Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel

The paper presents the transportation of viscoelastic fluid with fractional Maxwell model by peristalsis through a channel under long wavelength and low Reynolds number approximations. The propagation of wall of channel is taken as sinusoidal wave propagation (contraction and relaxation). Homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are used to obtain the analytical approximate solutions of the problem. The expressions of axial velocity, volume flow rate and pressure gradient are obtained. The effects of fractional parameters (α), relaxation time (λ₁) and amplitude (?) on the pressure difference and friction force across one wavelength are calculated numerically for different particular cases and depicted through graphs.     

微极流体蠕动泵经由滑移边界管道输送的Stokes流动

计及管道边界条件滑移的影响,研究微极流体蠕动泵,经由圆柱形管道输运的Stokes流动.壁面运动的控制方程为正弦波方程.使用润滑理论,得到了轴向速度、微转动向量、流函数、压力梯度、摩擦力和机械效率的解析数值解.用图形表示出构成参数,如像耦合参数、微极参数和表征蠕流泵特性的滑移参数、摩擦力和俘获现象的影响.数值计算表明,当耦合参数较大时,需要蠕动泵的压力更大,而微极参数和滑移参数正相反.俘获团块的大小随耦合参数和微极参数的减小而缩小,而随滑移参数的增大而缩小.     

Mathematical modelling of flow control in a tundish using electro-magnetic forces

The control of flow in a tundish is important for improving the quality of the steel. Dams, Wiers and Pouring chamber are some of the devices used for controlling the flow in the tundish. The investigation about the role of electromagnetic forces as a replacement for these devices is an objective for the present work. Thus, 3-D MHD simulation was performed to study the effect of electromagnetic forces on flow behaviour in the tundish. The MHD model developed for carrying out the simulation was validated with the analytical solution of the Hartman problem. The results obtained shows improvement in the desired characteristics for inclusion flotataion with magnetic flow modifier of optimum strength of magnetic field.     

Dynamic lot-sizing in sequential online retail auctions

Retailers often conduct non-overlapping sequential online auctions as a revenue generation and inventory clearing tool. We build a stochastic dynamic programming model for the seller’s lot-size decision problem in these auctions. The model incorporates a random number of participating bidders in each auction, allows for any bid distribution, and is not restricted to any specific price-determination mechanism. Using stochastic monotonicity/stochastic concavity and supermodularity arguments, we present a complete structural characterization of optimal lot-sizing policies under a second order condition on the single-auction expected revenue function. We show that a monotone staircase with unit jumps policy is optimal and provide a simple inequality to determine the locations of these staircase jumps. Our analytical examples demonstrate that the second order condition is met in common online auction mechanisms. We also present numerical experiments and sensitivity analyses using real online auction data.     

A class of exact solutions and physical behaviour of magnetic field lines in plasma column

Using hodograph and Legendre transformation functions the basic equations are recast in terms of this function, and the conditions which this function should satisfy are stated. Several applications of this method are considered, and the geometry of magnetic field lines is discussed.     

Temperature dependent energy-dispersive X-ray diffraction and magnetic study of Fe/Al interface

In situ temperature dependent energy-dispersive structural and magnetic study of electron beam evaporated Fe/Al multilayer sample (MLS) has been investigated. The structural studies show the formation of an intermixed FeAl transition layer of a few nanometers thick at the interface during deposition, which on annealing at 300 °C transforms to B2FeAl intermetallic phase. Magnetization decreases with increase in temperature and drops to minimum above 300 °C due to increase in anti-ferromagnetic interlayer coupling and formation of nonmagnetic FeAl phase at the interface. The Curie temperature (T_c) is found to be 288 °C and is much less than that of bulk bcc Fe.     

On the density of integral sets with missing differences from sets related to arithmetic progressions

For a given set M of positive integers, a problem of Motzkin asks for determining the maximal density μ(M) among sets of nonnegative integers in which no two elements differ by an element of M. The problem is completely settled when |M|?2, and some partial results are known for several families of M for |M|?3, including the case where the elements of M are in arithmetic progression. We consider some cases when M either contains an arithmetic progression or is contained in an arithmetic progression.     

Improvement in the Performance of Composite Cathode via Solid Electrolyte for High Electrochemical Performance of Li–S Battery

Commercialization of Li–S in present scenario is obstructed by poor performance of cathode and its compatibility with electrolyte used. Here in this work, in order to improve the electrochemical performance all solid state Li–S battery, solid electrolyte (SE) formed by composition of lithium sulfide (Li₂S) and phosphorus pentasulfide (P₂S₅) combinedly called LPS is used. The modified carbon in the form of graphene oxide (GO) and reduced graphene oxide (rGO) as additive is used to provide better electron conduction pathway. High conductivity of the order 10⁻⁴ S cm⁻¹ of prepared LPS overcomes the major drawback of insulating nature of sulfur. The coin cells are fabricated by using above mentioned material as a cathode material, LPS as SE, and lithium foil as anode. The prepared nanocomposites are characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) to study structural and morphological properties. Energy dispersive X-ray spectroscopy (EDS) images of the cathode surface confirms the uniform spreading of material. The electrochemical performance of coin cell is studied by Galvanostatic charge-discharge plot at 0.1 C to check the compatibility of composite and electrolyte prepared. The cells having additive material GO and rGO with host sulfur show better results as compared to the cell having pristine sulfur.