The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking ...The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.展开更多
We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P estimates resolve a problem left open in previous...We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P estimates resolve a problem left open in previous work.Our argument is based on duality technique and direct estimation of operators.As a consequence of our result,we deduce the L^P boundedness of a class of fractional Marcinkiewicz integral operators.展开更多
A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of th...A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of the one-fluid Euler solvers,differing from them by the presence of a void ratio transport-equation.The model and the system of equations to be simulated are presented.Results are displayed for shock and expansion tube problems,shock-bubble interaction and underwater explosion.Close agreement with reference solutions,obtained from explicit finite volume approaches,is demonstrated.Different numerical methods are additionally displayed to provide comparable and improved computational efficiency to the model and the system of equations.The overall procedure is therefore very well suited for use in general two-phase fluid flow simulations.展开更多
In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that...In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L^1(S^n-1).展开更多
文摘The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.
文摘We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P estimates resolve a problem left open in previous work.Our argument is based on duality technique and direct estimation of operators.As a consequence of our result,we deduce the L^P boundedness of a class of fractional Marcinkiewicz integral operators.
基金The authors gratefully thank K.Tang and A.Beccantini fromthe Commissariata l’Energie Atomique for having provided the numerical solutions computed with their sevenequation model.The second author would like to particularly acknowledge the support provided by the German Jordanian University through the project SEED-SNRE 7-2014.
文摘A compressible and multiphase flows solver has been developed for the study of liquid/gas flows involving shock waves and strong expansion waves leading to cavitation.This solver has a structure similar to those of the one-fluid Euler solvers,differing from them by the presence of a void ratio transport-equation.The model and the system of equations to be simulated are presented.Results are displayed for shock and expansion tube problems,shock-bubble interaction and underwater explosion.Close agreement with reference solutions,obtained from explicit finite volume approaches,is demonstrated.Different numerical methods are additionally displayed to provide comparable and improved computational efficiency to the model and the system of equations.The overall procedure is therefore very well suited for use in general two-phase fluid flow simulations.
文摘In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L^1(S^n-1).
