Cooperative plasticity due to the motion of disorientation and phase separation boundaries

Conclusions As has already been noted above, the theory of planar defects organically includes the mechanics of twinning, grain boundaries, Somigliani dislocations, translational dislocations, disclination, and dispiration. The fundamental propositions of the theory and methods of giving the tensor T are listed in Table 4. The mathematical formalism remains the same throughout, and it is applicable to both discrete objects (it is then necessary to conserve the -function apparatus), and to a continuous (then appropriate smoothing is needed, which usually reduces to replacement of the multiplication procedure by the normal n or by the direction , to operations of finding the gradient, divergence, and curl of regular expressions, and discarding the -functional), In particular, the problem of thermoelasticity is formulated successfully by such a method in the terminology of the present theory.In a broad sence of the word, the development of the theory should be perceived as an extension of the concept of imperfection to defects of sufficiently arbitrary origin. A completely developed formalism was worked out earlier for just linear defects; in the symbols used here, for the case b=b₀ + X (r – r₀) for constant b₀,, and r₀, and without taking account of processes on the boundary S if the linear defect contained such a feature. Let us emphasize that to describe three-dimensional defects occurring because of homogeneous distortion = (V)., it is sufficient to use the apparatus of just the theory of planar defects since the fundamental phenomena are associated with precisely the presence of boundaries and in a formal plane, with the spatial derivatives of , they are always expressed in terms of the functional (S), while in the case of finite surface gradients in terms of (L). The time derivatives of the distortion T, i.e., is written down in the developed representations in terms of the form with all the resulting consequences.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 83–102, June, 1981.     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.     

On the stability of spin waves at finite temperatures

The temperature dependent exchange stiffnessD, defined for long wavelength spin waves by=Dq ², is calculated for very weak itinerant ferromagnets. It is found that for a general single band of d-electrons,D reduces to a very simple form givingD(T)=D(0)/ ₀ in the limit ₀0. The stability condition for spin waves at finite temperatures is thenD(0) > 0 and/ ₀ > 0, where is the relative occupation ± spin sub-bands and ₀ its value at 0°K.The authors are grateful to E. P. Wohlfarth for helpful discussions.     

Logically independent von Neumann lattices

Three definitions of logical independence of two von Neumann latticesP₁,P₂ of two sub-von Neumann algebras ₁, ₂ of a von Neumann algebra are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called logical independence is the strongest:A B 0 for any 0 A P₁, 0 B P₂. Propositions relating logical independence ofP₁,P₂ toC ^*-independence,W ^* independence, and strict locality of ₁, ₂ are presented.     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

Spectral properties of a periodically kicked quantum Hamiltonian

We study the spectral properties of the Floquet operator for the periodically kicked HamiltonianH(t) =H ₀+ ₊ ^– (t–nT),H ₀ being self-adjoint and pure point. We show that the Floquet operator is pure point for almost every , if is cyclic forH ₀ and has absolutely convergent expansion in the basis of eigenstates ofH ₀. When this last condition is not satisfied, the Floquet operator can have a continuous spectrum, as we show by an example.     

Der Einfluss von Fremdstoffgehalt auf einige Kenngrössen der Verfestigungskurven von Zinkeinkristallen

Zusammenfassung Es wurde der Einfluß von Fremdstoffgehalt: auf die kritische Schubspannung ₀, den Verfestigungskoeffizient _A im BereichA der Verfestigungskurve; die Längea _A des BereichsA, und die Schubspannung _A am Ende des BereichsA, von Zinkeinkristallen untersucht. Es konnte gezeigt werden, daß der Einfluß von Fremdstoffgehalt auf den Wert der kritischen Schubspannung vorwiegend indirekter Natur ist. Die Abnahme des Verfestigungskoeffizienten mit zunehmendem Fremdstoffgehalt kann an Hand erhöhter Leerstellenkonzentration erklärt werden. Das Auftreten des BereichsB wird im Zusammenhang mit der Entstehung von Frankschen Halbversetzungen erwogen.

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₀, _A , _A . , . . .

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Herrn P. Sirotek bin ich für den Umbau und die Instandsetzung des Polanyiaparates zu Dank verpflichtet. Mein Dank gehört ferner Herrn J. Voráek, für die präzise Durchführung der polarographischen Analysen, Frau I. Ejemová und M. Postránecká, für die Verrichtung der Orientierungsbestimmungen und Rechenarbeiten. Gleichzeitig möchte ich Frl. Svobodová meinen herzlichen Dank aussprechen — sie hat, auf Anregung des Lehrstuhls für mathematische Statistik an der mathematisch-physikalischen Fakultät der Karlsuniversität in Prag, mit großem Verständnis die statistische Auswertung der Meßergebnisse durchgeführt. Herrn Dr. F. Kroupa und Ing. B. esták bin ich für das Durchlesen des Manuskripts sowie wertvolle Hinweise zu Dank verpflichtet. Mein besonderer Dank für zahlreiche fruchtbare Diskussionen und Anregungen gilt Herrn P. Kratochvíl. Herrn Prof. Dr. A. Seeger danke ich ganz besonders für Kritik des Manuskripts und wertvolle Ratschläge.     

Kinetics of phase separation in ramified polymer blends of arbitrary topology

We present here a theoretical study of kinetics of phase separation within a mixture made of two chemically incompatible ramified polymers. For simplicity, we assume that they have the same topology. We are interested in the variation of the relaxation rate, _q, versus the wave number q, in the vicinity of the spinodal temperature. The kinetics is governed by local (Rouse) and reptation motions (faster and slower modes). For qR_G 1 (R_G being the gyration radius), kinetics is entirely controlled by local motions where each chain moves inside its own tube, and we show that the corresponding characteristic frequency, ^{-1}_q, scales as ^{-1}_{q G}q⁶, where _G is a known topological factor. For qR_G 1, however, kinetics is rather dominated by long-wavelength (reptation) motions where unlike ramified polymers creep inside a long tube. For this case, we find that ^{-1}_q ( 0 )q² (_c - ), where ( 0 ) is another known topological factor that represents the total mobility of free monomers belonging to connected chains and reticulation points, and _c accounts for the critical value of the segregation parameter. Finally, the derived relaxation rate must be compared to that relative to a linear polymer mixture.     

R andRτ ratios at the five-loop level of perturbative QCD

We study perturbative QCD at the five-loop level. In particular we considerR = _tot(e ⁺ e ^– hadrons)/(e ⁺ e ^{– + –}) andR = ( v+hadrons)/( ev). We use our method to estimate the five-loop coefficients. As a result, we obtain _s (M _z ) = 0.1186(11) and _s (34 GeV) = 0.1396(16), which are accurate at the 1% level. We also findR = 3.8350(18), which is consistent withR and is accurate to 0.05%.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

Absence of asymptotic-time symmetry breaking in zero-bias spin-boson model with partial relaxation

The symmetric spin-boson model without external field is treated for any type of coupling to the boson bath and any initial bath density matrix. With initially fully aligned spin (_z (0)= =1), the proof is given that a partial relaxation (_z (+) t1<) implies that there is no asymptotic-time (up-and-down) symmetry breaking (i.e. that _z (+)=0). For the problem of a particle (interacting with free bosons) in a symmetric double well without spatial symmetry breaking before the infinite time limit, this means that att + the particle distribution becomes symmetric (irrespective of the full initial asymmetry) unless the particle fully remains (att + ) in Ihe starting well.     

The ground state energy of a Bose gas with Coulomb interaction II

LetH _N be the quantum mechanical Hamiltonian for a neutral system of 2_N charged particles, each of unit charge. The HamiltonianH _N is assumed to act on wave functions inL ²(^6N ) which satisfy Bose statistics. It is shown that if the kinetic energy of is sufficiently small, then |H _N |–CN ^7/5 for some universal constantC.Research supported by U.S. National Science Foundation Grant DMS 8600748     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

ПРИМЕНЕНИЕ ПАРАМАГН ИТНОГО РЕЗОНАНСА ДЛЯ ИССЛЕДОВАНИЯ РЕАКЦИЙ СВОБОДНЫХ РА ДИКАЛОВ

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The use of paramagnetic resonance in studying the reactions of free radicals

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, .     

Two-body correlations and pair formation in the two-dimensional Coulomb gas

We investigate pair correlations in the two-dimensional Coulomb gas made up of two species of point ions carrying electric charges Z₁ e(>0) and Z₂ e(<0), and interaction by the logarithmic Coulomb potential. This system is known to be classically stable for couplings=e ²/k _BTc=2/¦Z₁Z₂¦ (whereT is the temperature). Correlations between equally charged ions are shown to be greatly modified at short distances, in the range _c/2<< _c, due to gradual ion condensation. The usual integral equations for the pair correlation functions admit no solutions in that range. Preliminary Monte Carlo simulations for the symmetric case (Z₁=–Z₂) reveal a striking chemical equilibrium between tightly bound ion pairs and free ions, which is reasonably well described by a simple Bjerrum model.     

A solvable model exhibiting a glass-like transition

A nonlinear equation of motion of an overdamped oscillator exhibiting a glass-like transition at a critical coupling constant _c is presented and solved exactly. Below _c , in the fluid phase, the oscillator coordinatex(t) decays to zero, while above _c , in the amorphous phase, it decays to a nonzero infinite time limit. Near _c the motion is slowed down by a nonlinear feedback mechanism andx(t) decays exponentially to its long time limit with a relaxation time diverging as (1 – / _c )^–3/2 and (/ _c –1)^–1 for < _c and > _c respectively. At _c x(t) exhibits a power law decay proportional tot ^– with exponent -1/2.     

Asymptotic behaviour of spin-momentum distribution observables for fermion fields with cut-off self-coupling

In a previous paper asymptotic creation and annhilation operatorsa _± ^# have been constructed by the Kato-Mugibayashi method from the creation and annihilation operatorsa ^# for spin 1/2 fields with an interaction Hamiltonian density which is an evendegree polynomial in the field with ultra-violet cut-off and its derivatives. For any eigenvector of the total HamiltonianH=H ₀+H _I partial isometries _± have been defined so thata _± ^# equal _± a ^# *_± on the ranges _± of _±. Since the existence of a groundstate ofH has been proved, the existence of at least one pair _± follows. The purpose of this paper is to show that for any _± orthogonal to the distribution of spins and momenta of the interacting Schrödinger states exp[–itH]_± approaches fort the distributions of spins and momenta of the free state exp[–itH ₀] if a wave-amplitude renormalization is carried out in _±. This is achieved by studying the expectation values of the operators in themaximally abelian W*-algebra generated by operators of the form a*a, in terms of whichany information about spins and momenta can be expressed.Supported in part by the National Research Council of Canada.     

Multinucleon antiproton annihilations in deuterium

Rare annihilation reactions for stopped antiprotons in deuterium ¯pdMN; M, whereM stands for, or other heavy mesons, are considered using the two-step model described by the triangle diagram. It was found that the probabilities of these processes are comparable with those for ¯pd^– p. The study of all Pontecorvo reactions is very important for the goals of meson spectroscopy as well as for understanding the high momentum components of the deuteron wave function.Dedicated to the memory of M. Gmitro.We would like to thanks P. P. Temnikov who brings our attention to the necessity of considering the reactions (7). We have benefited also from many discussions with C. Guaraldo, D. E. Kharzeev and L. A. Kondratyuk on these topics.     

Analysis of conformal-invariant scattering amplitudes for the two-dimensional world model

The explicit form of the conformal-invariant phase shift analysis in thes-channel for a scattering process involving two incoming and two outgoing particles is derived for the two-dimensional world model. The high energy behaviour of the scattering amplitudes is determined completely (up to a constant factor) by the requirement of conformal invariance. It is not possible to obtain this high energy limit by neglecting the masses right from the beginning. The main mathematical problem is the determination of the Clebsch-Gordan coefficients forSU ₀(1, 1) in the momentum basis.     

Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR