Influence of the size distribution of granules and of their attractive interaction on the percolation threshold in granulated alloys

Numerical simulation was applied to study the influence of the size distribution of granules and the interaction between them on the percolation threshold in granulated metal-insulator alloys. An alloy model was considered in which metal granules have two characteristic sizes, l and L (with L>l), and the size distribution of granules of greater size L having an average value of approximately L ₀ is described by a normal distribution with a standard deviation d, by a step function with a halfwidth d, or by a delta function. A model with attraction between granules and mechanisms of trapping of an additional granule by an already developed cluster with a characteristic trapping range R was also considered. The percolation threshold significantly grows with the ratio L ₀/l and with R for both two-and three-dimensional cases and tends to flattening at large L/l or R. The calculated results make it possible to explain the high percolation threshold observed for the majority of granulated alloys.     

Spin-glass phase in the ensemble of amphoteric impurities in a semiconductor

The transition to the spin-glass phase at T = 0 has been found for a two-dimensional ensemble of amphoteric impurities with charge transfer. The characteristics of the charge clustering found in specimens at low temperatures have been investigated. The finite size scaling with the critical exponents v = 0.95 ± 0.05, η = 0.75 ± 0.05 has been found for the spin-glass susceptibility _χSG(L,T) and Binder parameter g(L,T).     

Conductance distribution near the Anderson transition

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for quasi-one-dimensional systems of size L ^d–1 × L _z , characterizing by parameters L/ξ and L _z /L (ξ is the correlation length, d is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension d = 2 + ? obtained in the framework of the σ-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small g and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at g = 1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apart of this singularity, the critical distribution for d = 3 is well described by the present theory. One-parameter scaling for the whole distribution takes place under condition, that two independent parameters characterizing this distribution are functions of the ratio L/ξ.     

g-factor of magnesium particles of diameter between 10 and 30 Å

ESR measurements of Mg particles smaller than about 40 Å show evidence for a quantum size effect on the g-value. The large g-shift of our bulk Mg has allowed us to follow the evolution of the g-factor as a function of particle size. The theoretical model of Myles and Buttet, which predicts a gradual change from the bulk g-value to the free electron g-value when the size decreases is in qualitative agreement with the experimental data.     

Phonon coupling effects in magnetic moments of magic and semimagic nuclei

Phonon coupling (PC) corrections to magnetic moments of odd neighbors of magic and semimagic nuclei are analyzed within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional by S. A. Fayans et al. The perturbation theory in g _L ² is used where g _L is the phonon-particle coupling vertex. A model is developed with separating non-regular PC contributions, the rest is supposed to be regular and included into the standard TFFS parameters. An ansatz is proposed to take into account the so-called tadpole term which ensures the total angular momentum conservation with g _L ² accuracy. An approximate method is suggested to take into account higher-order terms in g _L ² . Calculations are carried out for four odd-proton chains, the odd Tl, Bi, In, and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to the magnetic moment in magic nuclei is, as a rule, negligible. In non-magic nuclei considered it is noticeable and, with only one exception, negative. On average it is of the order of ?(0.1–0.5)µ _N and improves the agreement of the theory with the data. Simultaneously we calculated the gyromagnetic ratios g _L ^ph of all low-lying phonons in ²⁰⁸Pb. For the 3 ₁ ^? state it is rather close to the Bohr-Mottelson model prediction whereas for other L phonons, two 5^? and six positive parity states, the difference from the Bohr-Mottelson values is significant.     

The absence of cut-off effects for the fixed-point action in one-loop perturbation theory

In order to support the formal renormalization group arguments that the fixed-point action of an asymptotically free model gives cut-off independent physical predictions in one-loop perturbation theory, we calculate the finite-volume mass gap m(L) in the non-linear σ-model. No cut-off effect of the type g⁴ (a/L)ⁿ is seen for any n. The results are compared with those of the standard and tree level improved symanzik actions.     

Approximate estimate of the form of molecular vibrations

Detailed polarized absorption and emission spectra are presented for anthracene and some of its methyl and methoxy derivatives in rigid solution at 77°K. PPP-SCF calculations show that no new states are introduced below 5 eV by the substitution. The observed effects of chemical substitution on state ordering, polarizations, and oscillator strength correlate quite well with the predictions of the PPP-SCF calculations. A vibrational analysis of the anthracene polarization spectra is carried out. In the near uv long-axis polarized absorption and fluorescence of anthracene, two vibronic origins are identified as a 1630 cm^?1b_1g molecular vibration and a weak 60 cm^?1b_g type of lattice vibration. All long-axis polarized structure in the near uv absorption can be assigned to Franck-Condon progressions built upon these vibronic origins in the ¹L_a band (which is electronically short-axis polarized). Differences in the spectral integrated transition intensity (oscillator strength) between the absorption and the emission reveal an additional long-axis component in the high energy region of the ¹L_a absorption which could be evidence for the hidden ¹L_b band in anthracene. However, there is no clear cut structural evidence for this state in the polarization spectrum. This hidden transition is made allowed by methoxy substitution. In the symmetric 2,3-dimethoxyanthracene, the ¹L_b band appears at 365 nm as a new transition. In 2-methoxyanthracene the ¹L_a and the ¹L_b are strongly mixed. The anomalous short-axis polarization of the ¹L_b band, predicted by the theory for 2-methoxyanthracene, is confirmed by the polarization data. Methoxy substitution also reveals new weak bands, located between the ¹L_b and ¹B_b bands, of B_1g and A_1g parentage, which are successfully predicted by the PPP-SCF calculations.     

Quark mixing angles in the left-ringt symmetric model with lightW R fromK 0-K 0 mixing

K _L?K _S mass difference and the CP violation parameter, ?, of theK ⁰ ? \(\overline {K^0 } \) system are used to set bounds on the right-handed Cabibbo-like angle and the CP violating phase angle in the left-right symmetric electroweak model of four quarks. The corresponding mixing and phase angles in typical left-right asymmetric models (g _L≠g _R) are also determined.     

Saturated absorption spectroscopy: Elimination of crossover resonances with the use of a nanocell

It is demonstrated that the velocity-selective optical pumping/saturation resonances of the reduced absorption in a Rb vapor nanocell with thickness L = λ, 2λ, and 3λ (resonant wavelength λ = 780 nm) allow for the complete elimination of crossover (CO) resonances. We observe well-pronounced resonances corresponding to the F _g = 3 → F _e = 2, 3, and 4 hyperfine transitions of the ⁸⁵Rb D₂ line with line widths close to the natural width. A small CO resonance located midway between F _g = 3 → F _e = 3 and F _g = 3 → F _e = 4 transitions appears only for L ≥ 4λ. The D₂ line (λ = 852 nm) in a Cs nanocell exhibits a similar behavior. From the amplitude ratio of the CO and VSOP resonances, it is possible to determine the thickness of the column of alkali vapor in the range of 1–1000 μm. The absence of the CO resonances for nanocells with L ～ λ is attractive for the frequency reference application and for studying the transitions between the Zeeman sublevels in external magnetic fields.     

A two dimensional theoretical model for describing gain coefficient in N2-lasers and the model validity for CVL and excimer lasers

Based on our previously reported measurements on the gain-value in a N₂- laser and numerical calculations, we introduce a method to obtain an analytical expression for the small signal gain, g₀, where the dependency of g₀ on the laser geometrical configuration, including electrodes length and gap separation, is demonstrated. For this study one- and two-dimensional approaches for the photon density have been applied independently to determine gain-parameter, where for explaining the observed dependency of the gain-parameter on the laser electrodes separation, d_AMP, which was found experimentally and explained by an empirical expression of the type g₀ = r + q/d_AMP, with r and q some constants, realization of introducing an extra dimension along the gap separation was unavoidable. For the electrodes length, l_AMP, we have already shown that an empirical equation of the type g₀ = m + n/l_AMP, with m and n some constants, is consistent with the measurements corresponding to N₂-lasers. With this realization, it is proved that the gain-parameter in N₂-lasers can be written as g₀^{above threshold} = m″ + g_0z(γ_L^z, z) + g_0y(γ_L^y, y), where it consists of two independent gain-values along the electrodes length (z) and gap separation (y) with the corresponding power losses given by γ_L^z and γ_L^y. m″ is a very small quantity showing that laser is operating slightly above the threshold. The results of this calculation are consistent with our recent measurements and also other reported N₂-laser gain values measured under moderate current density conditions. To check the validity of the model for other types of lasers, the reported gain-values for copper vapor lasers of different laser tube radii, R_AMP, and tube lengths, l_AMP, have been examined using the one-dimensional model of either g₀(R_AMP) or g₀(l_AMP) and the consistency with the observed measurements was found to be quite satisfactory. The model was also found to be valid for the excimer lasers of different types, different gas mixtures and pressures at a constant input operational voltage. Due to limited numbers of the reported experimental measurements, for the graphs preparation of g₀(l_AMP) in excimer lasers we used the observed data at V₀ = 30 kV and also some variations of the input voltages in the range of ΔV ≅ 20 kV have been adopted. The results for both cases were found to be consistent with the proposed one-dimensional model.     

Exact asymptotic form for the β function in quantum electrodynamics

It is shown that the asymptotic form of the Gell-Mann-Low function in quantum electrodynamics can be determined exactly: β(g) = g for g → ∞, where g = e ² is the running fine-structure constant. This solves the problem of electrodynamics at small distances L (for which dependence g ∞ L ^?2 holds) and completely eliminates the problem of “zero charge.”     

Linear-chain ferromagnetism in the one-dimensional compounds CoCl2(pyrazole)2 and CoCl2(indazole)2

Two linear-chain compounds of formula CoCl₂L₂, with L = pyrazole (pz) and indazole (indz), have been investigated with the aid of IR, far-IR, ligand field and ESR spectra. Magnetic susceptibility data have been collected in the temperature region 4.2–80 K. Analysis of the susceptibility data in terms of the Ising model yielded the values of the ferromagnetic intrachain exchange constants J = 7.2(6) and 7.4(9) cm^-1 for the pz and indz compound, with corresponding g-values of g∥ = 7.9(7), g⊥ = 4.6(9) and g∥ = 10.8(9), g⊥ = 3(1), respectively. The results are discussed and compared with the similar compound CoCl₂(pyridine)₂. The influence of the bridge geometry and of the π-bonding properties of the organic ligands on the exchange constant are considered for the explanation of different J-values. It is suggested that the π-bonding properties of the organic ligand influence the magnitude of the superexchange constant to a great extent.     

Decoupled magnetic subsystems in the random mixture FepCo1-p(C5H5NO)6(ClO4)2

Specific heat data on the random mixtures Fe_pCo_1-pL₆(ClO₄)₂, where L = C₅H₅NO, are presented. The Fe and Co magnetic atoms have competing anisotropies since the pure Fe and Co compounds are known to be good examples of the simple cubic, $\text{S =}\text{1}\text{2}$, Ising and XY magnet, respectively. The experimental data show the two magnetic subsystems in the mixtures to be almost completely decoupled, which is a consequence of the fact that the crystal field anisotropies of the Fe²⁺ and Co²⁺ ions, yielding g_∥ ? g_⊥ and g_⊥ ? g_∥, respectively, are very strong compared to the magnetic exchange interactions. Consequently the two magnetic subsystems experience one another as nonmagnetic impurities. A model is presented which explains these results, as well as those previously found for related random mixtures, in terms of two interpenetrating percolation clusters.     

GPU-based single-cluster algorithm for the simulation of the Ising model

We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L = 4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L = 256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.     

Matter fields and metric deformations in multidimensional unified theories

This paper describes a first study of the effects due to including matter fields in generalized Kaluza-Klein (KK) theories with nonabelian compact gauge group G and nontrivial fibres $\text{V}$^K. The approach is based on the first-order Einstein-Cartan (EC) general relativity in (4 + K) dimensions. In the EC theory there are two basic mechanisms which can lead to a spontaneously compactified KK background geometry R⁴ × $\text{V}$^K: (A) a particular kind of energy-momentum density matter condensate in the quantized ground state, or (B) a particular kind of spin-density matter condensate. If (A) or (B) are operating, the inconsistencies usually found between the KK ansatz and the matter-free EC theory are avoided. Mechanism (B) works only when $\text{V}$^K is parallelizable. It is shown that the expansion of matter fields in normal modes on $\text{V}$^K implies that one must include deformations of the Yang-Mills (YM) potentials contained in the usual KK metrics. We discuss and characterize one class of such deformations. As a case study, we consider fibres $\text{V}$^K ～ G′, where G′ is a semisimple compact Lie group. We allow for the “maximal” YM gauge group G_L′ × G_R′. We carry out the harmonic analysis for spinor fields and study the mass spectrum and YM quantum numbers of the normal modes. We rely on mechanism (B) to provide a curvature-free connection (“parallelization”) on $\text{V}$^KG′ by means of a suitable vertical constant torsion. Minimal YM couplings are of size $\text{l}\text{L}\text{≡ g}$, where l is the Planck length and L is the length of the fibre; nonminimal YM couplings are of size L. Nonzero masses are of size L^?1. The massless modes are found and discussed. There would be no massless modes if the parallelizing vertical torsion were absent. This torsion also implies the vanishing of the cosmological constant. When the theory is restricted to massless modes, the YM deformations disappear and the dimensional reduction to four dimensions yields an effective YM theory, which is renormalizable at energies far below L^?1: the effective theory is obtained by letting L → 0 with g ? 1 fixed and by neglecting all masses of order L^?1; g corresponds to the bare YM coupling constant. The surviving effective YM gauge group is G_L′ and the matter fields are in a particular representation of G_L′ × G_R′, corresponding to the zero mass eigenvalue. Explicit examples are discussed for G′ = SU(2) and G′ = SU(3).     

A generalization of the inhomogeneity measure for point distributions to the case of finite size objects

The statistical measure of spatial inhomogeneity for n points placed in χ cells each of size k×k is generalized to incorporate finite size objects like black pixels for binary patterns of size L×L. As a function of length scale k, the measure is modified in such a way that it relates to the smallest realizable value for each considered scale. To overcome the limitation of pattern partitions to scales with k being integer divisors of L, we use a sliding cell-sampling approach. For given patterns, particularly in the case of clusters polydispersed in size, the comparison between the statistical measure and the entropic one reveals differences in detection of the first peak while at other scales they well correlate. The universality of the two measures allows both a hidden periodicity traces and attributes of planar quasi-crystals to be explored.     

Yang-Lee zeros of triangular Ising antiferromagnets

In our previous research, by combining both the exact enumeration method (microcanonical transfer matrix) for a small system (L=9) with the Wang-Landau Monte Carlo algorithm for large systems (to L=30) we obtained the exact and approximate densities of states g(M,E), as a function of the magnetization M and exchange energy E, for a triangular-lattice Ising model. In this paper, based on the density of states g(M,E), the precise distribution of the Yang-Lee zeros of triangular-lattice Ising antiferromagnets is obtained in a uniform magnetic field as a function of temperature for a 9×9 lattice system. Also, the feasibility of the Yang-Lee zero approach combined with the Wang-Landau algorithm is demonstrated; as a result, we obtained the magnetic exponents for triangular Ising antiferromagnets at various temperatures.     

The prediction of traffic noise using a scale model

This paper describes the development of means of using a scale model of a road and its surrounding urban environment to predict L_eq, L₁₀ and other measures of traffic noise. The model described is that of the Centre Scientifique et Technique du Batiment, Grenoble, France. The problems involved in the development include allowance for relative sound absorption between real life and the model situation, the constraints on the accuracy of the results due to noise source variations on the model and the effects of the finite size of the model.     

The magnetic moments and halflives of the 5/2− states in199Hg and197Hg and the discrepancies in the experimental hyperfine fields at Hg in Fe

The Larmor-precession frequencies for¹⁹⁷Hg in Fe have been determined to beω _L = 1291 ±25 MHz at 293 K andω _L = 1334±25 MHz at 105 K. For¹⁹⁹Hg in Feω _L =1372±50 MHz has been measured at 293 K. The half-lives of the 5/2^? states in¹⁹⁷Hg and¹⁹⁹Hg have been remeasured asT _1/2(¹⁹⁷Hg)=8.1±0.16 nsec andT _1/2(¹⁹⁹Hg)=2.45±0.05 ns, respectively. The magnetic moment of the 5/2^? 158keV state in¹⁹⁹Hg was redetermined by the integral perturbed angular correlation method in an external magnetic field of 47kG asμ(5/2 ^? ) = 0.905±0.091 nm. With this new value consistency for the magnetic hyperfine fields at Hg in Fe measured with the TDPAC-method and with the NMR/ON-method is obtained. This fact is used to determine theg-factors of the 5/2^? states in¹⁹⁷Hg and¹⁹⁹Hg more precisely fromω _L -values given above:g(¹⁹⁷Hg)=0.342(6);g(¹⁹⁹Hg)=0.352(13). The magnetic moments of the first excited 2⁺ states in^198–204Hg isotopes which rely on calibrations with the¹⁹⁹Hg-g-factor, are revised.