Response of Cu single crystals to high loading rates

The present paper deals with dynamic response of Cu single crystals to high loading rates. Cu crystals were loaded with transient stress waves along several crystallographic directions ([110], [100] and [¯135]). The response is expressed in terms of stress wave attenuation. The obtained results indicate that there are at least 2 basic regions where different mechanisms of plastic strain are working.The paper also involves a critical analysis of the used Hopkinson split bar technique. The analysis clearly indicates that the interpretation of experimental results can not be generally done by means of the function(). The obtained results may be described in terms of relaxation processes, analogously as in case of shock waves. This procedure also makes possible to describe the results in terms of dislocation dynamics. The possible connection between elastic precursor decay curves and the stress distribution in a specimen loaded with the Hopkinson split bar technique is briefly outlined.     

Interdeffusion in the Co-Ni system-III. Intrinsic diffusion coefficients

The intrinsic diffusion coefficients¯D _Co and¯D _Ni in the Co—Ni system have been calculated with the use of the interdiffusion coefficient values, concentration gradient data (Part I) and from the observed inert markers displacements (Part II). The Darken euqations [1] were used in these calculations and for comparison's sake an attempt was made to apply the Van Loo treatment as well [2, 3].The experimental difficulties related to the determination of the diffusants concentration in the Kirkendall interface are discussed. A simple method had been worked out which enabled us to determine this concentration from the Darken equations, from inert markers velocity and from the penetration curves data.The activation enthalpies¯ H _Co and¯ H _Ni have been calculated from the temperature dependence of the intrinsic diffusion coefficients;¯ H _Co values are slightly higher than¯ H _Co values. The magnitude of the observed Kirkendall effect has been analyzed and compared with the results obtained in some other binary FCC and BCC systems.     

Effect of a dislocation forest on the bauschinger effect during the twinning of zinc single crystals

A study was made of the effect of a dislocation in the {{11¯22}} 11¯23 system (pyramidal slip) on the characteristics of the Bauschinger effect during the twinning of single crystals of zinc and of the alloy Zn + 0.6% Cu. The dislocation forest retards the backward motion of the twinning dislocations, leading to the effect.Translated from Izvestiya VUZ. Fizika, No. 5, pp. 101–104, May, 1971.In conclusion the authors thank candidates of physicomathematical sciences F. F. Lavrent'yev for useful discussion.     

The\bar pp \to e^ + e^ - reaction at rest and the hierarchy of the annihilation ranges

A new procedure is devised to evaluate the proton form-factor at the ¯pp threshold from experimental data on ¯ppe ⁺ e ^– annihilation at rest. Comparison of the ¯ppe ⁺ e ^– and¯pp ^+– processes reveals that annihilation ranges for various channels are ranked in line with quark dynamics.This work has been funded in part by the German Federal Minister for Research and Technology (BMFT) under the contract number 06HD756     

Nonequilibrium thermodynamics of lasing and bistable optical systems

A simple model of nonlinear optical systems exhibiting instability—such as in laser action and in bistable absorption—is presented that provides a prototype of nonequilibrium thermodynamics on a statistical basis. The adiabatic reduction of the atomic degrees of freedom in a revised Langevin treatment establishes a fully consistent framework in which the active electromagnetic field mode is in contact with two thermal reservoirs (the cavity and the atoms) as well as being acted upon by an external field. The results are summarized by the first and second laws,dE=W+Q _c +Q _A anddS Q_c/¯T_c+Q_A/¯T_A, with the statistical mechanical representations of the entities therein exhibiting the nature of the mode; i.e., (a) a heat-engine structure operating between two reservoirs of temperatures¯T _c > 0 and¯T _A < 0 for the laser, and (b) a nonlinear response against external work balanced by a single reservoir (¯ T _c = ¯T _A ) for the absorptive bistability.Originally presented at the Taniguchi Symposium, October 1979.⁴⁴     

Updating the effective range expansion of low-energyN \bar N-scattering

Low energyN¯N scattering is reanalyzed using the new data on annihilation cross-sections from CERN [1], the¯np-absorption measurement from BNL [2] and the annihilation width of the 2p state in antiprotonic hydrogen [3]. Imposing the condition that the imaginary part of the effective range is negative we find low energy scattering parameters which interpolate between the existing ITEP [4] and CERN/Heidelberg [5] values.Supported by the BMFT-grant 06 HD 756     

Geometric and Crystallographic Characterization of WC Surfaces and Grain Boundaries in WC-Co Composites

Electron backscattered diffraction has been used to determine the orientation of WC crystals in a WC-Co composite and atomic force microscopy has been used to measure the shapes of planar sections of the same crystals. A stereological analysis has been used to determine that {101¯0} prism facets and the {0001} basal planes are the WC surfaces that are most frequently in contact with Co. Further, the WC habit is an approximately equiaxed trigonal prism bound by three prism facets and two basal facets. An analysis of 15,600 grain boundaries shows that certain interfaces occur with a frequency that is much higher than would be expected in a random distribution and that the grain boundary habit planes also have {101¯0} and {0001} orientations. Eleven percent of all the observed WC-WC interfaces are 90° twist boundaries about [101¯0]. Two types of boundaries with a 30° rotation about [0001], a twist and an asymmetric tilt, comprise 3% of the population.     

Surface self-diffusion on Pt(110): Directional dependence and influence of surface-energy anisotropy

The decay of periodic surface profiles by surface self-diffusion is simulated by numerically solving the phenomenological equations for this process. The crystalline nature of the surface is taken into account by introducing an anisotropic surface free energy,(). Depending on the degree of anisotropy of(), the decay kinetics and the shapes of the profiles are largely different. A comparison with measurements of profile decay on Pt(l10) single crystal surfaces shows that the anisotropy in() along the [1¯10] azimuth should be about 2–3%, while that along the [001] azimuth is expected near 8%. In the latter case large amplitude profiles exhibit (111) faceting and slow decay kinetics which are non-exponential. The rate of surface self-diffusion on Pt(110) is anisotropic with the [1¯10] direction being faster than the [001] direction.     

The interactions¯pp→¯nπ− p at 22·4 GeV/c

The interactions¯pp¯n ^– p are compared with predictions of several models for diffraction dissociation and the validity of these models is tested.     

Effects of current pulses on the mobility of fast-moving dislocations

Selective etching has been applied to the mobilities of pyramidal dislocations in the {11¯22} 11¯23 system in Zn single crystals in the quasiviscous region in the simultaneous presence of mechanical treatment and current flow in order to establish the mechanisms whereby current pulses affect metal plasticity. The dislocation dynamics may be related to the current density and mechanical loading, which is examined in relation to the possible current-effect mechanisms. The dynamic retardation constant has been estimated and it has been found that the nonpolar pinch effect and direct force action from the current are decisive.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 5–8, August, 1991.We are indebted to A. M. Roshchupkin and I. L. Bataronov for discussions and critical comments.     

The coherent K L 0 C → K S 0 C regeneration at high energies

New experimental results on the coherentK _L ⁰ C K _S ⁰ C regeneration in the momentum range 10p30 GeV/c are presented. For the quantity (f ₀–¯f ₀/k (where f₀ and¯f ₀ are theKC and¯K ⁰C forward scattering amplitudes andk is the wave number) we have obtained: arg (f ₀–¯f ₀)/k=–126±14 and ¦(f ₀–¯f ₀/k¦ p ^{–0.62±0.14} These results are well described by a simple Regge pole model including only the (-trajectory exchange in thet-channel with the intercept (0) close to 0.4.Presented at the IV International Symposium on High Energy and Elementary Particle Physics, Warszaw, September 1975.     

Tensorial representation of the Dirac equation

We discuss tensor representations of the Dirac equation using a geometric approach. We find that the mass zero Dirac equations can be represented by Maxwell equations having a source which obeys the empty space wave equation. We also obtain a relation for the source in terms ofE andH. In the case of mass not equal to zero a difficulty is encountered in removing the constant spinors¯ _Aand¯ _A.We find that the arbitrary constant spinors can be eliminated in a spinor theory based on the Klein-Gordon equation.     

Angular distribution and polarization of K*(890) in ¯pp annihilation at 5.7 GeV/c

We have studied angular distributions ofK ^*(890) and found strong angular asymmetry forward-backward in ¯K ^*/K ^* in the centre of mass system. The ¯K ^* are produced predominantly in original direction of ¯p while theK ^* follow the proton directions. We also looked for angular distributions and-matrix elements in the rest system ofK ^*. We did not find any strong deviation from the isotropy distributions. In our research the corresponding matrix element for the angular distribution acoording to transversity axis has been found, ₀₀=0·37 ±0·05.     

Restoration of universality for the rod-to-coil transition scaling in the infinite-dimensionality limit: Exact results for directed walks

We derive scaling forms for the thermodynamic and correlation quantities for the turn-weighted fully and partially directed self-avoiding walks on the hypercubic lattices ind2. In the grand canonical (fixed fugacity per step) ensemble, the conformational rod-to-coil transition sets up in the regimew¯N=O(1), wherew is the weight of each 90° turn and¯N is the (fugacity-dependent) average number of steps. Contrary to the conventional critical phenomena wisdom, the scaling functions for the two different walk models, directed and partially directed, become universal only in the limitd.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

On the physical interpretation and the mathematical structure of the combinatorial hierarchy

The combinatorial hierarchy model for basic particle processes is based on elementary entities; any representation they may have is discrete and two-valued. We call themSchnurs to suggest their most fundamental aspect as concatenating strings. Consider a definite small number of them. Consider an elementary creation act as a result of which two different Schnurs generate a new Schnur which is again different. We speak of this process as a discrimination. By this process and by this process alone can the complexity of the universe be explored. By concatenations of this process we create more complex entities which are themselves Schnurs at a new level of complexity. Everything plays a dual role in which something comes in from the outside to interact, and also serves as a synopsis or concatenation of such a process. We thus incorporate the observation metaphysic at the start, rejecting Bohr's reduction to the haptic language of common sense and classical physics. Since discriminations occur sequentially, our model is consistent with a fixed past-uncertain future philosophy of physics. We demonstrate that this model generates four hierarchical levels of rapidly increasing complexity. Concrete interpretation of the four levels of the hierarchy (with cardinals 3,7,127,2¹²⁷-110³⁸) associates the three levels which map up and down with the three absolute conservation laws (charge, baryon number, lepton number) and the spin dichotomy. The first level represents +, –, and ± unit charge. The second has the quantum numbers of a baryon-antibaryon pair and associated charged meson (e.g.,n¯n,p¯n,p¯p,n¯p, ⁺ , ⁰, ^– ). The third level associates this pair, now including four spin states as well as four charge states, with a neutral lepton-antilepton pair (e¯e orv¯v), each pair in four spin states (total, 64 states)—three charged spinless, three charged spin-1, and a neutral spin-1 mesons (15 states), and a neutral vector boson associated with the leptons; this gives 3+15+3×15=63 possible boson states, so a total correct count of 63+64=127 states. Something likeSU ₂×SU ₃ and other indications of quark quantum numbers can occur as substructures at the fourth (unstable) level. Breaking into the (Bose) hierarchy by structures with the quantum numbers of a fermion, if this is an electron, allows us to understand Parker-Rhodes' calculation ofm _p /m _e =1836.1515 in terms of our interpretation of the hierarchy. A slight extension gives us the usual static approximation to the binding energy of the hydrogen atom, ² m _e c ² . We also show that the cosmological implications of the theory are in accord with current experience. We conclude that we have made a promising beginning in the physical interpretation of a theory which could eventually encompass all branches of physics.Work supported by the Department of Energy under contract number EY-76-C-03-051.     

A new bundle completion for parallelizable space-times

The Schmidt [9]b-boundaryM, for completing a space-timeM, has several desirable features. It is uniquely determined by the space-time metric in an elegant geometrical manner. The completed space-time is¯M=M M, where¯M= ⁺ M/O ⁺ and ⁺ M is the Cauchy completion (with respect to a toplogical metric induced by the Levi-Cività connection) of a component of the orthonormal frame bundle having structure groupO ⁺. ThenM consists of the endpoints of incomplete curves inM that have finite horizontal lifts in ⁺ M, and ifM= we say thatM isb-complete. It turns out thatM isb-complete if and only ifO ⁺ M is complete. This criterion for space-time completeness is stronger than geodesic completeness and Beem [1] has shown that this remains so even for the restricted class of globally hyperbolic space-times. Clarice [3] has shown that for such space-times the curvature becomes unbounded as theb-boundary is approached.Now ifM, then ⁺ M may contain degenerate fibers; thus the quotient topology for¯M is non-Hausdorff and precludes a manifold structure. Precisely this has been demonstrated by Bosshard [2] for Friedmann space-time, casting doubt on the physical significance of the completion. The only neighborhood of the Friedmann singularity is the whole of¯M, and in the closed model initial and final singularities are identified inM. Similarly, Johnson [7] showed that the completion of Schwarzschild space-time is non-Hausdorff because of degenerate ibers in¯O ⁺ M.Here we introduce a modification of the Schmidt procedure that appears to be useful in avoiding fiber degeneracy and in promoting a Hausdorff completion. The modification is to introduce an explicit vertical component into the metric forO ⁺ M by reference to a standard section, that is, to a parallelizationpMO ⁺ M We prove some general properties of thisp-completion and examine the particular case of a Friedmann space-time where there is a fairly natural choice of parallelization.     

Efficient β-formulation for the FEM analysis of leaky modes in general anisotropic channel waveguides

An efficient method to model guided and leaky modes of anisotropic dielectric waveguides with arbitratry dielectric tensor ¯¯ is presented. This method takes advantage of a particular -formulation approach of the finite element method (FEM), leading to an optimized use of the computational resources.     

Recrystallization of cold-rolled copper and the fourier analysis of the elastic anisotropy

The presence in cold-rolled electrolytic copper sheet of a texture of the type {134}, [4¯85] has been established by x-ray methods and by analysis of the elastic anisotropy. The modulus diagrams of the sheet are described by a Fourier series of the form: E = r₀ – r₂ cos2 + r₄ · cos 4.After annealing at temperatures up to 160 °, the free term in the expansion slowly increases, while the amplitudes of the second and fourth harmonics remain unchanged. Above 160 ° the second harmonic gradually disappears in the course of recrystallization, and the amplitude of the fourth harmonic increases at the same time. The modulus diagram is described by the series E = r₀ + r₄ cos 4.Fourier analysis reveals the steady development of the orientation (100) [001], even in the initial stages of recrystallization, although x-rays show no traces of the new structure up to 250 °.