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## Acoustic Manipulation

Magnetic levitation is a method by which an object is suspended with no support other than magnetic fields. However, magnetic levitation requires the suspended objects are composed of magnetic materials. Acoustic counterpart can be used to manipulate the micro objects without limited requirement of metallic materials, i.e., material independent.

Nowadays, most of applications using the acoustic radiation forces are based on Gor'kov potential theorem, which requires that the particles do not affect the potential distribution (i.e., Rayleigh region). Obviously, to manipulate the Rayleigh particles, the forces derive from Gor'kov's theorem is accurate enough as the scattering phenomenon from the particles play insignificant role in the region.

However, in the cases of manipulating or levitating the Mie particles, the scattering phenomenon from reflection of the probe particle itself and rescattering phenomenon from the reflection of other particles toward the probe partible become significant and nonnegligible.

Additional boundary conditions due to the existence of Mie particles will affect the forces distribution and make the problem become much more complicated for Gor'kov's method. As a result, finite element method (FEM) or finite differential method (FDM) are commonly used to solve the governing partial differential equations (PDE) so that obtain the radiation forces.

In addition, in terms of dynamically manipulating problem, the boundary conditions of the Mie particles must be adjusted and resetting with time elapsing as their positions keep changing at different moments.

In order to simplify the problem, with the help of the translational addition theorem and the partial-wave expansion method, the radiation forces can be expressed as several explicit formulas in which the boundary conditions are involved into the formulas themselves so that it is not necessary to keep resetting the boundary conditions when the particles change the positions.

On this Lagrange's viewpoint, the radiation forces act on certain particles can be calculated effectively by avoiding calculating numerical solution at all grid nodes in the computational domain and adjusting the boundary conditions for every time step.

Therefore, it is possible to fill the gap on the topics of particles patternings and dynamically manipulating problems related to Mie particles.

Nowadays, most of applications using the acoustic radiation forces are based on Gor'kov potential theorem, which requires that the particles do not affect the potential distribution (i.e., Rayleigh region). Obviously, to manipulate the Rayleigh particles, the forces derive from Gor'kov's theorem is accurate enough as the scattering phenomenon from the particles play insignificant role in the region.

However, in the cases of manipulating or levitating the Mie particles, the scattering phenomenon from reflection of the probe particle itself and rescattering phenomenon from the reflection of other particles toward the probe partible become significant and nonnegligible.

Additional boundary conditions due to the existence of Mie particles will affect the forces distribution and make the problem become much more complicated for Gor'kov's method. As a result, finite element method (FEM) or finite differential method (FDM) are commonly used to solve the governing partial differential equations (PDE) so that obtain the radiation forces.

In addition, in terms of dynamically manipulating problem, the boundary conditions of the Mie particles must be adjusted and resetting with time elapsing as their positions keep changing at different moments.

In order to simplify the problem, with the help of the translational addition theorem and the partial-wave expansion method, the radiation forces can be expressed as several explicit formulas in which the boundary conditions are involved into the formulas themselves so that it is not necessary to keep resetting the boundary conditions when the particles change the positions.

On this Lagrange's viewpoint, the radiation forces act on certain particles can be calculated effectively by avoiding calculating numerical solution at all grid nodes in the computational domain and adjusting the boundary conditions for every time step.

Therefore, it is possible to fill the gap on the topics of particles patternings and dynamically manipulating problems related to Mie particles.