Multiple scattering in random media I. Restricted two-body additive approximation

We present a microscopic theory of the problem of finding the properties of a particle interacting with potentials located at random sites. The sites are governed by a general probability distribution. The starting point is the multiple scattering equations for the amplitude k ₁|T |k ₂ in terms of the individual scattering amplitudes k ₁|T |k ₂. We work with quantitiesA defined by k ₁|T |k ₂=k ₁|T |k ₂exp[i(k ₁–k ₂)R ]. The theory is based on a splitting of the fundamental equation forA into equations for the mean A and the fluctuationsAA . Neglect of the fluctuations yields the quasicrystalline approximation. We rearrange the equation forAA to isolate the collective part of the fluctuations. We then make the simplest microscopic truncation which is thatAA is a restricted two-body additive function of the site positions. With the contribution of the collective fluctuations, this yields results forA that are accurate to ordert ⁴.Work supported in part by the National Science Foundation under Contract No. NSF DMRWork supported in part by the National Science Foundation under Contract No. NSF DMR     

Permeability of microscale fibrous porous media using the lattice Boltzmann method

The permeabilities of microscale fibrous porous media were calculated using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Two models of the microscale fibrous porous media were constructed based on overlapping fibers (simple cubic, body-centered cubic). Arranging the fibers in skew positions yielded two additional models comprising non-overlapping fibers (skewed simple cubic, skewed body-centered cubic). As the fiber diameter increased, the fibers acted as granular inclusions. The effects of the overlapping fibers on the media permeability were investigated. The overlapping fibers yielded permeability values that were a factor of 2.5 larger than those obtained from non-overlapping fibers, but the effects of the fiber arrangement were negligible. Two correlations were obtained for the overlapping and non-overlapping fiber models, respectively. The effects of the rarefaction and slip flow are also discussed. As the Knudsen number increased, the dimensionless permeability increased; however, the increase differed depending on the fiber arrangement. In the slip flow regime, the fiber arrangement inside the porous media became an important factor.     

Convergence of the Finite Difference Scheme for a Fast Diffusion Equation in Porous Media

We are concerned with an implicit scheme for the finite difference solution to a nonlinear parabolic equation with a multivalued coefficient that describes the fast diffusion in a porous medium. The boundary conditions contain the multivalued function as well. We prove the stability and the convergence of the scheme, emphasizing the precise nature of convergence in this specific case, and compute the error level of the approximating solution. The method is aimed to simplify the numerical computations for the solutions to equations of this type, without performing an approximation of the multivalued function. The theory is illustrated by numerical results.     

Effective binuclear Pd(II) complexes for Suzuki reactions in water

A series of new ionic binuclear Pd(II) complexes supported by water‐soluble bis(α‐diimine) ligands were prepared and employed as catalysts for the palladium‐catalyzed Suzuki reaction in aqueous media. The binuclear nature of the complexes increased the reaction rate, while electronic and steric modification of the ligand frameworks had a remarkable influence upon the catalytic activity of the palladium complexes. The catalysts were shown to be homogeneous through mercury poisoning experiments and complexes could be recycled more than 10 times without loss of catalytic activity. Copyright © 2013 John Wiley & Sons, Ltd.     

Conductivity as a Sensor for Monitoring Relative Magnesium Corrosion Rates in Real‐time,in Serum‐containing Media under Cell Culture Conditions

Because controlling the corrosion rate of magnesium metal will be crucial to the success of biomedical implants containing pure magnesium or magnesium alloys, many ways have been sought to improve in vitro tests to analyze corrosion rates, and also to identify new methods of preparing or post‐processing magnesium. In this work, for an in vitro assay, we explored the use of a commercially available conductivity sensor to study magnesium corrosion under cell culture conditions that duplicate many physiologically appropriate parameters. With this sensor, we studied the corrosion of two previously untested magnesium single crystal samples that differed in surface treatments that could alter corrosion rates. The results show that the relative conductivity changes in (mS/cm) over the total time of immersion were proportional to the corrosion rates in (mm/y) and also to the total magnesium released, as detected by inductively coupled plasma mass spectrometry (ICP‐MS).     

Cross‐coupling reactions using porous multipod Cu2O microcrystals as recoverable catalyst in aqueous media

Porous multipod Cu₂O microcrystals were found to be an efficient, highly recyclable and eco‐friendly catalyst for the cross‐coupling reactions of aryl halides and terminal alkynes with high yields in aqueous media. Noteworthy, the Cu₂O catalyst can be reused for several times without significant decrease in catalytic activity.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

Fly‐Ash‐Supported Synthesis of 2‐Mercaptobenzothiazole Derivatives under Microwave Irradiation

Microwave‐assisted, solvent‐free alkylation and acylation of 2‐mercaptobenzothiazole has been attempted using silica gel, alumina, and a new solid support, fly ash. Fly ash, a waste generated at thermal power stations, could be used as solid support just as efficiently as commercial supports. The additional features of methodology include a much faster reaction, easy workup, higher yields, higher purity of the products, and an ecofriendly approach.     

Surface influence on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel

Low-field nuclear magnetic resonance techniques are employed to extract information about the effects introduced by the interaction with the surface on the rotational and translational dynamics of molecules confined inside a mesoporous carbon xerogel. The molecules under study were water, cyclohexane, and hexane. They were chosen due to their different interaction strength with the carbonaceous matrix. Frequency dependent longitudinal relaxation measurements, using the fast field cycling technique, allowed extraction of the fractal dimension of the carbon xerogel surface. It was observed that the measured value is influenced by the molecule affinity to the surface. Diffusion measurements, using the pulse field gradient technique, have revealed that the stronger interaction with the surface of cyclohexane and hexane molecules leads to an increased diffusive tortuosity, as compared with water.     

带有媒体影响上限的传染病模型研究

媒体报道对传染病的传播有着一定的影响,但它并不是影响其传播的本质因素.通过建立一个具有分段感染率的传染病模型来刻画媒体报道对传染病传播影响的饱和性.分析了系统各平衡态的局部稳定性,同时利用排除极限环的存在性证明了各平衡态的全局稳定性.最后,通过模拟来验证我们的理论分析.