/usr/share/meep-openmpi/casimir.scm is in libmeep-openmpi8 1.3-3build4.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 | ;given m1 m2, make a composit index n; the inverse is casimir-source-info below
; m1 = r-c, m2 = c => r = m1+m2; n - s = m2 => n = m2 + s; s = (sum_(k=1)^r k)
; => n = m2 + (sum_(k=1)^(m1+m2) k) = m2 + 1/2 (m1+m2) * (m1+m2+1)
(define (make-casimir-src-index m1 m2) (+ m2 (* (/ 2) (+ m1 m2) (+ m1 m2 1))))
; return a list (source-vol mx my mz)
; given the volume integration-vol and n, pick out the appropriate side and mx my mz to use
; sides are ordered by decreasing weight
; weights are w(side, m) = area(side)/total area * 1/(m+1)^4, a rough estimate of the
; contribution to the stress tensor from that side and that m
(define (casimir-source-info integration-vol n)
(define (modround x n) (modulo (inexact->exact (round x)) n))
(define (get-src-index n) ;given n, extract out the two values of m for 3-d
(let* ((s 0) ;sum of diagonals
(r 0) ;row intersection
(c 0));column intersection
(while (< (+ s r) n)
(set! r (+ r 1))
(set! s (+ s r)))
(set! c (- n s))
(list (- r c) c)))
(let* ((min-corner (meep-volume-get-min-corner integration-vol))
(max-corner (meep-volume-get-max-corner integration-vol))
(size-vec (vector3- max-corner min-corner))
(center-vec (vector3+ (vector3-scale 0.5 size-vec) min-corner))
(sx (vector3-x size-vec))
(sy (vector3-y size-vec))
(sz (vector3-z size-vec))
(xshift (vector3 (/ sx 2) 0 0))
(yshift (vector3 0 (/ sy 2) 0))
(zshift (vector3 0 0 (/ sz 2))))
(if (and (> sy 1e-15) (> sz 1e-15)) ;3d cartesian: n = 6*f(m1,m2) + s
(let* ((s (modround n 6))
(nr (/ (- n s) 6))
(ms (get-src-index nr)) ;get (m1 m2)
(m1 (first ms))
(m2 (second ms))
(x-const (vector3 0 sy sz))
(y-const (vector3 sx 0 sz))
(z-const (vector3 sx sy 0))
(center-list
(list (vector3- center-vec xshift) (vector3+ center-vec xshift)
(vector3- center-vec yshift) (vector3+ center-vec yshift)
(vector3- center-vec zshift) (vector3+ center-vec zshift)))
(m-list
(list (vector3 0 m1 m2) (vector3 0 m1 m2) (vector3 m1 0 m2)
(vector3 m1 0 m2) (vector3 m1 m2 0) (vector3 m1 m2 0)))
(orientation-list (list -1 1 -1 1 -1 1))
(size-list
(list x-const x-const y-const y-const z-const z-const))
(surface-vol
(volume (center (list-ref center-list s)) (size (list-ref size-list s))))
(surface-m (list-ref m-list s)))
(print "Computing in 3d\n")
(list surface-vol
(vector3-x surface-m) (vector3-y surface-m) (vector3-z surface-m)
(list-ref orientation-list s) 1))
(if (= dimensions -2) ;cylindricals - must make sure that the volume has only r >= 0
(let* ((3-sides? (if (<= (vector3-x min-corner) 0) true false)) ;volume passes through the origin
(s (if 3-sides? (modround n 3) (modround n 4)))
(nr (if 3-sides? (/ (- n s) 3) (/ (- n s) 4))) ;reduced index
(ms (get-src-index nr)) ;extract out both m-phi and m-dct
(m-phi (first ms))
(m-dct (second ms))
(DR (if 3-sides? (/ 1 resolution) 0)) ;cannot include r = 0!!
(sr (- (vector3-x max-corner) (+ (max 0 (vector3-x min-corner)) DR)))
(r-cen (+ (* 0.5 sr) (max 0 (vector3-x min-corner)) DR))
(new-center-vec (vector3 r-cen 0 (vector3-z center-vec)))
(r-shift (vector3 (/ sr 2) 0 0))
(z-shift (vector3 0 0 (/ sz 2)))
(r-const-size (vector3 0 0 sz))
(z-const-size (vector3 sr 0 0))
(center-list ;if 3-sides? = true, only first 3 list elements are used
(list (vector3- new-center-vec z-shift) (vector3+ new-center-vec z-shift)
(vector3+ new-center-vec r-shift) (vector3- new-center-vec r-shift)))
(m-list
(list (vector3 m-dct m-phi 0) (vector3 m-dct m-phi 0)
(vector3 0 m-phi m-dct) (vector3 0 m-phi m-dct)))
(orientation-list (list -1 1 1 -1))
(size-list
(list z-const-size z-const-size r-const-size r-const-size))
(surface-vol
(volume (center (list-ref center-list s)) (size (list-ref size-list s))))
(surface-m (list-ref m-list s)))
(print "Computing in Cylindrical coordinates: m-phi = "m-phi", m-dct = "m-dct", 3-sides? = "3-sides?"\n")
(list surface-vol
(vector3-x surface-m) (vector3-y surface-m) (vector3-z surface-m)
(list-ref orientation-list s) (if (or (= s 0) (= s 1)) 1 0)))
(let* ((s (modround n 4)) ;2d or quasi-3d cartesian: n = 4m + s, no ambiguity in m
(m (/ (- n s) 4))
(x-const-size (vector3 0 sy )) ;sz may be non-zero for quasi-3d systems
(y-const-size (vector3 sx 0 ))
(center-list
(list (vector3- center-vec xshift) (vector3+ center-vec xshift)
(vector3- center-vec yshift) (vector3+ center-vec yshift)))
(m-list
(list (vector3 0 m 0) (vector3 0 m 0) (vector3 m 0 0) (vector3 m 0 0)))
(orientation-list (list -1 1 -1 1))
(size-list
(list x-const-size x-const-size y-const-size y-const-size))
(surface-vol
(volume (center (list-ref center-list s)) (size (list-ref size-list s))))
(surface-m (list-ref m-list s)))
(print "Casimir.scm: working in 2 dimensions\n")
(print " Surface center: "(list-ref center-list s)"\n")
(print " Surface size: "(list-ref size-list s)"\n")
(list surface-vol
(vector3-x surface-m) (vector3-y surface-m) (vector3-z surface-m)
(list-ref orientation-list s) 1))))))
;compute the casimir force for a single n and single polarization
;n contains both the side number and the harmonic expansion index
(define (casimir-force-contrib force-direction integration-vol n Sigma T source-component gt . step-funcs)
(define (cos-func X mx my mz source-vol)
(let*
((min-corner (meep-volume-get-min-corner source-vol))
(max-corner (meep-volume-get-max-corner source-vol))
(size-vec (vector3- max-corner min-corner))
(X-start (vector3+ X (vector3-scale 0.5 size-vec)))
(sx (vector3-x size-vec))
(sy (vector3-y size-vec))
(sz (vector3-z size-vec))
(x (vector3-x X-start))
(y (vector3-y X-start))
(z (vector3-z X-start))
(kx (if (> sx 1e-15) (/ (* mx pi) sx) 0))
(ky (if (> sy 1e-15) (/ (* my pi) sy) 0))
(kz (if (> sz 1e-15) (/ (* mz pi) sz) 0))
(Nx (if (> sx 1e-15) (/ (if (= mx 0) 1 2) sx) 1))
(Ny (if (> sy 1e-15) (/ (if (= my 0) 1 2) sy) 1))
(Nz (if (> sz 1e-15) (/ (if (= mz 0) 1 2) sz) 1)))
(* (sqrt (* Nx Ny Nz)) (cos (* kx x)) (cos (* ky y)) (cos (* kz z)))))
(let* ((ft (meep-type source-component))
(source-info (casimir-source-info integration-vol n))
(source-vol (first source-info))
(mx (second source-info))
(my (third source-info)) ;m-phi in cylindrical coordinates
(mz (fourth source-info))
(source-orientation (fifth source-info))
(dt (/ Courant resolution)))
(if (= ft E-stuff)
(begin
(set! global-D-conductivity Sigma)
(set! global-B-conductivity 0))
(begin
(set! global-B-conductivity Sigma)
(set! global-D-conductivity 0)))
(if (eq? dimensions -2)
(begin (print "Cylindricals: m = "my" and (nr nz) = ("mx", "mz")\n")
(print " surface center = "(meep-volume-center source-vol)"\n")
(print " source size = "(vector3-
(meep-volume-get-max-corner source-vol)
(meep-volume-get-min-corner source-vol)))
(set! m my))) ;set exp(i m phi) field dependence
(set! sources
(list (make source
(src (make custom-src ; delta function pulse
(src-func (lambda (t) (/ 1 dt)))
(start-time (* -0.25 dt))
(end-time (* 0.75 dt))
(is-integrated? false)))
(center (meep-volume-center source-vol))
(size (vector3- (meep-volume-get-max-corner source-vol)
(meep-volume-get-min-corner source-vol)))
(component source-component)
(amp-func (lambda (p) (cos-func p mx my mz source-vol))))))
(reset-meep)
(init-fields)
(let* ((counter 0)
(force-integral 0))
(define (integrate-function)
(let* ((f-temp (meep-fields-casimir-stress-dct-integral
fields
force-direction
(meep-component-direction source-component)
mx (if (eq? dimensions -2) 0 my) mz
ft source-vol)))
(set! force-integral
(+ force-integral
(imag-part (* (list-ref gt counter) dt
source-orientation
(if (eq? dimensions -2)
(* (if (eq? my 0) 1 2)
(real-part f-temp))
f-temp)))))
(set! counter (+ counter 1))))
(apply run-until (cons (- T 1) (cons integrate-function step-funcs)))
force-integral)))
;%%%%%%%%%%%%%%%%%%%%% BLOCH PBCS %%%%%%%%%%%%%%%%%%%%%%
;here the source is specified in
;the form exp(i k x), k = pi/L (m + k_red),
;m = (mx,my,mz) are integers (reciprocal lattice vectors
;k_red = (kx,ky,kz) is in the 1st BZ, m an integer
;source-vol is assumed to occupy one entire plane intersecting
;the computational cell, so we don't need to extract out
;its information - there is only one side to it
;pass the vector (mx my mz) and (kx ky kz) ready-made, since
;this surface consists of only one face
(define (casimir-force-contrib-bloch force-direction source-vol k-vec Sigma T source-component gt . step-funcs)
;sources of the form exp(i g x); surface integration in
;casimir.cpp integrates against exp(-i g x)
(define (casimir-bloch-func X gx gy gz source-vol)
(let*
((min-corner (meep-volume-get-min-corner source-vol))
(max-corner (meep-volume-get-max-corner source-vol))
(size-vec (vector3- max-corner min-corner)) ;crossection of computational cell
(sx (vector3-x size-vec))
(sy (vector3-y size-vec))
(sz (vector3-z size-vec))
(x (vector3-x X))
(y (vector3-y X))
(z (vector3-z X))
(Kx (if (> sx 1e-15) (/ (* gx pi) 1) 0)) ;phase winding is independent of unit cell size
(Ky (if (> sy 1e-15) (/ (* gy pi) 1) 0))
(Kz (if (> sz 1e-15) (/ (* gz pi) 1) 0))
(Nx (if (> sx 1e-15) (/ sx) 1))
(Ny (if (> sy 1e-15) (/ sy) 1))
(Nz (if (> sz 1e-15) (/ sz) 1)))
(* (sqrt (* Nx Ny Nz)) (exp (* (sqrt -1) (+ (* Kx x) (* Ky y) (* Kz z)))))))
(let* ((ft (meep-type source-component))
(dt (/ Courant resolution))
;Bloch phases - exp( i * (2*pi*m + pi*k) x/L)
(gx (vector3-x k-vec))
(gy (vector3-y k-vec))
(gz (vector3-z k-vec)))
(set! force-complex-fields? true)
(set! k-point (vector3-scale 0.5 k-vec))
(if (= ft E-stuff)
(begin
(set! global-D-conductivity Sigma)
(set! global-B-conductivity 0))
(begin
(set! global-D-conductivity 0)
(set! global-B-conductivity Sigma)))
(set! sources
(list (make source
(src (make custom-src
(src-func (lambda (t) (/ 1 dt)))
(start-time (* -0.25 dt))
(end-time (* 0.75 dt))
(is-integrated? false)))
(center (meep-volume-center source-vol))
(size (vector3- (meep-volume-get-max-corner source-vol)
(meep-volume-get-min-corner source-vol)))
(component source-component)
(amp-func (lambda (p) (casimir-bloch-func p gx gy gz source-vol))))))
(reset-meep)
(init-fields)
(let* ((counter 0)
(force-integral 0))
(define (integrate-function)
(set! force-integral
(+ force-integral
(imag-part (* (list-ref gt counter) dt
(meep-fields-casimir-stress-dct-integral
fields
force-direction
(meep-component-direction source-component)
gx gy gz
ft source-vol true)))))
(set! counter (+ counter 1)))
(apply run-until (cons (- T 1) (cons integrate-function step-funcs)))
force-integral)))
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