Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in,for example,variable-radius arteries.With respect to the nonlinear waves in an artery full of blood with certain aneurysm...Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in,for example,variable-radius arteries.With respect to the nonlinear waves in an artery full of blood with certain aneurysm,pulses in a blood vessel,or features in a circulatory system,this paper symbolically computes out an auto-B?cklund transformation via a noncharacteristic movable singular manifold,certain families of the solitonic solutions,as well as a family of the similarity reductions for a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers equation.Aiming,e.g.,at the dynamical radial displacement superimposed on the original static deformation from an arterial wall,our results rely on the axial stretch of the injured artery,blood as an incompressible Newtonian fluid,radius variation along the axial direction or aneurysmal geometry,viscosity of the fluid,thickness of the artery,mass density of the membrane material,mass density of the fluid,strain energy density of the artery,shear modulus,stretch ratio,etc.We also highlight that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.展开更多
To alleviate the bio-inert of Ti alloys as hard tissue implants, Ti–35Nb–7Zr–xCPP（calcium pyrophosphate,x = 5, 10, 15, 20 wt%） composites were prepared by mechanical alloying（MA） and following spark plasma sint...To alleviate the bio-inert of Ti alloys as hard tissue implants, Ti–35Nb–7Zr–xCPP（calcium pyrophosphate,x = 5, 10, 15, 20 wt%） composites were prepared by mechanical alloying（MA） and following spark plasma sintering（SPS）. Mechanical behaviours and in vitro bioactivity of these composites were investigated systematically. Results showed that the composites consisted of β-Ti matrix, α-Ti, and metal–ceramic phases such as CaO, CaTiO3, CaZrO3, and TixPy. With increasing CPP content, the composites had higher strength（over 1500 MPa） and higher elastic modulus, but suffered almost zero plastic deformation together with lower relative density. When the CPP contents were 5 and 10 wt%,the compressive elastic moduli were 44 and 48 GPa, respectively, which were close to those of natural bones. However, the compressive elastic modulus of the composites increased significantly when CPP contents exceed 10 wt%, thus deteriorating the mechanical compatibility of the composites owing to more α-Ti and metal–ceramic phases. Besides, the surface of Ti–35Nb–7Zr–10CPP composite was deposited as a homogeneous apatite layer during soaking in simulated body fluid（SBF）. It indicates a good bioactivity between the implant materials and living bones.展开更多
Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation i...Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-B?cklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and B?cklund transformations are different from those in the existing literature. All of our results are dependent on the waterwave dispersive power.展开更多
基金Project(31160262)supported by the National Natural Science Foundation of ChinaProject(2013DH012)supported by the Innovation Platform Construction Project of Science and Technology of Yunnan Province,China
基金supported by the National Natural Science Foundation of China under Grant Nos.11871116 and 11772017the Fundamental Research Funds for the Central Universities of China under Grant No.2019XD-A11.
文摘Recent theoretical physics efforts have been focused on the probes for nonlinear pulse waves in,for example,variable-radius arteries.With respect to the nonlinear waves in an artery full of blood with certain aneurysm,pulses in a blood vessel,or features in a circulatory system,this paper symbolically computes out an auto-B?cklund transformation via a noncharacteristic movable singular manifold,certain families of the solitonic solutions,as well as a family of the similarity reductions for a variable-coefficient generalized forced–perturbed Korteweg–de Vries–Burgers equation.Aiming,e.g.,at the dynamical radial displacement superimposed on the original static deformation from an arterial wall,our results rely on the axial stretch of the injured artery,blood as an incompressible Newtonian fluid,radius variation along the axial direction or aneurysmal geometry,viscosity of the fluid,thickness of the artery,mass density of the membrane material,mass density of the fluid,strain energy density of the artery,shear modulus,stretch ratio,etc.We also highlight that the shock-wave structures from our solutions agree well with those dusty-plasma-experimentally reported.
基金supported by the National Natural Science Foundation of China (No. 31160197)the Innovation Platform Construction Project for Science and Technology, Yunnan Province (No. 2013DH012)the Analysis and Testing Foundation of Kunming University of Science and Technology (No. 2016T20090120)
文摘To alleviate the bio-inert of Ti alloys as hard tissue implants, Ti–35Nb–7Zr–xCPP（calcium pyrophosphate,x = 5, 10, 15, 20 wt%） composites were prepared by mechanical alloying（MA） and following spark plasma sintering（SPS）. Mechanical behaviours and in vitro bioactivity of these composites were investigated systematically. Results showed that the composites consisted of β-Ti matrix, α-Ti, and metal–ceramic phases such as CaO, CaTiO3, CaZrO3, and TixPy. With increasing CPP content, the composites had higher strength（over 1500 MPa） and higher elastic modulus, but suffered almost zero plastic deformation together with lower relative density. When the CPP contents were 5 and 10 wt%,the compressive elastic moduli were 44 and 48 GPa, respectively, which were close to those of natural bones. However, the compressive elastic modulus of the composites increased significantly when CPP contents exceed 10 wt%, thus deteriorating the mechanical compatibility of the composites owing to more α-Ti and metal–ceramic phases. Besides, the surface of Ti–35Nb–7Zr–10CPP composite was deposited as a homogeneous apatite layer during soaking in simulated body fluid（SBF）. It indicates a good bioactivity between the implant materials and living bones.
基金supported by the National Nature Science Foundation of China under Grant No.11871116Fundamental Research Funds for the Central Universities of China under Grant No. 2019XD-A11。
文摘Water waves are one of the most common phenomena in nature, the studies of which help energy development, marine/offshore engineering, hydraulic engineering, mechanical engineering, etc. Hereby, symbolic computation is performed on the Boussinesq–Burgers system for shallow water waves in a lake or near an ocean beach. For the water-wave horizontal velocity and height of the water surface above the bottom, two sets of the bilinear forms through the binary Bell polynomials and N-soliton solutions are worked out, while two auto-B?cklund transformations are constructed together with the solitonic solutions, where N is a positive integer. Our bilinear forms, N-soliton solutions and B?cklund transformations are different from those in the existing literature. All of our results are dependent on the waterwave dispersive power.
