Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations

A new ordinary differential inequality without global solutions is proposed. Comparison with similar differential inequalities in the well‐known concavity method is performed. As an application, finite time blow up of the solutions to nonlinear Klein–Gordon equation and generalized Boussinesq equation is proven. The initial energy is arbitrary high positive. The structural conditions on the initial data generalize the assumptions used in the literature for the time being. Copyright © 2015 John Wiley & Sons, Ltd.     

Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

Strong solutions to 3D compressible magnetohydrodynamic equations with Navier‐slip condition

We consider the short time strong solutions to the compressible magnetohydrodynamic equations with initial vacuum, in which the velocity field satisfies the Navier‐slip condition. The Navier‐slip condition differs in many aspects from no‐slip conditions, and it has attracted considerable attention in nanoscale and microscale flows research. Inspired by Kato and Lax's idea, we use the Lax–Milgram theorem and contraction mapping argument to prove local existence. Moreover, under the Navier‐slip condition, we establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of L^∞ norm of the deformation tensor D(u). Copyright © 2015 John Wiley & Sons, Ltd.     

Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique

We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd.     

Viscous flow in a mixed compression intake

Numerical simulation of the flow in a two‐dimensional mixed compression intake is carried out by solving unsteady viscous compressible equations using a stabilized finite element method. The effect of bleed in starting/unstarting of the intake and controlling the buzz instability is investigated in detail. Higher bleed leads to an increase in the ability of the intake to sustain larger back‐pressure for stable operation. The amount of bleed and its location is varied to understand its effect on the performance of the intake. Two kinds of unsteady oscillations are observed: ‘little’ and ‘big’ buzz. The frequency of the both kinds of buzz oscillations is found to be super‐harmonic of the fundamental acoustic frequency of intake modeled as an open‐closed organ pipe. The frequency as well as amplitudes of the big buzz cycles is larger than those of the little buzz. The little‐ and big‐buzz are found to occur for low‐ and high‐subcritical state of the intake and are very similar to Ferri and Dailey criteria, respectively. Buzz is eliminated when relatively high bleed is implemented, both, upstream and downstream of the throat. The effect of rate of change of back‐pressure on the start/unstart of the intake is investigated. Two situations are considered. The first case is that of an intake where the back‐pressure remains below the critical value. It is found that the intake remains started if the change in back‐pressure is gradual. However, it unstarts if the back‐pressure is changed relatively rapidly. The second set of simulations is an attempt to model the situation where the back‐pressure at the exit of the intake exceeds the critical value and a logic is incorporated in the feed back loop of the fuel modulation to start the intake. Low rate of change of pressure is unsuccessful in starting the intake. Relatively high rates result in either a quick starting of the intake or a slow unstart. Copyright © 2010 John Wiley & Sons, Ltd.     

Er3+/Yb3+共掺杂La2TiO5荧光粉体的制备及上下转换荧光性质研究

使用溶胶-凝胶法制备了Er³⁺单掺及Er³⁺/Yb³⁺共掺La₂TiO₅荧光粉体样品。经过1 100 ℃下3 h的煅烧,得到了较好的微晶。X射线粉末衍射测试表明样品中不含杂质相。扫描电镜观察表明样品颗粒范围为100~300 nm。紫外激发光谱中,在250~320 nm范围内出现Er离子和临近配位氧离子之间强烈的电荷转移跃迁峰,在350~500 nm出现Er离子f-f跃迁尖锐的吸收峰。在378 nm激发下,Er离子发射强烈的特征绿光(546 nm, ⁴S_3/2-⁴I_5/2),当Er离子物质的量分数达到1%,发射峰强度达到最大。在980 nm激发下的上转换光谱中,Yb离子的共掺杂有效的敏化上转换发光强度。详细讨论了样品的上下转换发光机理及相应能量传递过程。同时测试了样品的荧光衰减和量子产率。     

Synthesis,Characterization and Properties of a Novel Environmentally Friendly Mono Azo Disperse Dye and Its Application on Polyethylene Terephthalate (PET)

The aim of this research is to achieve the synthesis of a novel mono azo disperse dye containing both a β‐naphthyl acetate group and carboxylic acid ester group and application on PET fabric. In this study the dyeing properties have also been investigated. The synthesized dye was characterized using UV‐Vis, FTIR, ¹H NMR and ¹³C NMR spectroscopic techniques. To investigate alkali‐clearability, both alkali‐hydrolysis behavior and the effect of its fastness properties with regard to PET fabric were examined. This dye showed a reasonable level of hydrolysis under relatively mild alkaline conditions. The application of the dye to PET fabric showed good leveling and building up properties. Estimating fastness properties of the dyed fabric showed excellent wash, rubbing fastness, good light and sublimation fastness. The results furthermore displayed that the synthesized dye offers the option of alkali‐clearing process over that of a conventional reduction‐clearing process. Therefore, the value of Chemical Oxygen Demand (COD), Biological Oxygen Demand (BOD) and water pollution as well as the expenditure of production were decreased.     

一类非线性四阶波动方程初边值问题解的有限时间爆破

研究四阶带有阻尼项的非线性波动方程的解的初边值问题,利用位势井方法,证明了当初值满足一定条件时解发生爆破.将有关该系统爆破性质的研究结果一般化,通过证明得到了该系统较好的性质.     

Challenges and strategies in the preparation of large‐volume polymer‐based monolithic chromatography adsorbents

To date, the number of published reports on the large‐volume preparation of polymer‐based monolithic chromatography adsorbents is still lacking and is of great importance. Many critical factors need to be considered when manufacturing a large‐volume polymer‐based monolith for chromatographic applications. Structural integrity, validity, and repeatability are thought to be the key factors determining the usability of a large‐volume monolith in a separation process. In this review, we focus on problems and solutions pertaining to heat dissipation, pore size distribution, “wall channel” effect, and mechanical strength in monolith preparation. A template‐based method comprising sacrificial and nonsacrificial techniques is possibly the method of choice due to its precise control over the porous structure. However, additional expensive steps are usually required for the template removal. Other strategies in monolith preparation are also discussed.