Numerical Simulation for Solute Transport in Fractal Porous Media

A modified Fokker-Planck equation with continuous source for solute transport in fractal porous media is considered. The dispersion term of the governing equation uses a fractional-order derivative and the diffusion coefficient can be time and scale dependent. In this paper, numerical solution of the modified Fokker-Planck equation is proposed. The effects of different fractional orders and fractional power functions of time and distance are numerically investigated. The results show that motions with a heavy tailed marginal distribution can be modelled by equations that use fractional-order derivatives and/or time and scale dependent dispersivity

On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering

We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean eld particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter, yielding what seems to be the first results of this kind in this subject

Isogeometric analysis for functionally graded microplates based on modified couple stress theory

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates.Comment: 57 pages, 14 figures, 18 table

Multipole Expansion for the Electron-Nucleus Scattering at High Energies in the Unified Electroweak Theory

The article presents the multipole expansion for the electron-nucleus scattering cross section at high energies within the framework of the unified electroweak theory. The electroweak currents of the nucleus are expanded into simple components with definite angular momentum, which are called the multipole form factors. The multipole expansion of the cross section is a consequence of the above expansion. Besides the familiar electromagnetic form factors, there are weak form factors related to weak interactions, corresponding to the vector and axial (pseudovector) weak currents. We do not use the impulse approximation, the multipole form factors are calculated directly, using only the Born approximation. We will present some examples in the next paper.Comment: 7 pages, 0 figur

Foreword

This work reports on the performances of ohmic contacts fabricated on highly p-type doped 4H-SiC epitaxial layer selectively grown by vapor-liquid-solid transport. Due to the very high doping level obtained, the contacts have an ohmic behavior even without any annealing process. Upon variation of annealing temperatures, it was shown that both 500 and 800 °C annealing temperature lead to a minimum value of the Specific Contact Resistance (SCR) down to 1.3×10−6 Ω⋅cm2. However, a large variation of the minimum SCR values has been observed (up to 4×10−4 Ω⋅cm2). Possible sources of this fluctuation have been also discussed in this paper

Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory

Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory is presented. The core of sandwich beam is fully metal or ceramic and skins are composed of a functionally graded material across the depth. Governing equations of motion and boundary conditions are derived from the Hamilton’s principle. Effects of power-law index, span-to-height ratio, core thickness and boundary conditions on the natural frequencies, critical buckling loads and load–frequency curves of sandwich beams are discussed. Numerical results show that the above-mentioned effects play very important role on the vibration and buckling analysis of functionally graded sandwich beams

Modelling of the low-impulse blast behaviour of fibre–metal laminates based on different aluminium alloys

A parametric study has been undertaken in order to investigate the influence of the properties of the aluminium alloy on the blast response of fibre–metal laminates (FMLs). The finite element (FE) models have been developed and validated using experimental data from tests on FMLs based on a 2024-O aluminium alloy and a woven glass–fibre/polypropylene composite (GFPP). A vectorized user material subroutine (VUMAT) was employed to define Hashin’s 3D rate-dependant damage constitutive model of the GFPP. Using the validated models, a parametric study has been carried out to investigate the blast resistance of FML panels based on the four aluminium alloys, namely 2024-O, 2024-T3, 6061-T6 and 7075-T6. It has been shown that there is an approximation linear relationship between the dimensionless back face displacement and the dimensionless impulse for all aluminium alloys investigated here. It has also shown that the residual displacement of back surface of the FML panels and the internal debonding are dependent on the yield strength of the aluminium alloy

A Planarity Test via Construction Sequences

Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. The approach is different from previous planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm runs in linear time and computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise

Vibration and buckling of composite beams using refined shear deformation

Vibration and buckling analysis of composite beams with arbitrary lay-ups using refined shear deformation theory is presented. The theory accounts for the parabolical variation of shear strains through the depth of beam. Three governing equations of motion are derived from the Hamilton’s principle. The resulting coupling is referred to as triply coupled vibration and buckling. A two-noded C1 beam element with five degree-of-freedom per node which accounts for shear deformation effects and all coupling coming from the material anisotropy is developed to solve the problem. Numerical results are obtained for composite beams to investigate effects of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads and corresponding mode shapes

Static behaviour of functionally graded sandwich beams using a quasi-3D theory

This paper presents static behaviour of functionally graded (FG) sandwich beams by using a quasi-3D theory, which includes both shear deformation and thickness stretching effects. Various symmetric and non-symmetric sandwich beams with FG material in the core or skins under the uniformly distributed load are considered. Finite element model (FEM) and Navier solutions are developed to determine the displacement and stresses of FG sandwich beams for various power-law index, skin-core-skin thickness ratios and boundary conditions. Numerical results are compared with those predicted by other theories to show the effects of shear deformation and thickness stretching on displacement and stresses