On the number of distinct prime factors of an odd perfect number

It is not known whether or not there exists an odd perfect number. We describe an algorithmic approach for showing that if there is an odd perfect number then it has t distinct prime factors, and we discuss its application towards showing that t9.     

A theoretical and numerical evaluation of the steady-state burning rate of vertically oriented PMMA slabs

The steady state burning rate of vertically oriented slabs of poly-methyl-methacrylate (PMMA) is numerically investigated. Model predictions are compared with measurements and results of the laminar boundary layer (LBL) theory. The numerical model provides a solution of the Favre-averaged Navier–Stokes equations coupled with sub-models for turbulence, combustion, soot production and radiation. The modelling of condensed phase processes is based on the one-dimensional heat transfer equation and pyrolysis is treated as a phase change using the latent heat approach. Results show that the pyrolysing region can be divided into three regions. In the laminar part of the flow (Gr _x < 4.3 × 10⁷), the predicted normalised burning rate, [mdot]″ _p x/μ_∞, is a power-law function of Gr _x with an exponent close to that of the LBL theory, surface re-radiation being the primary source of discrepancies. From the LBL theory for free flow, it is demonstrated that the local burning rate is inversely proportional to the shear velocity gradient. This is globally confirmed by numerical model results. At Gr _x = 4.3 × 10⁷ the change in slope of the burning rate observed experimentally, which indicates the end of the laminar flow region, is reproduced numerically. From Gr _x = 2.5 × 10⁹ model results show that the surface mass flux of pyrolyzate increases with x, in agreement with experimental data in literature.     

Study of absorption spectra of gasolines and other hydrocarbon mixtures in the second overtone region of the CH<Subscript>3</Subscript>, CH<Subscript>2</Subscript>, CH groups

We have obtained experimental and model absorption spectra for individual hydrocarbons (toluene, benzene, n-heptane, and iso-octane) and their mixtures in the near IR range (λ = 1080–1220 nm). We model the spectra of nonsynthetic gasolines obtained under the same conditions by combining the spectra of three pure hydrocarbons. We show that the octane number of the studied gasoline is linearly related to the toluene (or benzene) concentrations in the model mixture. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 157–161, March–April, 2007.     

Structural,thermal and ion transport studies on nanocomposite polymer electrolyte-{(PEO + SiO<Subscript>2</Subscript>):NH<Subscript>4</Subscript>SCN} system

Development and characterisation of polyethylene oxide (PEO)-based nanocomposite polymer electrolytes comprising of (PEO-SiO₂): NH₄SCN is reported. For synthesis of the said electrolyte, polyethylene oxide has been taken as polymer host and NH₄SCN as an ionic charge supplier. Sol–gel-derived silica powder of nano dimension has been used as ceramic filler for development of nanocomposite electrolytes. The maximum conductivity of electrolyte ∼2.0 × 10⁻⁶ S/cm is observed for samples containing 30 wt.% silica. The temperature dependence of conductivity seems to follow an Arrhenius-type, thermally activated process over a limited temperature range.     

Bound on vertical heat transport at large Prandtl number

We prove a new upper bound on the vertical heat transport in Rayleigh-Bénard convection of the form under the assumption that the ratio of Prandtl number over Rayleigh number satisfies where the non-dimensional constant c₀ depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) bound (modulo logarithmic correction) on vertical heat transport for the infinite Prandtl number model for convection due to Constantin and Doering [P. Constantin, C.R. Doering, Infinite Prandtl number convection, J. Stat. Phys. 94 (1) (1999) 159-172] and Doering, Otto and Reznikoff [C.R. Doering, F. Otto, M.G. Reznikoff, Bounds on vertical heat transport for infinite Prandtl number Rayleigh-Bénard convection, J. Fluid Mech. 560 (2006) 229-241]. It also improves a uniform (in Prandtl number) bound for the Nusselt number [P. Constantin, C.R. Doering, Heat transfer in convective turbulence, Nonlinearity 9 (1996) 1049-1060] in the case of large Prandtl number.     

近独立子系系统的统计规律(四)——巨正则分布函数

根据吉布斯系综理论导出了由任意数目刚性粒子构成的力学系统的巨正则分布函数、化学势及粒子数和能量涨落公式.并介绍了刚球模型下,对二维和三维近独立子系系统巨正则分布的计算机模拟,结果与理论完全一致.     

Polymer and surface roughness effects on the drag crisis for falling spheres

We make time resolved velocity measurements of steel spheres in free fall through liquid using a continuous ultrasound technique. We explore two different ways to induce large changes in drag on the spheres: 1) a small quantity of viscoelastic polymer added to water and 2) altering the surface of the sphere. Low concentration polymer solutions and/or a pattern of grooves in the sphere surface induce an early drag crisis, which may reduce drag by more than 50% compared to smooth spheres in pure water. On the other hand, random surface roughness and/or high concentration polymer solutions reduce drag progressively and suppress the drag crisis. We also present a qualititative argument which ties the drag reduction observed in low concentration polymer solutions to the Weissenberg number and normal stress difference.     

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using φ-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of φ-mapping. In our solution, the flux of this soliton is naturally quantized.     

旋转热管生物反应器的流场模拟研究

采用热管技术对传统生物反应器进行革新,自主开发出一种适用于多种生物反应的新型生物反应器,提出了将热管本身作为搅拌轴的设计思想,同时以计算流体力学(CFD)为基础建立旋转热管生物反应器的数学模型,计算了不同雷诺数下此类搅拌轴的功率准数,并得到了功率曲线。采用标准k-ε湍流模型成功模拟了反应器内的速度分布,为反应器的优化设计提供了基础。     

Operator Formulas Involving Generalized Stirling Number Derived by Virtue of Normal Ordering of Vacuum Projector

By virtue of the normal ordering of vacuum projector we directly derive some new complicated operator identities, regarding to the generalized Stirling number.