A viscous incompressible fluid occupying the space theta < pi/2 and bounded by the wall theta=pi/2 of a spherical polar coordinate system (r,theta,phi), is stirred by a line vortex along the line theta=0 which is s...
A viscous incompressible fluid occupying the space theta < pi/2 and bounded by the wall theta=pi/2 of a spherical polar coordinate system (r,theta,phi), is stirred by a line vortex along the line theta=0 which is switched on at time t=0. The line vortex is perpendicular to the wall. The development of the flow configuration is considered for the case where the poloidal flow is weak and does not affect the structure of the inducing azimuthal flow. The problem is formulated in terms of the similarity variable r/2(nut)1/2 and the polar angle theta, where nu is the kinematic viscosity of the fluid. An analytical solution is constructed for the azimuthal flow. At any given station r the steady azimuthal velocity field is, practically, reached within time r2/nu. The equations governing the poloidal flow are coupled partial differential equations of mixed elliptic-parabolic type which are transformed to equations that are elliptic throughout the solution domain. These equations are solved numerically using the methods of successive overrelaxation and fast Fourier transform. The results show that the poloidal flow in a meridional plane at time t forms closed loops about the point r almost-equal-to 1.58(nut)1/2, theta=pi/4, where the velocity has only an azimuthal component. The case of a diffusing configuration from the steady state, due to switching off at t=0 of the agent generating the flow, is also considered. For this case the poloidal field consists of open streamlines and at t=2r2/nu its intensity is a very small fraction of that associated with the steady state.
In the present paper, we investigate the instability, adiabaticity, and controlling effects of external fields for a dark state in a homonuclear atom-tetramer conversion that is implemented by a generalized stimulated...
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In the present paper, we investigate the instability, adiabaticity, and controlling effects of external fields for a dark state in a homonuclear atom-tetramer conversion that is implemented by a generalized stimulated Raman adiabatic passage. We analytically obtain the regions for the appearance of dynamical instability and study the adiabatic evolution by a newly defined adiabatic fidelity. Moreover, the effects of the external field parameters and the spontaneous emissions on the conversion efficiency are also investigated.
India's primary source of income is agriculture. Farmers in India have differing perspectives on how to integrate technology into their farming operations. However, farmers lack the knowledge necessary to put tech...
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In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and tran...
In this paper, we present the derivation of a multicontinuum model for the coupled flow and transport equations by applying multicontinuum homogenization. We perform the multicontinuum expansion for both flow and transport solutions and formulate novel coupled constraint cell problems to capture the multiscale property, where oversampled regions are utilized to avoid boundary effects. Assuming the smoothness of macroscopic variables, we obtain a multicontinuum system composed of macroscopic elliptic equations and convection–diffusion–reaction equations with homogenized effective properties. Finally, we present numerical results for various coefficient fields and boundary conditions to validate our proposed algorithm.
An iterative scheme is proposed for numerically solving the integro-differential equations arising in geomagnetic induction problems. The method is tested successfully on two simple models, both involving an infinite ...
An iterative scheme is proposed for numerically solving the integro-differential equations arising in geomagnetic induction problems. The method is tested successfully on two simple models, both involving an infinite strip. The results indicate that for induction problems generally, the iterations should converge rapidly. It is believed that the method will have applications in other fields of interest.
Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equat...
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Spatial instability frequency noise radiation at waves associated with low- shallow polar angles in the chevron jet are investigated and are compared to the round counterpart. The Reynolds-averaged Navier-Stokes equations are solved to obtain the mean flow fields, which serve as the baseflow for linear stability analysis. The chevron jet has more complicated instability waves than the round jet, where three types of instability modes are identified in the vicinity of the nozzle, corresponding to radial shear, azimuthal shear, and their integrated effect of the baseflow, respectively. The most unstable frequency of all chevron modes and round modes in both jets decrease as the axial location moves downstream. Besides, the azimuthal shear effect related modes are more unstable than radial shear effect related modes at low frequencies. Compared to a round jet, a chevron jet reduces the growth rate of the most unstable modes at down- stream locations. Moreover, linearized Euler equations are employed to obtain the beam pattern of pressure generated by spatially evolving instability waves at a dominant low frequency St = 0.3, and the acoustic efficiencies of these linear wavepackets are evaluated for both jets. It is found that the acoustic efficiency of linear wavepacket is able to be reduced greatly in the chevron jet, compared to the round jet.
It is pointed out that in the point-ion formulation of the modified Poisson–Boltzmann equation the pair distribution function has a power decay parallel to the surface. The relationship of the modified Poisson–Boltz...
It is pointed out that in the point-ion formulation of the modified Poisson–Boltzmann equation the pair distribution function has a power decay parallel to the surface. The relationship of the modified Poisson–Boltzmann results to recent cluster-analysis work on the structure of the surface of an electrolyte solution is also mentioned.
The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (SF6) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and contro...
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The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (SF6) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation *** vortex dynamics of the Richtmyer-Meshkov instability and the turbulent mixing induced by the KelvinHelmholtz instability are discussed.A modified reconstruction model is proposed to predict the circulation for the shock triangular gas-cylinder interaction *** typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are *** the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present *** analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin-Helmholtz vortices can gain energy from the mean flow in ***,small scale flow structures are generated therein by means of nonlinear ***,the occasional 'pairing' between a vortex and its neighboring vortex will trigger the merging process of vortices and,finally,create a large turbulent mixing zone.
High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for th...
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High-order strong stability preserving(SSP)time discretizations are often needed to ensure the nonlinear(and sometimes non-inner-product)strong stability properties of spatial discretizations specially designed for the solution of hyperbolic ***-derivative time-stepping methods have recently been increasingly used for evolving hyperbolic PDEs,and the strong stability properties of these methods are of *** our prior work we explored time discretizations that preserve the strong stability properties of spatial discretizations coupled with forward Euler and a second-derivative ***,many spatial discretizations do not satisfy strong stability properties when coupled with this second-derivative formulation,but rather with a more natural Taylor series *** this work we demonstrate sufficient conditions for an explicit two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and Taylor series *** call these strong stability preserving Taylor series(SSP-TS)*** also prove that the maximal order of SSP-TS methods is p=6,and define an optimization procedure that allows us to find such SSP *** types of these methods are presented and their efficiency ***,these methods are tested on several PDEs to demonstrate the benefit of SSP-TS methods,the need for the SSP property,and the sharpness of the SSP time-step in many cases.
The quadratic convection term in the incompressible Navier-Stokes equations is considered as a nonlinear forcing to the linear resolvent operator, and it is studied in the Fourier domain through the analysis of intera...
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