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.     

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.     

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.     

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)     

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.     

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.     

Quasiclassical analysis of the spectra of two groups of central potentials

A method is suggested for analyzing the spectra of central attractive potentials either with Coulomb singularity (intra-atomic potentials) or finite at zero point (potentials in spherical clusters and nuclei). It is shown that, if the orbital degeneracy is removed, then $\varepsilon _{nl} - \varepsilon _{n0} \cong a_{\varepsilon _{n0} } (l + 1/2)^2 $ for small l in the shell n. In atoms and ions, the coefficient a _ε is nonnegative, so that the energy in the n shell increases with l. The validity of this formula for the inner electrons is illustrated by calculating the spectrum of the mercury atom. In cluster potentials, the opposite situation, as a rule, occurs: the larger l, the lower the corresponding level (a _ε<0). However, in the soft potentials of small clusters, spectral regions with different signs of a _ε coexist and the orbitally degenerate level exists in the spectral region where a _ε=0. Aluminum clusters Al_N are taken as an example to find out how the position of the region with the degenerate level varies with varying cluster size N, and it is found that this region is “pushed out” to higher energies with an increase in N. In this connection, the presence of multiply ionized Al_N clusters of the corresponding size in a low-temperature aluminum plasma is discussed.     

Thermodynamic theory of the equation of state of materials

A universal derivation of the thermodynamic equations on the basis of a combined analysis of the exact relations for any material — the virial theorem, the shock adiabat, and the differential thermodynamic identity relating the thermic and caloric equations of state of matter — is given. This combination makes it possible to reduce the fundamental problem of thermodynamics to a boundary-value problem of mathematical physics. Analytic relations T _s=T(P _s,ρ _s and T _s=T(D,u) are obtained for classical systems. Zh. Tekh. Fiz. 68, 1–9 (October 1998)     

The kinetics of the photolysis of thin films of lead iodide

The kinetics of the photolysis of thin films of PbI₂ have been followed using a quartz crystal microbalance method. Rate as a function of temperature, light intensity and wavelength has been determined. The influence of grain size and gaseous ambient has also been investigated. Three ranges of kinetics were identified. Initial; associated with nucleation and surface chemical reactions. Intermediate; associated with photolysis without the intervention of optically absorbing product, gives $\text{(}\text{?θ}\text{?t}\text{)}{}_{\mathrm{T}}\text{,λ,I ∝ T}$. Terminal; attenuation due to lead particles, gives $\text{(}\text{?θ}\text{?t}\text{)}{}_{\mathrm{T}}\text{,λ,I ∝ t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$.Results show that iodine is generated at the solid/vacuum interface and lead is generated in the bulk. Photolysis is described by phenomenological equations involving bulk and surface recombination of hole/electron pairs plus photolysis. A mechanism is proposed in which the rate determining step is anion vacancy diffusion from the surface, the activation energy for photolysis and anion vacancy diffusion being the same.     

Extreme compression behaviour of equations of state

The extreme compression (P→∞) behaviour of various equations of state with K′_∞>0 yields (P/K)_∞=1/K′_∞, an algebraic identity found by Stacey. Here P is the pressure, K the bulk modulus, K^′=dK/dP, and K′_∞, the value of K^′ at P→∞. We use this result to demonstrate further that there exists an algebraic identity also between the higher pressure derivatives of bulk modulus which is satisfied at extreme compression by different types of equations of state such as the Birch–Murnaghan equation, Poirier–Tarantola logarithmic equation, generalized Rydberg equation, Keane's equation and the Stacey reciprocal K-primed equation. The identity has been used to find a relationship between λ_∞, the third-order Grüneisen parameter at P→∞, and pressure derivatives of bulk modulus with the help of the free-volume formulation without assuming any specific form of equation of state.     

Investigation of stability of ordered manganites

Cation-ordered manganites of the PrBaMn₂O₆ system have been obtained using a two-stage synthesis and characterized with respect to the chemical composition, crystal structure, magnetic and magnetotransport properties, and the stability of the ordered state on heating. The physical properties of the cation ordered PrBaMn₂O₆ manganites obtained using this method significantly differ from the properties of cation disordered Pr_0.50Ba_0.50MnO₃ synthesized by means of the conventional ceramic technology and depend on the degree of ordering of the Pr³⁺ and Ba²⁺ cations. In particular, the cation-disordered Pr_0.50Ba_0.50MnO₃ has a cubic perovskitelike unit cell \((SG = Pm\bar 3m,Z = 1)\), while cation-ordered PrBaMn₂O₆ has a tetragonal unit cell (SG = P4/mmm, Z = 2). Cation states in the system under study are reversible. The cation-ordered PrBaMn₂O₆ state remains stable upon heating in an oxidizing medium (P[O₂] = 1 bar) up to 1300°C. The ordering of the Pr³⁺ and Ba²⁺ cations leads to a significant increase in the critical temperatures of phase transitions. In particular, PrBaMn₂O₆ with the maximum degree of ordering is a metallic ferromagnet with the Curie temperature T_C～320 K, whereas T_C of a fully disordered sample is on the order of 140 K. The samples with intermediate degrees of ordering contain two magnetic phases. Slightly below T_C, all such samples exhibit a metal-insulator transition and a peak of the magnetoresistance, which amounts to approximately 10 and 65% in a magnetic field of 9 kOe for the fully ordered PrBaMn₂O₆ and disordered Pr_0.50Ba_0.50MnO₃, respectively. The results are interpreted in terms of the Goodenough-Kanamori empirical rules for indirect exchange interactions with allowance for the degree of ordering of the Pr³⁺ and Ba²⁺ cations.     

Elastic constants of single crystals of the three phases of In---Pb alloys

In a study of the elastic behaviour of the InPb alloys, the elastic stiffness tensor components of crystals of each of the three phases (fct, $\text{c}\text{a}\text{> 1}$; fct, $\text{c}\text{a}\text{> 1}$; fcc) have been obtained as a function of temperature from pulse superposition measurements of ultrasonic wave velocities. Comparison of the elastic stiffness constants obtained for a fct ($\text{c}\text{a}\text{> 1}$) 5 atm.% Pb alloy with those of In itself and those of InTl and InCd alloys, establishes for this phase that alloying with Pb, as with TI and Cd, enhances the softening of the acoustic [110] phonon mode, polarization [1$\text{1}$0] near the Brillouin zone centre. The elastic properties of a 17 atm.% Pb crystal, which is in the fct ($\text{c}\text{a}\text{> 1}$) phase, are quite different from those shown by In alloys in the fct ($\text{c}\text{a}\text{> 1}$ phase; in particular the response to a shear stress is remarkably isotropie: there is no phonon mode softening in this alloy. Neither is there softening of this mode (which corresponds at the zone centre to the shear stiffness $\text{1}\text{2}$(C₁₁;C₁₂)) in crystals of the fee phase — in complete contrast to the dominating influence of the softening of $\text{1}\text{2}$(C₁₁;C₁₂) in the InTl and InCd fee alloys. In fact for a fcc In-75 atm.% Pb alloy the anistropy ratio for shear $\text{2C}{}_{44}\text{(C}{}_{11}\text{C}{}_{12}\text{)}$ is close to unity. The transitions between the three phases of the InPb alloys are markedly first order and acoustic mode softening has a much smaller influence on the elastic behaviour of the fct ($\text{c}\text{a}\text{< 1}$) and fcc InPb alloys than it has on the fct ($\text{c}\text{a}\text{< 1}$) InPb, InCd and InTl alloys.     

Asymptotics of Determinants of Bessel Operators

 For aL ^∞ (ℝ₊)∩L ¹ (ℝ₊) the truncated Bessel operator B _τ (a) is the integral operator acting on L ² [0,τ] with the kernel