A new method to find homoclinic and heteroclinic orbits

A new series method is provided for continuous-time autonomous dynamical systems, which can find exact orbits as opposed to approximate ones. The method can reduce the connecting orbit problem as a boundary value problem in an infinite time domain to the initial value problem. It consists of transforming time to the logarithmic scale, substituting a power series around each fixed point of interest for each of the unknown functions into the system, and equating the corresponding coefficients. When solving for the power series coefficients, additional parameters are used in order to find the intersections of the unstable manifold and the stable manifold of the equilibria. This paper demonstrates how the new method allows to obtain heteroclinic and homoclinic orbits in some well-known cases, such as Nagumo system, stretch-twist-fold flow or mathematical pendulum.     

Determination of Aluminum Traces in Hemodialysis and Tap Water Using Standard Method's Procedure Modified and Flow Injection Ionic Exchange Preconcentration

Abstract

A procedure for the spectrophotometric determination of aluminum traces in water using a flow injection (FI) preconcentration system has been proposed. The flow system was made up of a peristaltic pump, an injector‐commutator, and a minicolumn filled with 300.0 mg of Amberlite IR‐120 cationic exchange resin. After the preconcentration step, aluminum was eluted by a 4.0 mol l^?1 HCl solution. In a second stage, out of the flow system, the eluate was neutralized with a 4.0 mol l^?1 NaOH solution. The aluminum was submitted to the reaction with eriochrome cyanine to form a chelate in solution buffered to pH 5.85, according to the Standard Method's procedure with some modifications, and this was followed by spectrophotometric detection. Chemical and flow variables were studied in the preconcentration system. The precision of the proposed method was calculated for a solution containing 46.8 µg l^?1 of Al(III), when 40.0 ml of solution were preconcentrated (n=7), and their respective relative standard deviation (RSD) was 1.8%. The detection limit obtained was 1.7 µg l^?1 of Al(III) (sample volume=40.0 ml). The proposed method was successful in determining aluminum in water certified reference material.     

Internal flow numerical simulation of a cross‐flow fan in refrigerant operating condition using user‐defined functions

In the paper, a cross‐flow fan in refrigerant operating condition is systematically simulated using user‐defined functions. Three‐dimensional simulations are acquired with Navier–Stokes equations coupled with k–ε turbulence model, and internal flow characteristics of an indoor split‐type air conditioner are obtained, which is mainly composed of cross‐flow fan and heat exchanger. It has systematically been simulated in the isothermal flow condition that the performance of cross‐flow fan may be reduced easily with dry or humid air, and in the refrigerant operating condition in which user‐defined functions are applied to the humid air, considered as a mixture of dry air and vapor. A density‐modulated function is adopted to deal with the condensation of the vapor at the heat‐transfer region approximately. The results show flow mechanism of the two gas‐phase flow, including phase‐vary process. The distribution of the parameters is not uniform at the inlet of the machine, the intensity and position of pressure and velocity vary along the axial direction of the fan, the distribution of vapor volume fraction and turbulent intensity in heat‐transfer region is obtained, and the external characteristic data of the indoor machine are obtained and analyzed. Compared with the experimental data, the calculated characteristic curves and designed parameters are on target. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd.     

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes–Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions.     

气体钻水平井环空冲蚀能量分析

在建立水平井流动方程的基础上,通过气固两相流动基本数学模型的求解数值模拟不同工况条件下的气固混合物冲蚀能量,得出了冲蚀能量的变化规律。算例数值模拟显示:环空速度剖面主要由注气量大小决定,机械钻速的影响不大;相同注气量条件下,机械钻速降低与井下岩屑浓度等比例下降;注气量的增加能提高井眼净化程度,但不如降低机械钻速效果明显;环空总冲蚀能中气体冲蚀能量占绝对主要地位,岩屑冲蚀能量只占极小部分,在相同注气量条件下总冲蚀能量基本相同;岩屑冲蚀能量主要取决于机械钻速,机械钻速越大井底产生岩屑越多冲蚀能力越强,相同机械钻速条件下,较大注气量能提供较大岩屑运移速度,提高了岩屑冲蚀能量。     

Radiometrie Investigations into Gas-Solid-Fluidized Beds

Investigations made into a gas-solid-fluidized bed model reactor, aiming at obtaining statements about the spatial and time density distributions within the fluidized bed and the correlation between the state of the turbulent layer and a characteristic measured quantity as well as variation of a physical property of the solid. statisticl evaluation techniques are indispensable, owing to the elementary actions occuring within the fluidized bed reactor and their random nature. Such parameters of the fluidized bed could be determined from a totality of individual measurements for measuring periods of 10 ms per single measurement by use of a miniature measuring probe within the interior of the fluidized bed reactor. This probe consisted of a beta-radition source and a Si-surface barrier-layer detector.     

A hybrid DSMC/Navier–Stokes frame to solve mixed rarefied/nonrarefied hypersonic flows over nano‐plate and micro‐cylinder

We extend a hybrid DSMC/Navier–Stokes (NS) approach to unify the DSMC and the NS simulators in one framework capable of solving the mixed non‐equilibrium and near‐equilibrium flow regions efficiently. Furthermore, we use a one‐way state‐based coupling (Dirichlet–Dirichlet boundary‐condition coupling) to transfer the required information from the continuum region to the rarefied one. The current hybrid DSMC–NS frame is applied to the hypersonic flows over nanoflat plate and microcylinder cases. The achieved solutions are compared with the pure DSMC and NS solutions. The results show that the current hybrid approach predicts the surface heat transfer rate and shear stress magnitudes very accurately. Some important conclusions can be drawn from this study. For example, although the shock wave region would be a non‐equilibrium region, it is not necessary to use a pure DSMC simulator to solve it entirely. This is important when the researchers wish to predict the surface properties such as velocity slip, temperature jump, wall heat flux rate, and friction drag magnitudes accurately. Our investigation showed that our hybrid solution time would be at least 40% (for the flat plate) and 35% (for the cylinder) of the time that must be spent by a pure DSMC solver to attain the same accuracy.Copyright © 2013 John Wiley & Sons, Ltd.     

Film thickness measurements in liquid–liquid slug flow regimes

At present there is significant interest in the development of small scale medical diagnostic equipment. These devices offer faster processing times and require smaller sample volumes than equivalent macro scale systems. Although significant attention has been focused upon their outputs, little attention has been devoted to the detailed fluid mechanics that govern the flow mechanisms within these devices. Conventionally, the samples in these small scale devices are segmented into distinct discrete droplets or slugs which are suspended in an organic carrier phase. Separating these slugs from the channel wall is a very thin film of the organic carrier phase.The magnitude of this film is the focus of the present study and the effects of sample slug length and carrier phase fluidic properties on the film are examined over a range of Capillary numbers. A non-intrusive optical technique was used to capture images of the flow from which the magnitude of the film was determined.The experimental results show that the film is not constant along the length of the slug; however above a threshold value for slug length, a region of constant film thickness exists. When compared with existing correlations in the literature, the experimental data showed reasonable agreement with the Bretherton model when the Capillary number was calculated based on the mean two phase flow velocity. However, significant differences were observed when the Capillary number was redefined to account for the mean velocity at the liquid interface, i.e., the mean slug velocity.Analysis of the experimental data revealed that it fell into two distinct flow regimes; a visco-capillary regime and a visco-inertial regime. A modified Taylor expression is presented to estimate the magnitude of the film for flows in the visco-capillary regime while a new model is put forward, based on Capillary and Weber numbers, for flows in the visco-inertial regime. Overall, this study provides some novel insights into parameters, such as aqueous slug length and carrier phase fluidic properties, that affect the thickness of the film in liquid–liquid slug flow regimes.     

FRACTURE ASSESSMENT OF AN INTERFACE CRACK BETWEEN TWO DISSIMILAR MAGNETOELECTROELASTIC MATERIALS UNDER HEAT FLOW AND MAGNETOELECTROMECHANICAL LOADINGS

A magnetoelectrically permeable interface crack between two semi-infinite magnetoelectroelastic planes under the action of a heat flow and remote magnetoelectromechanical loadings is considered, where the assumption of frictionless contact between two dissimilar halfplanes is adopted. Not only the solutions of the interface crack problem are presented in an explicit form, but also the general condition for the transition from a perfect thermal contact of two magnetoelectroelastic bodies to their separation is given.     

Surrogate-based modeling and dimension reduction techniques for multi-scale mechanics problems

Successful modeling and/or design of engineering systems often requires one to address the impact of multiple "design variables" on the prescribed outcome.There are often multiple,competing objectives based on which we assess the outcome of optimization.Since accurate,high fidelity models are typically time consuming and computationally expensive,comprehensive evaluations can be conducted only if an efficient framework is available.Furthermore,informed decisions of the model/hardware’s overall performance rely on an adequate understanding of the global,not local,sensitivity of the individual design variables on the objectives.The surrogate-based approach,which involves approximating the objectives as continuous functions of design variables from limited data,offers a rational framework to reduce the number of important input variables,i.e.,the dimension of a design or modeling space.In this paper,we review the fundamental issues that arise in surrogate-based analysis and optimization,highlighting concepts,methods,techniques,as well as modeling implications for mechanics problems.To aid the discussions of the issues involved,we summarize recent efforts in investigating cryogenic cavitating flows,active flow control based on dielectric barrier discharge concepts,and lithium(Li)-ion batteries.It is also stressed that many multi-scale mechanics problems can naturally benefit from the surrogate approach for "scale bridging."