Effective magnetic properties of a composite material with circular conductive elements

Effective magnetic properties of a composite meta-material consisting of periodically arranged circular conductive elements are studied theoretically. A general expression for the effective bulk permeability is obtained with mutual effects and lattice ordering being taken into account. The resonance frequency of the permeability is found to be strongly dependent on the size and shape of the unit cell. Frequency dispersion of the permeability is studied with special attention paid to the frequency range, where negative values of the permeability are possible. Corresponding recommendations for optimisation of the meta-materials with negative permeability are made. The results are confirmed by numerical simulations of the finite structure behaviour in an external magnetic field. Received 19 April 2002 Published online 31 July 2002     

Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

The plasticity of the Cu(H2O) 6 2+ Jahn-Teller complex affected by lattice strains and cooperative interactions

The EPR spectra evolution of Cs₂Zn_1?x Cu_x(ZrF₆)₂ · 6H₂O (x=0.01, 0.6, 0.8, and 1.0) in the temperature range 4.2–330 K and the x-ray structure analysis of the compound with x=1.0 in the range 150–327 K show that the Jahn-Teller (JT) complex Cu(H₂O)₆ coordination sphere undergoes a plastic deformation. The observed effect is due to the combined influence of small lattice strains existing in the paraphase and a new one appearing as a result of a ferroelastic phase transition and increasing with decreasing temperature below T _c . It is proved that both cooperative interactions between JT complexes and ferroelastic strain stabilize a certain JT configuration. The problem of instability of a JT configuration compressed at T ～ 265 K is discussed.     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

On the Determination of the Absolute Intensities of Vibrational-Rotational Lines of XY3 Molecules with C 3v Symmetry

Analytical formulas are derived that describe the dependences of the transition probabilities in vibrational-rotational spectra of XY₃-type molecules with C _3v symmetry on the rotational quantum numbers.     

Gluon jets from quarkonia

A detailed analysis is made within perturbative QCD of the decays into gluon jets of P-wave and S-wave quarkonia (J^PC = 0⁺⁺, 1⁺⁺, 2⁺⁺, 1^+? and 0^?+, 1^??). For all those states we compute to leading non-trivial order in α_s the conventional fraction f(?, δ) of the jet-like hadronic final states, characterized by the back-to-back cone of half angle δ, in which all but a small fraction ? of the total energy is emitted. To the same order we give also the average values of thrust momenta and spherocity distributions.     

The Lefschetz number of an involution on the space of harmonic cusp forms ofSL 3

Inventiones mathematicae -     

The frequency scale of speech intonation.

In intonation research, prominence-lending pitch movements have either been described on a linear or on a logarithmic frequency scale. An experiment has been carried out to check whether pitch movements in speech intonation are perceived on one of these two scales or on a psychoacoustic scale representing the frequency selectivity of the auditory system. This last scale is intermediary between the other two scales. Subjects matched the excursion size of prominence-lending pitch movements in utterances resynthesized in different pitch registers. Their task was to adjust the excursion size in a comparison stimulus in such a way that it lent equal prominence to the corresponding syllable in a fixed test stimulus. The comparison stimulus and the test stimulus had pitches running parallel on either the logarithmic frequency scale, the psychoacoustic scale, or the linear frequency scale. In one-half of the experimental sessions, the test stimulus was presented in the low register, while the comparison stimulus was presented in the high register, and, conversely, for the other half of the sessions. The result is that, in all cases, stimuli are matched in such a way that the average excursion sizes in different registers are equal on the psychoacoustic scale.     

实验研究二维圆柱后尾流中涡脱落的有序和混沌现象

本文给出了在Re=50—400范围内二维圆柱后涡脱落的有序和混沌现象的一些初步实验结果。涡脱落由有序到混沌的转捩发生在Re=184.6—193.5之间,但是它不是通过准周期途径。在涡脱落频率与Re数的关系曲线上有两个间断。在Re=70处的间断可能对应于倾斜涡脱落模式的变化,在Re≈193.5处的第二间断对应于由有序到混沌状态的转捩。     

Stability of vertices in random boolean cellular automata

Based on computer simulations, Kauffman (Physica D, 10, 145-156, 1984) made several generalizations about a random Boolean cellular automaton which he invented as a model of cellular metabolism. Here we give the first rigorous proofs of two of Kauffman's generalizations: a large fraction of vertices stabilize quickly, consequently the length of cycles in the automaton's behavior is small compared to that of a random mapping with the same number of states; and reversal of the states of a large fraction of the vertices does not affect the cycle to which the automaton moves.