Specific propagation directions of acoustic waves for piezoelectric and nonpiezoelectric media

I reanalyze the problem of the existence of longitudinal normals inside the symmetry planes of piezoelectric crystals belonging to the symmetry class mm2. The equations determining components of longitudinal normals situated outside the symmetry planes for media of this symmetry are discussed. It is proven that nonpiezoelectric media of rhombic symmetry could have 4 or 8 distinct acoustic axes. Examples of nonpiezoelectric elastic media of monoclinic symmetry without acoustic axes are given. The method of determination of the components of acoustic axes for piezoelectric media of arbitrary symmetry is presented. With the help of this method, I discuss the problem of acoustic axes for piezoelectric media of the symmetry class mm2. The text was submitted by the author in English.     

The crystal structure of the prototypic ceramic superconductor BaPbO3: An X-ray and neutron diffraction study

The structure of the distorted perovskite BaPbO₃ was studied with high-resolution X-ray diffraction at 300 K and 26 K and with neutron diffraction at 300 K. Simultaneous refinement of the neutron and X-ray data sets (300 K) using the Rietveld method yields a monoclinic structure with the space groupI 2/m and lattice parametersa=6.0278 (1) Å,b=6.0664(1) Å,c=8.5109(1) Å, and =90.083 (2)^o. The tilting of the oxygen octahedra is given asa ^– a ^– c ⁰ in Glazer's notation [11]. The monoclinic angle corresponds to the angle between the cubic directions [110] _c and _c . This is in contrast to the observations in BaBiO₃. The structure of BaBiO₃ has the same space groupI 2/m, the similar dimensions of the unit cell and the same tilt system, but = ([110] _c , [001] _c ) as the monoclinic angle. As a consequence there is only one type and size of, PbO₆ octahedra but two types of octahedra in BaBiO₃. This fact may influence the occurrence of superconductivity in solid solutions (Ba(Pb_1–x Bi _x )O₃ containing a large fraction of lead by enhancing valence fluctuations.     

The orientation of water molecules in monoclinic Li2SO4·H2O investigated by light scattering

Directional dispersion of the highest frequency B-phonon branch associated with the ω₃-vibration of H₂O in monoclinic Li₂SO₄·H₂O has been measured by means of Raman spectroscopy for varying wave vector directions perpendicularly to the twofold symmetry axis. The minimum and maximum frequency indicates those directions for which there exist purely transverse and longitudinal waves, respectively. Since the dipole moment of the ω₃-vibration is parallel to the H-H-direction the wave normals of the TO- and LO-modes allow a direct conclusion in regard to the orientation of the crystal water molecules. Our result is in good agreement with previous NMR-measurements.     

Zur nichtlinearen Theorie der Strahl-Plasma-Wechselwirkung I

Beam-plasma-interaction is theoretically investigated on the basis of the non-linear Vlasov equation. The case of amplifying longitudinal waves is described by a non-linear approximation including “quasilinear” and mode-coupling terms. By evaluating the electric field vector E(x, t) and the distribution functions f_a(x, v, t) for the beam and plasma electrons in Fourier series and approximating the non-oscillating parts of the f_a by the first terms in an expansion using Hermite polynomials in velocity space a system of ordinary differential equations for the complex wave number k, the mean and thermal velocities and the quasimoments b_as is obtained, which can be solved numerically, if terms with E for which m + n > 3 are neglected. The numerical results will be given in a further part of the paper.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. I. General Theory and Square-Lattice Chromatic Polynomial

We study the chromatic polynomials (= zero-temperature antiferromagnetic Potts-model partition functions) P _G (q) for m×n rectangular subsets of the square lattice, with m8 (free or periodic transverse boundary conditions) and n arbitrary (free longitudinal boundary conditions), using a transfer matrix in the Fortuin–Kasteleyn representation. In particular, we extract the limiting curves of partition-function zeros when n, which arise from the crossing in modulus of dominant eigenvalues (Beraha–Kahane–Weiss theorem). We also provide evidence that the Beraha numbers B ₂,B ₃,B ₄,B ₅ are limiting points of partition-function zeros as n whenever the strip width m is 7 (periodic transverse b.c.) or 8 (free transverse b.c.). Along the way, we prove that a noninteger Beraha number (except perhaps B ₁₀) cannot be a chromatic root of any graph.     

Generalization ability and information gain of clock-model perceptrons

We study the generalization abilityg _Q ofQ-state Clock-model perceptrons for (i) Hebbian and for certain Non-Hebbian learning procedures, namely (ii) learning with maximal stability, (iii) zero stability and (iv) optimal generalization, for the case of random training sets. Among other results we find thatg _Q behaves quite different in the Hebbian and in the Non-Hebbian cases in the limitQ. E.g. in the Hebbian case for finite ,g _Q vanishes always 1/Q, whereas in the Non-Hebbian cases considered,g _Q converges forQ to a non-trivial continuous functiong (), which vanishes for <2, but increases rapidly for >2. This means that for (ii), (iii) and (iv), as a function of atQ=, there is a 2nd-order phase transition from a non-generalizing phase for 2 to a generalizing phase for >2. Different behaviour of the Hebbian and Non-Hebbian cases, respectively, is also observed for the information gain obtained through learning. For the particular case of AdaTron Learning, which is identical to case (ii), we find a geometrical formulation forg _Q (), which is applicable to more general models.     

Tight-binding study of structural and electronic properties of silver clusters

Tight-binding model is developed to study the structural and electronic properties of silver clusters. The ground state structures of Ag clusters up to 21 atoms are optimized by molecular dynamics-based genetic algorithm. The results on small Ag_n clusters (n = 3-9) are comparable to ab initio calculations. The size dependence of electronic properties such as density of states, s-d band separation, HOMO-LUMO gap, and ionization potentials are discussed. Magic number behavior at Ag₂, Ag₈, Ag₁₄, Ag₁₈, Ag₂₀ is obtained, in agreement with the prediction of electronic ellipsoid shell model. We suggest that both the electronic and geometrical effect play significant role in the coinage metal clusters. Received 7 August 2000     

Hyperthermal surface-collisions of water cluster cations

Size-selected, protonated water cluster cations (H₂O)_nH⁺, 4 n 32, are scattered at normal incidence from the surface of a diamond-coated silicon wafer at collision energies 0 E _coll 500 eV. The size distribution of collision-induced fragment-ions and the ion yield of scattered particles are analyzed, using a secondary time-of-flight mass spectrometer, as a function of the cluster size, n, and the collision energy, E _coll. Even at low impact energies only very small fragment-ions can be detected, with a maximum fragment size of 35% of the colliding parent cluster ions. For clusters consisting of more than 10 molecules, the protonated water dimer (H₂O)₂H⁺ becomes the predominant fragment-ion. The total charge survival yield obeys a nonlinear increase with cluster size; for the largest clusters investigated, more than 35% of the impacting ions survive the surface collision in the cationic charge state.     

Self-similarity and scaling of wave function for binary quasiperiodic chains associated with quadratic irrationals

By establishing the correspondence between the substitution rule (aa ⁿb; ba) and the transformation on the value of =tan by1/(n+) in the cut-and-project (CP) method, it is proved that the necessary and sufficient conditions for a binary quasiperiodic (QP) sequence made by the CP method to be self-similar is that is a quadratic irrational (QI) number. And, vice versa, the necessary condition for a binary self-similar sequence generated by the substitution rule to be obtainable by the CP method is that the corresponding substitution rule can be rewritten as a simple composition of transformations with the type (aa ⁿb; ba). To illustrate some physical properties of the self-similar QP chains associated with QI numbers, we analyze the scaling behaviour of the wave function atE=0 for an off-diagnonal tight-binding model. It is shown that the wave function atE=0 grows at most by a power-law for the QP lattices, characterized by a special class of QI numbers. For the QP chains associated with general QI numbers, with the same logic, the typical scaling behaviour of the wave function is conjectured to be the same.     

Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions II: Numerical description and application

A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how to choose the value of . It is found that the should be taken as functions of the momentum transfer and multipolarity . Illustrations are carried out by calculating the cross-sections for some typical transitions n _a l _a -n _b l _b of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys. Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle. Received 6 April 1999     

The emission of neutral clusters in sputtering

The mass, angle, and energy resolved emission of neutral clusters in sputtering was studied for a variety of metals and semiconductors. The main phenomena and results are the following: (i) Cluster emission from a series of transition metals reveals a prominent contribution of clusters to the total flux of ejected particles but there is no simple scaling of cluster intensities with the average sputtering yields. With increasing number of constituents, relative intensities of neutral clusters decrease much faster than those of secondary-ion clusters. (ii) The relative intensities of clusters emitted from amorphous and crystalline semiconductors are identical, but the energy spectra of Ge _n -clusters (n = 1–4) sputtered from Ge (111) peak at a slightly higher energy (1 eV) as compared to spectra taken from amorphous Ge. The intensities of all Ge _n -clusters exhibit the same dependence on emission angle; this holds for both the amorphous and crystalline Ge-sample. (iii) The flux of neutral monomers, dimers, and trimers sputtered from Cu(111), Ni(111), and Ag(111) crystals shows a pronouncedly anisotropic emission along the 110 lattice directions which is ascribed to a momentum alignment in the anisotropic part of the collision cascade. Energy spectra taken along 110 peak at higher energies than those obtained from a random emission angle.     

Energy relaxation in aϕ 4 with long range interactions

We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential of ⁴-type and infinite range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions <E _n(t)E _n > of the fluctuations of the one-particle energiesE _n(t) decays exponentially. The corresponding relaxation time is proportional toN and is given by (T, N) =N₀(T). The temperature dependent time scale ₀ can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode coupling approximation and by a perturbative approach. Both results agree in leading order in 1/N. It is speculated that any interaction of range generates a timescale .     

Measurement of the electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆

The electric form factor of the neutron, G_E,n, has been measured at the Mainz Microtron by recoil polarimetry in the quasielastic D(¯e, e¯n)p reaction. Three data points have been extracted at squared four-momentum transfers Q ² = 0.3, 0.6 and 0.8 (GeV/c)². Corrections for nuclear binding effects have been applied.This revised version was published online in March 2005. In the previous version, the email address of one author was inadvertently assigned to multiple authors.     

Multiscaling and multifractality in an one-dimensional Ising model

Scaling properties of the Gibbs distribution of a finite-size one-dimensional Ising model are investigated as the thermodynamic limit is approached. It is shown that, for each nonzero temperature, coarse-grained probabilities of the appearance of particular energy levels display multiscaling with the scaling length ℓ = 1/M _n, where n denotes the number of spins and M_n is the total number of energy levels. Using the multifractal formalism, the probabilities are argued to reveal also multifractal properties. Received 10 July 2000 and Received in final form 6 November 2000     

Spectral‐Luminescent Properties of Certain Substituted Arylpolyenes and Their Features

We investigated fluorescence and fluorescence excitation spectra of five substituted diphenylpolyenes with the number of double bonds in the chain n = 2 or n = 3 and substituents NO₂, N(CH₃)₂, and NH₂ in different media (toluene and noctane) at low (77 and 4.2 K) temperatures. The duration of fluorescence () and the quantum yield of fluorescence () of the four compounds investigated were measured at room temperature. The influence of the electron donoracceptor interaction in one of the compounds on its spectralluminescent properties has been analyzed.     

Core size effects on electrodeposition of gold nanoparticles attached with biferrocene derivatives

Biferrocene-modified gold nanoparticles (Au_n-BFc) comprising 1.7, 2.2 and 2.9 nm in average core diameter, d, were synthesized by a substitution reaction of octyl thiolate-covered nanoparticles with biferrocene-terminated alkanethiol, 1-(9-thiononyl-1-one)-1, 1-biferrocene (BFcS). All sizes of Au_n-BFc undergo two-step oxidation reactions in 0.1 mol dm^-3 Bu₄NClO₄-CH₂Cl₂ and consecutive potential scans including the second oxidation process lead to the formation of an adhesive redox-active gold nanoparticle film on an electrode. The thickness of the Au_n-BFc film is controllable by the number of potential scans. The scanning tunneling microscope images reveal that the Au_n-BFc (d = 2.9 nm) film forms many domains of the assembled Au_n-BFcs, especially the particles are isotropically assembled in line.     

Superradiating 4P-4S-3P cascade of sodium vapour arising on the leading edge of the exciting laser pulse

Investigations of the superradiating cascade of sodium vapour 4P-4S-3P ₁ = 2.21 µm and ₂=1.14 µm) arising on the leading edge of the exciting laser pulse were carried out. The dependences of the actual delay time _D of the ₁ pulse on the population rise time of the laser-excited 4P state were measured and compared with those calculated following the existing theoretical model. The dependence of the actual delay time _D on the inverse density of excited atoms 1/N* is also presented. Analysis of this dependence revealed the influence of the Doppler dephasing and of the second, ₂, transition on the formation of the ₁ superradiance.     

Invasion Percolation and the Incipient Infinite Cluster in 2D

 We establish two links between two-dimensional invasion percolation and Kesten's incipient infinite cluster (IIC). We first prove that the k ^th moment of the number of invaded sites within the box [−n, n]×[−n, n] is of order (n ²π _n ) ^k , for k≥1, where π _n is the probability that the origin in critical percolation is connected to the boundary of a box of radius n. This improves a result of Y. Zhang. We show that the size of the invaded region, when scaled by n ²π _n , is tight. Secondly, we prove that the invasion cluster looks asymptotically like the IIC, when viewed from an invaded site v, in the limit |v|→∞. We also establish this when an invaded site v is chosen at random from a box of radius n, and n→∞. Received: 3 December 2000 / Accepted: 3 December 2002 Published online: 18 February 2003 RID="⋆" ID="⋆" Present address: CWI, PNA 3, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. E-mail:jarai@cwi.nl Communicated by M. Aizenman     

Exactly solvable models through the generalized empty interval method,for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E _n(t)'s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of E _n(t)'s are closed, are given. Received 25 September 2002 / Received in final form 3 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: mamwad@iasbs.ac.ir