Statistics of photocounts of blinking fluorescence of quantum dots

The blinking of quantum dots under the action of laser radiation is described based on a model of a binary (two-state) renewal process with on (fluorescent) and off (non fluorescent) states. The T _on and T _off sojourn times in the on and off states are random and power-law distributed with exponents 0 < α < 1 and 0 < β < 1; the averages of the on and off times are infinite. As a consequence of this, the Gaussian statistics is inapplicable and the process is described using a more general statistics. An equation for the density of distribution p(t _on|t) of the total on time during the observation time t is derived that contains derivatives of fractional orders α and β. A solution to this equation is found in terms of fractional stable distributions. The Poisson transform of the density p(t _on|t) leads to the photon counting distribution and determines the fluorescence statistics. It is demonstrated that, if a blinking process with exponents α < β is implemented, then, at fairly long times, the on time will considerably prevail over the off time, i.e., blinking will be suppressed. This behavior is evidenced by the types of distributions of the total fluorescence time, the decay of relative fluctuations, and the Monte Carlo simulated trajectories of the process.     

Estimates of annoyance of sounds of different character

The character of a sound is defined as the weighted combination of all acoustic factors, not contained in $\text{L}{}_{\mathrm{<mtext>A</mtext>}}$, contributing to its annoyance.From this definition it follows that differences in annoyance due to sounds with equal $\text{L}{}_{\mathrm{<mtext>A</mtext>}}$ are differences in sound character. For the concept of sound character to have real significance it is necessary that listeners agree on the annoyance due to sounds with equal $\text{L}{}_{\mathrm{<mtext>A</mtext>}}$.This paper describes a listening experiment with a variety of sounds of equal $\text{L}{}_{\mathrm{<mtext>A</mtext>}}$. The annoyance due to the sounds was rated by twelve subjects. Their individual ratings show significant agreement. Moreover, their average rating correlates well (0·90) with the ratings obtained by Terhardt and Stoll in a similar experiment.     

Simulation of the contours of spectral lines of closed-ARC radiation

Simulated contours of self-reversed lines of Tl at 535 nm (7²S_1/2−6²P_3/2) and 378 nm (7²S_1/2-6²P_1/2) in alternating-current closed-arc radiation in mercury vapor with an addition of Tll were compared with experimental contours. It is shown that while a single self-reversed contour has many different sets of model parameters that ensure coincidence of experimental and calculated profiles, in the case of operation with a large data file of contours that correspond to different directions of observation along chords perpendicular to the discharge axis, and with different lines that have a common level, such a set of parameters becomes virtually unique. Instantaneous spatial distributions of Hg and Tl atoms in the ground state and of Tl atoms in the 6²P_3/2 state are determined and the parameters of the van der Waals broadening of the 7²S_1/2 level are found. It is shown that a considerable “red” shift of absorption contours in the outer layers of the discharge is observed. The results obtained contradict the presumed existence of local thermodynamic equilibrium in the given discharge. Reported at the Conference “Plasma Physics and Plasma Technologies,” Minsk, September 15–19, 1997 Petrozavodsk State University, 33, Lenin Ave, Petrozavodsk, 185640, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 5, pp. 761–768, September–October, 1998.     

Pb-Mg-Al合金腐蚀机理的电子理论研究

为了了解Pb-Mg-Al合金腐蚀的物理本质, 本文采用基于第一性原理的赝势平面波方法系统地计算了Pb-Mg-Al合金中各物相的结合能、费米能级和局域态密度等电子结构参数, 分析了合金的电化学腐蚀机理. 计算结果表明：Pb-Mg-Al合金中各主要组成物相稳定性大小关系为 Mg₁₇Al₁₂>Mg₂Pb>Mg;Mg,Mg₂Pb和Mg₁₇Al₁₂的费米能级存在E_f(Mg)>E_f(Mg₂Pb)>E_f(Mg₁₇Al₁₂)的关系, 说明Mg最容易失去电子, Mg₂Pb次之, Mg₁₇Al₁₂最难;局域态密度表明, 在同样的外界条件下, 体系中Mg相和Mg₂Pb相对于Mg₁₇Al₁₂均处于不稳定的状态, 容易失去电子, 即容易发生腐蚀. Pb-Mg-Al合金体系中不同物相的费米能级差构成了电化学腐蚀的电动势, 导致电子从费米能级高的Mg相和Mg₂Pb相流向费米能级低的Mg₁₇Al₁₂相, 使Pb-Mg-Al合金发生腐蚀.     

Application of symmetry groups of four-dimensional space in spectroscopy of crystals

A method of classification of many-electron states that involves symmetry groups of four-dimensional space is developed. Taking into account the spatial and temporal symmetry, the selection rules for electric and magnetic dipole transitions are investigated. The reduction relations for the irreducible representations of the orthogonal group O ₄ and the group R ₄ of pure rotations of the four-dimensional space on the groups and O _h ⁴ and O ⁴ of the four-dimensional cube and of the octahedron on the three-dimensional groups O _h and D _6h of the cubic and hexagonal systems, respectively, are obtained. The four-dimensional classification of the levels of the spin-orbit interaction of rare earth ions for the intermediate reduction on the group of the four-dimensional cube is performed. With the help of the irreducible representations of the O ₄ group, the selection rules of magnetic and forbidden electric dipole transitions, as well as of intercombination transitions, are investigated.     

Extension of the module of invertible transformations. Classification of integrable systems

We demonstrate that for the systems of equations, which are invariant under a point group or possess conservation laws of the zeroth or first order, a nontrivial extension of the module of invertible transformations is possible. That simplifies greatly a classification of the integrable systems of equations. Here we present an exhaustive list and a classification of the second order systems of the formu _t =u _xx +f(u, v, u _x v _x ), –v _t=v _xx +g(u, v, u _x ,v _x ), which possess the conservation laws of higher order. The reduction group approach allows us to define the Lax type representations for some new equations of our list.     

Republication of: Exact solutions of the field equations of the general theory of relativity

This is an English translation of a paper by Pascual Jordan, Jürgen Ehlers and Wolfgang Kundt, first published in 1960. The original paper was part 1 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (The other parts of the series will be printed as Golden Oldies in the future.) The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. It is accompanied by an editorial note written by G. F. R. Ellis, and by the biographies of the authors: P. Jordan (written by A. Krasiński) and W. Kundt (written by himself). The biography of J. Ehlers is contained elsewhere in the same issue of GRG, which is devoted to his memory. An editorial note to this paper and a biography can be found in this issue preceding this Golden Oldie and online via doi:. Original paper: Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt, Strenge L?sungen der Feldgleichungen der Allgemeinen Relativit?tstheorie. Akademie der Wissenschaften und der Literatur, Abhandlungen der Mathematisch-naturwissenschaftliche Klasse Nr 2S (1960), pp. 21–105. Reprinted with the kind permission of the Academy of Sciences and Literature, Mainz, and of the authors: Jürgen Ehlers and Wolfgang Kundt. Translated by Anita Ehlers, Anita.Ehlers@t-online.de, and by Manfred Trümper, manfred@truemper.fr, with ample help from Wolfgang Kundt. P. Jordan (Deceased July 31, 1980) J. Ehlers (Deceased May 20, 2008)

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Effect of ultrasound on the kinetics of anti-solvent crystallization of sucrose

The effect of ultrasound on the kinetics of anti-solvent crystallization of sucrose was studied. The influence of temperature, stirring rate, supersaturation and ultrasonic power on the anti-solvent crystallization of sucrose was investigated. The relationship between infrared spectral characteristic band of sucrose and supersaturation was determined with an online reaction analyzer. The crystal size distribution of sucrose was detected by a laser particle-size analyzer. Ultrasound accelerated the crystallization process, and had no impact on the crystal shape. Abegg, Stevens and Larson model was fitted to the experimental data, and the results were the following: At 298.15 K, the average size of crystals was 133.8 μm and nucleation rate was 4.87 × 10⁹ m⁻³·s⁻¹ without ultrasound. In an ultrasonic field, the average size was 80.5 μm, and nucleation rate was 1.18 × 10¹¹ m⁻³·s⁻¹. Ultrasound significantly reduced the average size of crystals and improved the nucleation rate. It was observed that the crystal size decreased with the increase of stirring rate in silent environment. When the stirring rate increased from 250 to 400 rpm, the average size decreased from 173.0 to 132.9 μm. However, the stirring rate had no significant impact on the crystal size in the ultrasonic field. In addition, the activation energy of anti-solvent crystallization of sucrose was decreased, and the kinetic constant of nucleation rate was increased due to the effect of ultrasound. In the ultrasonic field, the activation energy was reduced from 20422.5 to 790.5 J·mol⁻¹, and the kinetic constant was increased from 9.76 × 10² to 8.38 × 10⁸.     

Limit of Fluctuations of Solutions of Wigner Equation

We consider fluctuations of the solution W _ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W _ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W _ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.     

Anomalies of the electronic properties of alloys in the presence of variation of the local magnetic moments

The concentration dependences of the electronic properties (residual electrical resistivity, diffusion thermoelectric power, normal Hall effect, and low-temperature specific heat) and the magnetic characteristics (magnetization and paramagnetic susceptibility) of quasibinary (Pd_xPt_1−x )₃Fe, Pt₃Mn_xFe_1−x , (Pd_xAu_1−x )₃Fe, and Sc_xTi_1−x Fe₂ alloys are investigated. A relationship is established between the anomalous behavior of the kinetic properties and the variation of the local magnetic moments. The absence of corresponding anomalies in the concentration dependence of the specific heat indicates that the density of states at the Fermi level does not change significantly and, therefore, that the conventional Mott two-band model cannot be used to describe the anomalies in the properties of the alloys in question. A single interpretation of the sum-total of the experimental results is given on the basis of the theory of local fluctuations of the electron spin density in metal magnets. Fiz. Tverd. Tela (St. Petersburg) 39, 1257–1262 (July 1997)     

Fracto-mechanoluminescence and mechanics of fracture of solids

The present paper explores the correlation between fracto-mechanoluminescence and fracture of solids and thereby provides a clear understanding of the physics of fracto-mechanoluminescence. When a fluorescent or non-photoluminescent crystal is fractured impulsively by dropping a load on it, then initially the mechanoluminescence (ML) intensity increases linearly with time, attains a maximum value I_m at a particular time t_m and later on it decreases exponentially with time. However, when a phosphorescent crystal is fractured impulsively by dropping a load on it, then initially the ML intensity increases linearly with time, attains a maximum value I_m at a particular time t_m and later on it decreases initially at a fast rate and then at a slow rate. For low impact velocity the value of t_m is constant, however, for higher impact velocity t_m decreases logarithmally with the increasing impact velocity. Whereas the peak ML intensity I_m increases linearly with the impact velocity, the total ML intensity I_T, initially increases linearly with the impact velocity and then it tends to attain a saturation value for higher values of the impact velocity. The value of t_m increases logarithmally with the thickness of crystals, I_m increases linearly with the area of cross-section of crystals and I_T increases linearly with the volume of crystals. Generally, the ML of non-irradiated crystals decreases with increasing temperature of crystals. Depending on the prevailing conditions the ML spectra consist of either gas discharge spectra or solid state luminescence spectra or combination of the both. On the basis of the rate of generation of cracks and the rate of creation of new surface area of crystals, expressions are derived for the ML intensity and they are found to explain satisfactorily the temporal, spectral, thermal, crystal-size, impact velocity, surface area, and other characteristics of ML. The present investigation may be useful in designing of damage sensors, fracture sensors, ML-based safety management monitoring system, fuse-system for army warheads, milling machine, etc. The present study may be helpful in understanding the processes involved in earthquakes, earthquake lights and mine-failure as they basically involve fracture of solids.     

Heat of formation of solid solution of alkali halides

Based on a semicontinuum model, the electrostatic, the polarisation, and the repulsive energy change of a lattice is calculated numerically, as a function of the relaxation of the nearest neighbouring ions of a substitutional impurity in an alkali halide crystal. It is found that for a particular displacement, the total energy change of the lattice is a minimum. Thus the heat of formation of a dilute solid solution is obtained. Here, we report calculations on the heat of formation of the following systems-Na⁺ in LiCl, Li⁺ in NaCl, K⁺ in NaCl, Na⁺ in KCl, Rb⁺ in NaCl, Na⁺ in RbCl, F^? in NaCl, Cl^? in NaF. Br^? in NaCl and Cl^? in NaBr.     

Structure of turbulent flows of incompressible fluids and the parametrization of turbulence

The structure of stationary isotropic, homogeneous turbulence in an incompressible fluid with Re ≫ 1 set into motion by a force with amplitude f ₀ and spatial and temporal time scales of r ₀ and τ ₀, respectively, is examined. It is found that, depending on the magnitude of the force that sets the fluid into motion, three fundamentally different turbulent stationary states of the fluid can develop and the dimensionless parameters responsible for transitions from one state to another, γ=f ₀ τ ₀ ² /r ₀ and Γ=γ ^4/3 Re, are determined. It is shown that for γ≪1 and Γ≪1 a Kolmogorov spectrum with E(k)∝1/k ^5/3 develops in the inertial range. During the transition to turbulent flows driven by large amplitude forces f ₀, i.e., during the transition to a regime with γ≪1 and Γ ≫ 1, a segment of the spectrum with E(k)∝1/k ² develops near the viscous range and “detaches” the Kolmogorov spectrum from the viscous range. Further increases in the amplitude f ₀ of the force, i.e., approaching the parameter range with γ≫1 and Γ≫1, causes the entire inertial range to be “occupied” by a spectrum E(k)∝1/k ², and outside the inertial range, large scale structures with a characteristic size extending to γ ^2/5 r ₀ begin to be generated. In the regime with Γ≪1, the power dissipated per unit mass of fluid is independent of the viscosity, but on going to turbulent regimes with Γ≫1, the viscous losses begin to depend on the viscosity of the fluid. The “turn-off” of viscous dissipation for Γ≫1 shows that a drag crisis can occur simply as the source power is increased, without any further conditions. With this method for the excitation of turbulence, the Loitsyanskii integral diverges for arbitrary values of γ and Γ. A physical mechanism is proposed to explain the readjustment of the spectrum of the turbulent fluctuations at different γ and Γ. These results have all been obtained neglecting intermittency. Zh. éksp. Teor. Fiz. 116, 1630–1647 (November 1999)     

Neutron-interferometric measurement of the coherent scattering length of the isotopes of silver

Employing a new measuring scheme with the D 18 Neutron Interferometer at the ILL, Grenoble, the thermal neutron coherent scattering lengthb _c for bound atoms of natural Ag,¹⁰⁷Ag and¹⁰⁹Ag have been measured at the wavelengthλ=1.8742 Å. The results, corrected for composition and density of the actual samples, are nat Ag:b _c =5.922 (7) fm¹⁰⁷Ag:¹⁰⁷ b _c =7.555 (11) fm¹⁰⁹Ag:¹⁰⁹ b _c =4.165 (11) fm The result is in agreement with an earlier value obtained with the interferometer for nat Ag (5.932 (6)) using a different measuring scheme and a totally different sample. For nat Ag and¹⁰⁷Ag the values determined interferometrically are ?0.05 and ?0.08 fm smaller, repectively, than those measured with the Christiansen filter method.     

Determination of imaginary components of anomalous scattering of some elements from experimental data

Using the Bijvoet difference data reported in the literature for four compounds,viz./it, zinc sulphide, L-α-glyceryl phosphoryl ethanolamine monohydrate, 1-β-arabinofurinosyl cytosine hydrochloride and lithium aluminium oxide, the anomalous dispersion components Δf″ of the stronger anomalous scatterer in each case is calculated accepting the theoretical values for the lighter anomalous scatterers. For MoKα radiation the values turn out to be Δf″ z _n=1.470 (85), and for CuKα Δf″ _P=0.430 (25) Δf″ _C1=0.715 (18) and Δf″ _A1=0.264 (21). Contribution No. 421 from the Department of Crystallography and Biophysics, University of Madras, Guindy Campus, Madras 600025.     

Estimation of the absorption coefficients of the surfaces of classrooms

Measurements of early-decay time and multivariable linear-regression techniques were used to estimate the 125-8000-Hz octave-band absorption coefficients of eight types of surfaces in university classrooms. The eight types were ‘hard surfaces’, ‘paneled surfaces’ (including hard seats and windows), ‘glued-on acoustical tiles’, ‘suspended acoustical ceilings’, ‘carpeted surfaces’, ‘upholstered seats’, ‘porous absorbers’ and ‘Helmholtz-resonator absorbers’. In general, resulting estimates were statistically significant, physically realistic and in good agreement with previous results. Values for suspended acoustical ceilings were significantly lower than published data.     

A method of reduction of Einstein's equations of evolution and a natural symplectic structure on the space of gravitational degrees of freedom

A program is outlined which addresses the problem of thereduction of Einstein's equations, namely, that of writing Einstein's vacuum equations in (3+1)-dimensions as anunconstrained dynamical system where the variables are thetrue degrees of freedom of the gravitational field. Our analysis is applicable for globally hyperbolic Ricci-flat spacetimes that admit constant mean curvature compact orientable spacelike Cauchy hypersurfaces M with degM=0 andM not diffeomorphic toF ₆, the underlying manifold of a certain compact orientable flat affine 3-manifold. We find that for these spacetimes, modulo the extended Poincaré conjecture and the use of local cross-sections rather than a global cross-section, (3+1)-reduction can be completed much as in the (2+1)-dimensional case. In both cases, one gets as the reduced phase space the cotangent bundleT ^* T _M of theTeichmüller space T _M of conformal structures onM, whereM is a given initial constant mean curvature compact orientable spacelike Cauchy hypersurface in a spacetime (V, g _V ), and one gets reduction of the full classical non-reduced Hamiltonian system with constraints to a reduced Hamiltonian system without constraints onT ^* T _M . For these reduced systems, the time parameter is the parameter of a family of monotonically increasing constant mean curvature compact orientable spacelike Cauchy hypersurfaces in a neighborhood of a given initial one. In the (2+1)-dimensional case, the Hamiltonian is the area functional of these hypersurfaces, and in the (3+1)-dimensional case, the Hamiltonian is the volume functional of these hypersurfaces.     

Evaluation of optical parameters of some tellurite glasses

Evaluation of optical parameters of tellurite glasses in the form: 80TeO₂-5TiO₂-(15-x) WO₃-xA_nO_m, where xA_nO_m = 0.01, 1, 3, 5 Nb₂O₅ or 0.01, 0.1, 1, 3 Nd₂O₃ or 0.01, 0.1, 1, 3, 5, 7 Er₂O₃ mol% will be carried out. The optical parameters will be focused on calculating molar refractivity, molar polarizability, oxide ion polarizability, molar cation polarizability, optical basicity, metallization and number of polarizable atoms per unit volume for every glass composition in order to interpret the refractive index of these glasses.