平板几何迁移算子的特征值问题

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Hybrid nanofluid flow induced by an exponentially shrinking sheet

The flow and heat transfer induced by an exponentially shrinking sheet with hybrid nanoparticles is investigated in this paper. The alumina (Al₂O₃) and copper (Cu) nanoparticles are suspended in water to form Al₂O₃–Cu/water hybrid nanofluid. In addition, the effects of magnetohydrodynamic (MHD) and radiation are also taken into account. The similarity equations are gained from the governing equations using similarity transformation, and their solutions are obtained by the aid of the bvp4c solver available in Matlab software. Results elucidate that dual solutions exist for suction strength S > S_c and shrinking strength λ > λ_c. The critical values S_c and λ_c for the existence of the dual solutions decrease with the rising of the solid volume fractions of Cu, φ₂ and the magnetic parameter, M. Besides, the skin friction and the heat transfer rate increase with the increasing of φ₂ and M for the upper branch solutions. The increasing of radiation, R leads to reduce the surface temperature gradient which implies to the reduction of the heat transfer rate for both branches when λ < 0 (shrinking sheet). The stability of the dual solutions is determined by the temporal stability analysis, and it is discovered that only one of them is stable and physically applicable.     

Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation

The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000.     

Interplay of Hole Transfer and Host–Guest Interaction in a Molecular Dyad and Triad: Ensemble and Single‐Molecule Spectroscopy and Sensing Applications

A new molecular dyad consisting of a Cy5 chromophore and ferrocene (Fc) and a triad consisting of Cy5, Fc, and β‐cyclodextrin (CD) are synthesized and their photophysical properties investigated at both the ensemble and single‐molecule levels. Hole transfer efficiency from Cy5 to Fc in the dyad is reduced upon addition of CD. This is due to an increase in the Cy5‐Fc separation (r) when the Fc is encapsulated in the macrocyclic host. On the other hand, the triad adopts either a Fc‐CD inclusion complex conformation in which hole transfer quenching of the Cy5 by Fc is minimal or a quasi‐static conformation with short r and rapid charge transfer. Single‐molecule fluorescence measurements reveal that r is lengthened when the triad molecules are deposited on a glass substrate. By combining intramolecular charge transfer and competitive supramolecular interaction, the triad acts as an efficient chemical sensor to detect different bioactive analytes such as amantadine hydrochloride and sodium lithocholate in aqueous solution and synthetic urine.