Magnetization coils without iron core for high field intensities

A new theory of rectangular coils without an iron core is described which amends the old one of Fabry and Bitter. It enables us to compute field intensities in coils having very small openings, which the old theory could not do.

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TheS=1/2 Heisenberg antiferromagnet on the triangular lattice: Exact results and spin-wave theory for finite cells

We study the ground state properties of theS=1/2 Heisenberg antiferromagnet (HAF) on the triangular lattice with nearest-neighbour (J) and next-nearest neighbour (J) couplings. Classically, this system is known to be ordered in a 120° Néel type state for values-<1/8 of the ratio of these couplings and in a collinear state for 1/8<<1. The order parameter and the helicity /gC of the 120° structure are obtained by numerical diagonalisation of finite periodic systems of up toN=30 sites and by applying the spin-wave (SW) approximation to the same finite systems. We find a surprisingly good agreement between the exact and the SW results in the entire region-<<1/8. It appears that the SW theory is still valid for the simple triangular HAF (=0) although the sublattice magnetisation is substantially reduced from its classical value by quantum fluctuations. Our numerical results for the order parameterM of the collinear order support the previous conjecture of a first order transition between the 120° and the collinear order at 1/8.     

О СУЩЕСТВОВАНИИ ОТРИ ЦАТЕЛЬНОГО ЯВЛЕНИЯ БАРКГАУЗЕНА

. . , . , . , . coo , 13. 5. 1954 . - .     

Double cascade transitions of gamma rays from radiative capture on Co59

Pairs of gamma quanta, giving a sum equal to the binding energy of the last neutron in a Co⁶⁰ isotope, were studied during radiation capture on a Co⁵⁹ nucleus. The energies of the gamma quanta giving such cascades were determined and an attempt was made to determine the relative intensities of the different cascades.

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- Co⁵⁹

Co⁵⁹ -, Co⁶⁰. -, , .

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In conclusion the authors thank J. Vávra for cooperation in the measurements.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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On the dynamics of excitations in disordered systems

A new, time-local (TL) reduced equation of motion for the probability distribution of excitations in a disordered system is developed. ToO(k²) the TL equation results in a Gaussian spatial probability distribution, i.e, P(r, t) = [(2)^1/2]^–dexp(-r²/2²), where = (t) is a correlation length, andr = ¦r¦. The corresponding distribution derived from the Hahn-Zwanzig (HZ) equation is more complicated and assumes the asymptotic (r ) form: P(r, s)(s ^d )^–1exp(–r/) · (r/)^(1-d)/2 where = (s),d is the space dimensionality, ands is the Laplace transform variable conjugate tot. The HZ distribution generalizes the scaling form suggested by Alexanderet al. ford= 1. In the Markov limit (t)t, (s)1/s, and the two distributions are identical (ordinary diffusion).     

The classical theory of nuclear spin interaction in a ferromagnet

The Hamiltonian of nuclear spin interaction in a ferromagnet is derived by the classical method, which introduces the precession of nuclear spin into the equation of motion for magnetization. From this it is shown that the interaction Hamiltonian also depends on the magnitude and sign of nuclear precession frequency _N and the damping constant of ferromagnetic resonance A. The calculation of these parameters makes the Suhl [1] quantum mechanical derivation of the Hamiltonian of nuclear spin interaction in a ferromagnet more accurate. The influence of these parameters on the relaxation timeT ₂ is also discussed and is applied to the case of cubic cobalt.

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. , _N . , [1] - . ₂ .

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In conclusion the author thanks Dr. L. Valenta for significant remarks and valuable advice on this work. He also thanks J. Kvasnica and Z. roubek for suggestive discussions.     

The spectrum of a quasiperiodic Schrödinger operator

The spectrum (H) of the tight binding Fibonacci Hamiltonian (H _mn= _m,n+1+ _m+1,n + _m,n v(n),v(n)= ((n–1)), 1/ is the golden number) is shown to coincide with the dynamical spectrum, the set on which an infinite subsequence of traces of transfer matrices is bounded. The point spectrum is absent for any , and (H) is a Cantor set for 4. Combining this with Casdagli's earlier result, one finds that the spectrum is singular continuous for 16.On leave from the Central Research Institute for Physics, Budapest, Hungary     

ДАЛЬНЕЙШИЕ ИССЛЕДОВ АНИЯ ФИЛЬТРА ДВОЙНОГ О ЛУЧЕПРЕЛОМЛЕНИЯ

, 4, (1954), 53. . .     

Some applications of the discrete fourier transform to problems of crystal lattice deformation II

The method elaborated in [1] is applied to the solution of some problems for a plane lattice and the linear chain. The method can be used to investigate deformations around crystal lattice defects.

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, [1] . .

     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Exact results for the asymmetric simple exclusion process with a blockage

We present new results for the current as a function of transmission rate in the one-dimensional totally asymmetric simple exclusion process (TASEP) with a blockage that lowers the jump rate at one site from one tor<1. Exact finitevolume results serve to bound the allowed values for the current in the infinite system. This proves the existence of a nonequilibrium phase transition, corresponding to an immiscibility gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state. A series expansion inr, derived from the finite systems, is proven to be asymptotic for all sufficiently large systems. Padé approximants based on this series, which make specific assumptions about the nature of the singularity atr=1, match numerical data for the infinite system to 1 part in 10⁴.     

МОДЕЛИРОВАНИЕ ЭЛЕКТ РОННО-ОПТИЧЕСКИХ СИС ТЕМ С ОСЕВОЙ СИММЕТРИЕЙ П РИ ПОМОЩИ СЕТИ СОПРОТИВЛЕНИЙ

The paper explains the theory of modelling electrostatic fields by a resistance network. The conditions, which the resistance network must satisfy, are derived and the question of modelling electrodes of different shapes is solved. The finished network and the results obtained on it when modelling a jet for a linear h-f accelerator of electrons are described. Particular attention is paid to the influence of a space charge, the modelling of which is an advantage of this method.

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Piron's axioms for quantum mechanics: A reply to Foulis and Randall

In their paper A note on Misunderstandings of Piron's Axioms for Quantum Mechanics, Foulis and Randall undertake a reply to our critique of Piron's question-proposition system (qp-s) which appeared in previous issues of this journal. In the present paper, we want briefly to refute the points of criticism raised by Foulis and Randall (FR). We argue that the misunderstandings are not ours, and we prove it.     

The Statistics of the Trajectory of a Certain Billiard in a Flat Two-Torus

We consider a billiard in the punctured torus obtained by removing a small disk of radius >0 from the flat torus ², with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. Let (), and respectively R(), denote the first exit time (length of the trajectory), and respectively the number of collisions with the side cushions when ² is being identified with [0,1)². We prove that the probability measures on [0, ) associated with the random variables and R are weakly convergent as 0⁺ and explicitly compute the densities of the limits. Research partially supported by ANSTI grant C6189/2000.     

Local energy flux and the refined similarity hypothesis

In this paper we demonstrate the locality of energy transport for incompressible Euler equations both in space and in scale. The key to the proof is the proper definition of a local subscale flux, _t (r), which is supposed to be a measure of energy transfer to length scales <l at the space point r. Kraichnan suggested that for such a quantity the refined similarity hypothesis will hold, which Kolmogorov originally assumed to hold instead for volume-averaged dissipation. We derive a local energy-balance relation for the large-scale motions which yields a natural definition of such a subscale flux. For this definition a precise form of the refined similarity hypothesis is rigorously proved as a big-O bound. The established estimate is _t (r)=O(l _3h-1) in terms of the local Hölder exponenth at the point r, which is also the estimate assumed in the Parisi-Frisch multifractal model. Our method not only establishes locality of energy transfer, but it also clarifies the physical reason that convection effects, which naively violate locality, do not contribute to the subscale flux. In fact, we show that, as a consequence of incompressibility, such effects enter into the local energy balance only as the divergence of a spatial current. Therefore, they describe motion of energy in space and cancel in the integration over volume. We also discuss theorems of Onsager, Eyink, and Constantinet al. on energy conservation for Euler dynamics, particularly to explain their relation with the Parisi-Frisch model. The Constantinet al. proof may be interpreted as giving a bound on the total flux, _t =d ^d r _t (r), of the form _t (r)=O(l _z3h-1), wherez ₃ is the third-order scaling exponent (or Besov index), in agreement with the multifractal model. Finally, we discuss how the local estimates are related to the results of Caffarelli-Kohn-Nirenberg on partial regularity for solutions of Navier-Stokes equations. They provide some heuristic support to a scenario proposed recently by Pumir and Siggia for singularities in the solutions of Navier-Stokes with small enough viscosity.     

Релятивистские волн овые уравнения ддя ча стиц со спином 3/2

3/2.     

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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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.