Approximation of transient temperatures in complex geometries using fractional derivatives

It is shown that time-dependent temperatures in a transient, conductive system can be approximately modeled by a fractional-order differential equation, the order of which depends on the Biot number. This approximation is particularly suitable for complex shapes for which a first-principles approach is too difficult or computationally time-consuming. Analytical solutions of these equations can be written in terms of the Mittag-Leffler function. The approximation is especially useful if a suitable fractional-order controller is to be designed for the system.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang     

Physical processes underlying the development of shear turbulence

A physical model of the development of turbulence in free shear flows is proposed. The model is based on the results of numerical simulations of turbulent flow development. The main ideas of the proposed theory of turbulence are stated as follows: the onset of turbulence begins with the formation of large vortices; spectral energy transfer involves both direct and inverse cascades; and the inertial range of the energy spectrum develops as a result of concurrent direct and inverse cascades. The dominant physical factors that determine the spectrum include Joukowski forces.     

Computing the sound power in non-uniform flow

An expression for the sound power in an annular duct with swirling mean flow is derived in the high-frequency limit relevant to fan aeroacoustics. The sound power is expressed in terms of the duct normal modes which are computed for several mean flows. It is shown that the mean flow non-uniformity modifies both the pressure-dominated modes and the expression for the sound power. The pressure-dominated modes are not orthogonal and thus one must account for interference between the different radial modes. The interference effects are small for the case of a potential mean flow. For a vortical mean flow interference terms may become significant.     

First-principles calculations of the hyperfine fields on ligands in fluorides

In solid-state physics, a crystal lattice is frequently approximated by an array of interacting ions. In this case, the wave functions of individual ions are assumed to be a fairly good zeroth approximation in calculating the matrix elements of the interaction Hamiltonian of electrons and nuclei of the lattice from first principles. Use of the second-quantization method is proposed for such calculations in the basis of these functions. As an example, the electron transition amplitude from a ligand to the central ion is estimated. The results agree well with the experimental data.