No abstract

The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and numerically. Mathematical derivations reveal that, for gradient reconstruction based on the Green-Gauss theorem (the GG methods), if the summation of first-and-lower-order terms does not counterbalance in the discretized integral process, which rarely occurs, second-order accurate approximation of face midpoint value is necessary to produce at least first-order accurate gradient. However, gradient reconstruction based on the least-squares approach (the LSQ methods) is at least first-order on arbitrary unstructured grids. Verifications are performed on typical isotropic grid stencils by analyzing the relationship between the discretization error of gradient reconstruction and the discretization error of the face midpoint value approximation of a given analytic function. Meanwhile, the numerical accuracy of gradient reconstruction methods is examined with grid convergence study on typical isotropic grids. Results verify the phenomenon of accuracy degradation for the GG methods when the face midpoint value condition is not satisfied. The LSQ methods are proved to be at least first-order on all tested isotropic grids. To study gradient accuracy effects on inviscid flow simulation, solution errors are quantified using the Method of Manufactured Solutions (MMS) which was validated before adoption by comparing with an exact solution case, i.e., the 2-dimensional (2D) inviscid isentropic vortex. Numerical results demonstrate that the order of accuracy (OOA) of gradient reconstruction is crucial in determining the OOA of numerical solutions. Solution accuracy deteriorates seriously if gradient reconstruction does not reach first-order.

β-cyclodextrin(βCD)-based star polymers have attracted much interest because of their unique structures and potential biomedical and biological applications. Herein, a well-defined folic acid (FA)-conjugated and disulfide bond-linked star polymer ((FA-Dex-SS)-βCD-(PCL)14) was synthesized via a couple reaction between βCD-based 14 arms poly(ε-caprolactone) (βCD-(PCL)14) and disulfide-containing α-alkyne dextran (alkyne-SS-Dex), and acted as theranostic nanoparticles for tumor-targeted MRI and chemotherapy. Theranostic nanoparticles were obtained by loading doxorubicin (DOX), and superparamagnetic iron oxide (SPIO) particles were loaded into the star polymer nanoparticles to obtain ((FA-Dex-SS)-βCD-(PCL)14@DOX-SPIO) theranostic nanoparticles. In vitro drug release studies showed that approximately 100% of the DOX was released from disulfide bond-linked theranostic nanoparticles within 24 h under a reducing environment in the presence of 10.0 mM GSH. DOX and SPIO could be delivered into HepG2 cells efficiently, owing to the folate receptor-mediated endocytosis process of the nanoparticles and glutathione (GSH), which triggered disulfide-bonds cleaving. Moreover, (FA-Dex-SS)-βCD-(PCL)14@DOX-SPIO showed strong MRI contrast enhancement properties. In conclusion, folic acid-decorated reduction-sensitive star polymeric nanoparticles are a potential theranostic nanoparticle candidate for tumor-targeted MRI and chemotherapy.

In order to simulate the under control self-propelled swimming of bionic fishes, a coupling method of hydrodynamics/kinematics/motion-control is presented in this paper. The Navier-Stokes equations in the arbitrary Lagrangian-Eulerian framework are solved in parallel based on the computational domain decomposition to simulate the unsteady flow field efficiently. The flow dynamics is coupled with the fish dynamics in an implicit way by a dual-time stepping approach. In order to discretize the computational domain during a wide range maneuver, an overset grid approach with a parallel implicit hole-cutting technique is adopted and coupled with morphing hybrid grids around the undulation body. The motion control of the fish swimming is realized by a deep reinforcement learning algorithm, which makes the fish model choose proper undulation manner according to a specific purpose. By adding random disturbances in the training process of fish swimming along a straight line, a simplified two-dimensional fish model obtains the ability to swim along a specific trajectory. Then in subsequent tests, the two-dimensional fish model is able to swim along more complex curves with obstacles. Finally, the starting process of a three-dimensional tuna-like model is simulated preliminarily to validate the ability of the coupling method for three-dimensional complex configurations. The numerical results demonstrate that this study could be used to explore the swimming mechanism of fishes in complex environments and to guide how robotic fishes can be controlled to accomplish their tasks.