On the asymptotic behaviour of infinite gradient systems

We consider gradient systems of infinitely many particles in one-dimensional space interacting via a positive invariant pair potential with a hard core. The main assumption is that is strictly convex within the rangeR of (whereR is a fixed number ). Under some technical conditions we prove the following theorems: Let the initial distribution be given by a translation invariant point process onR ¹. Then there exists only one extreme equilibrium state with a given intensityI() satisfyingI()R ^–1, and all ergodic initial distributions with an intensityI()R ^–1 converge weakly ast to the extreme equilibrium state with the same intensity.     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

Dependence of characteristics of hysteresis loops on dislocation densities for low-alloy Cr-Mo steel

The microstructure of specimens of low-alloy Cr-Mo steel subjected to various heat treatments and various plastic deformations is studied by transmission electron microscopy. The observations indicate that the decisive factors which control the coercive forceH _c, the initial permeability _i and the Rayleigh constant are the density and the arrangement of dislocations. The precipitates have only a secondary effect. The observed linear dependencesH _c ^1/2, _i ^–1/2, ^–1 ( —dislocation density) are in full agreement with the theoretical predictions.Dedicated to Academician Vladimír Hajko on the occasion of his 65th birthday.     

Existence d'orbites quasi-periodiques dans les attracteurs de Birkhoff

For each number between the lower and the upper rotation number of the Birkhoff attractor of a dissipative monotone twist map, there is a periodic or quasi-periodic orbit with rotation number .     

The Becker-Döring cluster equations: Basic properties and asymptotic behaviour of solutions

Existence and uniqueness results are established for solutions to the Becker-Döring cluster equations. The density is shown to be a conserved quantity. Under hypotheses applying to a model of a quenched binary alloy the asymptotic behaviour of solutions with rapidly decaying initial data is determined. Denoting the set of equilibrium solutions byc ⁽⁾, 0 _s , the principal result is that if the initial density _{0 s} then the solution converges strongly toc ^(o), while if ₀ > _s the solution converges weak* toc ^(s). In the latter case the excess density ₀– _s corresponds to the formation of larger and larger clusters, i.e. condensation. The main tools for studying the asymptotic behaviour are the use of a Lyapunov function with desirable continuity properties, obtained from a known Lyapunov function by the addition of a special multiple of the density, and a maximum principle for solutions.     

A study of the ϱ0 meson polarization in π− p reaction at 5 GeV/c

Experimental data on ⁰ meson polarization in ^– p reaction at 5 GeV/c are presented. Change in ⁰ meson polarization for mesons produced at smallP ² and atP ² 0·3 or produced in backward direction in CMS is demonstrated. Natural explanation of these phenomena is one pion exchange mechanism and mechanism of quark-antiquark annihilation as observed for ⁰ meson production in¯pp reactions.The authors are indebted to Ján Piút, Richard Lednický, V. S. Rumiancev and N. K. Koutsidi for discussions and critical comments.     

The problem of recurrence for Lorentz processes

We prove that, for the planar Lorentz process with a periodic configuration of scatterers, the quasi-local CLT of the gaussian {log n} type holds for any >1. Consequently, for arbitrary >3/2, the probabilities that, at the moment of thenth reflection, this process lies in a square of size log n are asymptotically gaussian. This implies that these events occur for infinitely many values ofn (i.e. a weaker form of recurrence).Dedicated to Professor Ya. G. Sinai on the occasion of his 50th birthday     

A global analysis approach to the general relativistic fluid ball problem

That a self-gravitating perfect fluid in empty space has a spherical equilibrium configuration if it is static-i.e., nonrotating-is considered physically evident, but has not yet been rigorously derived from Einstein's field equations together with suitable asymptotic conditions. In this paper the global analysis techniques developed recently mainly by Fischer, Marsden, and Cantor are used to derive the result that if a family of static perfect fluid solutions with fixed total gravitational massm and fixed equation of state(p) satisfying 0 p and 0 d/dp < depends differentiably on a parameter and contains the spherically symmetric solution then it must consist of solutions diffeomorphic to the spherically symmetric one.Partially supported by the National Sciences and Engineering Research Council, grant No. A8059.     

More surprises in the general theory of lattice systems

I use Israel's methods to prove new theorems of ubiquitous pathology for classical and quantum lattice systems. The main result is the following: Let be any interaction and be any translation-invariant equilibrium state for (extremal or not). Then there exists a sequence { _k } of interactions converging to , having extremal (or even unique) translation-invariant equilibrium states _k , such that { _k } converges to . In certain situations the perturbations _k – can be chosen to lie in a cone of antiferromagnetic pair interactions. I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r ² interaction (Thouless effect).     

There is no equivalence between ϱ′(1250) and inelastic effects in e+e−→π+π−

The analysis of all existing pion form factor data by a model respecting the fundamental principles, including (770), (1250) and (1600) contributions without inelastic effects and depending just on the physical parameters is carried out. The comparison of the obtained results with a previous analysis performed by means of a model with only (770) and (1600) contributions and inelastic effects confirmes the conclusions of Novosibirsk experimental group that the (1250) contribution and inelastic effects in e⁺e^–+– are indistinguishable. However, theoretically predicted behaviours of the P-wave isovector phase shift and the inelasticity from both models and their comparison with existing data unambiguously favour the model with (770), (1600) and inelastic contributions.We are indebted to Dr. D. Krupa who called our attention to the concise (in comparison with our original diagrammatized presentation) and transparent algebraic proof, given in the text by (30)–(33). One of us (A. Z. D.) would like to thank Professor Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics in Trieste.     

Is the Free Electromagnetic Field a Consequence of Maxwell's Equations or a Postulate?

It is generally accepted that solutions of so called free Maxwell equations for = 0 (null charge density at every point of the whole space) describe a free electromagnetic field for which flux lines neither begin nor end in a charge). In order to avoid ambiguities and unacceptable approximation which have place in the conventional approach in respect to the free field concept, we explicitly consider three possible types of space regions: (i) isolated charge-free region, where a resultant electric field with the flux lines which either begin or end in a charge is zero in every point, for example, inside a hollow conductor of any shape or in a free-charge universe; (ii) non-isolated charge-free region, where this electric [see (i)] field is not zero in every point; and (iii) charge-neutral region, where point charges exist but their algebraic sum is zero. According to these definitions a strict mathematical interpretation of Maxwell's equations gives following conclusions: (1) In isolated charge-free regions electric free field cannot be unconditionally understood neither as a direct consequence of Maxwell's equations nor as a valid approximation: it may be introduced only as a postulate; nevertheless, this case is compatible is the existence of a time-independent background magnetic field. (2) In both charge-neutral and non-isolated charge-free regions, where the condition = function or = 0 respectively holds, Maxwell's equation for the total electric field have non-zero solutions, as in the conventional approach. However, these solution cannot be strictly identified with the electric free field. This analysis gives rise to the reconsideration of the free-electromagnetic field concept and leads to the simplest implications in respect to charge-neutral universe.     

Observation of the spin alignment of the ϱ0-meson produced in ¯pp interactions at 22.4 and 5.7 GeV/c

Studying the ⁰-meson production in ¯pp interactions at 22.4 GeV/c and in 4-prong anníhilation channels of ¯pp interactions at 5.7 GeV/c, we have observed an essential ⁰-meson spin alignment. The values of the ₀₀ element of the ⁰-meson spin density matrix (thez-axis is directed along the normal to the production plane) are equal to 0.08 ± 0.07 and 0.55 ± 0.03, respectively, i.e. the ⁰-meson spin lies preferably in the production plane. The absence of such an effect in pp interactions at 12 and 24 GeV/c and also the essentially larger ⁰ production cross section in ¯pp interactions at these energies make it possible to connect the observed ⁰-meson spin alignment with the annihilation processes. The character of the observed spin alignment is unexpected from the point of view of usual models, e.g. multiperipheral models. This effect could be described by the spontaneous polarization of quarks and antiquarks during the state preceding their recombination into mesons.Dedicated to Professor Ivan Úlehla on the occasion of his sixtieth birthday.The authors would like to express their gratitude to the CERN-Prague collaboration for permission to use their data on ¯pp interactions at 5.7 GeV/c. The authors are also indebted to A. M. Baldin, S. B. Gerasimov and H. I. Miettinen for valuable discussions, to the technicians and assistants at all laboratories for their work.     

Phase-modulus correlations for forward-scattering amplitudes without the Froissart bound

The role of the Froissart-Martin bound in obtaining rigorous phase-modulus asymptotic correlations for forward scattering is examined. A general form of the asymptotic upper bound on the total cross section covering the majority of cases occuring in weak interactions as well as in model field theories is assumed and its consequences for the asymptotic- correlations are drawn, being the ratio ReF/ImF for the crossing-even forward scattering amplitudeF. It is shown that the form of the correlations depends in an essential way on the absolute bound on assumed. Generalizations to the crossing-odd amplitude as well as to non-forward scattering are pointed out.On leave of absence from theAll Union Polytechnical Institute, Moscow, Pavel Korchagin Street, 22, USSR.Discussions with V.Alda, P.Kolá and R.ály are gratefully acknowledged.     

The van der Waals limit for classical systems. I. A variational principle

We consider the thermodynamic pressurep(, ) of a classical system of particles with the two-body interaction potentialq(r)+ ^v K(r), where is the number of space dimensions, is a positive parameter, and is the chemical potential. The temperature is not shown in the notation. We prove rigorously, for hard-core potentialsq(r) and for a very general class of functionsK(s), that the limit 0 of the pressurep(, ) exists and is given by where the limit and the supremum can be interchanged. Here is a certain class of nonnegative, Riemann integrable functions,D is a cube of volume |D|, anda ⁰() is the free energy density of a system withK=0 and density . A similar result is proved for the free energy.     

Symmetry and equilibrium states

Within the general framework ofC*-algebra approach to mathematical foundation of statistical mechanics, we prove a theorem which gives a natural explanation for the appearance of the chemical potential (as a thermodynamical parameter labelling equilibrium states) in the presence of a symmetry (under gauge transformations of the first kind). As a symmetry, we consider a compact abelian groupG acting as *-automorphisms of aC*-algebra (quasi-local field algebra) and commuting (elementwise) with the time translation automorphisms _t of . Under a technical assumption which is satisfied by examples of physical interest, we prove that the set of all extremal _t -KMS states (pure phases) ofG-fixed-point subalgebra (quasi-local observable algebra) of satisfying a certain faithfulness condition is in one-to-one correspondence with the set of all extremalG-invariant _t · _t -KMS states ^– of with varying over one-parameter subgroups ofG (the specification of being the specification of the chemical potential), where the correspondence is that the restriction of ^– to is .     

Humidity dependence of the atmospheric absorption coefficient in the transparency windows centered at 0.88 and 0.73 MM

A dependence is investigated of the absorption coefficient of atmospheric water vapor on absolute air humidity in the spectral intervals =11.1+12.0 and 13.2+14.3 cm^–1 by a radiospectrometer with a multipass vacuum cell. Measurements are carried out in the humidity range 3+23 g/m³ at 140 m length of the optical path.Parts of the absorption coefficient linearly and quadratically depending on have been separately defined from the experimental data. In particular, it has been obtained for the centers of transparency windows: (=0.73mm) [dB/km]=1.68 (±0.08) +0.019 (±0.004) ², (=0.88 mm) [dB/km]=0.83 (±0.06) +0.013 (±0.002) ². The given values correspond to the temperature of 306 K and the pressure of dry air of 735 Torr.A comparison is made between our results and theoretical calculations and data of other measurements.     

Electrical resistivity of stretched and twisted 99.70% pure silver

Samples of anneald pure silver (99·70 wt.%) have been subjected to tensile and/or twisting deformations at room temperature. It has been found that the electrical resistivity () of the stretched silver samples decreases monotonically with the increase of tensile stress. Negative values are obtained for the stress coefficient of resistivity (SCR) both in the elastic and plastic regions, contrary to the twisted samples where positive values are obtained. The resistivity () increases almost linearly with the number of twist turns in the case of unidirectional mode of twist, whereas in the case of the bidirectional one, () increases non-linearly with the number of reversed twist turns. In such case, () obeys a function of exponential type. Moreover, the accompanying axial strain for the bidirectional mode of twist is found to be larger than that for the unidirectional one by approximately one order of magnitude.The authors would like to express their deep thanks to Prof. Dr. H. H. Hassan, Physics Department, Faculty of Science, Cairo Univ., for his critical comments and suggestions.     

Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals

We establish an analogue of Weyl's classical theorem for the asymptotics of eigenvalues of Laplacians on a finitely ramified (i.e., p.c.f.) self-similar fractalK, such as, for example, the Sierpinski gasket. We consider both Dirichlet and Neumann boundary conditions, as well as Laplacians associated with Bernoulli-type (multifractal) measures onK. From a physical point of view, we study the density of states for diffusions or for wave propagation in fractal media. More precisely, let (x) be the number of eigenvalues less thanx. Then we show that (x) is of the order ofx ^d S/2 asx+, where the spectral exponentd _S is computed in terms of the geometric as well as analytic structures ofK. Further, we give an effective condition that guarantees the existence of the limit ofx ^–d S/2(x) asx+; this condition is, in some sense, generic. In addition, we define in terms of the above spectral exponents and calculate explicitly the spectral dimension ofK.The research of Michel L. Lapidus was partially supported by the National Science Foundation under Grant DMS-8904389 (transferred to the University of California as grant DMS-9196085) and Grant DMS-9207098, as well as by Yale University     

On shear-free motion of charged perfect fluid obeying an equation of state in general relativity

In this note, a spherically symmetric charged perfect fluid executing shear-free motion has been investigated under the assumption of validity of an equation of state. Mashoon and Partovi [4] have studied this problem and have established several theorems giving the properties of such fluid distributions. We find that there is one more solution which is new. It is characterized by three parameters, one of which is the charge parameter. In the limit of vanishing charge the metric goes over to the Wyman metric [2]. It has been shown that the solution does not match with the Reissner-Nordström solution at a boundary and hence it is not suitable to represent a bounded system. We have also discussed the possibility of this solution representing the physical universe. We have found that the solution after a proper choice of constants may satisfy the physical requirements3p,d/dp 1 but will violate the condition /1 wherep, , and represent, respectively, the pressure, matter density, and charge density of the fluid. Therefore, the charged Wyman solution is unsuitable to represent the physical universe. Thus we conclude that for a charged perfect fluid distribution executing shear-free motion the field equations do not admit any physically meaningful solution if we assume the validity of an equation of state.This paper was partially presented at the 12th meeting of Indian Association for General Relativity and Gravitation and the symposium on Applications of General Relativity to Astrophysics and Cosmology held at Puna, India, November 9–12, 1983.     

MHD laminar thin-film flow along a vertcal wall

An accelerating magnetohydrodynamic laminar flow of an electrically conducting fluid under the influence of gravity and in presence of transverse magnetic field is investigated in the paper. Using a cubic polynomial for the velocity profile inside the boundary layer, the momentum integral equation is solved numerically by Runge-Kutta method to determine the boundary layer thickness and the corresponding film thickness is then calculated for the entrance region. The effect of magnetic field on these solutions is shown in graphical form.List of symbols u, v local velocity components - p pressure - density - kinematic viscosity - viscosity= - electrical conductivity - g acceleration due to gravity - U _s (x) inviscid core velocity - h(x) film thicknes - (x) boundary layer thickness - M Hartmann number - B ₀ external magnetic field The authors remain thankful to the referee for some helpful criticisms.