard in are considered. In the first, a compact form of the hyperspherical equations leads to their complex contracted representation. Employing these contracted equations, a proof is given of Courant's nodal-symmetry intersection theorem for diagonal eigenstates of spherical-like quantum billiards in . The second topic addresses the first-excited-state theorem for the spherical quantum billiard in . Wavefunctions for this system are given by the product form, ( )Z _q+()Y ⁽ⁿ⁾ , where is dimensionless displacement, is angular-momentum number, qis an integer function of dimension, Z() is either a spherical Bessel function (nodd) or a Bessel function of the first kind (neven) and represents (n– 1) independent angular components. Generalized spherical harmonics are written . It is found that the first excited state (i.e., the second eigenstate of the Laplacian) for the spherical quantum billiard in is n-fold degenerate and a first excited state for this quantum billiard exists which contains a nodal bisecting hypersurface of mirror symmetry. These findings establish the first-excited-state theorem for the spherical quantum billiard in . In a third study, an expression is derived for the dimension of the th irreducible representation (irrep) of the rotation group O(n) in by enumerating independent degenerate product eigenstates of the Laplacian.     

Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

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.

     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

Black-Hole Entropy as Causal Links

We model a black hole spacetime as a causal set and count, with a certain definition, the number of causal links crossing the horizon in proximity to a spacelike or null hypersurface . We find that this number is proportional to the horizon's area on , thus supporting the interpretation of the links as the horizon atoms that account for its entropy. The cases studied include not only equilibrium black holes but ones far from equilibrium.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.