Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

Decay of Re186

The decay of Re 186 was investigated with a double focusing spectrometer and scintillation spectrometer. Four transitions were observed with energies of 122·7±0·1 keV, 137·2 keV, 632·2±1·5 keV and 768·2±1·5 keV and the relative-ray intensities 18, 246, 0·9 and 1 respectively. TheK-conversion coefficients determined for low-energy transitions are in good agreement with the theoretical values ( _K ^122·7 =0·53±0·05, _K ^137·2 =0·44±0·02). The relative intensities of theK, L, M andN conversion lines were also determined for these transitions:KL _I +IIL _III M=1·20±0·201·32±0·20 1±0·150·57±0·08 for 122·7 keV transition,KL _I +IIL _III MN=1·57±0·081· 72±0080·70±0·030·20±0·01 for 137·2 keV transition. In the beta spectrum two groups were observed with the end points of 1076±3 keV and 939±3 keV and relative intensities 74±4% and 21±4% respectively. For the branching ofK-capture it was found that 1·5% populates the 122·7 keV level and 3·5% the ground state. The decay scheme from the present results is proposed.The authors would like to thank M. Buriánek and V. Kopiva for help in the measurements.     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Corrections to cluster-radius scaling for branched polymers and percolation

We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent . We find -0.640±0.004 and =0.87±0.07 for isotropic animals in 2d, and =0.64±0.06 in 3d. For directed lattice animals we argue that the leading correction has= or= ; we also estimate =0.82±0.01 and 0.69 ±0.01 ind=2, 3 respectively. For percolation clusters at and abovep _c, we find (p _c) =0.58±0.06 and (p>p _c)=0.84±0.09 in 2d, and (p _c)=0.42±0.11 and (p>p _c)=0.41 ±0.09 in 3d.     

Decay of Cs134m

The decay of the isomeric state of Cs¹³⁴ was studied. The decay half-timeT _1/2=2·93±0·05 hours was determined. From measurements carried out by means of a spectrometer with short lens, scintillation measurements and chemical separations, the non-existence of the weak decay of this state was proved, contrary to statements found previously in the literature (maximum possible intensity 0·02%, compared to the value of 1% found in the literature). The spectrum of conversion electrons was measured by a double-focusing spectrometer, and the following transition energies were determined: 127·3±0·3 keV (E3) and 138·4±0·4 keV (M4) (K:L:M+N is 92 100 27 for the 127·3 keV transition, and 206 100 31 for the 138·4 keV transition). The conversion coefficient of the 127 keV transition was measured, resulting in a value of _k =2·55±±0·4. The ratio of transition intensities isI ₁₃₈ I ₁₂₇=5·7 1000.     

The internal friction of longitudinal oscillations in ferromagnetic materials

The paper deals with the theory of the new magnetomechanical phenomenon in an alternating field [6, 7]. The first part concerns the internal friction of longitudinal oscillations of a ferromagnetic material in the shape of a wire in a constant magnetic field. It is assumed that the medium in which the sample oscillates is conducting and has a certain permeability. Equations defining the magnetic field in the oscillating material are derived from the basic thermodynamic relations. The term describing the non-conservative force component in a complex formulation is used to determine the internal friction. A general relation between the internal friction and the magnetic field is derived, as well as other expressions, which are a simplification of it. The second part of the paper deals with internal friction in an alternating field. It is shown that the solution can be transformed to the sum of the internal frictions of the different harmonic oscillations, which are obtained as a partial solution of the problem on the assumption that the elastic oscillations in interaction with the field oscillations are separated into their harmonic components. The calculation then becomes that of the internal friction considered in the first part of the paper. In this case the internal friction significantly depends on the field amplitude. The functional dependence of the internal friction peak on the frequency of the mechanical oscillations is also calculated. The agreement of the theory with experiment is satisfactory.

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Multifractality and scaling in disordered mesoscopic systems

We suggest a new method for investigating scaling properties of mesoscopic observables and their distributions in disordered systems showing metal-insulator transition. In such systems quantum interference effects lead to multifractal structure of eigenstates on scales much smaller than the correlation length of the transition which can be described by a set of exponents, thef() spectrum. The analysis off() spectra can be extended to any scaling variable. Multifractality is an indication for broad distributions of these variables. If the transition is governed by one correlation length only then thef() spectra of normalized scaling variables must be universal. The critical exponentv of the correlation length is determined by the value (0) wheref() takes its maximum and the scaling exponent of normalizationxv ^–1=(0)+x. As an illustrative example we calculate numerically thef() spectra of eigenstates in the critical regime of 2d disordered electron systems in high magnetic fields. We find similarf() spectra indicating universal log-normal distributions of scaling variables.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Phase transitions in gallium nanodroplets detected by dielectric spectroscopy

Both theoretical and experimental works give evidence that gallium exhibits solid phases labelled , , , besides the stable phase strongly dependent both on the size and the confinement conditions. An experimental technique was used based on capacitance and conductance measurements vs. temperature in the audiofrequency range. This technique is particularly sensitive to the conditions of the investigated particle surface that plays a fundamental role in the melting and more generally in the phase transition processes. In particular the strict relation between the derivative of the capacitance with respect to the temperature, dC/dT, and the entropy of the system is considered. In gallium nanoparticles 20 nm in radius, only the phase is shown to occur. Further the transition to liquid phase was detected. The melting process was found to start about 65 K below the full melting temperature value. In the case of particles 10 nm in radius, where different metastable phases may occur, the capacitance vs. temperature curve was found to display abrupt changes of the slope. The singularities are associated to a well defined transition temperature.     

The asymmetric contact process on a finite set

The contact process onZ has one phase transition; let _c be the critical value at which the transition occurs. Let _N be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants ₁() and ₂() such that if < _c , lim _{N N} /logN = 1/₁(); if > _c , lim _N log _N /N = ₂(); if = _c , lim _{N N} /N= and lim _{N N} /N ⁴=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values _c1< _c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for < _c1 and > _c2. We show that for [ _c1< _c2), lim _{N N} /N=-1/, (where _i is an edge speed) and for = _c2, lim _N log _N /logN=2 in probability.     

Notes on the classical and the nonrelativistic limits in quantum mechanics

A method is presented which can be used to discuss both the classical and also the nonrelativistic limit of quantum mechanics. A one-to-one correspondence may be established between the asymptotic convergence of the resolvent and that of the timedependent solution. In so far as the question of dynamics is concerned we investigate the relation between families of nonrelativistic Hamiltonians and the corresponding Dirac-Hamiltonians when c± or when c±0. The nonrelativistic free theory formally shows the same pattern when ±0 (the classical limit) or when ±. The investigation finally shows how the asymptotic convergence of the relativistic theory can take place under some fairly general conditions of the radiation field.     

Static and dynamic critical phenomena of the two-dimensionalq-state Potts model

Theq-state Potts model on the square lattice is studied by Monte Carlo simulation forq=3, 4, 5, 6. Very good agreement is obtained with exact results of Kiharaet al. and Baxter for energy and free energy at the critical point. Critical exponent estimates forq=3 are0.4,0.1,1.45, in rough agreement with high-temperature series extrapolation and real space renormalization-group methods. The transition forq=5, 6 is found to be a very weakly first-order transition, i.e., pronounced pseudocritical phenomena occur, specific heat, susceptibility, etc. (nearly) diverge at the first-order transition temperature. Dynamics is associated to the model in the same way as for the kinetic Ising model, and the nonlinear slowing down of the order parameter and of the energy is studied. The dynamic exponent is estimated to be (=zv)1.9. Within our accuracy noq dependence is detected. The relaxation is found to be consistent with dynamic scaling predictions, and dynamic scaling functions associated with the nonlinear relaxation are estimated.     

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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Сцинтилляционный сп ектрометр с сложение м импулъсов от двух кри сталлов

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On the electroluminescence of ZnS at low voltages

The possibility of explaining non-zero electroluminescence brightness below the minimum ionization voltage by the influence of thermal velocities of electrons is pointed out; the derived voltage dependence of electroluminescence brightness agrees with the measurements in [1].

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ZnS

; [1].

     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

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The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

Excited-state absorption and third-order optical nonlinearities in symmetric π-electron organic molecules

Excited-State Absorption (ESA), Two-Photon Absorption (TPA) and the third-order polarizability (;,, – ) have been investigated for a model dichloride derivative of a symmetrically substituted benzylidene analine (SBAC), using a multielectron configuration-interaction procedure. The calculations indicate that SBAC exhibits ESA across the visible region of the spectrum, but that it is not as extensive as for molecules such as the phthalocyanines. The magnitude of the third-order polarizability is dominated by resonance enhancement from a very strongA _g B _u one-photon absorption. The calculated off-resonance value for (;,, – ) suggests that SBAC is a potential candidate for ultrafast switching applications.     

On the invariant sets of a family of quadratic maps

The Julia setB for the mappingz (z–)² is considered, where is a complex parameter. For 2 a new upper bound for the Hausdorff dimension is given, and the monic polynomials orthogonal with respect to the equilibrium measure onB are introduced. A method for calculating all of the polynomials is provided, and certain identities which obtain among coefficients of the three-term recurrence relations are given. A unifying theme is the relationship betweenB and -chains ± (± (± ...), which is explored for –1/42 and for with ||1/4, with the aid of the Böttcher equation. ThenB is shown to be a Hölder continuous curve for ||<1/4.Supported by NSF Grant MCS-8104862Supported by NSF Grant MCS-8002731     

The contrast gain in a guest-host nematic display due to a periodic boundary condition

The mean square tilt angle of a nematic slab with finite anchoring energy and periodic boundary conditions has been theoretically investigated, as a function of the slab geometry and of the reduced extrapolation length. If the anchoring strength is free-surfacelike, the contrast is affected by a loss 10% at room temperature if the ratio between the anchoring pitch and the cell thickness is 0.5.Glossary anchoring pitch - h cell thickness - /h - ( = x/, = y/h) reduced coordinates - (, ) local tilt angle - elastic constant - w_a anchoring energy anisotropy - b=/w _a de Gennes-Kleman extrapolation length - B=b/h reduced extrapolation length - T _NI nematic-isotropic transition temperature - :=(T/T _NI ) – 1 reduced temperature - easy axis direction - _MAX - _± ² mean square tilt angle along the boundary - () absorbance coefficients of the p-dye - r /: dichroic ratio - c contrast - G contrast gain - S order parameter     

The crystal structure of copper dipyridine dibromide Cu(C5H5N)2Br2

The X-ray structural analysis of copper dipyridine dibromide was carried out. The substance is monoclinic, its space group isP2₁/n, having the lattice constantsa=8.30 kXU,b=17.72 kXU,c=4.04 kXU,=96°,Z=2. The localization of the heavy atoms was carried out by means of the projections of the Patterson functionsP(u, v) andP(v, w), which provided the bases for determining the signs of the majority of structure factors. The projections of the electron density(x, y) and(y, z) were calculated on the basis of these data. The positions of the atoms were refined three times by methods of differential syntheses and by geometrical analysis. The structure of CuPy₂Br₂ is very close to that of CuPy₂Cl₂ [1], [2], differing from it primarily in the orientation of the symmetry elements with respect to the crystallographic axes. In both structures the copper atom is octahedrally coordinated with four halogen and two nitrogen atoms. The nitrogen atoms and two bromine atoms are bound to the copper covalently in the structure of the bromine derivative, as follows from the length of the bonds (Cu-N 1.99 kXU, Cu-Br, 2.46 kXU), while the remaining two bromine atoms are bound to the copper by weaker bonds and mediate the chain formation of molecules in the direction of thec axis.

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Cu(C₅H₅N)₂Br₂

. , 2₁/ ==8,30 kX,b=17,72 kX,=4,04 kX,=96°,z=2. (, v) P(v, w), . (, ) (, z). . CuPy₂Br₂ u₂1₂, . . , (-N 1,99 kX, u-r 2,46 kX), .

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The authors thank M. Serátor for supplying the crystal samples and for initiating the work, the management of the Institute of Technical Physics, Czechoslovak Academy of Sciences, in Prague and especially Dr. A. Línek for making it possible to calculate some of the Fourier maps on the special computer Elika and finally A. lechtová for carefully calculating the Fourier maps and structure factors.

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The first stage of this work was reported on at the 3rd State Conference on Inorganic Chemistry, held in Bratislava from June 29th to July 4th, 1959.     

Magnetic anisotropy in thin ferromagnetic films

The magnetic properties of thin ferromagnetic films are studied taking into account the magnetic anisotropy term in the Hamiltonian. In the second approximation equations are obtained for the magnetization of the monatomic layers parallel to the surface of the thin film. From these equations one obtains the Curie temperature, which depends on the thickness of the thin film and the ratio a between the anisotropy constant and the exchange energy between two neighbours. A value can be chosen for such that the thin film becomes ferromagnetic only for a thickness greater than a definite value and in this manner the theoretical results can be fitted to the experimental data. The situation in cobalt thin films is dealt with in particular.

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The author extends his thanks to the research workers of CIFA 1 as well as to Dr. L. Valenta for information on the same subject.