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.     

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.

     

ИЗОТОПЫ ФТОРА F19 И F21 В МОДЕЛИ НИЛЬССОНА

Energy levels and electromagnetic properties of fluorin isotopes in the Nilsson's model with Coriolis mixing are investigated. Position of the F¹⁹ levels is satisfactorily explained up to the energy of 4·5 MeV. Concerning the F²¹ it seems that the shell model will better correspond to the F²¹ nucleus.

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. , .     

Polarization of photo-luminescence of ZnS: Cu monocrystals

Different models of luminescence centres are discussed on the basis of measurements of the composition of ZnS monocrystal photo-luminescence in different polarizations and temperature dependence of the degree of polarization. Those of the models submitted by Birman, which assume the polarization to be due to the different force of the oscillators for transitions withEc andEc, or models assuming luminescence polarization to be due to the orientation of the luminescence centres, agree with the results of experiments, i.e. the temperature independence of the degree of polarization and the conformable spectral composition of both polarizations. It is also shown that measurements made up to now of the degree of polarization must be taken as orientational as a consequence of the depolarizing influence of the diffused rays of luminescence on its value.

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ZnS: Cu

ZnS , . , . . , , , E E, , . , , - .

     

Feynman integral and complex classical trajectories

Let _t be an analytic solution of the Schrödinger equation with the initial condition . Let _t be the solution of the Schrödinger equation with the initial condition =, where is an analytic function. When 0, then _t (x) _t (x)¹ ( _t (x)), where _t (x) trajectory starting from x. We relate this result to Feynman's sum over trajectories and complex stochastic differential equations.     

О взаимодействии экс итонов с колебаниями кристаллической реш етки

, - . : - . - .     

Method of moments in analysis of x-ray diffraction lines

A general relation between the moments of the functionsf,g, andh, in the integral equationh(x)=f(y)g(x–y) dy, is derived. This enables any moment of the unknown functionf to be calculated from the moments of the functionsg andh. In particular, if certain assumptions are fulfilled, the moments of the components of the doublet can be calculated with advantage from the moments of the total profile. The statistical significance of the moment characteristics is also emphasized.

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f, g, h h(x)=f(y)g(x–) dy, f g h. , . .

     

A contribution to the semi-focusing method with a flat polycrystalline sample

Condition are derived for the approximate focusing of diffraction lines in the chosen, relatively wide angular region, using the semi-focusing method with a flat sample, if a bent crystal monochromator is employed. The form of the absorption factor for a flat polycrystalline sample is derived for the case of uniform oscillation of the sample in the angular region ± around the axis of the camera.

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, . ± , .

     

Enhancement of activated decay of metastable states by resonant pumping

We consider the effect of a high-frequency pumping cost on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequency(E) is assumed to be weak on the scale of thermal energy,_E(0)T(0)T/V₀ (0)[_E(0) is the derivative of(E) atE= 0,V ₀ is the barrier height,V ₀ T]. The quadratic-in- contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, when = n(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦-(0)¦ and is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v _E (0)T/, and the resonance mismatch, [ —(0)]/. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov ^–1. In this regime, the dependence on is stepwise: the pumping contribution is large for v > 0 and small for v < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs of andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

ЧАстИЧНО пОгРУжЕННы И БлОк В кВАДРАтНОИ РЕ шЕткЕ

( ) , . , . [1] , , .

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Partially inserted block in square lattice

The paper gives a theory of the partially inserted block (control rod) in a reactor of finite height, consisting of a square lattice of fuel blocks and a moderator. The partially inserted block replaces the block of the original lattice which was located in the axis of cylindrical symmetry of the reactor. The results obtained agree with the relations for a homogeneous medium in paper [1] and are thereby justified for homogeneized reactors.

     

Unbounded derivations and invariant states

Let be a von Neumann algebra with a cyclic and separating vector . Let =i[H, ·] be the spatial derivation implemented by a selfadjoint operatorH, such thatH=0. Let be the modular operator associated with the pair (, ). We prove the equivalence of the following three conditions:1)H is essential selfadjoint onD(), andH commutes strongly with .2) The restriction ofH toD() is essential selfadjoint onD(^1/2) equipped with the inner product(|)_#=(|)+(^1/2|^1/2), , D(^1/2).3) exp (itH) exp (–itH)= for anyt.We show by an example, that the first part of 1),H is essential selfadjoint onD(), does not imply 3). This disproves a conjecture due to Bratteli and Robinson [3].Part of this work was done while O.B. was a member of Zentrum für interdisziplinäre Forschung der Universität Bielefeld     

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.     

On the theory of ferromagnetic thin films

As is known, the second approximation in the calculation of the partition function by the traces method of ferromagnetic thin films gives wrong results for the coordination number equal to eight. In order to obtain correct results even for this case, the third order approximation of the partition function is developed and thus the magnetic properties of body-centred cubic iron thin films are studied. The dependence of the Curie temperature on the thickness, for different values of the ratio between the anisotropy constant and the exchange energy between two neighbours, is discussed. A value can be chosen for this ratio such that the thin film becomes ferromagnetic only for a thickness greater than a definite value.

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, . , , (Fe). . , - .

     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.     

ВЛИЯНИЕ ПРЕДВАРИТЕЛ ЬНОГО ОСВЕЩЕНИЯ ha ХАРАКТЕРИСТИКИ МЕДН ОЗАКИСНЫХ ВЫПРЯМИТЕ ЛЕЙ

, 150° , . - . -. . ( ).     

ВлИьНИЕ стАцИОНАРНО гО РАсслОЕНИь НА ДВИж УЩИЕсь слОИ В тлЕУЩЕМ РАжРьД Е B Ne

The paper describes a new experimentally found phenomenon of the effect of standing stratification on the parameters of moving striations in the positive column of a glow discharge.

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. . M. Hobaky