Optimal estimation of reactivity ratios for acrylamide/acrylic acid copolymerization

Reactivity ratios for the important acrylamide (AAm)/acrylic acid (AAc) copolymerization system exhibit considerable scatter in previously published literature, and therefore, there is a need for more definitive values for these reactivity ratios. An appropriate methodology, based on the error‐in‐variables‐model (EVM) framework along with a direct numerical integration procedure, is applied in order to determine reliable reactivity ratios. The reliability of the results is confirmed with extensive and independent replication. Furthermore, via an EVM‐based criterion for the design of experiments using mechanistic models, optimal feed compositions are calculated, and from these optimal reactivity ratios are estimated for the first time (r_AAm = 1.33 and r_AAc = 0.23) based on information from the full conversion range. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4819–4827     

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."     

Multiscale Lagrangian fluid dynamics simulation for polymeric fluid

We have developed a simulation technique of multiscale Lagrangian fluid dynamics to tackle hierarchical problems relating to historical dependency of polymeric fluid. We investigate flow dynamics of dilute polymeric fluid by using the multiscale simulation approach incorporating Lagrangian particle fluid dynamics technique (the modified smoothed particle hydrodynamics) with stochastic coarse‐grained polymer simulators (the dumbbell model). We have confirmed that our approach is well in agreement with the macroscopic results obtained by a constitutive equation corresponding to the dumbbell model, and observed that microscopic thermal fluctuation appears in macroscopic fluid dynamics as dispersion phenomena. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 886–893, 2010     

Diffusion from within a Spherical Body with Partially Blocked Surface: Diffusion through a Constant Surface Area

Diffusion from spherical bodies has been a subject of interest since the earliest times of modern sciences and a few equivalent analytical formulations of the problem are taught in engineering textbooks dealing with cooling rates of hot spheres. However, all these former studies assume that the diffusing material is transferable to/from the surrounding space through the whole surface of the spherical body. Conversely, the development of nanoscience and the improved knowledge of microscopic biological events have evidenced that diffusion from spherical bodies is a ubiquitous problem. It often occurs in situations where the nanosphere surfaces are not isotropic and partly impermeable to diffusing materials. This work elaborates on this issue and theoretically establishes that—with some specific allowance—the basic analytical equation of diffusion from/to fully accessible spherical bodies may be used.     

Niobium oxide solid catalyst: esterification of fatty acids and modeling for biodiesel production

Biodiesel can be obtained from fatty acid raw materials through esterification. The reactivity of lauric, palmitic, stearic, oleic, and linoleic fatty acids with methanol using powdered niobic acid as a heterogeneous catalyst was investigated in this work, both experimentally (in a batch reactor) and theoretically. A 2³ experimental design was used, with methanol/fatty acid molar ratio, catalyst concentration, and temperature as main factors. An empirical model demonstrated that temperature is the most important variable. Fourteen heterogeneous and 56 homogeneous‐like kinetic models were tested. A homogeneous‐like model considering zero order for all species and inhibition by water was the most adequate for experiments without catalyst. A homogeneous‐like model considering a second‐order reaction in relation to the fatty acid and no water inhibition was the most adequate for niobic acid catalyzed reaction. Molecular modeling confirmed the experimental results showing that the reactivity is directly related to the increase of unsaturated bonds and the reduction of carbon chain length. The polarity of the fatty acid is determinant in the reactivity. At the molecular level, reaction occurs between the HOMO orbital of methanol and LUMO orbitals of fatty acids and reactivity is higher when the energy difference between these orbitals is lower. Copyright © 2010 John Wiley & Sons, Ltd.     

Local existence of multiple positive solutions to a singular cantilever beam equation

By constructing suitable cone and control functions, we prove some local existence theorems of positive solutions for a singular fourth-order two-point boundary value problem. In mechanics, the problem is called cantilever beam equation. Furthermore, we improve a famous method appeared in the studies of singular boundary value problems. The approximation theorem of completely continuous operators and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type play important parts in this work.     

Asymptotic behavior of intermediate points in the differential mean value theorem of divided differences with repetitions

By the explicit representation for the divided differences with repetitions involving cycle index of symmetric groups, this paper deals with the asymptotic behavior of the intermediate point of the mean value theorem of divided differences with repetitions. Our results generalize some recent interesting results such as the asymptotic expansions of the immediate points of the Taylor formula and the differential mean value theorem of divided differences with distinct points.     

Evaluation of linear and nonlinear convection schemes on multidimensional non‐orthogonal grids with applications to KVLCC2 tanker

Almost all evaluations of convection schemes reported in the literature are conducted using simple problems on uniform orthogonal grids; thus, having limited contribution when solving industrial computational fluid dynamics (CFD), where the grids are usually non‐orthogonal with distortions. Herein, several convection schemes are assessed in uniform and distorted non‐orthogonal grids with emphasis on industrial applications. Linear and nonlinear (TVD) convection schemes are assessed on analytical benchmarks in both uniform and distorted grids. To evaluate the performance of the schemes, four error metrics are used: dissipation, phase and L₁ errors, and the schemes' effective order of accuracy. Qualitative and quantitative deterioration of these error metrics as a function of the grid distortion metrics are investigated, and rigorous verifications are performed. Recommendations for effective use of the convection schemes based on the range of grid aspect ratio (AR), expansion ratio (ER) and skewness (Q) are included. A ship hydrodynamics case is studied, involving a Reynolds averaged Navier–Stokes simulation of a bare‐hull KVLCC2 tanker using linear and nonlinear convection schemes coupled with isotropic and anisotropic Reynolds‐stress (ARS) turbulence models using CFDShip‐Iowa v4. Predictions of local velocities and turbulent quantities from the midships to the nominal wake plane are compared with experimental fluid dynamics (EFD), and rigorous verification and validation analyses for integral forces and moments are performed for 0° and 12° drift angles. Best predictions are observed when coupling a second‐order TVD scheme with the anisotropic turbulence model. Further improvements are observed in terms of prediction of the vortical structures for 30° drift when using TVD2S‐ARS coupled with DES. Copyright © 2009 John Wiley & Sons, Ltd.     

Laguerre-Gauss collocation method for initial value problems of second order ODEs

This paper proposes a new collocation method for initial value problems of second order ODEs based on the Laguerre-Gauss interpolation. It provides the global numerical solutions and possesses the spectral accuracy. Numerical results demonstrate its high efficiency.     

A note on transfer function model specification with noisy closed‐loop input data

We assume that the input in a transfer function noise model is determined by a proportional‐integral‐derivative controller that is subject to noise. We show how such a noisy feedback in the input series affects the standard Box–Jenkins method of specifying the transfer function model. Our findings have important implications for the analyst who uses the traditional Box–Jenkins approach. The analyst will be led to estimate an incorrect transfer function model if feedback (exact or noisy) is present. Copyright © 2009 John Wiley & Sons, Ltd.