Continuum and discretum—Unified field theory and elementary constants

Unitary field theories and SUPER-GUT theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian ^(1–3) ) structured vacuum according the quantum theory of unitary fields (Dirac, ^(4,5) and Heisenberg ^(6–8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against all transformations and which depend on nothings (Planck ^(9–11) ). A satisfactory unitary theory has to involve these constants like the mathematical numbers. Today, Planck's conception of the three elementary constants , c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also.According to Popper's theory ^(12–16) of induction, such unitary theories are universal explaining theories. The fundamental constants involve the complementarity between the universal statements in unitary theory and the basic statements in the language of classical observables.     

Nonlinear optimization simplified by hypersurface deformation

A general strategy is advanced for simplifying nonlinear optimization problems, the ant-lion method. This approach exploits shape modifications of the cost-function hypersurface which distend basins surrounding low-lying minima (including global minima). By intertwining hypersurface deformations with steepest-descent displacements, the search is concentrated on a small relevant subset of all minima. Specific calculations demonstrating the value of this method are reported for the partitioning of two classes of irregular but nonrandom graphs, the prime-factor graphs and the pi graphs. We also indicate how this approach can be applied to the traveling salesman problem and to design layout optimization, and that it may be useful in combination with simulated annealing strategies.     

The complex conductivity of the plasma of a d-c glow discharge in Ne

In paper [1] Fang derived an expression for the complex conductivity of plasma assuming that the distribution function of the electrons is Maxwellian and the collision frequency is directly proportional to their velocity. Since the assumptions are approximately satisfied in the positive column of a d-c glow discharge in Ne, the applicability of Fang's relation is investigated for this case.

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[1] , . , .

     

A cell dynamical system model of chemical turbulence

A cellular-automaton-like caricature of chemical turbulence on an infinite one-dimensional lattice is studied. The model exhibits apparently turbulent space-time patterns. To make this statement precise, the following problems or points are discussed: (1) The infinite-system-size limit of such cell-dynamical systems and its observability is defined. (2) It is proved that the invariant state in the large-system-size limit of the turbulent phase exhibits spatial patterns governed by a Gibbs random field. (3) Potential characteristics of turbulent space-time patterns are critically surveyed and a working definition of (weak) turbulence is proposed. (4) It is proved that the invariant state of the turbulent phase is actually (weak) turbulent. Furthermore, we conjecture that the turbulent phase of our model is an example of a K system that is not Bernoulli.     

К КИНЕТИКЕ ФОТОПРОВОДИМОСТИ СЕ ЛЕНА

- 65 –150 °. 0,2 . - , .     

Renormalization Group study of a critical lattice model

The Renormalization Group is used to study the correlation functions of a nonlocal hierarchical model mimicking the ()⁴ model, dipole gas and the like. It is shown that the infrared behaviour of the correlations is that of the massless gaussian 1/2c()()².     

On the positivity of correlations in nonequilibrium spin systems

We consider Ising spin systems, equivalently lattice gases evolving under discrete- or continuous-time Markov processes, i.e., stochastic cellular automata or interacting particle systems. We show that for certain spin-flip probabilities or rates and suitable initial states the expectation values of products of spin variables taken at equal or different times are nonnegative; they satisfy the same inequalities as the equal-time correlations of ferromagnetic systems in equilibrium (first Griffiths inequality). Extensions of FKG inequalities to time-displaced correlations are also discussed.     

ВОЗМОЖНОСТЬ ИССЛЕДО ВАНИЯ ХОДА ИСКАЖЕНИЙ РЕШЕТКИ В КРИСТАЛЛИКАХ ПРИ ПО МОЩИ РЕНТГЕНОВСКИХ Л УЧЕЙ РАЗНОЙ ДЛИНЫ ВОЛНЫ

, . , (K , , ), - , -. -, 25 a 1956.     

БЕТАТРОННЫЕ КОЛЕБАН ИЯ В УСКОРИТЕЛЕ С ОБЩИМ ПО ЛЕМ II

, , . , I. . . , .

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Betatron oscillations in an accelerator with a general field. II

In the second part of the theory of an accelerator with a generalized field the author solves the dynamics of particles in a stationary approximation (without acceleration). The trajectories of the particles in the neigbourhood of the equilibrium orbit are related to it as betatron oscillations. An analysis of betatron oscillations includes the region of stability determined by means of Routh-Hurwitz criterion, damping, resonance effects and field perturbations. A general matrix method is presented permiting the inclusion of all the focusing structures used in accelerators.

     

The Hamiltonian systems on the Poisson structure of the quasi-classical limit of GL q (∞)

We consider the Hamiltonian systems on the Poisson structure of GL() which is introduced from the quantum group GL _q () by the so-called quasi-classical limit of GL _q (). Furthermore, we show that the Toda lattice hierarchy is a Hamiltonian system of this structure.     

Cooling-rate dependence of the residual energy of a one-dimensional configurational glass model

For a one-dimensional configurational glass model we have performed molecular dynamical calculations. The Newtonian equation of motion was solved numerically including a damping term. The residual energye _res() as a function of the damping constant , exhibits a power law behavioure _res(),0.061; in an intermediate range of . This behaviour can be explained as the freezing of a certain type of two level systems with an excitation energy and a barrier heightB. The exponent is approximately equal to /B. This relationship is justified analytically.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

The influence of compression on the absorption of AgBr single crystals

The influence of compression on the edge of self absorption of AgBr single crystals was studied. The measurements were performed at a temperature of –180°C. The shift of the edge of self absorption was studied both in the field of elastic and plastic deformations. The shift of the absorption edge towards the UV end of the spectrum was determined in the field of elastic deformations and towards the i.r. end in the field of plastic deformations. After the ending of the deformation and after unloading the crystal the return of the absorption edge towards the original position was observed.

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AgBr

AgBr. –180°C. , . , — . .

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The author thanks Prof. Dr. L. Zachoval and K. K. Vacek C. Sc. for their interest in this work and for many comments given during the work.     

Buoyancy forces in magnetic fluids

The ponderomotive force on a macroscopic body in a magnetic fluid is calculated by a hydrodynamic approach. The resulting equations are generally valid, neither small susceptibilities nor stationarity are assumed. The simple and widely-used formulaV(M-M ^bg )H is recoverd in linear order of ; magnetostrictive effects are shown to contribute in the order ³. The expressions derived here are definite and unambiguous, they do not depend on whether one starts from a theory in terms ofH, or in terms ofB: the correct evaluation of the contribution dV[-p] resolves the apparent contradiction between the force density expressions ₀ MH, orMB.     

АНТИПРОТОННАЯ СХЕМА β-РАСПАДА

, .     

Remarks on the modular operator and local observables

In this paper we give a characterization of the modular group of a von Neumann algebra , with a cyclic and separating vector, which provides at the same time a necessary and sufficient condition so that two von Neumann algebras ₁ and ₂, such that ₁₂, are the mutual commutants, i.e. ₁=₂.An application is made to the duality property in Quantum Field Theory, and we give a sufficient condition for PCT invariance in a theory of local observables.Partially supported by C.N.R.     

Zum Problem der Exoelektronenemission

Zusammenfassung Es wurden einige neue Versuche über die Exöelektronenemission aus Alkalihalogeniden durchgeführt und auf Grund derer Ergebnisse und aller bis jetzt bekannten experimentallen Kenntnisse die Hauptfragen der Exoelektronenemission diskutiert.

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Ich habe die angenehme Pflicht meinen Mitarbeitern Milada Kotíková und Václav Stelka zu danken. Herrn G. Sc. Stanislav Koc danke ich für das sorgfältige Durchlesen des Textes und Herrn Dr. A. Bohun für das Borgen seiner im Drucke sich befindenden Arbeiten.     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

High energy electrons in the earth's radiation belts

Special experiments performed aboard the space stations Salyut-6-SoyuzProgress, Salyut-7-Soyuz T-13-Kosmos-1669, and the artificial earth satellite IK Bolgariya-1300 discovered, significant electron and positron fluxes with energies of more than decades of MeV in the earth's radiation belts. Spatial and angular characteristics of these fluxes have been studied. Study of the charge ratio of the electron-positron component has shown that it is electron-based. This indicates that in outer space near the earth some efficient mechanism capable of accelerating electrons to energies of more than decades of MeV exists.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 38–43, September, 1986.The authors consider it their pleasant duty to express gratitude to V. M. Gracev, S. V. Koldashov, A. V. Popov, and S. E. Ulin for their preparation of the equipment and conduct of the experiments.     

On the approximate formulation of the orthogonalized plane-wave method

An approximate method, analogical to the orthogonalized plane-wave method, is used to calculate the energy at a number of points in the Brillouin zone of lithium and the results are compared with the energy values calculated by the OPW method. Some of the general properties of the matrix elements of the repulsive potential are discussed and correlation with other methods carried out.

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In conclusion the author thanks Dr. Glasser for communicating the numerical values of the wave function and K. Trnková for carrying out the numerical calculations.     

Two repulsive lines on disordered lattices

We investigate the ground-state properties of two lines with on-site repulsion on disordered Cayley tree and (Berker) hierarchical lattices, in connection with the question of multiple pure states for the corresponding one-line problem. Exact recursion relations for the distribution of ground-state energies and of the overlaps are derived. Based on a numerical study of the recursion relations, we establish that the total interaction energy on average is asymptotically proportional to the width of the ground-state energy fluctuation of a single line for both weak and strong (i.e., hard-core) repulsion. When the lengtht of the lines is finite, there is a finite probability of ordert ^–a for (nearly) degenerate, nonoverlapping one-line ground-state configurations, in which case the interaction energy vanishes. We show thata= (t ) on hierarchical lattices. Monte Carlo transfer matrix calculation on a (1+1)-dimensional model yields the same scaling for the interaction energy but ana different from =1/3. Finitelength scalings of the distribution of the interaction energy and of the overlap are also discussed.