Elastic stress around linear dislocation in anisotropic medium

Relations are derived for the elastic stress field around a linear dislocation in an infinite medium with general anisotropy. The strongly deformed material around the core of the dislocation is cut out in the shape of an elliptic cylinder. The conditions of a free surface are used on the boundary thus formed. The calculation of the field around a crack in a crystal, the model of which was proposed by Fujita in [9], is given as an example.

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. , , , . , [9] .

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The author thanks Dr. F. Kroupa for valuable discussions and all-round help in solving the problem and Z. Hemanová for performing the numerical calculations.     

An example of a generalized Brownian motion

We present an example of a generalized Brownian motion. It is given by creation and annihilation operators on a twisted Fock space ofL ²(). These operators fulfill (for a fixed –11) the relationsc(f)c ^* (g)–c ^* (g)c(f)=f,g1 (f, g L ²()). We show that the distribution of these operators with respect to the vacuum expectation is a generalized Gaussian distribution, in the sense that all moments can be calculated from the second moments with the help of a combinatorial formula. We also indicate that our Brownian motion is one component of ann-dimensional Brownian motion which is invariant under the quantum groupS U(n) of Woronowicz (with =v ²).     

РЕАКЦИЯ (γ, р) НА КАДМИИ И ОЛОВЕ

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(, p) Reaction on cadmium and tin

A study is made of the nuclear photoeffect on Sn and Cd where, in contrast to most of the experiments with this effect up to now, discrete rays were used. The paper complements paper [3], the experimental arrangement of which it has taken over. Several interesting results were obtained — particularly the discreteness of the energy spectrum and the unconventional form of the angular distribution. With tin, the top proton shell of which is completely occupied, the shape of the energy spectrum corresponds to the Wilkinson theory of gigant resonance; with cadmium the energy spectrum is similar to the evaporation spectrum. The angular distributions of the photoprotons of both elements do not satisfy the commonly used relations corresponding to existing theories of nuclear photoeffect. They can, however, be described quite well by empirical equations which contain associated Legendre polynomials of different orders. With both elements the results have features of both a direct and a collective process. The paper gives results, a satisfactory explanation of which would require a new theory including both types of processes.

     

The lattice deformation and the energy of antiphase boundaries in Fe-Si alloys

The lattice deformation across the antiphase boundary and the energy of both types (a/2111 anda(100) of antiphase boundaries lying in {110} plane are calculated using a series of three interatomic potentials fitted to experimental data. It is shown that the relaxation of atomic planes in the vicinity of antiphase boundary is important for thea/2111 antiphase boundary and is negligible for a 100 antiphase boundary in the DO₃ structure.The author is grateful to Dr. F.Kroupa and to Dr. A.Gemperle for valuable discussions.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

Relativistic multiconfiguration time-dependent self-consistent-field theory for molecules

A relativistic multiconfiguration time-dependent self-consistent-field theory is constructed for molecules. Equations are derived for relativistic response functions, and their solutions are found in general form for multielectron molecules. Within the adopted approach, the equivalence of the results of relativistic calculations of the oscillator strengths in the molecules is demonstrated by using equations in length and velocity. A relativistic formalism is formulated for the Liouville-Dirac-Fock self-consistent field; this formalism may be very effective in molecular calculations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, 29–34, October, 1991.     

A complete proof of the Feigenbaum conjectures

The Feigenbaum phenomenon is studied by analyzing an extended renormalization group map . This map acts on functions that are jointly analytic in a position variable (t) and in the parameter () that controls the period doubling phenomenon. A fixed point ^* for this map is found. The usual renormalization group doubling operatorN acts on this function ^* simply by multiplication of with the universal Feigenbaum ratio ^*= 4.669201..., i.e., (N ^*(,t)= ^*( ^* ,t). Therefore, the one-parameter family of functions, ^* , ^* (t)=( ^*(,t), is invariant underN. In particular, the function ₀ ^* is the Feigenbaum fixed point ofN, while ^* represents the unstable manifold ofN. It is proven that this unstable manifold crosses the manifold of functions with superstable period two transversally.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

, , . , . .

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The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

Properties of theL p -solutions of linear impulsive equations in a banach space

Conditions for the existence ofL _p-solutions (1p) of linear impulsive equations in a Banach space are found.     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й ИЗГИБА У ПБЕЗОЭЛЕКТРИЧЕСКИ Х СТЕРЖНЕЙ

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Logic of likelihood

The notion of probability is generalized to that of likelihood, and a natural logical structure is shown to exist for any physical theory which predicts likelihoods. Two physically based axioms are given for this logicai structure to form an orthomodular poset, with an order-determining set of states. The results strengthen the basis of the quantum logic approach to axiomatic quantum theory.     

К определению самопр оизволъной иамагниченности В об ласти точки кыри

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Magnetic moments of proton drip-line nuclei13O and9C

The magnetic moments of the proton drip-line nuclei¹³O(I = 3/2^–,T _1/2 = 8.6 ms) and 9C(I = 3/2^–,T _1/2 = 126 ms) have been determined for the first time through the combined techniques of polarized radioactive nuclear beams and-NMR detection. The observed magnetic moments are ¦(¹³O)¦ = 1.3891 ±0.0003 _N and ¦(⁹C)¦ = 1.3914 ±0.0005 _N. Spin expectation values are deduced to be 0.76 and 1.44 for¹³O and⁹C, respectively. While the of¹³O is consistent with the systematics from isospinT= 1/2 mirror pairs, the of⁹C is unusually large, even far larger than the single particle value, = 1.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

Bremsstrahlung spectrum in beta decay

The spectrum of the bremsstrahlung due to the complete slowing down in aluminium of beta particles belonging to the continuous spectrum, was calculated for an arrangement, in which the beta emitter is completely enclosed in an absorber. The Bethe-Heitler cross-section, corrected by an empirical factor, was used. A table is given which makes it possible to calculate bremsstrahlung spectra of beta emitters with their maximal energy between 0·6 MeV and 2·0 MeV; the necessary additional calculations are quite simple. The error in the calculation is practically determined by the uncertainty in the determination of the cross-section and is equal to about 10%.

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Scaling in the mean of the p+p→π0+X inclusive reaction data and the energy dependence of Feynman variable

We have studied the p+p⁰+X inclusive reaction data of Carey et al. in the framework of the scaling in the mean hypothesis first proposed by Dao et al. These data have been used to obtain the gamma ray spectrum in terms of the average value of the Feynman variablex, written as x.A comparison with the observed gamma ray spectrum at Mt. Chacaltaya by the Japanese and Brazilian Group gives the energy dependence of x at very high energy.     

Damage created by high-current-density implants of phosphorus into 〈100〉 and 〈111〉 silicon wafers

The damage left by high-current-density, 9 A/cm², implants of 120 keV phosphorus into 100 and 111 silicon oriented substrates was investigated as a function of the fluence in the range 4×10¹⁵–1.5×10¹⁶/cm². The samples were analyzed by 2 MeV He⁺ channeling and transmission electron microscopy. Initially a buried amorphous layer forms at low fluences until the wafer temperature saturates at 450 °C at a fluence of 4.5×10¹⁵/cm². As the fluence is further increased ion-assisted regrowth of this initial buried amorphous layer takes place and is 2 to 2.5 times faster (with respect to ion fluence) for 100 substrates than for 111 substrates. At higher fluences, most of the residual damage is located at a depth equal to the sum of the projected range and of the straggling. In the regrown layers twins are found in both orientations, and in some cases a hexagonal silicon phase is present at high fluences. The results are compared with the ion assisted regrowth of amorphous layers at well defined temperatures in the 250°–400 °C range.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.