The optimal control related to Riemannian manifolds and the viscosity solutions to Hamilton–Jacobi–Bellman equations

In this paper we study the optimal stochastic control problem for stochastic differential equations on Riemannian manifolds. The cost functional is specified by controlled backward stochastic differential equations in Euclidean space. Under some suitable assumptions, we conclude that the value function is the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation which is a fully nonlinear parabolic partial differential equation on Riemannian manifolds.     

Performance Effects of Exploratory and Exploitative Innovation Strategies and the Moderating Role of External Innovation Partners

In today's dynamic environment, the involvement of external partners in the innovation process is frequently assumed to be a panacea to cut costs while improving outcomes. In this study, we scrutinize how different collaboration types influence the effects of exploitative and exploratory innovation strategies on new product development (NPD) performance. For our analyses, we draw on a survey comprising a sample of 254 technology-based German firms. Our findings indicate that exploitative strategies are best pursued without comprehensive external collaborations, while the involvement of several partners in a balanced approach is most promising for exploratory strategies. Joint exploration with competitors, in particular, shows the highest effects on NPD performance. The paper discusses the findings and provides several implications for future research.     

Numerical simulation of particulate processes for control and estimation by spectral methods

Results of application of pseudospectral methods, also known as spectral collocation methods, to practical particulate processes including growth, nucleation, aggregation, and breakage are presented. For growth‐dominated processes, a considerable reduction in model dimension can be achieved; for pure aggregation and breakage they form a viable option. To handle problems that include aggregation, breakage, and growth phenomena simultaneously, we introduce a hybrid algorithm combining the advantages of spectral methods and cell average or fixed pivot methods for aggregation and breakage. Results are shown for analytical examples as well as real processes taken from the fields of granulation and crystallization. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2309–2319, 2012     

Catalytic and kinetic study of methanol dehydration to dimethyl ether

Dimethyl ether (DME), as a solution to environmental pollution and diminishing energy supplies, can be synthesized more efficiently, compared to conventional methods, using a catalytic distillation column for methanol dehydration to DME over an active and selective catalyst. In this work, using an autoclave batch reactor, a variety of commercial catalysts are investigated to find a proper catalyst for this reaction at moderate temperature and pressure (110–135 °C and 900 kPa). Among the γ-alumina, zeolites (HY, HZSM-5 and HM) and ion exchange resins (Amberlyst 15, Amberlyst 35, Amberlyst 36 and Amberlyst 70), Amberlysts 35 and 36 demonstrate good activity for the studied reaction at the desired temperature and pressure. Then, the kinetics of the reaction over Amberlyst 35 is determined. The experimental data are described well by Langmuir–Hinshelwood kinetic expression, for which the surface reaction is the rate determining step. The calculated apparent activation energy for this study is 98 kJ/mol.     

Modelling and prediction of bioethanol production from intermediates and byproduct of sugar beet processing using neural networks

The aim of this work was to model and predict the process of bioethanol production from intermediates and byproduct of sugar beet processing by applying artificial neural networks. Prediction of one substrate fermentation by neural networks had the same input variables (fermentation time and starting sugar content) and one output value (ethanol content, yeast cell number or sugar content). Results showed that a good prediction model could be obtained by networks with single hidden layer. The neural network configuration that gave the best prediction for raw or thin juice fermentation was one with 8 neurons in hidden layer for all observed outputs. On the other side, the optimal number of neurons in hidden layer was found to be 9 and 10 for thick juice and molasses, respectively. Further, all substrates data were merged, which led to introducing an additional input (substrate type) and defining all outputs optimal network architecture to 3-12-1. From the results the conclusion was that artificial neural networks are a good prediction tool for the selected network outputs. Also, these predictive capabilities allowed the application of the Garson's equation for estimating the contribution of selected process parameters on the defined outputs with satisfactory accuracy.     

Mass transfer simulation of biodiesel synthesis in microreactors

A coupled nonlinear mathematical model for the mass transfer of the species involved in the transesterification reaction between soybean oil and methanol in a parallel plates geometry microreactor is presented. The set of partial differential equations that governs the concentration profile of these species were obtained from the general mass balance equation for the case of isothermal flow and steady state with constant physical properties. The velocity profile was obtained from the Navier-Stokes equations assuming fully developed stratified laminar flow for two immiscible Newtonian fluids, with a plane interface between them, based on experimental observation of this flow pattern. The second order kinetic equations for the species were developed assuming homogeneous and reversible chemical reactions and these equations were written as source terms in the main equations. The mathematical model was solved using the hybrid method known as Generalized Integral Transform Technique (GITT). The simulation results were critically compared with those obtained by using the COMSOL multiphysics platform, showing a good agreement between the hybrid and fully numerical simulations. The effects of governing parameters such as residence time, temperature and microreactor dimensions were investigated. It was observed that higher triglycerides conversion rates occurred at higher temperatures and residence times and lower microreactor depths.     

Modeling of a DC glow discharge in a neon–xenon gas mixture at low pressure and with metastable atom densities

The physical properties of Ne–Xe DC glow discharges at low pressure are reported for a gap length of 1 cm for the first time in the literature. The model deals specifically with the first three moments of Boltzmann's equation and includes the radiation processes and metastable atom densities. The spatio-temporal distributions of the electron and neon and xenon ion densities, the neon and xenon metastable atom densities, the electric potential and the electric field as well as the mean electron energy are presented at 1.5 Torr and 250 V. The current–voltage characteristic is shown at 3 Torr, and it is compared with previous work for pure neon gas. The model is validated theoretically and experimentally in the case of pure gas.     

From a compressible fluid model to new mass conserving cavitation algorithms

This study investigates two algorithms proposed to solve a new cavitation model. This new cavitation model is based on a compressible Reynolds equation in which the density–pressure relation is obtained from a barotropic–isentropic assumption. It can be viewed as an approximation of the Jakobson–Floberg–Olsson/Elrod Adams cavitation model. Two algorithms are proposed to solve it. The first one is explicit and needs an important number of nodes. The second is implicit and can be used for steady-state and unsteady problems. Its implementation is easy and needs only minor modifications for a computer code in which cavitation is ignored. It can also be used to compute the solution of the usual J.F.O./E.A. model. Faster convergence is obtained using a relaxation parameter.     

A high accurate static contact angle algorithm based on Hough transformation

The static contact angle for blurry drop images is more intricate to obtain. To improve the accuracy of the Hough transformation for the static contact angle calculation, the water drop images with different volumes are generated by the Laplace equation, and the influence of the volume on the accuracy of the Hough transformation is analyzed. The results reveal that the circle Hough transformation is particularly well suited to the cases with small drop volume. At the same time, the critical water drop volume value corresponding to a contact angle error of 3° is given, a modified Hough transformation algorithm in conjunction with the critical water drop volume is proposed, and at the same time, the accuracy of the static contact angle calculation for blurry water drop images is significantly improved. The proposed algorithm is a powerful approach to estimate the static contact angle for blurry water drop images.     

Analysis and design of smart mandrels using shape memory polymers

Based on the thermomechanical mechanism of shape memory polymers (SMPs), the three-dimensional thermomechanical constitutive equation that can be used in the ABAQUS finite element simulation was derived. Then this paper compiled UMAT subroutine and simulated the thermomechanical behaviors of SMP smart mandrels. In addition, the properties of shape fixity and shape recovery ratio of SMP were considered in detail. Finally, filament winding experiments were proceeded on bottle-shaped and air duct-shaped mandrels and the simple and efficient demoulding of SMP mandrels were verified. The results showed the feasibility of SMP as the smart mandrels from practical application in the future.