Correlations and spectra of an intermittent chaos near its onset point

A one-parameter family of piecewise-linear discontinuous maps, which bifurcates from a periodic state of periodm, (m=2, 3,...) to an intermittent chaos, is studied as a new model for the onset of turbulence via intermittency. The onset of chaos of this model is due to the excitation of an infinite number of unstable periodic orbits and hence differs from Pomeau-Manneville's mechanism, which is a collapse of a pair of stable and unstable periodic orbits. The invariant density, the time-correlation function, and the power spectrum are analytically calculated for an infinite sequence of values of the bifurcation parameter which accumulate to the onset point _c from the chaos side - _c > 0. The power spectrum near=0 is found to consist of a large number of Lorentzian lines with two dominant peaks. The highest peak lies around frequency=2/m with the power-law envelope l/¦-(2/m)¦⁴. The second-highest peak lies around o = 0 with the envelope l/¦¦². The width of each line decreases as, and the separation between lines decreases as/lg3^–1. It is also shown that the Liapunov exponent takes the form-/m and the mean lifetime of the periodic state in the intermittent chaos is given bym ^–1(ln ^–1+1).     

Dielectric properties of titanium and gadolinium doped MgO single crystals

The dielectric properties of titanium doped magnesium oxide (Ti/MgO) and gadolinium doped magnesium oxide (Gd/MgO) single crystals have been measured at room temperature over the frequency range 500 Hz to 50 kHz. For both the crystals, the dielectric constant is found to be independent of frequency and the ac conductivity Re{_ae} agrees well with the relation Re{_ae} ⁿ , being the angular frequency with n=0.84±0.05 for Ti/MgO andn=0.81±0.03 for Gd/MgO. The data fits well with the relation ^n–1(n<1), being the dielectric loss factor. An explanation may be found on the basis of the hopping phenomenon.     

Determination of the far infrared optical constants of η-doped bulk CdxHg1?xTe (CMT) by dispersive fourier transform spectroscopy

Far infrared phase and amplitude reflectivity measurements have been made on two bulk Cd_xHg_1–xTe mixed crystals with composition x=0.29 and x=0.22 by dispersive Fourier transform spectroscopy (DFTS). The results have been used to calculate the real and imaginary parts of the dielectric function (, ) from the Fresnel relations. A plasma contribution is observed in the spectra in addition to the phonon response. For both samples a broad but weak reflection band around 95–105 cm^–1 is observed as well as the expected two-oscillator response from the HgTe-like and CdTe-like optical phonons. This feature is attributed to absorption due to phonon combination bands, but it is too broad to enable assignments to be made. There is no evidence of additional features in the CdTe region due to clustering.     

Spectral behavior of quasi periodic potentials

Spectral properties of Schrödinger operators of the typeH =–+V, where is the Laplacian,V a quasiperiodic potential and a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as is increased.Research supported in part by grant NSF MCS 7900813     

One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ¹ It is known that equilibrium (i.e., time-invariant attractive) states for this model are translationally invariant Gaussian ones, with the mean 0, which satisfy some linear relations involving the interaction quadratic form. The natural parameter characterizing equilibrium states is the spectral density matrix function (SDMF)F(), [– , ). Time evolution of a space profile of local equilibrium parameters is described by a space-time SDMFF(t;x, ) t, xR ¹. The hydrodynamic equation forF(t; x, ) which we derive in this paper means that the normal mode profiles indexed by are moving according to linear laws and are mutually independent. The procedure of deriving the hydrodynamic equation is the following: We fix an initial SDMF profileF(x, ) and a familyP ,>0 of mean 0 states which satisfy the two conditions imposed on the covariance of spins at various lattice points: (a) the covariance at points close to the value ^–1 x in the stateP is approximately described by the SDMFF(x, ); (b) The covariance (on large distances) decreases with distance quickly enough and uniformly in. Given nonzerotR ¹, we consider the states P _–1 ,>0, describing the system at the time moments ^–1 t during its harmonic time evolution. We check that the covariance at lattice points close to ^–1 x in the state P _–1 is approximately described by a SDMFF(t;x, ) and establish the connection betweenF(t; x, ) andF(x,).     

Accurate calculation of functional determinants

A dependence of the functional determinant of the operator from the family D() satisfying the condition D()=fD()+D()f on the parameter m² of infrared regularization is found in the regularization method using a generalized function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 27–32, June, 1988.     

Changes in the properties of dielectric material T-8000 produced by irradiation with electrons and protons

In studying the dielectric properties of material T-8000, a difference was discovered in the effects of electron and proton irradiation on dielectric permeability () and dielectric loss angle tangent (tan ). It is assumed that upon irradiation with protons having higher energy (4.25 MeV) the processes of titanium, zirconate, and barium ion displacement occur with greater probability than upon irradiation with electrons whose energy does not exceed 1.2 MeV. This causes the differences in the changes in tan and of the T-8000 material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 46–49, March, 1974.     

The physical nature of the production of moving striations in a d-c discharge plasma

The physical nature of the stratification of the d-c discharge plasma is found and physically interpreted. The interpretation is based on the mathematical expression of the production of periodic structure in plasma after an aperiodic disturbance, derived from an extremely simplified system of equations. Only three basic phenomena occurring in the plasma of each d-c discharge are included: a) the dependence of the rate of ionization on the electron temperature and hence on the electric field, b) the production of space charges due to the different rates of diffusion of the electrons and ions, c) the creation of additional electric fields due to the creation of space charges. The interactions of these phenomena gives rise to a chain, expanded in time and space, which leads to the production of moving striations. In agreement with experiment this structure is developed only on the side towards the anode from the place where the equilibrium state is disturbed.

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. (9, 10) (4, ), . , , : ) , , ; ) , ; ) , . , , — — . , .

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In conclusion the authors thank J. Fousek, J. Kaczér and M. Novák for carefully reading this paper and for valuable remarks, and J. Holub for carrying out the numerical and graphical work.     

Asymptotic theory of multidimensional chaos

A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.     

Equilibrium state of toroidal electron beam

The paper deals with the collective behaviour of electrons which rotate in a magnetic field used in a betatron. It is shown experimentally that there exists strong interaction between the electrons, which leads to the rapid formation of the equilibrium state with characteristic distribution of the charge density in the cross-section of the toroidal beam. The corresponding relaxation time is of the order of 1 sec. A statistical theory of the equilibrium beam is elaborated. Its main result is that the effective radius of the beam is a function of two parameters, one of which is proportional to the thermal energy of the electrons and the other to the perveance of the beam. The charge contained in a toroidal beam of given effective cross-section is equal to the product of the charge the beam would contain at zero temperature and a coefficient, which is a function of the temperature of the beam. Its value is unity at zero temperature and rapidly decreases with increasing temperature. The cause of cooling of the beam is shown.

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, . , , . 1S. . , , — I/(E₀/q)^3/2 (I — , ₀ — q ). , , , , , . . .

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Now Institute of Vacuum Electronics, Czechosl. Acad. Sci., Prague.

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In conclusion the author thanks J. Luká and L. Hyttych for invaluable help in the experiments, A. Rajský for constructing the electronic apparatus and J. Sokol for preparing the miniature probe.     

Change in primary extinction during decomposition of supersaturated solid solution II. Al-Cu 4% alloy-formation of G.P. zones

The change in integrated intensity of the (200) reflections of a solid solution during the formation of G.P. zones was measured and compared with the change in the character of the diffuse streaks corresponding to them. It was found that the. formation of G.P. zones does not lead to a decrease in primary extinction despite the great changes in the distribution of the copper atoms. It was shown that the formation of a precipitate accompanied by the formation of crystallographically incoherent boundaries greatly decreases the primary extinction.

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. II. 1-u 4%: [. . ]

(200) . . , . , . . , . , , , .

     

Kinetic limits of the HPP cellular automaton

We study the Boltzmann-Grad limit in various versions of the two-dimensional HPP cellular automaton. In the completely deterministic case we prove convergence to an evolution that is not of kinetic type, a well-known phenomenon after Uchyiama's paper on the Broadwell gas, whereas the limiting equation becomes of kinetic type in the model with random collisions. The main part of the paper concerns the case where the collisions are deterministic and the randomness comes from inserting, between any two successive HPP updatings, ^- stirring updatings, <1 being any fixed positive number and a parameter which tends to 0. The initial measure is a product measure with average occupation numbers of the order of (low-density limit) and varying on distances of the order of ^–1. The limit as 0 of the system evolved for times of the order of ^-1- corresponds to the Boltzmann-Grad limit. We prove propagation of chaos and that the renormalized average occupation numbers (i.e., divided by) converge to the solution of the Broadwell equation. Convergence is proven at all times for which the solution of the Broadwell equation is bounded.     

Локалъная чувствите лъностъ фотокатодов фотоумножителей

. . .

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The local sensitivity of photo-multiplier photo-cathodes

The influence of the non-uniform distribution of the sensitivity of a photo-multiplier photo-cathode on the spectrum shape of the output pulses from a scintillation detector is studied. Methods of scanning the local sensitivity and determining its distribution function are described. The theory was compared qualitatively with measurement on a slow-neutron detector from a mixture of zinc sulphate and boric acid.

     

ОДНОНУКЛОННАЯ МОДЕЛ Ь ЯДРА. ЧАСТЬ I

. . , - , - , - .     

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.     

Dielectric properties of (K,Li)TaO3 crystals at superhigh frequencies

The dielectric-resonator method was used to study the dielectric constant and loss of K_1–xLi_xTaO₃ crystals for lithium contents x=0.02, 0.05, and 0.1 in the frequency of 0.5 GHz (in the temperature interval from 4.2 to 300 K) the dielectric constant, the static nonlinearity, and the dynamic nonlinearity were studied, the dielectric properties of K_1–xLi_xTaO₃ are determined simultaneously by the relaxation of impurity ions and by the soft mode, but at helium temperatures the contribution of the soft mode to predominates. The addition of lithium leads to a reduction of at 4.2 K and to a lessening of the steepness of the (t) curve. KTaO₃ crystals alloyed with lithium exhibited exceptionally low losses at helium temperatures (at 4.2 K in the range 12–14 GHz, tan =2 · 10^–5 for x=0.1). With a rise in temperature the loss increased just as in the case of unalloyed KTaO₃, but less steeply. Measurements of crystals with x=0.1 revealed considerable dispersion of the nonlinearity: the coefficient of static nonlinearity was an order of magnitude of magnitude higher than the coefficient of dynamic nonlinearity ₁ ^dyn, which was determined according to the efficiency of generation of the second harmonic.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–7, January, 1988.     

Resonant shielding of an inhomogeneous gyrotropic plasma slab

Conclusions The problem of the incidence of a plane TM electromagnetic wave on an isotropic, symmetric, resonance plasma slab (n=2, 4, 6, ...), discussed in [1], was solved by an iteration method in a recent paper [6]. The physical results found there are the same as those of [1]. Zhivulin and Makarov [6] then applied the iteration method to the analogous problem of a gyrotropic resonance plasma slab [7]. The analysis in these papers furnishes a clearer mathematical justification of the results of [1] and the present paper and thus of the method used there. The present method, which satisfies only a physical condition of rigor, is preferable to the mathematically more rigorous methods (in particular, the iteration method) because of its simplicity, its graphic nature, and its clear physical meaning. It also answers many questions which cannot be answered in the more rigorous approach because of the serious difficulties which arise (and which have not yet been overcome).N. G. Denisov has called our attention to the fact that complete shielding was actually found previously by Rytov and Yudkevich [8], who treated the problem of the incidence of a plane TE electromagnetic wave on a slab with a dielectric constant (x)=₁ – A₁/(a – x)² for x<0. (x)=₂ – A₂/(b + x)² for x>0, and ₁ – A₁/(a² = ₂ – A₂/b² in the plane x=0. In the limita0, b0, they found results corresponding to a slab with a dielectric constant having a first-order pole; it is in this case that complete shielding is achieved. This method for obtaining the corresponding results is analogous to the method used in [1] and the present paper. We also note that the distribution of the effective dielectric constant (6) in the immediate vicinity of the pole—where the contribution of the last term. (1–u)x², can be neglected—is the same as the distribution adopted in [8] if we seta-b-0, ₁ = ₂, A₁=A₂=u.Scientific-Research Institute of Radiophysics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 19, No. 8, pp. 1130–1141, August, 1976.     

Renormalization group approach for the site-bond percolation in structured stochastic environments

The quenched averaged percolation problem of a lattice with a given structure is analyzed. The structure is described by the static structure factorS(q)q ^–ain the regionq 0. As a result of the renormalization group, it follows that the critical behavior fora < 2 is the same as in the random percolation. In the case ofa=2 second universality class with=0 and=1/2+/8+ ²/32 is predicted.     

Photopyroelectric spectroscopy (P2ES) of electronic defect centers in crystalline n-CdS

The electrical and dielectric properties of mercuric iodide were studied at room temperature under various intensities and colours of light in the frequency range 1 Hz–10 kHz. In the high-frequency region (>40 Hz), the real part of the dielectric constant () is almost constant with frequency (f), colour and intensity of light. At lower frequencies, varies nearly as 1/f and monotonically increases with intensity (I) of the yellow (or green) light, whereas it is almost constant with red light intensity. This behaviour is discussed in the view of the different polarization contributions. The imaginary part of the dielectric constant () was found to vary as 1/f over the frequency range studied. This behaviour was observed whether the crystal was in dark or illuminated implying that the roomtemperature ac dark- or photo-conductivity () is independent of frequency. The observed variation of with intensity of yellow (or green) light was found to follow anI ^1/2 dependence and a weaker dependence for the red light. the red light. The conductivity behaviour is discussed in the view of the current theories.     

The influence of compression on the absorption of AgBr single crystals

The influence of compression on the edge of self absorption of AgBr single crystals was studied. The measurements were performed at a temperature of –180°C. The shift of the edge of self absorption was studied both in the field of elastic and plastic deformations. The shift of the absorption edge towards the UV end of the spectrum was determined in the field of elastic deformations and towards the i.r. end in the field of plastic deformations. After the ending of the deformation and after unloading the crystal the return of the absorption edge towards the original position was observed.

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AgBr

AgBr. –180°C. , . , — . .

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The author thanks Prof. Dr. L. Zachoval and K. K. Vacek C. Sc. for their interest in this work and for many comments given during the work.