Statistical mechanics of polymer networks of any topology

The statistical mechanics is considered of any polymer network with a prescribed topology, in dimensiond, which was introduced previously. The basic direct renormalization theory of the associated continuum model is established. It has a very simple multiplicative structure in terms of the partition functions of the star polymers constituting the vertices of the network. A calculation is made toO(²), whered=4–, of the basic critical dimensions _L associated with anyL-leg vertex (L1). From this infinite series of critical exponents, any topology-dependent critical exponent can be derived. This is applied to the configuration exponent _G of any networkG toO(²), includingL-leg star polymers. The infinite sets of contact critical exponents between multiple points of polymers or between the cores of several star polymers are also deduced. As a particular case, the three exponents ₀, ₁, ₂ calculated by des Cloizeaux by field-theoretic methods are recovered. The limiting exact logarithmic laws are derived at the upper critical dimensiond=4. The results are generalized to the series of topological exponents of polymer networks near a surface and of tricritical polymers at the-point. Intersection properties of networks of random walks can be studied similarly. The above factorization theory of the partition function of any polymer network over its constitutingL-vertices also applies to two dimensions, where it can be related to conformal invariance. The basic critical exponents _L and thus any topological polymer exponents are then exactly known. Principal results published elsewhere are recalled.     

Renormalization Group Analysis of the Self-Avoiding Paths on the d-Dimensional Sierpiński Gaskets

Notion of the renormalization group dynamical system, the self-avoiding fixed point and the critical trajectory are mathematically defined for the set of self-avoiding walks on the d-dimensional pre-Sierpiski gaskets (n-simplex lattices), such that their existence imply the asymptotic behaviors of the self-avoiding walks, such as the existence of the limit distributions of the scaled path lengths of canonical ensemble, the connectivity constant (exponential growth of path numbers with respect to the length), and the exponent for mean square displacement. We apply the so defined framework to prove these asymptotic behaviors of the restricted self-avoiding walks on the 4-dimensional pre-Sierpiski gasket.     

On the measurement of electronic spin-scattering anisotropy in the presence of magnetic interaction effects, using the dHvA Waveshape Analysis method

We derive an expression for the harmonic content of the oscillatory magnetization (de Haas-van Alphen effect) which is valid in the most general case, when the harmonic amplitudes and the relative harmonic phases of the pure Lifshitz-Kosevitch (LK) theory are modified by an arbitrary combination of magnetic interaction (MI), spin-scattering anisotropy (SSA) and exchange shift effects. The calculation produces several conclusions which bear directly upon the possibility of generally being able to determine separately the up-spin and down-spin conduction electron lifetimes in the presence of magnetic impurities, by means of measurements of the amplitudes and relative phase of the fundamental and second harmonic dHvA oscillations. We have shown that not only does SSA shift the first and second LK harmonics in phase, by amounts₁ and₂, but SSA also shifts the second harmonic magnetic interaction component by an amount 2₁. We find that, in general, the combined effect of both MI and SSA on the observable relative phase angle, (2 ₁–₂), can either add or cancel. In the limit in which the second harmonic is dominated by the MI component it can be shown that (2 ₁–₂) goes to , regardless of the amount of SSA, so that no useful information regarding SSA can be obtained from (2 ₁–₂) in this case. Measurable quantities and measurement techniques, for the determination of SSA, are discussed briefly.Research conducted at the University of Oregon with support from the National Science Foundation (USA).     

Neutron diffraction studies of the premartensitic transformation B2 → B19′ in Ti49Ni51 single crystals

We have studied structural changes in the high-temperature B2-phase in a large single crystal at temperatures near the premartensitic transformation B2 B19. We are the first to observe an extra 1/2 (110) reflection in neutron diffraction patterns taken along the [110]_B2 direction as the sample is cooled below 420 K, but still far from the martensite start temperature (M_s=180 K). This extra reflection heralds the formation of long-range order in atomic displacements with wave vectorq=(1/2±)[110]2/a. Premartensitic diffraction effects (caused by the development and correlation of lattice waves of atomic displacements with wave vectorsq ₁2/a[1/3, 1/3, 0] andq ₁2/1[1/3, 1/3] that were clearly visible in this same single crystal before the martensitic transformation B2 R, appeared at even lower temperatures with substantially lower intensities.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 56–61, January, 1995.     

Probability distribution of internal distances of a single polymer in good solvent

IfP _ij(x) is the probability distribution function of the scaled distancex between two elementsi andj of a long polymer in a good solvent, it is shown by Monte Carlo calculations that is in good agreement with out data for allx (B is a normalization constant). As a model we consider the freely jointed chain consisting ofN=160 rigid links. We estimate the exponents to ₀=0.27±0.01, ₀=2.44±0.02 (fori=1,j=N); ₁=0.55±0.06, ₁=2.60±0.15 (fori=1,j=N/2); ₂=0.9±0.1, ₂=2.48±0.06 (fori=N/4,j=3N/4). ₀ and ₀ are in agreement with ₀=1/(1-v) and ₀=(-1)/v proposed by Fisher and des Cloiseaux respectively, but we find concerning ₁ and ₂ that our estimates differ from recent -expansion calculations, by an amount of 20–30%. We analyse the crossover between the various exponents.     

Do quasiparticles in high-Tc superconductors condense like molecules of a perfect gas in the bose-Einstein condensation?

Far IR transmission spectra of very thin YBaCuO films in the 10–40 cm^–1 range have now sufficient accuracy and reproducibility to show that the number of quasiparticles at temperature <_c, _c being the transition temperature, do not follow a ⁴ law, but rather a ^1.5 one.     

Quantum particle-like configurations of the electromagnetic field

We construct explicitly three-dimensional localized solutions of the free Maxwell's equations with a phase expi(k x - t) which move like relativistic particles. The total field energyE of the moving lump is proportional to the frequency and its momentumP is proportional to the wave vectork, withE ² =P ² +M ². Further, if the angular momentum is different from zero, thenE =. These solutions thus model the wave-particle duality of quantum particles.     

P-wave charmonium decays into baryon and antibaryon pairs in quark pair creation model

A simple quark pair creation model is introduced to study exclusive decays of _{{c_J}} into baryon-antibaryon pairs. With this simple model, some exclusive decay processes, for example, _{c0} B¯ (B = ,⁰,^-) are investigated and their decay widths are evaluated by inclusion of the properties of outgoing baryons, and the results show that the strengthened decay channels _{{c_J}} ¯(J = 0, 2) are easily understood by considering only the color singlet contribution of P-wave charmonium.     

Stability of a Special Class of $$q_{ij}$$ -CCR and Extensions of Higher-Dimensional Noncommutative Tori

The -algebras A_{{q i}}, generated by generalised quon commutation relations are considered. The nuclearity of these algebras is proved. It is shown that A_{{q i}}, is isomorphic to the extension of a higher-dimensional noncommutative torus. Irreducible representations of A_{{q i}}, are considered. It is shown that the Fock representation is faithful.     

Gamma-ray spectroscopy in 110Sn and 111Sn

Excited states in ¹¹⁰Sn and ¹¹¹Sn nuclei have been investigated using in-beam -ray spectroscopic methods. An ¹⁶O beam with an energy of 60-80MeV was used to bombard a ⁹⁸Mo target. On the basis of the relative excitation functions, -ray angular distributions, - and -time distributions, -ray multiplicity and total energy data, the level schemes of ¹¹⁰Sn and ¹¹¹Sn have been studied and extended up to E_exc 11.5MeV, I = 24, and E_exc 11.1MeV and I = (51/2), respectively. An extension of the intruder, g.s. and negative-parity bands, as well as 5 new band-like structures are proposed in ¹¹⁰Sn. The nature of newly introduced collective band 8 as well as 10⁺ states fed in the decay of the collective band is discussed. In the ¹¹¹Sn nucleus an intruder band based on the 23/2^- state has been reinvestigated and the extension of the g.s. band and second negative-parity band is given. Evidence for neutron-core coupling in ¹¹¹Sn is found. The structure and systematics of excited states in light Sn isotopes is discussed.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

Faceting of Σ3 and Σ9 Grain Boundaries in Copper

Faceting is a well documented phenomenon known both for surfaces and interfaces, particularly, grain boundaries (GBs). Faceting can be considered as a phase transition when the original surface or GB dissociates onto flat segments whose energy is less than that of the original surface or GB. For the investigation of GB faceting a cylindrical Cu bicrystal with an island grain was grown by the Bridgman technique. Grain 1 in this bicrystal is completely surrounded by grain 2. The dissociation 9 3 + 3 proceeds during the growth of the bicrystal. The twins appear instead of {111}₁/{115}₂ or (110)_9CSL facet. GB faceting was studied at 1293 K, 1073 K, and 873 K. The profiles of the GB thermal groove were analysed by atomic force microscopy. Wulff-Herring plots and GB phase diagrams have been constructed for the 3, 9 and 9 + 3 GBs. With increasing temperature the facets with low-density CSL-planes disappear in the GB shape. GB roughening phase transition can be responsible for this phenomenon.     

On Essential Incompleteness of Hertz’s Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertzs experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertzs experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertzs crucial experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtzs electrodynamics did not contradict any of Hertzs experimental observations of transverse components as Maxwells theory predicted. Moreover, as we now know from recently published Hertzs dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertzs experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtzs theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method.     

Grain Boundary Wetting Statistic in Zn/Ga System and its Application to Grain Boundary Energy Spectrum Estimation

The grain boundary statistic in zinc polycrystals in contact with saturated Ga(Zn) melt has been studied. The misorientation angle distributions for zinc thin foil and zinc plates were obtained. The influence of the misorientation angle value on the wetting probability p of grain boundaries was observed. The grain boundary energy distribution parameters were obtained by using the p() relationship. The dihedral angles in triple lines of non-wetted zinc samples were also measured and their distribution was used to obtain the grain boundary energy distribution function. The parameters obtained by two different methods correspond to one other.     

Определение средней величины кристаллик ов кварца И графита на основани и первичной экстинкц ии

— —10 ^–4 —10 ^–2 . , . , , , , , .     

Differential algebras for quantum groups of type B, C, and D

We study higher order bicovariant differential calculi on the quantum groups O_q(N) and Sp _q (N). We show that the second antisymmetrizer exterior algebra _u is the quotient of the universal exterior algebra _u by the principal ideal generated by . Here denotes the unique up to scalars biinvariant 1-form. Moreover is central in _u and _u is an inner differential calculus. We show that the quadratic dual to the left-invariant algebra _{s L} is isomorphic to the reflection equation algebra. Let be an arbitrary left-covariant first order differential calculus. We show that the dimension of the space of left-invariant 2-forms in the universal exterior algebra equals the number of linearly independent quadratic-linear relations in the quantum tangent space.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

The quantum efficiency of the internal photo-electric effect in indium antimonide

A method is described for measuring the relative quantum efficiency of the internal photo-electric effect in semi-conductors by simultaneously measuring the photo-magnetoelectric and photo-conductive effect. The results of measurements on indium antimonide are given. The quantum efficiency begins to increase if the energy of the photon exceeds 0·47 eVat room temperature. The quantum efficiency as a function of the energy of the photon is analysed on the basis of the conception of impact ionization and it is shown that a study of the structure of this curve can supply information on the, band structure of a semi-conductor in the region of high energies of electrons and holes.

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. . , 0,47 eV . , .

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The authors thank M. Závtová and M. Vantuchová for efficient help with the measurements, K. mirous and V. Vrchovská for preparing the material, E. Antoník for critical remarks and M. Matyá and A. Müller for determining the constants of the material.     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].