Extensions of the sequential stochastic assignment problem

The sequential stochastic assignment problem (SSAP) allocates N workers to N IID sequentially arriving tasks so as to maximize the expected total reward. This paper studies two extensions of the SSAP. The first one assumes that the values of any two consecutive tasks are dependent on each other while the exact number of tasks to arrive is unknown until after the final arrival. The second extension generalizes the first one by assuming that the number of workers is also random. Optimal assignment policies for both problems are derived and proven to have the same threshold structure as the optimal policy of the SSAP.     

Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement

Permanent Magnet Synchronous Motor (PMSM) experiences chaotic behavior for a certain range of its parameters. In this case, since the performance of the PMSM degrades, the chaos should be eliminated. In this Letter, the control of the undesirable chaos in PMSM using Lyapunov exponents (LEs) placement is proposed that is also improved by choosing optimal locations of the LEs in the sense of predefined cost function. Moreover, in order to provide the physical realization of the method, nonlinear parameter estimator for the system is suggested. Finally, to show the effectiveness of the proposed methodology, the simulation results for applying this control strategy are provided.     

Nonlocal plate model for free vibrations of single-layered graphene sheets

Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.     

Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces without use of apex coordinates

Drop shape techniques, such as axisymmetric drop shape analysis, are widely used to measure surface properties, as they are accurate and reliable. Nevertheless, they are not applicable in experimental studies dealing with fluid configurations that do not present an apex. A new methodology is presented for measuring interfacial properties of liquids, such as surface tension and contact angles, by analyzing the shape of an axisymmetric liquid-fluid interface without use of apex coordinates. The theoretical shape of the interface is generated numerically as a function of surface tension and some geometrical parameters at the starting point of the interface, e.g., contact angle and radius of the interface. Then, the numerical shape is fitted to the experimental profile, taking the interfacial properties as adjustable parameters. The best fit identifies the true values of surface tension and contact angle. Comparison between the experimental and the theoretical profiles is performed using the theoretical image fitting analysis (TIFA) strategy. The new method, TIFA-axisymmetric interfaces (TIFA-AI), is applicable to any axisymmetric experimental configuration (with or without apex). The versatility and accuracy of TIFA-AI is shown by considering various configurations: liquid bridges, sessile and pendant drops, and liquid lenses.     

Crystal engineering in ionic liquids. The crystal structures of [Mppyr]3[NdI6] and [Bmpyr]4[NdI6][Tf2N

Single crystals of [mppyr][NdI6] and [bmpyr][NdI6][Tf2N] are the first surprising examples of how the cation of an ionic liquid determines the compound formation from an ionic liquid. Depending upon the variation of the length of the alkyl chain of the quaternary pyrrolidinium cation (C3 and C4, respectively), incorporation of the anion of the ionic liquid, [Tf2N]-, can either be evoked or suppressed.     

Homoleptic alkaline earth metal bis(trifluoromethanesulfonyl)imide complex compounds obtained from an ionic liquid

The first homoleptic alkaline earth bis(trifluoromethanesulfonyl)imide (Tf2N) complexes [mppyr]2[Ca(Tf2N)4], [mppyr]2[Sr(Tf2N)4], and [mppyr][Ba(Tf2N)3] were crystallized from a solution of the respective alkaline earth bis(trifluoromethanesulfonyl)imide and the ionic liquid [mppyr][Tf2N] (mppyr = 1,1-N-methyl-N-propylpyrrolidinium). In the calcium and strontium compounds, the alkaline earth metal (AE) is coordinated by four bidentately chelating Tf2N ligands to form isolated (distorted) square antiprismatic [AE(Tf2N)4]2- complexes which are separated by N-methyl-N-propylpyrrolidinium cations. In contrast, the barium compound, [mppyr][Ba(Tf2N)3], forms an extended structure. Here the alkaline earth cation is surrounded by six oxygen atoms belonging to three Tf2N- anions which coordinate in a bidentate chelating fashion. Three further oxygen atoms of the same ligands are linking the Ba2+ cations to infinite (infinity)(1)[Ba(Tf2N)3] chains.     

Effects of viscous dissipation on thermally developing forced convection in a porous saturated circular tube with an isoflux wall

The viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model. For the thermally developing region, a numerical study is reported while a perturbation analysis is presented to find expressions for the temperature profile and the Nusselt number for the fully developed region. The fully developed Nusselt number found by numerical solution for the developing region is compared with that of asymptotic analysis and a good degree of agreement is observed.     

Automated Conductometry Measurements of Simple Electrolytes and Micellar Solutions Using a Voltage Divider Technique

A new automated technique was developed for online monitoring of the conductance of a conductive type of cell. Shining metal electrodes were used for the conductometry measurements and the frequency of the input signal was swept from a few hertz to 1 MHz. A theoretical model was developed based on the voltage dividing technique. The model was in good agreement with the experimental results. Conductances of simple electrolytes such as HCl and micellar solutions were compared. Solutions of HCl with concentrations as low as 45 μmol⋅L⁻¹ were investigated. Critical micellar concentrations of two types of micelles, SDS and CPC, were also measured. It was shown that this voltage divider circuit can be used for automated online conductometric titrations.