Stochastic optimization of an urban rail timetable under time‐dependent and uncertain demand

Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two‐stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.     

Channel Coordination with Cooperative Advertising Considering Effect of Advertising on Willingness to Pay

In this paper, cooperative advertising in a manufacturer–retailer supply chain is studied. Advertising can enhance willingness to pay (WTP) of customers. This trade-off between the benefits of increasing WTP of customers and the advertising expenditure is a key to understanding the retailers optimal advertising decision. On the other hand, it is interesting to understand in which condition supporting the retailer for his advertising expenditure is beneficial for the manufacturer. In this study, in order to capture pricing and advertising strategies of the channel member, three non-cooperative games including Nash, Stackelberg retailer and Stackelberg manufacturer game-theoretic models are established. In spite of the related studies which restrict price in order to prevent negative demand, the proposed model allows channel members to increase their prices by enhancing WTP of customers. In this study, contrary to similar additive form demand functions applied in the co-op ad literature which limits their studies for cases that profit function is concave with respect to variables, optimal prices and advertising strategies are obtained for all the solution space. Surprisingly for the very high values of the advertising effect coefficient, a finite optimal advertising expenditure is achieved.     

Torus Knots and the Topological Vertex

We propose a class of toric Lagrangian A-branes on the resolved conifold that is suitable to describe torus knots on S ³. The key role is played by the \({SL(2, \mathbb{Z})}\) transformation, which generates a general torus knot from the unknot. Applying the topological vertex to the proposed A-branes, we rederive the colored HOMFLY polynomials for torus knots, in agreement with the Rosso and Jones formula. We show that our A-model construction is mirror symmetric to the B-model analysis of Brini, Eynard and Mariño. Compared to the recent proposal by Aganagic and Vafa for knots on S ³, we demonstrate that the disk amplitude of the A-brane associated with any knot is sufficient to reconstruct the entire B-model spectral curve. Finally, the construction of toric Lagrangian A-branes is generalized to other local toric Calabi–Yau geometries, which paves the road to study knots in other three-manifolds such as lens spaces.     

Preparation and electrochemical performances of nanoporous/cracked cobalt oxide layer for supercapacitors

Nanoporous/cracked structures of cobalt oxide (Co₃O₄) electrodes were successfully fabricated by electroplating of zinc–cobalt onto previously formed TiO₂ nanotubes by anodizing of titanium, leaching of zinc in a concentrated alkaline solution and followed by drying and annealing at 400 °C. The structure and morphology of the obtained Co₃O₄ electrodes were characterized by X-ray diffraction, EDX analysis and scanning electron microscopy. The results showed that the obtained Co₃O₄ electrodes were composed of the nanoporous/cracked structures with an average pore size of about 100 nm. The electrochemical capacitive behaviors of the nanoporous Co₃O₄ electrodes were investigated by cyclic voltammetry, galvanostatic charge–discharge studies and electrochemical impedance spectroscopy in 1 M NaOH solution. The electrochemical data demonstrated that the electrodes display good capacitive behavior with a specific capacitance of 430 F g^?1 at a current density of 1.0 A g^?1 and specific capacitance retention of ca. 80 % after 10 days of being used in electrochemical experiments, indicating to be promising electroactive materials for supercapacitors. Furthermore, in comparison with electrodes prepared by simple cathodic deposition of cobalt onto TiO₂ nanotubes(without dealloying procedure), the impedance studies showed improved performances likely due to nanoporous/cracked structures of electrodes fabricated by dealloying of zinc, which provide fast ion and electron transfer routes and large reaction surface area with the ensued fast reaction kinetics.     

Least-squares finite element methods for the Navier-Stokes equations for generalized Newtonian fluids

In this contribution we present the least-squares finite element method (LSFEM) for the incompressible Navier-Stokes equations. In detail, we consider a non-Newtonian fluid flow, which is described by a power-law model, see [1]. The second-order problem is reformulated by introducing a first-order div-grad system consisting of the equilibrium condition, the incompressibility condition and the constitutive equation, which are written in residual forms, see [2]. Here, higher-order finite elements which are an important aspect regarding accuracy for the present formulation are investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On solitary wave diffraction by multiple,in-line vertical cylinders

The interaction of solitary waves with multiple, in-line vertical cylinders is investigated. The fixed cylinders are of constant circular cross section and extend from the seafloor to the free surface. In general, there are N of them lined in a row parallel to the incoming wave direction. Both the nonlinear, generalized Boussinesq and the Green–Naghdi shallow-water wave equations are used. A boundary-fitted curvilinear coordinate system is employed to facilitate the use of the finite-difference method on curved boundaries. The governing equations and boundary conditions are transformed from the physical plane onto the computational plane. These equations are then solved in time on the computational plane that contains a uniform grid and by use of the successive over-relaxation method and a second-order finite-difference method to determine the horizontal force and overturning moment on the cylinders. Resulting solitary wave forces from the nonlinear Green–Naghdi and the Boussinesq equations are presented, and the forces are compared with the experimental data when available.     

A Modified Nested-Gridding for Upscaling–Downscaling in Reservoir Simulation

This article reports a numerical study of double-diffusive convection in a fluid-saturated vertical porous annulus subjected to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio (λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly.     

Rapid production of monodisperse cross-linked red blood corpuscle-like particles via scalable one-pot dispersion polymerization

Cross-linked polystyrene (PS) particles having red blood corpuscle (RBC)-like shape were synthesized by one-pot dispersion polymerization of styrene with ethanol/water mixture and ethylene glycol dimethacrylate (EGDMA) as the reaction medium and cross-linker, respectively. Monitoring of the reaction showed that RBC-like shape forms due to asymmetric shrinkage of a cross-linked network during the phase separation. In addition, three dimensional phase diagram was generated based on the yielded data that showed that the formation of such unique shape extremely depends on the polarity of the medium and injection time of the cross-linker. In situ synthesis of RBC-like particles, as promising biomaterials in targeted drug delivery and a model for the understanding of the cell behavior, via such fast and high solid content approach makes it to be conducive to subsequent scale up, i.e. potential commercial adoption.