Multiconfiguration Dirac–Fock calculations of Zn K-shell radiative and nonradiative transitions

Zinc K-shell radiative and radiationless transition rates are calculated using the multiconfiguration Dirac–Fock method. Correlation up to the 4p orbital is included in almost all transition rate calculations. Calculated radiative transition rates and transition probabilities are compared with Scofield's Dirac–Hartree–Slater and Dirac–Hartree–Fock calculations, presenting good agreement with the later. Radiative transition intensity ratios involving the strongest lines are compared with theoretical, experimental, and empirical-fit values. Most ratios are in close agreement with the empirical-fit values from NIST's Fundamental Parameters database. Calculated radiationless transition rates and ratios are compared with Chen et al.'s Dirac–Fock values and Safronova et al.'s Dirac–Fock values. The K-LL transition rates are overall lower than Chen et al.'s values, whereas the K-LX and K-XY transition rates are overall higher. Calculated K-LX/K-LL and K-XY/K-LL ratios are relatively close to the experimental values compared. Some calculated intensities relative to K-L are in good agreement with the experimental values, whereas others present worse agreement. The calculated fluorescence yield is higher than all theoretical, experimental, and empirical-fitted values compared, probably because the total radiationless transition rate value calculated in the present work is relatively low.     

Overview and calculation of X-ray K-shell transition yields for comprehensive data libraries

The simulation of atomic relaxation relies on data libraries with tabulated partial fluorescence yield values of radiative transitions, commonly derived from the Evaluated Atomic Data Library (EADL). However, recent studies support that the data library EADL could be improved by adopting Scofield's Hartree-Fock calculations instead of current Scofield's Hartree-Slater calculations. This work presents a bibliography overview of relevant atomic parameter values in order to verify the partial fluorescence yields presented in EADL. The references include libraries and articles, in which the atomic parameter values were theoretically calculated, experimentally measured, or obtained with semi-empirical and empirical fitting formulas. We present a comparison of total K-shell fluorescence yields and partial K-L₂, K-L₃, K-M₂, K-M₃ fluorescence yields that are either obtained directly from its references, or are derived from atomic parameters presented in these references. Additionally, we obtain comprehensive partial fluorescence yield values from the combination of semi-empirical and empirical fitting functions from different references. The comparisons performed in this work confirm that total K-shell, partial K-L₂, and partial K-L₃ fluorescence yield values, obtained from Scofield's Dirac-Slater calculations have better agreement with the most recent empirical values. Partial K-M₂, and partial K-M₃ fluorescence yield values obtained from Scofield's Dirac-Fock calculation have better agreement with the most recent empirical values. Therefore, further studies should be performed before changing the EADL data library.     

Modified Vonk's Method to Determine Crystallinity and Crystal Distortion in Polymers

Using a modified method developed from Vonk's method, detailed values of crystallinity and crystal disorder were obtained by wide angle X-ray diffraction (WAXD). In Vonk's method, the crystallinity (w) is determined by extrapolation of the WAXD experimental curve back to zero scattering angle, while the distortion factor (k) is determined by the inclination of the experimental curve at zero scattering angle. In our new method, both w and k are determined at the same time by using the least squares method. In order to show the efficiency of our method, the new fitting procedure was applied to the experimental values of polyethylene and polyethylene terephthalate as measured by Vonk, and the values of w and k determined by our new method were compared with those found by Vonk's method. The new fitting method has the advantage that it uses the whole experimental curve. Moreover, our modified Vonk's method enables us to discuss crystal distortions as arising from first-kind (thermal) disorder and second-kind (paracrystalline) disorder.     

Totally secure classical communication utilizing Johnson (-like) noise and Kirchoff's law

An absolutely secure, fast, inexpensive, robust, maintenance-free and low-power-consumption communication is proposed. The states of the information bit are represented by two resistance values. The sender and the receiver have such resistors available and they randomly select and connect one of them to the channel at the beginning of each clock period. The thermal noise voltage and current can be observed but Kirchoff's law provides only a second-order equation. A secure bit is communicated when the actual resistance values at the sender's side and the receiver's side differ. Then the second order equation yields the two resistance values but the eavesdropper is unable to determine the actual locations of the resistors and to find out the state of the sender's bit. The receiver knows that the sender has the inverse of his bit, similarly to quantum entanglement. The eavesdropper can decode the message if, for each bits, she inject current in the wire and measures the voltage change and the current changes in the two directions. However, in this way she gets discovered by the very first bit she decodes. Instead of thermal noise, proper external noise generators should be used when the communication is not aimed to be stealth.     

Solutions of Laplace's equation with simple boundary conditions,and their applications for capacitors with multiple symmetries

We find solutions of Laplace's equation with special boundary conditions, using a general curvilinear system of coordinates. We call this purely geometrical solutions Basic Harmonic Functions (BHF's). From them we obtain more general solutions with arbitrary constant values on the boundaries. Further, the BHF's are used to obtain the capacitance of many electrostatic configurations of conductors. Applications in complex geometries are given. Finally, expressions for electric fields between two conductors and surface charge densities are obtained in terms of generalized curvilinear coordinates. The present method can be extrapolated to other linear homogeneous differential equations.     

Thermodynamic and scaling behaviour in finite diffusion-limited aggregation

Rényi's entropies for diffusion-limited aggregates are studied as a function of the number N of particles contained in the aggregates. It is found that Rényi's values increase with log N in a linear fashion, and that the aggregates exhibit multifractal behaviour for finite values of N. When N → ∞, the aggregate has a monofractal structure. Rényi's entropies depend on the fractal dimension of the aggregate. When the fractal dimension increases, the values of K_q decrease for q ? 1> and increase for q > 1.     

Interfacial properties of Morse fluids

The interfacial properties as reflected in the interfacial tension values and the density profile of Morse fluids has been studied. The parameter range is chosen to coincide with that describing the behaviour of solid metals. The interfacial tension has been found to follow Guggenheim's and MacLeod's relations. However, the constants, while independent of temperature for each metal, are not the universal values predicted; with the exception of Macleod's exponent p. The density profile illustrates the change in densities across the interface dividing the coexisting vapour and liquid phases. The correlation length is also found to follow the universal relation with temperature, but again the constants, while independent of temperature, are dependent on the type of metal. The value of constant ν is found to be different for all five metals considered and is found to differ from the three-dimensional Ising model value of ν?=?0.630, which is also predicted by applying the Lennard–Jones model.     

Statistical properties of stock market indices of different economies

Daily changes in the logarithm of stock market index from 1997 to 2004 are analyzed for countries from three subgroups of economies classified by the International Monetary Fund (IMF): developing Asian countries, newly industrialized Asian economies and major advanced economies. For all markets, the daily changes are well fitted by a non-Gaussian stable probability density. The time evolution of the standard deviation of the daily changes for each market obeys a power law. However, the developing Asian countries have the smallest stable density characteristic parameters α and the largest exponents b of the power law, except China's SSEC and India's SENSEX. The values of α and b for these two markets are closer to those of the newly industrialized Asian economies; in particular, those for China's SSEC are close to those for Hong Kong's HSI. The values of α and b for the newly industrialized Asian economies are in between those for the developing Asian countries and major advanced economies, consistent with the results for generalized Hurst exponent [Physica A 324 (2003) 183]. The daily changes for the developing Asian countries and newly industrialized Asian economies have a weak long-range correlation, whereas the daily changes for the major advanced economies have a weak long-range anti-correlation.     

Efficient and accurate method for radiation transfer problems

An efficient method of analysis, which utilizes trial functions based on Case's eigenvalues, is developed for solving radiation transfer in an absorbing and scattering homogeneous semi-infinite plane-parallel medium subjected to externally incident radiation. Expressions for the forward and backward intensities, reflectivity and total radiation intensity are included. Numerical results are given and compared involving different forms of the externally incident radiation on the boundary surface. It is shown that the solution converges rapidly to the exact results and that lower-order solutions predict values of the physical parameters that are accurate to five figures in all values of the single-scattering albedos in the range 0.1 ≤ ω ≤ 1. The method has been also used to get approximate formulae for calculating Chandrasekhar's characteristic H-functions and their moments.     

Theoretical study on the structural,mechanical, electronic properties and QTAIM of CrB_4 as a hard material

Using the first-principles calculations based on spin density functional theory(DFT), we investigate the structure,elastic properties, and electronic structure of Pnnm-CrB4. It is found that Pnnm-CrB_4 is thermodynamically and mechanically stable. The calculated elastic properties such as the bulk modulus, shear modulus, Young's modulus, and Poisson's ratio indicate that CrB_4 is an incompressible material. Vicker's hardness of Pnnm-CrB_4 is estimated to be 26.3 GPa, which is in good agreement with the experimental values. The analysis of the investigated electronic properties shows that PnnmCrB_4 has the metallic character and there exist strong B–B and Cr–B bonds in the compound, which are further confirmed by Bader's quantum theory of atoms in molecules(QTAIM). Thermodynamic properties are also investigated.     

A Markoffian model for hadrons

The hadron is considered as a system consisting of other bound hadrons, the configuration state of which changes with the time. Its time development is described as a Markov process by Kolmogorov's equations. The stationary solution of Kolmogorov's equations for the Markoffian hadronic system makes it possible to calculate certain physical parameters for stable hadrons. The calculation of the magnetic moments of the proton and neutron in this model yields values which are in good agreement with the experimental data.     

Effects of surface and interface energies on the bending behavior of nanoscale multilayered beams

A modified continuum model of the nanoscale multilayered beams is established by incorporating surface and interface energies. Through the principle of minimum potential energy, the governing equations and boundary conditions are obtained. The closed-form solutions are presented and the overall Young's modulus of the beam is studied. The surface and interface energies are found to have a major influence on the bending behavior and the overall Young's modulus of the beam. The effect of surface and interface energies on the overall Young's modulus depends on the boundary condition of the beam, the values of the surface/interface elasticity constants and the initial surface/interface energy of the system. The results can be used to guide the determinations of the surface/interface elasticity properties and the initial surface/interface energies of the nanoscale multilayered materials through nanoscale beam bending experiments.     

Comparison of the simplicial method with Wilson's lattice gauge theory for U(1)3

In the simplicial version of lattice gauge theory, euclidean path integrals are approximated by tiling spacetime with simplexes and by linearly interpolating the fields throughout each simplex from their values at the vertices. This method is compared with Wilson's lattice gauge theory for U(1) in three dimensions. As a standard of comparison, the exact values of Creutz ratios of Wilson loops in the continuum theory are computed. Monte Carlo computations using the simplicial method give Creutz ratios within a few percent of the exact values for reasonably sized loops at β = 1,2,and10. Similar computations using Wilson's method give ratios that typically differ from the exact values by factors of two or more for 1 ⩽ β ⩽ 3.5 and that have the wrong β dependence. The better accuracy of the simplicial method is due to its use of the action and domain of integration of the exact theory, unaltered apart from the granularity of the simplicial lattice. Data on the action density and the mass gap are also presented.     

Fundamental frequencies of non-circular,elastic, hinged arcs

Lowest natural frequencies of elastic hinged arcs are calculated by using Rayleigh's principle. The effect of variable curvature is taken into account and the results are compared with values available in the open literature.     

Exact solution of Kramers' problem for piecewise parabolic potential profiles

This paper presents a general procedure for deducing exact time characteristics of Brownian diffusion in the high damping limit in piecewise parabolic pontential profiles.Our approach to solve this problem is based on the Laplace transform method for obtaining the desired time characteristics. For some concrete examples of piecewise parabolic profiles' exact values of metastable state decay times and bistable system relaxation times are found. These results are valid for any height of the potential barrier and coincide with Kramer's results for a high potential barrier. Conditions for the validity of Kramer's formula are also derived.     

The influence of grain size and texture on the Young's modulus of nanocrystalline nickel and nickel–iron alloys

Hardness and Young's modulus were measured by nanoindentation on a series of electrodeposited nanocrystalline nickel and nickel–iron alloys. Hardness values showed a transition from regular to inverse Hall–Petch behaviour, consistent with previous studies. There was no significant influence of grain size on the Young's modulus of nanocrystalline nickel and nickel–iron alloys with grain sizes greater than 20?nm. The Young's modulus values for nanocrystalline nickel and nickel–iron alloys for grain sizes less than 20?nm were slightly reduced when compared to their conventional (randomly oriented) polycrystalline counterparts. The observed trend with decreasing grain size was found to be consistent with composite model predictions that consider the influence of intercrystalline defects. However, there was some notable variability of the measured values when compared to the model predictions. Three theoretical relationships were used to characterise the anisotropic elastic behaviour of these materials. As a result, texture was also considered to have an influence on the measured Young's modulus and used to explain some of the observed variability for the entire grain size range (9.8–81?nm).     

Theoretical investigation on electronic structure and mechanical properties of cubic crystallographic structures with point defects in Al-based alloys

Electronic structure and mechanical properties of cubic crystallographic structures with point defects in Al-based alloys are investigated using the first-principles calculations. Equilibrium structural parameters and mechanical parameters such as bulk modulus, shear modulus, Young's modulus, Poisson's ratio and anisotropy are calculated and agreed well with experimental values. Effects of point defects on the electronic structures and mechanical properties of such cubic phases are further analyzed and discussed in view of the charge density and the density of states.     

Features of a setup for investigation of two-particle exclusive reactions with high transfer momentum

The technique of experimental design for electron and photon exclusive scattering on nucleons with transfer momentum values of the order of 10 GeV² is presented. The multichannel detectors providing the possibility to realize exclusive experiments with luminosity values of 10³⁹ cm^?2/s are described.     

Comparison of experimental microwave tunneling data with calculations based on Maxwell's equations

We compare microwave tunneling experiments using three types of potentials with calculations describing these systems, using only Maxwell's equations. The values obtained are identical within a very narrow error limit. Thus, microwave tunneling through evanescent waveguide regions, including superluminal tunneling velocities, is described by Maxwell's equations. The dispersion relation yields purely imaginary, complex, or real k-values. As an analogy, microwave tunneling presents an ideal tool for studying quantum mechanical tunneling.     

Is there a reality out there?

Joseph Bertrand's 1888 evidencing that assignment of a probability depends upon what one chooses to know or not and to control or not, congruent with Grad's 1961 evidencing that statistical entropy depends upon what one deems relevant or not in formalization and measurement, radically undermine common sense realism; mean values are symbols, but symbols of what? For that very reason, recent clever conceptualizations of the quantum measurement process via partial tracing do not restore realism: How could deliberate ignorance generate a reality? Beyond this, Born's and Jordan's quantal wavelike probability calculus, entailing algebraic nonseparability and spacetime nonlocality, blurs “reality” still more radically. Thus information stands out as the master word, with its two reciprocal aspects: knowledge and organization.