On the Boolean Model of Wiener Sausages

The Boolean model of Wiener sausages is a random closed set that can be thought of as a random collection of parallel neighborhoods of independent Wiener paths in space. It describes e.g. the target detection area of a network of sensors moving according to the Brownian dynamics whose initial locations are chosen in the medium at random. In the paper, the capacity functional of this Boolean model is given. Moreover, the one- and two-point coverage probabilities as well as the contact distribution function and the specific surface area are studied. In and , the one- and two-point coverage probabilities are calculated numerically by Monte Carlo simulations and as a solution of the heat conduction problem. The corresponding approximation formulae are given and the error of approximation is analyzed. Research supported by the grant GACR 201/06/0302.     

Poly(arylene ether) ionomers containing sulfofluorenyl groups: Effect of electron-withdrawing groups on the properties

For polymer electrolyte membrane fuel membrane cell (PEMFC) applications, the effect of electron-withdrawing groups on the properties of sulfonated poly(arylene ether) (SPE) ionomer membranes was investigated. A series of poly(arylene ether)s containing fluorenyl groups and electron-withdrawing groups (sulfone, nitrile, or fluorine) was synthesized, which were sulfonated with chlorosulfonic acid using a flow reactor to obtain the title ionomers. The ionomers had high molecular weight (M_n > 77 kDa, M_w > 238 kDa) and gave tough, ductile membranes by solution casting. The ion exchange capacity (IEC) of the membranes ranged from 1.6 to 3.5 mequiv/g as determined by titration. The electron-withdrawing groups did not appear to affect the thermal properties (decomposition temperature higher than 200 °C). The presence of nitrile groups, especially at positions meta to the ether linkages, improved the oxidative stability of the SPE membranes, while it led to a deterioration of the hydrolytic stability. The perfluorinated biphenylene groups were effective in providing high mechanical strength with reasonable dimensional change, probably due to a somewhat decreased water absorbability. The SPE membrane containing sulfone groups showed the highest proton conductivity (10⁻³-10⁻¹ S/cm) at 20-93% RH (relative humidity) and 80 °C. The nitrile-containing SPE membrane showed smaller apparent activation energies for oxygen and hydrogen permeability and is thus considered to be a possible candidate for applications in PEMFCs.     

Vibrational Properties of LaNb0.8M0.2O4-δ (M=As,Sb, V,and Ta)

LaNb_0.8M_0.2O_4-δ (where M=As, Sb, V, and Ta) oxides with pentavalent elements of different ionic sizes were synthesized by a solid-state reaction method. The vibrational properties of these oxides have been investigated. These studies revealed that the substituent element influences both Debye temperature value as well as the Raman active vibrational modes. Additionally, the low-temperature vibrational properties of LaNb_0.8Sb_0.2O_4-δ have been determined to show the phase transition occurrence at 260 K which is lower than previously reported.     

Numerical treatment of Casson nanofluid Bioconvectional flow with heat transfer due to stretching cylinder/plate: Variable physical properties

PurposeThe purpose of the current framework is to scrutinize the two-dimensional flow and heat transfer of Casson nanofluid over cylinder/plate along with impacts of thermophoresis and Brownian motion effects. Also, the effects of exponential thermal sink/source, bioconvection, and motile microorganisms are taken.Methodology/ApproachThe resulting non-linear equations (PDEs) are reformed into nonlinear ODEs by using appropriate similarity variables. The resultant non-linear (ODEs) were numerically evaluated by the use of the Bvp4c package in the mathematical solver MATLAB.FindingsThe numerical and graphical illustration regarding outcomes represents the performance of flow-involved physical parameters on velocity, temperature, concentration, and microorganism profiles. Additionally, the skin friction coefficient, local Nusselt number, local Sherwood number, and local microorganism density number are computed numerically for the current presented system. We noted that the velocity profile diminishes for the rising estimations of magnetic and mixed convection parameters. The Prandtl number corresponds with the declining performance of the temperature profile observed. The enhancement in the values of the Solutal Biot number and Brownian motion parameter increased in the concentration profile.OriginalityIn specific, this framework focuses on the rising heat transfer of Casson nanofluid with bioconvection by using a shooting mathematical model. The novel approach of the presented study is the use of motile microorganisms with exponential thermal sink/source in a Casson nano-fluid through a cylinder/plate. A presented study performed first time in the author’s opinion. Understanding the flow characteristics and behaviors of these nanofluids is crucial for the scientific community in the developing subject of nanofluids.     

Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.     

Ultrafine Metal–Organic Right Square Prism Shaped Nanowires

We report the structural design and control of electronic states of a new series of ultrafine metal–organic right square prism‐shaped nanowires. These nanowires have a very small inner diameter of about 2.0 Å, which is larger than hydrogen and similar to xenon atomic diameters. The electronic states of nanowires can be widely controlled by substitution of structural components. Moreover, the platinum homometallic nanowire shows a 100 times higher proton conductivity than a palladium/platinum heterometallic one depending on the electronic states.     

超强激光功率密度对等离子体中自生磁场和电子热传导的影响

应用多光子非线性康普顿散射模型、3维粒子模拟模型和数值计算方法,研究了超强激光与等离子体作用中自生磁场产生和电子热传导过程,提出了将非线性康普顿散射光作为改变等离子体自生磁场和电子热传导的新机制,给出了自生磁场最大饱和值和超热电子热传导的修正方程和数值计算结果。研究发现在时间为100~160范围内,自生磁场能量随入射激光功率密度增大而迅速增大,之后处于较高饱和阶段。增大的初始时刻较散射前提前了20,增大阶段的时间延长了30,饱和阶段增幅为40。入射激光功率密度为1019~1020W/cm2时,自生磁场强度最大模拟值为1.47104~3.75104T,单电子能谱峰值出现在3.3MeV和6.6MeV附近,能谱曲线在4~15 MeV和11~14.3MeV范围迅速衰减,在6.7MeV和13.2MeV以上时,超热电子有效温度为2.6MeV和4.5MeV,比无散射的理论值和拟合值均有一定增大。随入射激光强度增大,热流随激光脉冲一起向等离子体内流动的时间缩短,自生磁场限制热流的时间延长。并对所得结果给出了初步物理解释。     

石墨烯/聚乙烯界面导热性能的分子动力学模拟

采用非平衡分子动力学模拟(NEMD)方法研究了石墨烯/聚乙烯纳米复合材料的界面导热性能,主要考察了石墨烯层数、尺寸对界面热阻的影响.研究结果表明:当石墨烯层数为一层时,界面热导为46.79 MW/(m~2K),随着石墨烯层数的增加,界面热导下降;但石墨烯层数超过四层后,界面热导趋于恒定接近39.00 MW/(m~2K);随着石墨烯尺寸的增大,石墨烯中较长波长声子被引发并对界面热传导起到主要的作用,最终导致界面热导逐渐增大.     

Stepanov ergodic perturbations for some neutral partial functional differential equations

In this work, we give sufficient conditions for the existence and uniqueness of μ?pseudo almost periodic integral solutions for some neutral partial functional differential equations with Stepanov μ?pseudo almost periodic forcing functions. Our working tools are based on the variation of constant formula and the spectral decomposition of the phase space. To illustrate our main results, we give applications to a neutral model arising in physical systems, as well as an application to heat equations with discrete and continuous delay. Copyright © 2015 John Wiley & Sons, Ltd.