THe mechanism of the amplification of moving striations in a d-c discharge

To determine the mechanism of the amplification of moving striations one starts out from the processes which [3] showed to be decisive for the production of stratification of the plasma of a positive column. An analysis of the influence of other processes shows that the main processes leading to the decay of space charges and thus to a smoothing out of the inhomogeneities and thereby to the attenuation of the periodic structure, cannot by overcome by ionization phenomena caused by changes in the concentration of electrons but only partially compensated.It was found that the process which can lead to the predomination of the processes of amplification over the attenuation is the process of the spatial shift of the temperature deflections of the electrons with respect to the additional electric field, which is expressed in a simplified way by Eq. (12).By solving the extremely simplified basic equations it is proved that under favourable conditions this displacement can lead to both a time and a spatial amplification of the striations. Such a possibility is also verified quantitatively by substituting numerical values into the formulae obtained.

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, [3] . , , , , , ., , (12). , , . .

     

The lattice spacings of equilibrium solid solutions of silver in aluminium

This paper describes the measured dependence of the lattice spacings of equilibrium Al-Ag solid solutions on temperature and composition. The form of the lattice spacing composition curve is found to differ considerably from that for the supersaturated Al-Ag solid solutions. The differences between the spacings of equilibrium and quenched Al-Ag solid solutions plotted against the electron concentration yield a curve similar to that constructed from the analogous measurements on Al-Zn given by Ellwood. The differences can be attributed to the influence of changes accompanying the increased solute clustering introduced by quenching the solid solutions into the supersaturated state.

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Al-Ag . , Al-Ag . Al-Ag, (. . , ), Al-Zn, , . , .

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The author wishes to express her thanks to Ing. J. Lagek for his care in carrying out the chemical analysis of the aluminium-silver alloys. The careful density measurements of these alloys made by J. Bednfi [are greatly appreciated.     

Some results for the exponential interaction in two or more dimensions

We show that for the regularized exponential interaction :e : ind space-time dimensions the Schwinger functions converge to the Schwinger functions for the free field ifd>2 for all or ifd=2 for all such that ||>₀.Partially sponsored by the I.H.E.S. through the Stiftung Volkswagenwerk     

On the geometrization of electrodynamics

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion of spacetime. This conjecture is made feasible by the natural separation of the connection ^v into gravitational and electromagnetic parts ^v and ^v , respectively, related to the metric and to the torsion. When ^v is neglected in front of ^v , the affine geodesics are shown to become the equations of motion of charged particles with Lorentz force, for an appropriate choice of . Since ^v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when ^{v v} ).In addition to the factor q/m, the velocity of the test particle appears in . This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor.     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

Convergence of Nelson fiffusions

Let _t, _t ⁿ ,n1, be solutions of Schrödinger equations with potentials form-bounded by –1/2 and initial data inH ¹( ^d ). LetP, P ⁿ ,n1, be the probability measures on the path space =C(₊, ^d ) given by the corresponding Nelson diffusions. We show that if { _t ⁿ } _n1 converges to _t inH ¹( ^d ), uniformly int over compact intervals, then converges to in total variation t0. Moreover, if the potentials are in the Kato classK _d , we show that the above result follows fromH ¹-convergence of initial data, andK _d -convergence of potentials.     

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.     

Intersection properties of simple random walks: A renormalization group approach

We study estimates for the intersection probability,g(m), of two simple random walks on lattices of dimensiond=4, 4– as a problem in Euclidean field theory. We rigorously establish a renormalization group flow equation forg(m) and bounds on the -function which show that, ind=4,g(m) tends to zero logarithmically as the killing rate (mass)m tends to zero, and that the fixed point,g*, ind=4– is bounded by const' g*const. Our methods also yield estimates on the intersection probability of three random walks ind=3, 3–. For =0, these results were first obtained by Lawler [1].     

Collision Integrals for Attractive Potentials

Motivated by previous discussions of particle interactions under the Manev potential U(r)=–/r–/r ², we construct the collision integrals for attractive potentials U(r) satisfying the condition U(r) r ²– as r0 with 0. For =0, we obtain a Boltzmann-type integral with a collision law allowing spiral interactions and nonunique correspondence between impact parameter and scattering angle. For >0, an additional Smoluchowski-type coagulation integral arises. All these integrals are derived and possible applications are discussed.     

Semi-infinite Potts model and percolation at surfaces

The effects of surfaces on percolation are investigated near the bulk percolation threshold ind=6– dimensions. Using field-theoretic methods, this is done within the framework of a semi-infinite continuousq-state Potts model withq1. Renormalization-group equations are obtained which imply that the usual scaling laws for surface and bulk exponents are valid to all orders in , and the surface exponents at the ordinary and special transition are computed to order . Our result for ₁ ^ord is in conformity with the one by Carton.     

Weinberg Angle and Pion Beta Decay in the Spinor Strong Interaction Theory

From an isospin SU(2) × hypercharge U(1)gauge-invariant meson action for K⁺,^{+ +}, a prediction ofthe Cabbibo angle was obtained earlier. Using anotherresult of the spinor strong interaction theory that the s quark is only a littleheavier than the d quark, the above action can beextended to a weakly broken SU(3) one. The Weinbergangle is found to be 30° in the limit of this SU(3)symmetry. In the approximation and context entailing thislimit, the Weinberg angle can be removed from the listof undetermined fundamental parameters in electroweaktheory. The spinor strong interaction Lagrangian used above and applied to the decay⁺ e⁺ is shown tohold for ^{+ 0}e⁺ as well, renderingthe conserved vector current hypothesis hithertorequired to account for the latter decaysuperfluous.     

The Schrödinger equation and canonical perturbation theory

LetT ₀(, )+V be the Schrödinger operator corresponding to the classical HamiltonianH ₀()+V, whereH ₀() is thed-dimensional harmonic oscillator with non-resonant frequencies =(₁, ... , _d ) and the potentialV(q ₁, ... ,q _d) is an entire function of order (d+1)^–1. We prove that the algorithm of classical, canonical perturbation theory can be applied to the Schrödinger equation in the Bargmann representation. As a consequence, each term of the Rayleigh-Schrödinger series near any eigenvalue ofT ₀(, ) admits a convergent expansion in powers of of initial point the corresponding term of the classical Birkhoff expansion. Moreover ifV is an even polynomial, the above result and the KAM theorem show that all eigenvalues _n (, ) ofT ₀+V such thatn coincides with a KAM torus are given, up to order , by a quantization formula which reduces to the Bohr-Sommerfeld one up to first order terms in .     

Static and dynamic properties of XY systems with extended defects in cubic anisotropic crystallines

Static and dynamic critical behavior ofXY systems in cubic anisotropic crystallines, with extended defects (or quenched nonmagnetic impurities) strongly correlated along _d -dimensional space and randomly distributed ind – _d dimensions, were studied. These extended defects make the systems coordinate anisotropic, resulting in unique critical behavior due to competition between the cubic anisotropy and the coordinate anisotropy. The systems were analyzed by an ^1/2 (4 – d) type of expansion with double expansion parameters based on a renormalization-group (RG) approach. Critical exponents were calculated near the second-order phase transition point and the behavior of the first-order transition was evaluated near the tricritical point.     

Critical exponents for the self-avoiding random walk in three dimensions

We compute by direct Monte Carlo simulation the main critical exponents, , ₄, andv and the effective coordination number for the self-avoiding random walk in three dimensions on a cubic lattice. We find both hyperscaling relationsdv=2– anddv– 2 ₄+=0 satisfied ind = 3.     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

Interface formation and a structural phase transition for the spherical model of ferromagnetism

A detailed analysis is reported examining the local magnetic susceptibility (r), in relation to the correlation functionG(R) and correlation length , of a spherical model ferromagnet confined to geometry =L ^{d –d} × ^d ( ^d 2,d>2) under a continuous set oftwisted boundary conditions. The twist parameter in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For _j 0, jd-d, no seams are present except at infinity, whereas if _j = 1/2, impurity saturation occurs. For 0 < _j < 1/2 the physical domain _phys =D ^{d –d} × ^d (D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T ₀). Below that temperature (T>T ₀), seams are frozen at the same position (DL/2,d-d'=1), revealing a smoothly varying largescale structural phase transition.     

On the finite-size scalling equation for the spherical model

The mean spherical model with an arbitrary interaction potential, the Fourier transform of which has a long-wavelength exponent , 0<2, is considered under periodic boundary conditions and fully finite geometry ind dimensions, when <d<2. A new form of the finite-size scaling equation for the spherical field in the critical region is derived, which relates the temperature shift to Madelung-type lattice constants. The method of derivation makes use of the Poisson summation formula and a Laplace transformation of the momentumspace correlation function.On leave of absence from Institute of Mechanics and Biomechanics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria.     

Multicomponent field theories and classical rotators

It is shown that aD-component Euclidean quantum field, =(¹,...,^D), with ||⁴+|²| interaction, can be obtained as a limit of (ferromagnetic) classical rotator models; this extends a result of Simon and Griffiths from the caseD=1. For these Euclidean field models, it is then shown that a Lee-Yang theorem applies forD=2 or 3 and that Griffiths' second inequality is valid forD=2; a complete proof is included of a Lee-Yang theorem for plane rotator and classical Heisenberg models. As an application of Griffiths' second inequality forD=2, an interesting relation between the parallel and transverse two-point correlations is obtained.Research supported in part by the National Science Foundation under grant NSF MPS 74-04870.     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.