On the basis of Navier-Stockes equation and convection-diffusion equation, combined with surface tension and penetration models, the equations of moment and mass transfer between bubble and the ambient non-Newtonian l...On the basis of Navier-Stockes equation and convection-diffusion equation, combined with surface tension and penetration models, the equations of moment and mass transfer between bubble and the ambient non-Newtonian liquid were established. The formation of a single bubble from a submersed nozzle of 1.0 mm diameter and the mass transfer from an artificially fixed bubble into the ambient liquid were simulated by the volume-of-fluid （VOF） method. Good agreement between simulation results and experimental data confirmed the validity of the numerical method. Furthermore, the concentration distribution around rising bubbles in shear thinning non-Newtonian fluid was simulated. When the process of a single ellipsoidal bubble with the bubble deformation rate below 2.0 rises, the concentration distribution is a single-tail in the bubble＇s wake, but it is fractal when thebubble deformation rate is greater than 2.0. For the overtaking of two in-line rising bubbles, the concentration distribution area between two bubbles broadens gradually and then coalescence occurs. The bifurcation of concentration distribution appears in the rear of the resultant bubble.展开更多
[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectivel...[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectively.The largest eigenvalue of A_α(G) is called the A_α-spectral radius of G,denoted by ρ_α(G).In this paper,we give an upper bound on ρ_α(G) of a Hamiltonian graph G with m edges for α∈[1/2,1),and completely characterize the corresponding extremal graph in the case when m is odd.In order to complete the proof of the main result,we give a sharp upper bound on the ρ_α(G) of a connected graph G in terms of its degree sequence.展开更多
For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fi...For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ>0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.展开更多
The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They ...The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They develop the machinery of K-theory wrong-way maps in the context of orbifolds and use it to relate the quantization commutes with reduction phenomenon to Bott periodicity and the K-theory formulation of the Weyl character formula.展开更多
In this paper, a smooth repetitive osciflating wave traveling down the elastic walls of a non-uniform two- dimensional channels is considered. It is assumed that the fluid is electrically conducting and a uniform magn...In this paper, a smooth repetitive osciflating wave traveling down the elastic walls of a non-uniform two- dimensional channels is considered. It is assumed that the fluid is electrically conducting and a uniform magnetic field is perpendicular to flow. The Sisko fluid is grease thick non-Newtonian fluid can be considered equivalent to blood. Taking long wavelength and low Reynolds number, the equations are reduced. The analytical solution of the emerging non-linear differential equation is obtained by employing Homotopy Perturbation Method （HPM）. The outcomes for dimensionless flow rate and dimensionless pressure rise have been computed numerically with respect to sundry concerning parameters amplitude ratio , Hartmann number M, and Sisko fluid parameter bl. The behaviors for pressure rise and average friction have been discussed in details and displayed graphically. Numerical and graphical comparison of Newtonian and non-Newtonian has also been evaluated for velocity and pressure rise. It is observed that the magnitude of pressure rise is maximum in the middle of the channel whereas for higher values of fluid parameter it increases. Further, it is also found that the velocity profile shows converse behavior along the walls of the channel against multiple values of fluid parameter.展开更多
基金Supported by the National iqatural Science Foundation of China （21076139）.
文摘On the basis of Navier-Stockes equation and convection-diffusion equation, combined with surface tension and penetration models, the equations of moment and mass transfer between bubble and the ambient non-Newtonian liquid were established. The formation of a single bubble from a submersed nozzle of 1.0 mm diameter and the mass transfer from an artificially fixed bubble into the ambient liquid were simulated by the volume-of-fluid （VOF） method. Good agreement between simulation results and experimental data confirmed the validity of the numerical method. Furthermore, the concentration distribution around rising bubbles in shear thinning non-Newtonian fluid was simulated. When the process of a single ellipsoidal bubble with the bubble deformation rate below 2.0 rises, the concentration distribution is a single-tail in the bubble＇s wake, but it is fractal when thebubble deformation rate is greater than 2.0. For the overtaking of two in-line rising bubbles, the concentration distribution area between two bubbles broadens gradually and then coalescence occurs. The bifurcation of concentration distribution appears in the rear of the resultant bubble.
文摘[App1.Anal.Discrete Math.,2017,11(1):81-107] defined the A_α-matrix of a graph G as A_α(G)=αD(G)+(1-α)A(G),where α∈[0,1],D(G) and A(G) are the diagonal matrix of degrees and the adjacency matrix of G,respectively.The largest eigenvalue of A_α(G) is called the A_α-spectral radius of G,denoted by ρ_α(G).In this paper,we give an upper bound on ρ_α(G) of a Hamiltonian graph G with m edges for α∈[1/2,1),and completely characterize the corresponding extremal graph in the case when m is odd.In order to complete the proof of the main result,we give a sharp upper bound on the ρ_α(G) of a connected graph G in terms of its degree sequence.
基金supported by the National Natural Science Foundation of China(Nos.11171197,11371012)the Science Foundation of Weinan Normal University(Grant No.14YKS006)+4 种基金the Foundation of Mathematics Subject of Provincial Supporting Subject of Shaanxi Provincethe Civil-Military Integration Research Foundation of Shaanxi Province(No.13JMR12)the Fundamental Research Funds for the Central Universities(Nos.GK201402005,GK201301007)China Postdoctoral Science Foundation(No.2014M552405)the Natural Science Research Program of Shaanxi Province(No.2014JQ1010)
文摘For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ>0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.
文摘The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They develop the machinery of K-theory wrong-way maps in the context of orbifolds and use it to relate the quantization commutes with reduction phenomenon to Bott periodicity and the K-theory formulation of the Weyl character formula.
文摘In this paper, a smooth repetitive osciflating wave traveling down the elastic walls of a non-uniform two- dimensional channels is considered. It is assumed that the fluid is electrically conducting and a uniform magnetic field is perpendicular to flow. The Sisko fluid is grease thick non-Newtonian fluid can be considered equivalent to blood. Taking long wavelength and low Reynolds number, the equations are reduced. The analytical solution of the emerging non-linear differential equation is obtained by employing Homotopy Perturbation Method （HPM）. The outcomes for dimensionless flow rate and dimensionless pressure rise have been computed numerically with respect to sundry concerning parameters amplitude ratio , Hartmann number M, and Sisko fluid parameter bl. The behaviors for pressure rise and average friction have been discussed in details and displayed graphically. Numerical and graphical comparison of Newtonian and non-Newtonian has also been evaluated for velocity and pressure rise. It is observed that the magnitude of pressure rise is maximum in the middle of the channel whereas for higher values of fluid parameter it increases. Further, it is also found that the velocity profile shows converse behavior along the walls of the channel against multiple values of fluid parameter.
