Correction to: Practical framework for data-driven RANS modeling with data augmentation

Acta Mechanica Sinica -     

Fully-developed pipe and planar flows of multimode viscoelastic fluids

Two solutions are presented for fully-developed pipe and planar flows of multimode viscoelastic models. The fluids have a Newtonian solvent contribution and the polymer modes are described by the Phan-Thien—Tanner (PTT), the FENE-P or the Giesekus equation. The first solution is exact and can handle any number of modes, but is only semi-analytical. The second solution, which is presented only for the PTT model with a linear stress coefficient and the FENE-P model, can also handle any number of modes. It is based on a truncated series expansion and is completely analytical, but provides only an approximated solution. The complexity of the multimode solutions is investigated first with the exact semi-analytical method and it is shown that at high Deborah number flows the high-order stresses can become as important as the stress of the first mode. It is also under these conditions that the approximated analytical solution deviates from the exact semi-analytical solution. A criterion for the accurate use of the approximated solution is presented. Fortran codes are provided to obtain these solutions at the internet address at the end.     

Electrochemical oxidation of tetramethoxy precursor as a key step for the synthesis of coenzyme Q10

The feasibility of electrosynthesis of coenzyme Q₁₀ (1) by electrooxidation of tetramethoxy precursor (2) has been investigated at carbon, Pt and BDD anodes in a divided cell. The process strongly depends on the applied potential, anode material and water content of the solvent. At carbon anodes in CH₃CN/CH₂Cl₂ + 0.15 M Bu₄NBF₄ at proper operative conditions high faradic efficiency (>60%) and excellent selectivity (95–97%) of the target product were obtained.     

Time-dependent Green's functions for an anisotropic bimaterial with viscous interface

By virtue of the Stroh formalism, we derive the exact closed-form solutions for the time-dependent two-dimensional Green's functions due to a line force and line dislocation in an anisotropic bimaterial with a viscous interface. We first reduce the boundary value problem to two coupled homogeneous first-order partial differential equations, which can be solved using a decoupling technique. The full-field expressions of the time-dependent displacements and stresses due to the line force and line dislocation interacting with the viscous interface are obtained.     

An asymptotic approach to the problem of the free oscillations of a beam

Equations describing the free small longitudinal and transverse oscillations of a straight elastic beam of rectangular cross section are obtained using the plane linear theory of elasticity and the method of integrodifferential relations. The initial system of partial differential equations is reduced to a system of ordinary linear differential equations with constant coefficients. The effect of the geometrical and elastic characteristics of the beam on the frequency and form of the natural oscillations is investigated. For longitudinal motions it is shown that different types of natural displacements and internal stresses of the beam exist. For transverse oscillations, it is found that there are frequency zones corresponding to different forms of the solutions of the characteristic equation obtained using the proposed model.     

Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays

A delay-differential equation modelling a bidirectional associative memory (BAM) neural network with three neurons is investigated. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, its linear stability is investigated and Hopf bifurcations are demonstrated. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold reduction. Numerical simulation results are given to support the theoretical predictions.     

An estimate of the heat fluxes to the surface of blunt bodies moving at hypersonic velocity in the atmosphere

The problem of the chemically equilibrium three-dimensional boundary layer on a blunt body which is in motion in the atmosphere is considered. A solution of the system of equations of the boundary layer is found by the method of successive approximations, and simple analytic expressions are written in the first approximation for the surface friction and heat flux coefficients. Formulae are obtained in the final form for estimating the convective heat flux in the neighbourhood of the critical point of spherical blunting.     

Towards the synthesis of insulated oligoynes: A ring-closing-metathesis approach to molecular encapsulation

Masked hexayne 18 was prepared in 11 steps from commercially available reagents. The four butenyl substituents contained within the two arylsilane residues in 18 have been used in a double ring-closing-metathesis operation in an attempt to encapsulate the π-conjugated framework. When 18 was treated with Grubbs’ 1st generation metathesis catalyst however, double ring-closing metathesis provided macrocycle 19 as the major product in good yield. Reasons why the macrocycle in 19 crowns, rather than encapsulates, the π-conjugated framework are discussed.