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By Cho S.N.

The Casimir strength for charge-neutral, excellent 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 stumbled on to be beautiful. The repulsive Casimir strength stumbled on by way of Boyer for a round shell is a unique case requiring stringent fabric estate of the sector, in addition to the categorical boundary stipulations for the wave modes inside and out of the field. the required standards indetecting Boyer's repulsive Casimir strength for a sphere are mentioned on the finish of this thesis.

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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. 8) and after rearrangement, one obtains 3 ξ12 k −2 1 k1,i 2 + 2ξ1 k 3 −1 3 r0,i k1,i + 1 i=1 i=1 r0,i 2 2 − [ri ] = 0.

Reflection Dynamics ✄✂✄✂✄✂ ☞☛☞☛☞☛ Lx,1 ☎✆✝ ☎✆✝ ☎✆✝ ☎✝ ✄✂✄✂ ✄✂ Rrp,1 ✁ ✁ ✁ Lx,2 ☞☛☞☛☞☛ 1 R dpl Right Plate Left Plate Left Driven Plate ✁ ✁ ✁ 2 R rp,2 3 Rlp,3 Rlp,2 ^y ^x Right Driven Plate ✟✞✟✞✟✞ ✟✞✟✞✟✞ ✆✠✡ ✠✆✡ ✠✆✡ ✠✡ R dpr ^Z axis is out of the page! : A one dimensional driven parallel plates configuration. 16) of Appendix D1. The force shown in the above expression vanishes for the one dimensional case. This is an expected result. 4) in the Appendix D1. The summation there obviously runs only once to arrive at the expression, ∂Hns /∂ki = ns + 12 c.

For that system   R˙ rp,cm,α (t0 ) = R˙ lp,3 (t0 ) + R˙ rp,2 (t0 ) , 1 pvirtual−photon = Hns , (t0 ) ,  R˙ lp,cm,α (t0 ) = R˙ rp,1 (t0 ) + R˙ lp,2 (t0 ) . c For simplicity, assuming that the impact is always only in the normal direction, R˙ rp,cm,α (t0 ) = 2 Hns ,3 (t0 ) − Hns ,2 (t0 ) , mrp c R˙ lp,cm,α (t0 ) = 2 Hns ,1 (t0 ) − Hns ,2 (t0 ) , mlp c where the differences under the magnitude symbol imply field energies from different regions counteract the other. The details of this section can be found in Appendix D2.

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