Accurate Evaluation of Electrostatics for Macromolecules in Solution

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(303) n = 23, n = 64 θ. r. 100. 80. 60. 40. 20. 0. −20. −40. −60. −80. −100 −100. −80. −60. −40. −20. 0. 20. 40. 60. 80. 100. J) .& ) % ". Parameters: K+ = 2, ε− = 2, ε+ = 80, nr = 32, nθ = 96. 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 100 100. 50 50. 0 0 −50. −50 −100. −100. Computed Solution. J) 4& ) ) % " "0.

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(306) ( ) .( ! - = "##L ) )

(307) $ .. I -D$ . E C D E = D4<E 4 D $ . * .E ) I . nr = 23, nθ = 64 100. 80. 60. 40. 20. 0. −20. −40. −60. −80. −100 −100. −80. −60. −40. −20. 0. 20. 40. 60. 80. 100. J) 0& ) % . "# . !

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(310) )) - - (

(311)

(312) ) B . )

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(314) Parameters: K+ = 100, C = 10000, ε− = 2, ε+ = 80, nr = 32, nθ = 96. 2000 1500 1000 500 0 −500 −1000 −1500 −2000 −100 −50 0 50 100. −60. −80. −20. −40. 20. 0. 40. 60. 80. Computed solution truncated. J) 6& ) ) % . nr = 23, nθ = 64 100. 80. 60. 40. 20. 0. −20. −40. −60. −80. −100 −100. −80. −60. −40. −20. 0. 20. 40. 60. 80. 100. J) $& ) % 4 0 ,½ 4(047%#4 U "(../%#" U 7(76<%#0 "(<6$ 4(477%#. "(76/ .(.4.%#0 "(<7< 7(6$$%#4 "(<70 6($#0%#6 "(<<0 .("07%#4 "(<<$ 4& % )

(315) P) % 4(. + "0 4. .4 $0 0" ".7 // .6$ +. ½. ,. . "$.

(316) +. −. +. Parameters: K = 40, C = 5, ε = 2, ε = 80, n = 41, n = 128 θ. r. 1.5. 1. 0.5. 0. −0.5. −100. −1 −100. −50. −50. 0. 0 50. 50 100. 100 Computed solution truncated. J) /& ) ) % 4 −4. x 10 2.5 2 1.5 1 0.5 0 −0.5 100. 100. 50 50. 0 0 −50. −50 −100. −100. uh − uexact. J) 7& % ) ) % 4 "/.

(317) "# !. ! ) ) , ? :. F) ( % 4( 3 - = "./L = "6 ###( DE! ) = "( DE! G

(318) " ) :( ) J <""( Parameters: K+ = 1.27, C = 15000, ε− = 2, ε+ = 80, nr = 32, nθ = 96. 20 15 10 5 0 −5 −10 −15 −20 100 100. 50 50. 0 0 −50. −50 −100. −100. Computed solution truncated. J) <& ) ) % 0. 2 ) ) ) ) )

(319) ) ) ( ) ) ) ( DE ) )

(320) ) M ) ) ( DE ) 1) )

(321) B )

(322) Æ ) )( DE 9 F) ) B ( "7.

(323) Computed solution outdside of (including ) the interface. 6 4 2 0 −2 −4 −6 100 100. 50 50. 0 0 −50. −50 −100. −100. J) "#& ) ) ) I % 0 Parameters: K+ = 1.27, C = 9773, ε− = 2, ε+ = 80, nr = 32, nθ = 96. 15 10 5 0 −5. 100. −10. 50. −15 100. 0 50 −50. 0 −50 −100. −100. Computed solution truncate. J) ""& ) ) % 0 "<.

(324) Computed solution outdside of (including ) the interface. 6 4 2 0 −2. 100. −4. 50. −6 100. 0 50 −50. 0 −50 −100. −100. J) ".& ) ) ) I % 0 ) M

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