Unfamiliar Aspects of Bäcklund Transformations and an Associated Degasperis–Procesi Equation

We summarize the results of our recent work on Bäcklund transformations (BTs), particularly focusing on the relation between BTs and infinitesimal symmetries. We present a BT for an associated Degasperis–Procesi (aDP) equation and its superposition principle and investigate the solutions generated by applying this BT. Following our general methodology, we use the superposition principle of the BT to generate the infinitesimal symmetries of the aDP equation.     

New Effects in the Poly-N-Vinylcaprolactam/Titanium(IV) Oxides Nanocomposite System and Their Nature

Nanocomposites based on poly-N-vinylcaprolactam (PVC), characterized by different drying temperatures of aqueous PVC solution at 25°С (PVC25) and 40°С (PVC40), with titanium(IV) oxide nanoparticles (TONs) (η-phase (TP: TiO_{2 – x} · mH₂O) with a superstructure to the anatase structure and ordered solid solution with partial replacement of oxygen atoms in the η-phase with peroxo group O ₂ ^2– (PP: TiO _x (O₂)_{2 – x} · nH₂O)) have been obtained for the first time and characterized by X-ray diffraction and IR spectroscopy. It is found that a common feature of TP/PVC and PP/PVC obtained by dry mixing and grinding is the decrease in the number of water molecules for TP and PP in the interlayer space of the structure and their attachment to the PVC amide groups; the differences are related to the specificity of PVC behavior in these systems: mechanodestruction of PVC in PP/PVC40 and different numbers of water molecules in PVC25 and PVC40.     

Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

烧结温度对Cao.9(NaCe)0.05Bi2Nb2O9无铅压电陶瓷性能的影响

采用传统固相反应法制备了Ca0.9(NaCe)0.05Bi2 Nb2 O9铋层状无铅压电陶瓷.采用XRD、SEM、EDS及相关电学性能测试系统表征了样品的晶体结构、断面形貌、元素组成以及介电、压电、铁电等性能,探究不同烧结温度对于陶瓷性能的影响.结果表明:当烧结温度为1150℃时,样品的晶体结构单一均匀,呈现片层状结构,致密性较好,压电常数高达17 pC/N,介电损耗仅为0.42;,居里温度为908℃,并且具有很好的温度稳定性,说明固相反应法制备的Ca0.9(NaCe)0.05Bi2Nb2O9压电陶瓷最佳烧结温度为1150℃.     

An approach of dynamic mesh adaptation for simulating 3‐dimensional unsteady moving‐immersed‐boundary flows

In this paper, we present an approach of dynamic mesh adaptation for simulating complex 3‐dimensional incompressible moving‐boundary flows by immersed boundary methods. Tetrahedral meshes are adapted by a hierarchical refining/coarsening algorithm. Regular refinement is accomplished by dividing 1 tetrahedron into 8 subcells, and irregular refinement is only for eliminating the hanging points. Merging the 8 subcells obtained by regular refinement, the mesh is coarsened. With hierarchical refining/coarsening, mesh adaptivity can be achieved by adjusting the mesh only 1 time for each adaptation period. The level difference between 2 neighboring cells never exceeds 1, and the geometrical quality of mesh does not degrade as the level of adaptive mesh increases. A predictor‐corrector scheme is introduced to eliminate the phase lag between adapted mesh and unsteady solution. The error caused by each solution transferring from the old mesh to the new adapted one is small because most of the nodes on the 2 meshes are coincident. An immersed boundary method named local domain‐free discretization is employed to solve the flow equations. Several numerical experiments have been conducted for 3‐dimensional incompressible moving‐boundary flows. By using the present approach, the number of mesh nodes is reduced greatly while the accuracy of solution can be preserved.     

Unsymmetrical Pyrene‐Fused Phthalocyanine Derivatives: Synthesis,Structure, and Properties

Novel pyrene‐fused unsymmetrical phthalocyanine derivatives 2,3,9,10,16,17‐hexakis(2,6‐dimethylphenoxy)‐22,25‐diaza(2,7‐di‐tert‐butylpyrene)[4,5]phthalocyaninato zinc complex Zn[Pc(Pz‐pyrene)(OC₈H₉)₆] ( 1 ) and 2,3,9,10‐tra(2,6‐dimethylphenoxy)‐15,18,22,25‐traza(2,7‐di‐tert‐butylpyrene)[4,5]phthalocyaninato zinc compound Zn[Pc(Pz‐pyrene)₂(OC₈H₉)₄] ( 2 ) were isolated for the first time. These unsymmetrical pyrene‐fused phthalocyanine derivatives have been characterized by a wide range of spectroscopic and electrochemical methods. In particular, the pyrene‐fused phthalocyanine structure was unambiguously revealed on the basis of single crystal X‐ray diffraction analysis of 1 , representing the first structurally characterized phthalocyanine derivative fused with an aromatic moiety larger than benzene.