64 lines
3.6 KiB
Mathematica
64 lines
3.6 KiB
Mathematica
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function VDk = calculateVDCutoff(this,Params,Transf,TransfRad)
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% makes the dipolar interaction matrix, size numel(Params.kr) * numel(Params.kz)
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% Rmax and Zmax are the interaction cutoffs
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% VDk needs to be multiplied by Cdd
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% approach is that of Lu, PRA 82, 023622 (2010)
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% == Calulating the DDI potential in Fourier space with appropriate cutoff == %
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% Cylindrical (semianalytic)
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% Cylindrical infinite Z, polarized along x (analytic)
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% Spherical
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switch this.CutoffType
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case 'Cylindrical' %Cylindrical (semianalytic)
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Zcutoff = Params.Lz/2;
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alph = acos((Transf.KX*sin(Params.theta)*cos(Params.phi)+Transf.KY*sin(Params.theta)*sin(Params.phi)+Transf.KZ*cos(Params.theta))./sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2));
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alph(1) = pi/2;
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% Analytic part of cutoff for slice 0<z<Zmax, 0<r<Inf Ronen, PRL 98, 030406 (2007)
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cossq = cos(alph).^2;
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VDk = cossq-1/3;
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sinsq = 1 - cossq;
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VDk = VDk + exp(-Zcutoff*sqrt(Transf.KX.^2+Transf.KY.^2)).*( sinsq .* cos(Zcutoff * Transf.KZ) - sqrt(sinsq.*cossq).*sin(Zcutoff * Transf.KZ) );
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% Nonanalytic part
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% For a cylindrical cutoff, we need to construct a kr grid based on the 3D parameters using Bessel quadrature
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VDkNon = this.calculateNumericalHankelTransform(TransfRad.kr, TransfRad.kz, TransfRad.Rmax, Zcutoff);
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% Interpolating the nonanalytic part onto 3D grid
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fullkr = [-flip(TransfRad.kr)',TransfRad.kr'];
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[KR,KZ] = ndgrid(fullkr,TransfRad.kz);
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[KX3D,KY3D,KZ3D] = ndgrid(ifftshift(Transf.kx),ifftshift(Transf.ky),ifftshift(Transf.kz));
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KR3D = sqrt(KX3D.^2 + KY3D.^2);
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fullVDK = [flip(VDkNon',2),VDkNon']';
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VDkNon = interpn(KR,KZ,fullVDK,KR3D,KZ3D,'spline',0); %Last argument is -1/3 for full VDk. 0 for nonanalytic piece?
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VDkNon = fftshift(VDkNon);
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VDk = VDk + VDkNon;
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case 'CylindricalInfiniteZ' %Cylindrical infinite Z, polarized along x -- PRA 107, 033301 (2023)
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alph = acos((Transf.KX*sin(Params.theta)*cos(Params.phi)+Transf.KY*sin(Params.theta)*sin(Params.phi)+Transf.KZ*cos(Params.theta))./sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2));
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alph(1) = pi/2;
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rhoc = max([abs(Transf.x),abs(Transf.y)]);
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KR = sqrt(Transf.KX.^2+Transf.KY.^2);
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func = @(n,u,v) v.^2./(u.^2+v.^2).*(v.*besselj(n,u).*besselk(n+1,v) - u.*besselj(n+1,u).*besselk(n,v));
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VDk = -0.5*func(0,KR*rhoc,abs(Transf.KZ)*rhoc) + (Transf.KX.^2./KR.^2 - 0.5).*func(2,KR*rhoc,abs(Transf.KZ)*rhoc);
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VDk = (1/3)*(3*(cos(alph).^2)-1) - VDk;
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VDk(KR==0) = -1/3 + 1/2*abs(Transf.KZ(KR==0))*rhoc.*besselk(1,abs(Transf.KZ(KR==0))*rhoc);
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VDk(Transf.KZ==0) = 1/6 + (Transf.KX(Transf.KZ==0).^2-Transf.KY(Transf.KZ==0).^2)./(KR(Transf.KZ==0).^2).*(1/2 - besselj(1,KR(Transf.KZ==0)*rhoc)./(KR(Transf.KZ==0)*rhoc));
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VDk(1,1,1) = 1/6;
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case 'Spherical' %Spherical
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Rcut = min(Params.Lx/2,Params.Ly/2,Params.Lz/2);
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alph = acos((Transf.KX*sin(Params.theta)*cos(Params.phi)+Transf.KY*sin(Params.theta)*sin(Params.phi)+Transf.KZ*cos(Params.theta))./sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2));
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alph(1) = pi/2;
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K = sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
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VDk = (cos(alph).^2-1/3).*(1 + 3*cos(Rcut*K)./(Rcut^2.*K.^2) - 3*sin(Rcut*K)./(Rcut^3.*K.^3));
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otherwise
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disp('Choose a valid DDI cutoff type!')
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return
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end
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end
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