The integrable Boussinesq equation and it’s breather,lump and soliton solutions

The fourth-order nonlinear Boussinesq water wave equation, which explains the propagation of long waves in shallow water, is explored in this article. We used the Lie symmetry approach to analyze the Lie symmetries and vector fields. Then, by using similarity variables, we obtained the symmetry reductions and soliton wave solutions. In addition, the Kudryashov method and its modification are used to explore the bright and singular solitons while the Hirota bilinear method is effectively used to obtain a form of breather and lump wave solutions. The physical explanation of the extracted solutions was shown with the free choice of different parameters by depicting some 2-D, 3-D, and their corresponding contour plots.

     

CFD and Population Balance Modeling of Crude Oil Emulsions in Batch Gravity Separation—Comparison to Ultrasound Experiments

Water-in-oil emulsion destabilization and separation in a batch gravity separator was investigated experimentally and by numerical modeling. A multiphase computational fluid dynamics (CFD) was used with a population balance model (PBM) to model separation behavior of crude oil emulsions. The inhomogeneous discrete method is used to solve the population balance equations. Closure kernels are applied to model droplet–droplet coalescence. To describe the increase in emulsion viscosity with water concentration, an emulsion viscosity model was selected that predicted emulsion stability and the denser emulsion layer forming above the coalescing interface, otherwise known as the dense packed zone or layer (DPZ). The results from a commercial CFD code are compared to experimental data of the water fraction vertical distribution measured by low-power ultrasound in the batch separator. The predicted time-dependent profiles of water fraction in the separator were found to be in good agreement with the experimental measurements for the range of water content from 6 to 50%. The model predicts the effect of water fraction on the separation kinetics and the evolution of the DPZ. Further studies are underway to apply the models to emulsions from different types of crude oils.     

Exact and approximate solutions of time-fractional models arising from physics via Shehu transform

In this present investigation, we proposed a reliable and new algorithm for solving time-fractional differential models arising from physics and engineering. This algorithm employs the Shehu transform method, and then nonlinearity term is decomposed. We apply the algorithm to solve many models of practical importance and the outcomes show that the method is efficient, precise, and easy to use. Closed form solutions are obtained in many cases, and exact solutions are obtained in some special cases. Furthermore, solution profiles are presented to show the behavior of the obtained results in other to better understand the effect of the fractional order.     

Iterative methods for solving fourth- and sixth-order time-fractional Cahn-Hillard equation

This paper presents analytical-approximate solutions of the time-fractional Cahn-Hilliard (TFCH) equations of fourth and sixth order using the new iterative method (NIM) and q-homotopy analysis method (q-HAM). We obtained convergent series solutions using these two iterative methods. The simplicity and accuracy of these methods in solving strongly nonlinear fractional differential equations is displayed through the examples provided. In the case where exact solution exists, error estimates are also investigated.     

Influence of Transition Metal Cationization versus Sodium Cationization and Protonation on the Gas-Phase Tautomeric Conformations and Stability of Uracil: Application to [Ura+Cu]<Superscript>+</Superscript> and [Ura+Ag]<Superscript>+</Superscript>

The gas-phase conformations of transition metal cation-uracil complexes, [Ura+Cu]⁺ and [Ura+Ag]⁺, were examined via infrared multiple photon dissociation (IRMPD) action spectroscopy and theoretical calculations. IRMPD action spectra were measured over the IR fingerprint and hydrogen-stretching regions. Structures and linear IR spectra of the stable tautomeric conformations of these complexes were initially determined at the B3LYP/6-31G(d) level. The four most stable structures computed were also examined at the B3LYP/def2-TZVPPD level to improve the accuracy of the predicted IR spectra. Two very favorable modes of binding are found for [Ura+Cu]⁺ and [Ura+Ag]⁺ that involve O2N3 bidentate binding to the 2-keto-4-hydroxy minor tautomer and O4 monodentate binding to the canonical 2,4-diketo tautomer of Ura. Comparisons between the measured IRMPD and calculated IR spectra enable elucidation of the conformers present in the experiments. These comparisons indicate that both favorable binding modes are represented in the experimental tautomeric conformations of [Ura+Cu]⁺ and [Ura+Ag]⁺. B3LYP suggests that Cu⁺ exhibits a slight preference for O4 binding, whereas Ag⁺ exhibits a slight preference for O2N3 binding. In contrast, MP2 suggests that both Cu⁺ and Ag⁺ exhibit a more significant preference for O2N3 binding. The relative band intensities suggest that O4 binding conformers comprise a larger portion of the population for [Ura+Ag]⁺ than [Ura+Cu]⁺. The dissociation behavior and relative stabilities of the [Ura+M]⁺ complexes, M⁺ = Cu⁺, Ag⁺, H⁺, and Na⁺) are examined via energy-resolved collision-induced dissociation experiments. The IRMPD spectra, dissociation behaviors, and binding preferences of Cu⁺ and Ag⁺ are compared with previous and present results for those of H⁺ and Na⁺.

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Influence of short roughness strip on the turbulent boundary layer structure

Hot-wire measurements have been undertaken in a turbulent boundary layer which is subjected to an impulse in form of a short roughness strip with the aim of examining its influence on the structure of the turbulent boundary layer. The results indicate that, while the energy containing motion is shifted from low wave number to high wave number near the wall due to the interfering of the roughness strip with the near-wall structure, the reverse is the case in the outer region. While the anisotropy at small scale changes appreciably, there is no discernable change at the large scale when distance from the wall is increased as reflected in the collapses of spectra shear correlation coefficient at the low wave number. It further shows that the roughness strip alters the flow dynamics of the boundary layer as shown in the changes in the mixing length distribution.