Trapping,percolation, and anomalous diffusion of particles in a two-dimensional random field

We analyze from first principles the advection of particles in a velocity field with HamiltonianH(x, y)=¯ V ₁ y–¯ V ₂ x+W ₁ (y)-W ₂ (x), whereW _i , i=1, 2, are random functions with stationary, independent increments. In the absence of molecular diffusion, the particle dynamics are very sensitive to the streamline topology, which depends on the mean-to-fluctuations ratio=max(|¯V₁¦/; ¦¯V₂|/), with =|W ₁ |^21/2=rms fluctuations. Remarkably, the model is exactly solvable for 1 and well suited for Monte Carlo simulations for all , providing a nice setting for studying seminumerically the influence of streamline topology on large-scale transport. First, we consider the statistics of streamlines for=0, deriving power laws for p_nc(L) and (L), which are, respectively, the escape probability and the length of escaping trajectories for a box of sizeL, L » 1. We also obtain a characterization of the statistical topography of the HamiltonianH. Second, we study the large-scale transport of advected particles with > 0. For 0 < < 1, a fraction of particles is trapped in closed field lines and another fraction undergoes unbounded motions; while for 1 all particles evolve in open streamlines. The fluctuations of the free particle positions about their mean is studied in terms of the normalized variablest ^– v/2[x(t)–x(t)] andt ^–v/2 [y(t)-(t)]. The large-scale motions are shown to be either Fickian (=1), or superdiffusive (=3/2) with a non-Gaussian coarse-grained probability, according to the direction of the mean velocity relative to the underlying lattice. These results are obtained analytically for 1 and extended to the regime 0<<1 by Monte Carlo simulations. Moreover, we show that the effective diffusivity blows up for resonant values of ) for which stagnation regions in the flow exist. We compare the results with existing predictions on the topology of streamlines based on percolation theory, as well as with mean-field calculations of effective diffusivities. The simulations are carried out with a CM 200 massively parallel computer with 8192 SIMD processors.     

The strength of Einstein's equations

The strength of Einstein's empty-space field equations is computed anew and shown to be equal to the amount of initial data required for a local solution of the equations. This same amount of initial data is shown to be precisely that required for a set of 16 unknown first-order differential equations containing 10 field variables and having six identities of second order. The 10 field variables must be functions of second order in the metric coefficients. The 16 field equationsC , = 0 whereC is Weyl's conformal tensor, are shown to have the same properties as those of the unknown equations, suggesting thatC = 0 is a satisfactory local first-order formulation of Einstein's second-order empty-space field equations.     

On log-Sobolev inequalities for infinite lattice systems

For a system on an infinite lattice, we show that a Gibbs measure for a smooth local specification ={E } satisfying the Dobrushin uniqueness theorem also satisfies log-Sobolev inequality, provided it is satisfied for one-dimensional measures E _l .     

Interfacial properties in solid-stabilized emulsions

We prepared concentrated monodisperse oil-in-water emulsions stabilized by solid particles. The osmotic resistance, , of the emulsions was measured for different oil volume fractions above the random close packing ( ). The dimensionless osmotic resistance, /(/R) ( being the interfacial tension and R being the undeformed drop radius), was always substantially higher than the corresponding values obtained for surfactant-stabilized emulsions. It can be concluded that droplet deformation in solid-stabilized emulsions is not controlled by the capillary pressure, /R, of the non-deformed droplets but rather by 0/R, 0 being a parameter characterizing the rigidity of the droplets surfaces. The data can be interpreted considering that the interfacial layers are elastic at small deformations and exhibit plasticity at intermediate deformations. 0 corresponds to the surface yield stress, i.e. the transition between elastic and plastic regimes. We discuss the origin of the surface behavior considering the strong lateral interactions that exist between the adsorbed solid particles. We propose an independent measurement of 0 based on the critical bulk stress that produces droplet fragmentation in dilute emulsions submitted to shear. Finally, the bulk shear elastic modulus was measured as a function of and confirms many of the features revealed by the osmotic resistance.     

Iteration wave function for describing the (e, 2e) spectrum of the helium atom

The wave function of the ground state of the helium atom is derived by the variational-iteration technique with the Hylleraas-Eckart momentum representation of the wave function as a first approximation. This function is used to calculate the ratios of the differential cross sections (n=2)/(n=1) and (2p)/(2s) for helium ionized by an electron impact. The calculation is conducted in the plane-wave impulse approximation for symmetric noncoplanar kinematics of the (e, 2e) process. The results are compared with previous calculations in which variational wave functions of the configurational interaction type were used. Good agreement with the existing experimental data for (n=2)/(n=1) is obtained. The results are generalized to helium ions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 45–50, December, 1986.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

К ВОПРОСУ O КРИТИЧЕСКО Й ЧАСТОТЕ ПРИ ПРЕРЫВИСТОМ ОСВЕ ЩЕНИИ

c , c n , n AgBr. .     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

The temperature vibrations of urea molecules

The structural and dynamic parameters of urea at 112°K and 295°K were determined by the least squares method. The characteristic temperature of the torsional optical vibrations of a molecule about a C-O bond was determined and is in good agreement with the value determined by Raman scattering. The fractional X-coordinate of the nitrogen atom corrected for torsional vibrations was determined and it was found that the magnitude of the projection of the C-N bond in the given temperature range changes only within the limits of observational errors. A new method, called temperature difference synthesis, is described and it is shown that it is suitable for rapid qualitative determination of the thermal anisotropy of the vibrations of atoms in a crystal lattice.

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112°K 295°K. C-O , , . X- , C-N . , , , .

     

ВлИьНИЕ Cd НА пОглОЩЕН ИЕ NaCl

NaCl Cd , .

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The influence of Cd on the absorption of NaCl

Absorption measurements on uncoloured and X-rayed crystals of NaCl with different Cd-concentrations were made to show under what conditions the non-active form of this impurity may become the active form.

     

Proof of confinement of static quarks in 3-dimensionalU(1) lattice gauge theory for all values of the coupling constant

We study the 3-dimensional pureU(1) lattice gauge theory with Villain action which is related to the 3-dimensional -ferromagnet by an exact duality transformation (and also to a Coulomb system). We show that its string tension is nonzero for all values of the coupling constantg ², and obeys a bound const·m _D^–1 for smallag ², with =4²/g ² and . A continuum limita0,m _D fixed, exists and represents a scalar free field theory of massm _D. The string tension m _D ^–2 in physical units tends to in this limit. Characteristic differences in the behaviour of the model for large and small coupling constantag ² are found. Renormalization group aspects are discussed.Work supported in part by Deutsche Forschungsgemeinschaft     

The surface layer on a ferromagnetic. The energy of some periodic domain structures

Explicit solutions are found for a number of special cases of the potential problem of periodic charge distribution. The effect of uneven distribution of the charges of a Bloch wall on the magnetostatic energy is studied, the effective width of the Bloch wall is determined, an analytical expression is found for this distribution of poles and finally the effective height of the surface layer is also determined. An expression is derived for the orientation of the vectors of magnetization in the surface layer with respect to the easy directions of magnetization. The stability of the basic domain structure up to an inclination of 6°of the plane under observation to the direction of easy magnetization and the dimensions of the domains in periodic closure structures follow from the calculations.

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. , , , , . . , 6°,, , .

     

Untersuchungen über Versetzungen an Einkristall- und Polykristallplatten von AgCl

Zusammenfassung Beobachtungen der Versetzungen wurden an für optische Messungen hergestellten Platten des AgCl gemacht. Es wurde die Versetzungsdichte im Zusammenhang mit dem deformierenden Druck untersucht.

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AgCl

AgCl, . .

     

The iteration method in multiple scattering: The transfer equation

Using the iteration method, the author obtains the transfer equation for the scattering of electromagnetic waves in a system comprising a large number of statistically independent particles spherical in shape under the condition c^–1 1 c is the density of the number of particles, the scattering cross section for a single particle, and the wave number. The method is easily extended to the scattering of scalar waves.In conclusion the author expresses his thanks to V. E. Zuev and S. D. Tvorogov for their guidance and observations on the study.     

The effect of oxygen on the electric conductivity of a cuprous oxide single crystal

The effect of an excess of oxygen on the electric conductivity of a pre-illuminated and heated single crystal of Cu₂O is investigated. It is found that the influence of illumination on the electric conductivity, together with the concentration of impurities, increases with increasing oxygen pressure during annealing.

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, Cu₂O. , .

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In conclusion the author thanks E. Klier and J. Pastrak for valuable remarks and discussion.     

Changes in EPR spectrum of free radical species inγ-irradiated polyformaldehyde

We have found that gamma-irradiated polyformaldehyde does not exhibit the effect of the disappearance of the hyperfine structure of EPR spectrum as a function of the dose or the time passed since the end of irradiation, as was found earlier for a group of polymers having only C-C-C-C-atoms in the polymer chain. This difference in the change in the EPR of the polyformaldehyde (PFA) spectrum compared with the polymers with a -C-C-C-C- chain is explained by the impossibility of forming a conjugate double bond in the -C-O-C-O- chain in PFA.

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, , -, , , atom C-C-C-C-. ( ) C-C-C-C- , C-O-C-O- qu .

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The author thanks K. Vacek for many valuable discussions which helped this work.     

The distribution of ions and their valencies in manganese ferrites I. MnFe2O4+γ ferrites

A model for the distribution of cations in the spinel lattice of manganese ferrites MnFe₂O₄₊ was elaborated on the basis of the experimental studies of the basic magnetic quantities, electrical conductivity and magnetic relaxation of the given ferrites, taking into consideration their crystallographic properties. The conclusions following from this model are in good agreement with the experimental results obtained by us and by other authors both for stoichiometric manganese ferrite and for a ferrite where 0.

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I. MnFe₂O₄₊

, MnFe₂O₄₊ . , , , , , 0.

     

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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, . , . , , . , . .

     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

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