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言归正传,我们要证明的identity是关于Oseen张量的傅里叶变换,做小雷诺数流体力学的可能会用到,就是我们要用的Oseen Tensor里有这样一项: rirjr3 我们得到 F(rirjr3)=4πδijk2−8πkikjk4 这个玩意的傅里叶变换我想了一个比较tricky的办法,用来做其他傅里叶变换应该也很有效。
Fourth, the singular solution, based on a screened Oseen tensor, currently used in the above mentioned theories is simply wrong and fails to account for the incompressibility of the solvent. The actual singular solution, which has long been available, is discussed. In conclusion, it is pointed ...
We present Oseen equations on Lipschitz domains in a port-Hamiltonian context. Such equations arise, for instance, by linearization of the Navier-Stokes equations. In our setup, the external port consists of the boundary traces of velocity and the normal component of the stress tensor, and bounda...
of a vector n⃗ ∈R3n→∈R3 and a tensor T∈R9T∈R9. These 12 arguments are independent variables in the Frank-Oseen energy density FF.Next one should substitute T=∇⃗ n⃗ T=∇→n→.Let v⃗ =dn⃗ dtv→=dn→dt be the corresponding velocity field.OP...
Fast Q-tensor method for modeling the dynamics of defects in a liquid crystal director field. A fast Q-tensor method, which can model the defect dynamics in a liquid crystal director field, is presented. Conceptually based on the Oseen-Frank approac... GD Lee,PJ Bos,SH Ahn,... - 《Phy...
Further, the velocity deformation tensor is defined by 2.1. ALE formulation In order to handle the time-dependent domain, we now rewrite NSE (1) in an arbitrary Lagrangian–Eulerian form. Let be a reference domain, and define a family of bijective ALE mappings The reference domain can ...
To approximate the velocity, pressure, and stress tensor, we choose lowest equal-order FE triples p1 – p1 – p1dg respectively. It is well known that these elements don't satisfy the inf–sup (or LBB) condition. Owing to the violation of the essential stability condition, the system ...
In our setup, the external port consists of the boundary traces of velocity and the normal component of the stress tensor, and boundary control is imposed by velocity and normal stress tensor prescription at disjoint parts of the boundary. We employ the recently developed theory of port-...
The electric field distribution takes into account the whole 2D permittivity tensor for the transverse coordinates. Standard finite difference time domain methods together with an iterative method is applied to find an approximate solution to our coupled problem. A novel class of TBC is used to ...