Representation of the three-body Coulomb Green's function in parabolic coordinates: paths of integration

The possibility is discussed of using straight-line paths of integration in computing the integral representation of the three-body Coulomb Green's function. In our numerical examples two different integration contours are considered. It is demonstrated that only one of these straight-line paths provides that the integral representation is valid

Relativistic mask method for electron momentum distributions after ionization of hydrogen-like ions in strong laser fields

Wavefunction-splitting or mask method, widely used in the non-relativistic calculations of the photoelectron angular distributions, is extended to the relativistic domain within the dipole approximation. Since the closed-form expressions for the relativistic Volkov states are not available within the dipole approximation, we build such states numerically solving a single second-order differential equation. We calculate the photoelectron energy spectra and angular distributions for highly charged ions under different ionization regimes with both the direct and the relativistic mask methods. We show that the relativistic mask method works very well and reproduces the electron energy and angular distributions calculated by the direct method in the energy range where both methods can be used. On the other hand, the relativistic mask method can be applied for longer laser pulses and/or higher photoelectron energies where the direct method may have difficulties

Correction of some mechanical characteristics of human dentin under compression considering the shape effect

The paper is aimed to determine the true compression strength and Poisson's ratio of human dentin. The origin of the shape effect in dentin under compression is discussed, too. It was shown that the shape effect is mainly caused by the friction between the surface of the sample and the compression plates. Ratio d/h = 4 is the optimal proportion between the diagonal of compression surface and the height of dentin sample for compression testing. Inhomogeneous deformation takes place in the sample with a low aspect ratio whereas lateral deformation is suppressed in the sample with a high aspect ratio. There is significant difference between the conventional compression strength and the true compression strength. True compression strength of human dentin is 432 ± 16 MPa, the Young's modulus is 4.04 ± 0.12 GPa and Poisson's ratio of human dentin is 0.14 ± 0.04. © 2014 Elsevier B.V. All rights reserved.Russian Foundation for Basic Research, РФФИ: 14-08-31691The reported study was supported by RFBR , research project No. 14-08-31691

The parabolic Sturmian-function basis representation of the six-dimensional Coulomb Green's function

The square integrable basis set representation of the resolvent of the asymptotic three-body Coulomb wave operator in parabolic coordinates is obtained. The resulting six-dimensional Green's function matrix is expressed as a convolution integral over separation constants.Comment: 14 pages, 2 figure

Recovering Grammar Relationships for the Java Language Specification

Grammar convergence is a method that helps discovering relationships between different grammars of the same language or different language versions. The key element of the method is the operational, transformation-based representation of those relationships. Given input grammars for convergence, they are transformed until they are structurally equal. The transformations are composed from primitive operators; properties of these operators and the composed chains provide quantitative and qualitative insight into the relationships between the grammars at hand. We describe a refined method for grammar convergence, and we use it in a major study, where we recover the relationships between all the grammars that occur in the different versions of the Java Language Specification (JLS). The relationships are represented as grammar transformation chains that capture all accidental or intended differences between the JLS grammars. This method is mechanized and driven by nominal and structural differences between pairs of grammars that are subject to asymmetric, binary convergence steps. We present the underlying operator suite for grammar transformation in detail, and we illustrate the suite with many examples of transformations on the JLS grammars. We also describe the extraction effort, which was needed to make the JLS grammars amenable to automated processing. We include substantial metadata about the convergence process for the JLS so that the effort becomes reproducible and transparent

On some features of the shape effect in human dentin under compression

Contribution of inorganic and organic phases of human dentin in the shape effect under uniaxial compression is discussed. Comparison of the deformation behavior under compression of the samples with the different ratios between the diagonal of the compression surface and the height of quartz glass, aluminum oxide and PMMA with dentin samples having similar aspect ratios is carried out. In addition, the comparison of the deformation behavior of these materials under tensile stress is carried out. It has been shown that the shape effect of human dentin under compression is caused by the inorganic phase. The organic phase of dentin is responsible for the lowering of the Young's modulus and the compression strength and the increasing of its plasticity. Plasticity of the dentin can be additionally provided by its porosity, when the d/h ratio of the samples exceeds 1.5. © 2014 Elsevier B.V.Russian Foundation for Basic Research, РФФИ: 14-08-31691The reported study was supported by RFBR , research project no. 14-08-31691

Influences of the sample shape and compression temperature on the deformation behavior and mechanical properties of human dentin

Deformation behavior and mechanical properties of samples of human dentin having different geometries were studied under compression in liquid nitrogen. In this case, the plastic response of the collagen fibers in dentin was excluded. The findings were compared with the mechanical properties of dentin at room temperature. Such a comparison allows the plastic contribution of collagen in human dentin to be estimated for samples of different shapes. It was shown that the deformation behavior of human dentin under compression is similar at 77 K and 300 K. The dentin samples with low aspect ratio exhibited almost brittle behavior, whereas those with high aspect ratio were prone to considerable deformation. SEM study of the fracture surfaces of samples tested at room and liquid nitrogen temperatures has shown that they are similar. Examination of cracks on the compression surface of samples agrees with this conclusion. However, the mechanical characteristics of dentin depended on the temperature of testing. The compression strength and elastic deformation of dentin at 77 K are higher than these parameters at room temperature, while the plasticity of dentin at 77 K is lower. The plastic contribution of collagen fibers at room temperature was estimated on the basis of this comparison. The total plasticity of dentin is the sum of the contributions of both collagen and the geometry of the sample. The plasticity of dentin samples having a low aspect ratio is provided by collagen fibers only, while geometric factors are dominant for samples with a high aspect ratio. The contribution of collagen fibers to the plasticity of dentin depends on the geometry of samples with an intermediate aspect ratio. © 2014 Elsevier B.V.Russian Foundation for Basic Research, РФФИ: 14-08-31691The authors express the gratitude to Mrs. Sara Coles for her kind help. The reported study was supported by RFBR , research project No. 14-08-31691