Casimir force in non-planar geometric configurations by Cho S.N.

By Cho S.N.

The Casimir strength for charge-neutral, ideal conductors of non-planar geometric configurations were investigated. The configurations have been: (1) the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the round shell. The ensuing Casimir forces for those actual preparations were came across to be appealing. The repulsive Casimir strength stumbled on via Boyer for a round shell is a distinct case requiring stringent fabric estate of the field, in addition to the explicit boundary stipulations for the wave modes in and out of the field. the mandatory standards indetecting Boyer's repulsive Casimir strength for a sphere are mentioned on the finish of this thesis.

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It would then continue toward the plate, and depending on the orientation of plate at the time of impact, the wave-vector, now reflecting off the plate, would either escape to infinity or re-enter the hemisphere. The process repeats successively. In order to determine whether the wave that just escaped from the hemisphere cavity can reflect 27 3. : The plate-hemisphere configuration. back from the plate and re-enter the hemisphere or escape to infinity, the exact location of reflection on the plate must be known.

Equations of Motion for the Driven Parallel Plates The Unruh-Davies effect states that heating up of an accelerating conductor plate is proportional to its acceleration ¨ [2πck ] , where R ¨ is the plate acceleration. 10, can be used as a simple model to demonstrate the complicated sonoluminescense phenomenon for a bubble subject to a strong acoustic field. 31) of Appendix D2. 10. 33) for this linear coupled system can be written in 31 3. 34) ξ   R˙ 1 = R3 , R˙ 2 = R4 , ¨ 1 = ξrp + η1 R˙ 1 + η2 R˙ 2 = ξrp + η1 R3 + η2 R4 , R˙ 3 = R  ˙ ¨ 2 = ξlp + η3 R˙ 2 + η4 R˙ 1 = ξlp + η3 R4 + η4 R3 .

The subscript i of ri denotes “inner radius” and it is not a summation index. 5) are combined as 3 r0,i + ξ1 k −1 1 k1,i − ri Λ1,i eˆi = 0. 6) i=1 Because the basis vectors eˆi are independent of each other, the above relations are only satisfied when each coefficients 45 A. Reflection Points on the Surface of a Resonator of eˆi vanish independently, r0,i + ξ1 k −1 1 k1,i − ri Λ1,i = 0, i = 1, 2, 3. 7) The three terms Λ1,i=1 , Λ1,i=2 and Λ1,i=3 satisfy an identity 3 Λ21,i = 1. 7), Λ21,i is computed for each i : −2 Λ21,i = [ri ] r0,i 2 + ξ12 k −2 1 k1,i 2 + 2r0,i ξ1 k −1 1 k1,i , i = 1, 2, 3.

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