Positive-Part Moments via the Fourier–Laplace Transform

Integral expressions for positive-part moments E X₊^p\mathsf{E}\,X_{+}^{p} (p>0) of random variables X are presented, in terms of the Fourier–Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such an expression is given. This study was motivated by extremal problems in probability and statistics, where one needs to evaluate such positive-part moments.     

High-frequency diffraction corrections to backscattering cross sections from a rough three-dimensional surface

Diffraction corrections to scalar wave fields at perfectly free and rigid rough surfaces were derived by two iterations of the corresponding integral equations. These diffraction corrections to the pressure or normal velocity (which, in the geometrical optics limit, are doubled at perfectly rigid and free surfaces, respectively) were obtained with an accuracy of approximately 1k(2), where k is the wave number of incidence radiation. Based on these corrections to the surface fields, the backscattering cross sections at normal incidence from the statistically rough Gaussian surfaces were derived. It was found that for the gentle roughness, diffraction results in effective "smoothing" of roughness for rigid and free surfaces and increasing of the backscattering cross sections, but for a rigid surface with steep roughness, the "fictitious" surface can be more rough than the real one, and the diffraction corrections become negative.     

Model equations for the Eiffel Tower profile: historical perspective and new results

Model equations for the shape of the Eiffel Tower are investigated. One model purported to be based on Eiffel's writing does not give a tower with the correct curvature. A second popular model not connected with Eiffel's writings provides a fair approximation to the tower's skyline profile of 29 contiguous panels. Reported here is a third model derived from Eiffel's concern about wind loads on the tower, as documented in his communication to the French Civil Engineering Society on 30 March 1885. The result is a nonlinear, integro-differential equation which is solved to yield an exponential tower profile. It is further verified that, as Eiffel wrote, “in reality the curve exterior of the tower reproduces, at a determined scale, the same curve of the moments produced by the wind”. An analysis of the actual tower profile shows that it is composed of two piecewise continuous exponentials with different growth rates. This is explained by specific safety factors for wind loading that Eiffel & Company incorporated in the design of the free-standing tower. To cite this article: P. Weidman, I. Pinelis, C. R. Mecanique 332 (2004).     

Parameterization of electrostatic interactions for molecular dynamics simulations of heterocyclic polymers

The paper focuses on the problem of electrostatic interactions in molecular dynamics simulations of thermal properties of heterocyclic polymers. The study focuses on three thermoplastic polyimides synthesized on the basis of 1,3‐bis‐(3′,4‐dicarboxyphenoxy)benzene (dianhydride R) and three diamines: 4,4′‐bis‐(4″‐aminophenoxy) diphenylsulfone (diamine BAPS), 4,4′‐bis‐(4″‐aminophenoxy) biphenyl (diamine BAPB), and 4,4′‐bis‐(4''‐aminophenoxy) diphenyloxide (diamine BAPO). In the molecular dynamics simulations these polyimides were described by the Gromos53a5 force field. To parameterize the electrostatic interactions four methods of calculating the partial atomic charges were chosen: B3LYP/6–31G*(Mulliken), AM1(Mulliken), HF/6–31G*(Mulliken), and HF/6–31G*(ChelpG). As our parameterization is targeted to reproduce thermal properties of the thermoplastic polyimides, the choice of proper partial charges was finalized on a basis of the closest match between computational and experimental data for the thermal expansion coefficients of the polyimides below glass transition temperatures. Our finding clearly show that the best agreement with experimental data is achieved with the Mulliken partial atomic charges calculated by the Hartree‐Fock method with 6–31G* basis set. Furthermore, in addition to the thermal expansion coefficients this set of partial atomic charges predicts an experimentally observed relationship between glass transition temperatures of the three polyimides under study: . A mechanism behind the change in thermal properties upon the change in the chemical structure in considered polyimides may be related to an additional spatial ordering of sulfone groups due to dipole‐dipole interactions. Overall, the modified force‐field is proved to be suitable for accurate prediction of thermal properties of thermoplastic polyimides and can serve as a basis for building up atomistic theoretical models for describing other heterocyclic polymers in bulk. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 912–923     

Entropy enhancement and black hole microstates

We show that the entropy of fluctuating two-charge supertubes placed in three-charge scaling microstate solutions depends on their "effective" charges, which in strong magnetic fields can be much larger than their charges. This leads to a much larger entropy than one naively would expect. Since fluctuating supertubes source smooth geometries in certain duality frames, we propose that such an entropy enhancement mechanism might lead to a black-hole-like entropy coming entirely from configurations that are smooth and horizonless in the regime of parameters where the classical black hole exists.     

Measure extension by local approximation

Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned sense if and only if it is Carathéodory-measurable.     

Wave diffraction by rough interfaces in an arbitrary plane-layered medium

Abstract

The problem of electromagnetic wave scattering by a slightly rough interface in an arbitrarily layered medium is solved by a small-perturbation method. The bistatic amplitude of scattering as well as the scattering cross sections for statistically rough surfaces are calculated for linear polarized waves. Along with scattering into up-going waves in a homogeneous medium and scattering cross sections in down-going waves into a layered medium, scattering amplitudes from a rough interface in the arbitrarily layered medium are obtained.     

Validation of the Tessier scheme for speciation of metals in soil using the Bland and Altman test

The Tessier extraction method was used for speciation of Cu, Pb, Zn, As, Fe and Mn in a large concentration range in contaminated soil with various mineralogical compositions. The results were compared by X-ray fluorescence spectrometry (XRF) as a reference method using the Bland and Altman test. A sum of five fractions (exchangeable, bound to carbonates, Fe-Mn oxides, organic matter and residual forms) was compared with the total content determined on solid matrix by the reference method. A good agreement between the methods in the whole concentration range was found for Cu, Zn, As, and Fe. For Mn and Pb, XRF was found suitable to verify the sequential extraction only for concentrations above 250 mg kg⁻¹. This was a consequence of a poorer reproducibility of Pb extraction using the Tessier scheme due to a great difference in the mineralogical composition and the diversity of the Pb species identified in soil. The poorer result of Mn was attributed to the spectral interference of Fe in XRF. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.     

Wave diffraction by a concave statistically rough surface

We consider a statistically rough impedance surface that is concave on average in contrast to a plane. Backscattering from such a surface is considered based on the small perturbation theory method. The diffraction problem is divided into two parts which are considered separately: the problem of scattering by small roughness (assumed to be local) and the propagation of incident and scattered fields over a smooth large-scale concave surface. In contrast to the 'two-scale' scattering model, the zero-order unperturbed wavefield is not assumed to be specularly reflected from the local tangent plane to the smooth surface, but it is a solution of a corresponding diffraction problem. Two particular cases of smooth surfaces are considered: first, the inner surface of a concave cylinder with a constant radius and finite angular pattern, and second, a compound surface that consists of a coupled half-plane and the cylindrical surface mentioned above. In a geometrical optics limit and with propagation at low grazing angles, the analytical results for a zero-order (unperturbed) field are obtained for these two cases in the form of a series over multiple specular reflected fields. It is shown that these non-local processes lead to the essential increase in the backscattering cross section in comparison with the two-scale model and tangent-plane approach.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.