Computation of Thin-Walled Prismatic Shells

We consider a prismatic shell consisting of a finite number of narrow rectangular plates and having in the cross-section a finite number of closed contours (fig. 1(a)). We shall assume that the rectangular plates composing the shell are rigidly joined so that there is no motion of any kind of one plate relative to the others meeting at a given connecting line. The position of a point on the middle prismatic surface is considered to be defined by the coordinate z, the distance to a certain initial cross-section z = O, end the coordinate s determining its position on the contour of the cross-section

Torsional-flexural buckling of unevenly battened columns under eccentrical compressive loading

In this paper, an analytical model is developed to determine the torsional-flexural buckling load of a channel column braced by unevenly distributed batten plates. Solutions of the critical-buckling loads were derived for three boundary cases using the energy method in which the rotating angle between the adjacent battens was presented in the form of a piecewise cubic Hermite interpolation (PCHI) for unequally spaced battens. The validity of the PCHI method was numerically verified by the classic analytical approach for evenly battened columns and a finite-element analysis for unevenly battened ones, respectively. Parameter studies were then performed to examine the effects of loading eccentricities on the torsional-flexural buckling capacity of both evenly and unevenly battened columns. Design parameters taken into account were the ratios of pure torsional buckling load to pure flexural–buckling load, the number and position of battens, and the ratio of the relative extent of the eccentricity. Numerical results were summarized into a series of relative curves indicating the combination of the buckling load and corresponding moments for various buckling ratios.National Natural Science Foundation of China (NSFC) under grant number (No.) 51175442 and Sichuan International Cooperation Research Project under grant No. 2014HH002

On astrophysical solution to ultra high energy cosmic rays

We argue that an astrophysical solution to UHECR problem is viable. The pectral features of extragalactic protons interacting with CMB are calculated in model-independent way. Using the power-law generation spectrum $\propto E^{-\gamma_g}$ as the only assumption, we analyze four features of the proton spectrum: the GZK cutoff, dip, bump and the second dip. We found the dip, induced by electron-positron production on CMB, as the most robust feature, existing in energy range $1\times 10^{18} - 4\times 10^{19}$ eV. Its shape is stable relative to various phenomena included in calculations. The dip is well confirmed by observations of AGASA, HiRes, Fly's Eye and Yakutsk detectors. The best fit is reached at $\gamma_g =2.7$, with the allowed range 2.55 - 2.75. The dip is used for energy calibration of the detectors. After the energy calibration the fluxes and spectra of all three detectors agree perfectly, with discrepancy between AGASA and HiRes at $E> 1\times 10^{20}$ eV being not statistically significant. The agreement of the dip with observations should be considered as confirmation of UHE proton interaction with CMB. The dip has two flattenings. The high energy flattening at $E \approx 1\times 10^{19}$ eV automatically explains ankle. The low-energy flattening at $E \approx 1\times 10^{18}$ eV provides the transition to galactic cosmic rays. This transition is studied quantitatively. The UHECR sources, AGN and GRBs, are studied in a model-dependent way, and acceleration is discussed. Based on the agreement of the dip with existing data, we make the robust prediction for the spectrum at $1\times 10^{18} - 1\times 10^{20}$ eV to be measured in the nearest future by Auger detector.Comment: Revised version as published in Phys.Rev. D47 (2006) 043005 with a small additio

Braggoriton--Excitation in Photonic Crystal Infiltrated with Polarizable Medium

Light propagation in a photonic crystal infiltrated with polarizable molecules is considered. We demonstrate that the interplay between the spatial dispersion caused by Bragg diffraction and polaritonic frequency dispersion gives rise to novel propagating excitations, or braggoritons, with intragap frequencies. We derive the braggoriton dispersion relation and show that it is governed by two parameters, namely, the strength of light-matter interaction and detuning between the Bragg frequency and that of the infiltrated molecules. We also study defect-induced states when the photonic band gap is divided into two subgaps by the braggoritonic branches and find that each defect creates two intragap localized states inside each subgap.Comment: LaTeX, 8 pages, 5 figure

Non-minimal electrodynamics and resonance interactions in relativistic plasma

A three-parameter toy-model, which describes a non-minimal coupling of gravity field with electromagnetic field of a relativistic two-component electrically neutral plasma, is discussed. Resonance interactions between particles and transversal waves in plasma are shown to take place due to the curvature coupling effect.Comment: 6 pages, no figures, the short version of the talk at RUSGRAV-13, to be published in Gravitation and Cosmology, 2009, No.

Anomalous Coherent Backscattering of Light from Opal Photonic Crystals

We studied coherent backscattering (CBS) of light from opal photonic crystals in air at different incident inclination angles, wavelengths and along various [hkl] directions inside the opals. Similar to previously obtained CBS cones from various random media, we found that when Bragg condition with the incident light beam is not met then the CBS cones from opals show a triangular line shape in excellent agreement with light diffusion theory. At Bragg condition, however, we observed a dramatic broadening of the opal CBS cones that depends on the incident angle and [hkl] direction. This broadening is explained as due to the light intensity decay in course of propagation along the Bragg direction {\em before the first} and {\em after the last} scattering events. We modified the CBS theory to incorporate the attenuation that results from the photonic band structure of the medium. Using the modified theory we extract from our CBS data the light mean free path and Bragg attenuation length at different [hkl]. Our study shows that CBS measurements are a unique experimental technique to explore photonic crystals with disorder, when other spectroscopical methods become ambiguous due to disorder-induced broadening.Comment: 10 pages, 5 figure

Performance of CUF approach to analyze the structural behavior of slender bodies

This paper deals with the accurate evaluation of complete three-dimensional (3D) stress fields in beam structures with compact and bridge-like sections. A refined beam finite-element (FE) formulation is employed, which permits any-order expansions for the three displacement components over the section domain by means of the Carrera Unified Formulation (CUF). Classical (Euler-Bernoulli and Timoshenko) beam theories are considered as particular cases. Comparisons with 3D solid FE analyses are provided. End effects caused by the boundary conditions are investigated. Bending and torsional loadings are considered. The proposed formulation has shown its capability of leading to quasi-3D stress fields over the beam domain. Higher-order beam theories are necessary for the case of bridge-like sections. Various theories are also compared in terms of shear correction factors on the basis of definitions found in the open literature. It has been confirmed that different theories could lead to very different values of shear correction factors, the accuracy of which is subordinate to a great extent to the section geometries and loading conditions. However, an accurate evaluation of shear correction factors is obtained by means of the present higher-order theories

Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II