Kinetics of biofuel generation from deodorizer distillates derived from the physical refining of olive oil and squalene recovery

The recovery of squalene from deodorizer distillate derived from the physical refining of olive oil was evaluated by combining pressurized acidic esterification in a closed system with vacuum distillation. Esterification was carried out at 341, 359, 366, 391 and 395 K. The reaction at 395 K was found to be satisfactory as it decreased the acid value by 99.21% and generated a FAME concentration of 67.53% within 1 h. In order to demonstrate that the generation of FAME from deodorizer distillate was mainly due to the transformation of FFA, the reaction extent, which characterizes the reaction and simplifies calculations, was evaluated for FFA removal and the generation of FAME. Subsequent vacuum distillation allowed the separation of one fraction rich in FAME (94%), which can be used as a biofuel and accounted for 85% of the initial mass, and another fraction that was rich in squalene (78%) and may be used for manufacturing pharmaceutical products. The global squalene yield was 117 g kg⁻¹ initial deodorizer distillate.     

Optimum model extent for numerical simulation of tunnel inflow in fractured rock

The objective of this study is the introduction of an optimum model extent in discontinuous rock masses for tunnel inflow assessment using numerical models. Tunnel groundwater inflow is an important problem in tunneling, and numerical simulation is widely used for estimating the amount of tunnel inflow. An adequate size of the model domain is of very high importance when using such models. On the one hand, if the tunnel boundary is too close to the outer model boundary, the simulated inflow rate into the tunnel is significantly overestimated (which will be shown in the present study). On the other hand, if the model domain is very large, models may become “unhandy”, and simulations become very expensive with respect to computer memory and CPU. In this technical note, an approach is presented that derives an optimum model extent for numerical simulation of tunnel inflow in fractured rock. The approach uses the two-dimensional universal distinct element code (UDEC). The impact of different model parameters, such as tunnel radius, groundwater level, joint spacing, joint dip/dip direction and joint aperture on the optimum model extent has been evaluated. Based on the results, an optimum model extent chart is presented that allows modelers a quick determination of the optimum model extent as a function of the most significant parameters, which are the tunnel depth under the groundwater level, tunnel radius and joint spacing.     

Optimum lateral extent of soil domain for dynamic SSI analysis of RC framed buildings on pile foundations

This article describes a novel approach for deciding optimal horizontal extent of soil domain to be used for finite element based numerical dynamic soil structure interaction (SSI) studies. SSI model for a 12 storied building frame, supported on pile foundation-soil system, is developed in the finite element based software framework, OpenSEES. Three different structure-foundation configurations are analyzed under different ground motion characteristics. Lateral extent of soil domain, along with the soil properties, were varied exhaustively for a particular structural configuration. Based on the reduction in the variation of acceleration response at different locations in the SSI system (quantified by normalized root mean square error, NRMSE), the optimum lateral extent of the soil domain is prescribed for various structural widths, soil types and peak ground acceleration levels of ground motion. Compared to the past studies, error estimation analysis shows that the relationships prescribed in the present study are credible and more inclusive of the various factors that influence SSI. These relationships can be readily applied for deciding upon the lateral extent of the soil domain for conducting precise SSI analysis with reduced computational time.     

An improved convergence analysis for the Newton–Kantorovich method using recurrence relations

We generate a sequence using the Newton–Kantorovich method in order to approximate a locally unique solution of an operator equation on a Banach space under Hölder continuity conditions. Using recurrence relations, Hölder as well as centre-Hölder continuity assumptions on the operator involved, we provide a semilocal convergence analysis with the following advantages over the elegant work by Hernánde? in (The Newton method for operators with Hölder continuous first derivative, J. Optim. Theory Appl. 109(3) (2001), pp. 631–648.) (under the same computational cost): finer error bounds on the distances involved, and a more precise information on the location of the solution. Our results also compare favourably with recent and relevant ones in (I.K. Argyros, Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005), pp. 179–194; I.K. Argyros, Computational Theory of Iterative Methods, in Studies in Computational Mathematics, Vol. 15, C.K. Chui and L. Wuytack, eds., Elsevier Publ. Co., New York, USA, 2007; I.K. Argyros, On the gap between the semilocal convergence domain of two Newton methods, Appl. Math. 34(2) (2007), pp. 193–204; I.K. Argyros, On the convergence region of Newton's method under Hölder continuity conditions, submitted for publication; I.K. Argyros, Estimates on majorizing sequences in the Newton–Kantorovich method, submitted for publication; F. Cianciaruso and E. DePascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003), pp. 713–723; F. Cianciaruso and E. DePascale, Estimates of majorizing sequences in the Newton–Kantorovich method, Numer. Funct. Anal. Optim. 27(5–6) (2006), pp. 529–538; F. Cianciaruso and E. DePascale, Estimates of majorizing sequences in the Newton–Kanorovich method: A further improvement, J. Math. Anal. Appl. 322 (2006), pp. 329–335; N.T. Demidovich, P.P. Zabreiko, and Ju.V. Lysenko, Some remarks on the Newton–Kantorovich mehtod for nonlinear equations with Hölder continuous linearizations, Izv. Akad. Nauk Belorus 3 (1993), pp. 22–26 (in Russian). (E. DePascale and P.P. Zabreiko, The convergence of the Newton–Kantorovich method under Vertgeim conditions, A new improvement, Z. Anal. Anwendvugen 17 (1998), pp. 271–280.) and (L.V. Kantorovich and G.P. Akilov, Functional Analysis in Normed Spaces, Pergamon Press, Oxford, 1982; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations, Dokl. Akad. Nauk BSSR 38 (1994), pp. 20–24 (in Russian); B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957), pp. 166–169 (in Russian); Amer. Math. Soc. Transl. 16 (1960), pp. 378–382. (English Trans.).)     

扩展目标GMPHD滤波器的航迹维持算法

概率假设密度(PHD)滤波器提供了各目标在每个时刻的状态信息,但未形成航迹。该文提出了扩展目标高斯混合PHD(GMPHD)滤波器的航迹维持算法。首先对后验概率强度的每个高斯分量添加标签;其次在后验概率强度随着时间进行演化时,标签也随之演化;并通过航迹管理方案为扩展目标提供航迹。为提高GMPHD滤波器性能,提出了自适应的量测集划分法。最后通过仿真验证了提出算法的有效性。     

改进多种群遗传算法在墙土系统损伤识别中的应用

针对墙土系统损伤识别方法进行研究,提出了一种基于改进多种群遗传算法的墙土系统损伤识别方法。首先,建立了墙土系统动测简化模型,同时对土体发生损伤时墙土系统的特征方程进行理论分析,基于系统的特征方程构造目标函数;其次,对多种群遗传算法进行改进,改进的内容主要包括采用实数编码、采用自适应交叉概率、采用自适应变异概率;最后,利用改进多种群遗传算法分别进行了无噪声条件和噪声条件下的墙土系统损伤定位和定量研究。通过分析结果表明：无论对单处损伤还是多处损伤、单一损伤程度还是多损伤程度,按所提出的方法都能较好的识别出损伤位置和损伤程度,具有较强的抗噪声能力。因此,所提出的方法为墙土系统的损伤识别提供一种简单有效的途径。     

一种实用的加测陀螺坚强边的巷道贯通预计方法

针对巷道(隧道)贯通工程中存在的加测陀螺坚强边的曲线巷道贯通形式，通过建立新的坐标基准，将原有的数学模型进行简化，并进一步推导，获得该贯通形式下的最佳贯通点的位置和贯通允许区间的数学模型，从而为贯通误差预计提供了一种行之有效的方法。该方法也适用于加测陀螺坚强边的直线巷道贯通误差预计。     

浅谈反应进度和摩尔反应和引用单位反应概念

深入讨论了物理化学教学中的热化学部分中经常采用的反应进度和摩尔反应等重要概念,并采用摩尔反应概念时存在的一些问题和解决这些问题的方法。提出引用一种新的概念—单位反应概念,详细介绍单位反应概念并把它代替摩尔反应概念的优点。     

一类伪抛物型方程初边值问题

本文讨论和一些重要的物理过程有着密切关系的一类伪抛物方程的初边值问题。首先利用强制不等式和连续性方法推广了现有的线性问题解的存在惟一性结果,然后利用Hilbert空间中Leray-Schauder度的同伦不变性,给出了一类非线性伪抛物方程解的存在性定理。