The effective dielectric response of linear composites containing graded material is investigated under an applied electric field E_0.For the cylindrical inclusion with gradient dielectric function,ει(r)=b+cr,random...The effective dielectric response of linear composites containing graded material is investigated under an applied electric field E_0.For the cylindrical inclusion with gradient dielectric function,ει(r)=b+cr,randomly embedded in a host with dielectric constant εm,we have obtained the exact solution of local electric potential of the composite media regions,which obeys a linear constitutive relation D=εE,using hypergeometric function.In dilute limit,we have derived the effective dielectric response of the linear composite media.Furthermore,for larger volume fraction,the formulas of effective dielectric response of the graded composite media are given.展开更多
Two-dimensional viscous flow in a straight channel was studied. The steadyNavier-Stokes equations were linearized on the assumption of small disurbance from theCouette-Poiseuille flow, leading to an eigenvalue equatio...Two-dimensional viscous flow in a straight channel was studied. The steadyNavier-Stokes equations were linearized on the assumption of small disurbance from theCouette-Poiseuille flow, leading to an eigenvalue equation resembling the Orr-Sommerfeld equation.The eigenvalues determine the rate of decay for the stationary perturbation. Asymptotic forms of thedownstream eigenvalues were derived in the limiting cases of small and large Reynolds number, forthe flow with a general mass flux per unit width, and thus the work of Wilson (1969) and Stocker andDuck (1995) was generalized. The asymptotic results are in agreement with numerical ones presentedby Song and Chen (1995).展开更多
文摘The effective dielectric response of linear composites containing graded material is investigated under an applied electric field E_0.For the cylindrical inclusion with gradient dielectric function,ει(r)=b+cr,randomly embedded in a host with dielectric constant εm,we have obtained the exact solution of local electric potential of the composite media regions,which obeys a linear constitutive relation D=εE,using hypergeometric function.In dilute limit,we have derived the effective dielectric response of the linear composite media.Furthermore,for larger volume fraction,the formulas of effective dielectric response of the graded composite media are given.
文摘Two-dimensional viscous flow in a straight channel was studied. The steadyNavier-Stokes equations were linearized on the assumption of small disurbance from theCouette-Poiseuille flow, leading to an eigenvalue equation resembling the Orr-Sommerfeld equation.The eigenvalues determine the rate of decay for the stationary perturbation. Asymptotic forms of thedownstream eigenvalues were derived in the limiting cases of small and large Reynolds number, forthe flow with a general mass flux per unit width, and thus the work of Wilson (1969) and Stocker andDuck (1995) was generalized. The asymptotic results are in agreement with numerical ones presentedby Song and Chen (1995).
