�� sr !com.femlab.server.ModelFileHeader�D���% L tagst Lcom/femlab/util/FlStringList;L typesq ~ L vrsnt Lcom/femlab/util/FlVersion;xpw sr com.femlab.util.FlVersion��%�/B = I buildI majorL datet Ljava/lang/String;L extq ~ L nameq ~ L rcsq ~ L reactionExtq ~ L reactionNameq ~ xpw t q ~ t #COMSOL Reaction Engineering Lab 3.5t at COMSOL 3.5q ~ w [t $Name: $t $Date: 2008/12/03 17:02:19 $xur [Ljava.lang.String;��V��{G xp t modelinfot xfemt guit g1t g2t fem1uq ~ q ~ t femstructt guistructt drawq ~ t geomxsr com.femlab.api.client.ModelInfo�^���% L descrq ~ L docURLq ~ [ imaget [Bxpw pt"Model is with a rotating magnetic field in a cylinder with ferrofluid with boundary condition of omega=0. If this boundary condition is removed there is no flow. Parameters picked are similar to those from Chaves's papers normalized. Look at Calculation_normalized_velocity_alexchaves.xls pxuq ~ t�`
COMSOL 3.5
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$Name: $
$Date: 2008/12/03 17:02:19 $
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on
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FlNavierStokes
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{"x","y","z"}
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2
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_ns
Lagp2p1
static
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ref
off
{"lm3","lm4","lm5","lm6"}
ideal
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{1,1,1,1,1,1,1,1,2,1,1,1}
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noslip
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0
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0
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0.5
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gls
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navierstokes
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2
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ideal
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ref
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ideal
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ideal
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dir
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nB0Vm
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sym
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mu0_emnc*normH_emnc
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4221
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d2*M_yx-v_M_y_cd2*M_yy-w_M_y_cd2*M_yz+R_M_y_cd2,Vmz)"}{"-d(-u_M_z_cd3*M_zx-v_M_z_cd3*M_zy-w_M_z_cd3*M_zz+R_M_z_cd3,Vmx)","-d(-u_M_z_cd3*M_zx-v_M_z_cd3*M_zy-w_M_z_cd3*M_zz+R_M_z_cd3,Vmy)","-d(-u_M_z_cd3*M_zx-v_M_z_cd3*M_zy-w_M_z_cd3*M_zz+R_M_z_cd3,Vmz)"}{"-d(v,Vmx)","-d(v,Vmy)","-d(v,Vmz)"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"0","0","0"}{"-2*eta_ns*ux+p","-eta_ns*(uy+vx)","-eta_ns*(uz+wx)"}{"-eta_ns*(vx+uy)","-2*eta_ns*vy+p","-eta_ns*(vz+wy)"}{"-eta_ns*(wx+uz)","-eta_ns*(wy+vz)","-2*eta_ns*wz+p"}{"0","0","0"}{"-Dxx_s_di*sx-Dxy_s_di*sy-Dxz_s_di*sz","-Dyx_s_di*sx-Dyy_s_di*sy-Dyz_s_di*sz","-Dzx_s_di*sx-Dzy_s_di*sy-Dzz_s_di*sz"}{"-Dxx_M_x_cd*M_xx-Dxy_M_x_cd*M_xy-Dxz_M_x_cd*M_xz","-Dyx_M_x_cd*M_xx-Dyy_M_x_cd*M_xy-Dyz_M_x_cd*M_xz","-Dzx_M_x_cd*M_xx-Dzy_M_x_cd*M_xy-Dzz_M_x_cd*M_xz"}{"-Dxx_M_y_cd2*M_yx-Dxy_M_y_cd2*M_yy-Dxz_M_y_cd2*M_yz","-Dyx_M_y_cd2*M_yx-Dyy_M_y_cd2*M_yy-Dyz_M_y_cd2*M_yz","-Dzx_M_y_cd2*M_yx-Dzy_M_y_cd2*M_yy-Dzz_M_y_cd2*M_yz"}{"-Dxx_M_z_cd3*M_zx-Dxy_M_z_cd3*M_zy-Dxz_M_z_cd3*M_zz","-Dyx_M_z_cd3*M_zx-Dyy_M_z_cd3*M_zy-Dyz_M_z_cd3*M_zz","-Dzx_M_z_cd3*M_zx-Dzy_M_z_cd3*M_zy-Dzz_M_z_cd3*M_zz"}{"0","0","0"}{"0","0","0"}111111111111111111111
{"u","v","w","p","s","M_x","M_y","M_z","avgv","Vm"}
sqrt(u^2+v^2+w^2)wy-vzuz-wxvx-uysqrt(Vx_ns^2+Vy_ns^2+Vz_ns^2)ux+vy+wzrho_ns*U_ns*h/eta_nsrho_ns*(u*ux+v*uy+w*uz)+px-F_x_ns+if(gmg_level>0,0,-eta_ns*(2*uxx+uyy+vxy+uzz+wxz))rho_ns*(u*vx+v*vy+w*vz)+py-F_y_ns+if(gmg_level>0,0,-eta_ns*(vxx+uyx+2*vyy+vzz+wyz))rho_ns*(u*wx+v*wy+w*wz)+pz-F_z_ns+if(gmg_level>0,0,-eta_ns*(wxx+uzx+wyy+vzy+2*wzz))rho_ns*urho_ns*vrho_ns*weta_nsrho_nsnojac(1/max(2*rho_ns*sqrt(emetric(u,v,w)),48*eta_ns/h^2))0.5*nojac(if(u^2+v^2+w^2rho_ns*divU_nssx-Dxx_s_di*sx-Dxy_s_di*sy-Dxz_s_di*szsy-Dyx_s_di*sx-Dyy_s_di*sy-Dyz_s_di*szsz-Dzx_s_di*sx-Dzy_s_di*sy-Dzz_s_di*szsqrt(grad_s_x_di^2+grad_s_y_di^2+grad_s_z_di^2)sqrt(dflux_s_x_di^2+dflux_s_y_di^2+dflux_s_z_di^2)M_xx-Dxx_M_x_cd*M_xx-Dxy_M_x_cd*M_xy-Dxz_M_x_cd*M_xzM_x*u_M_x_cddflux_M_x_x_cd+cflux_M_x_x_cdM_xy-Dyx_M_x_cd*M_xx-Dyy_M_x_cd*M_xy-Dyz_M_x_cd*M_xzM_x*v_M_x_cddflux_M_x_y_cd+cflux_M_x_y_cdM_xz-Dzx_M_x_cd*M_xx-Dzy_M_x_cd*M_xy-Dzz_M_x_cd*M_xzM_x*w_M_x_cddflux_M_x_z_cd+cflux_M_x_z_cdu_M_x_cdv_M_x_cdw_M_x_cdsqrt(grad_M_x_x_cd^2+grad_M_x_y_cd^2+grad_M_x_z_cd^2)sqrt(dflux_M_x_x_cd^2+dflux_M_x_y_cd^2+dflux_M_x_z_cd^2)sqrt(cflux_M_x_x_cd^2+cflux_M_x_y_cd^2+cflux_M_x_z_cd^2)sqrt(tflux_M_x_x_cd^2+tflux_M_x_y_cd^2+tflux_M_x_z_cd^2)h*sqrt(beta_M_x_x_cd^2+beta_M_x_y_cd^2+beta_M_x_z_cd^2)/Dm_M_x_cd(Dxx_M_x_cd*u_M_x_cd^2+Dxy_M_x_cd*u_M_x_cd*v_M_x_cd+Dxz_M_x_cd*u_M_x_cd*w_M_x_cd+Dyx_M_x_cd*v_M_x_cd*u_M_x_cd+Dyy_M_x_cd*v_M_x_cd^2+Dyz_M_x_cd*v_M_x_cd*w_M_x_cd+Dzx_M_x_cd*w_M_x_cd*u_M_x_cd+Dzy_M_x_cd*w_M_x_cd*v_M_x_cd+Dzz_M_x_cd*w_M_x_cd^2)/(u_M_x_cd^2+v_M_x_cd^2+w_M_x_cd^2+eps)-Dxx_M_x_cd*M_xxx-Dxy_M_x_cd*M_xxy-Dxz_M_x_cd*M_xxz+M_xx*u_M_x_cd-Dyx_M_x_cd*M_xyx-Dyy_M_x_cd*M_xyy-Dyz_M_x_cd*M_xyz+M_xy*v_M_x_cd-Dzx_M_x_cd*M_xzx-Dzy_M_x_cd*M_xzy-Dzz_M_x_cd*M_xzz+M_xz*w_M_x_cd-R_M_x_cdM_xx*u_M_x_cd+M_xy*v_M_x_cd+M_xz*w_M_x_cd-R_M_x_cdDts_M_x_cdM_yx-Dxx_M_y_cd2*M_yx-Dxy_M_y_cd2*M_yy-Dxz_M_y_cd2*M_yzM_y*u_M_y_cd2dflux_M_y_x_cd2+cflux_M_y_x_cd2M_yy-Dyx_M_y_cd2*M_yx-Dyy_M_y_cd2*M_yy-Dyz_M_y_cd2*M_yzM_y*v_M_y_cd2dflux_M_y_y_cd2+cflux_M_y_y_cd2M_yz-Dzx_M_y_cd2*M_yx-Dzy_M_y_cd2*M_yy-Dzz_M_y_cd2*M_yzM_y*w_M_y_cd2dflux_M_y_z_cd2+cflux_M_y_z_cd2u_M_y_cd2v_M_y_cd2w_M_y_cd2sqrt(grad_M_y_x_cd2^2+grad_M_y_y_cd2^2+grad_M_y_z_cd2^2)sqrt(dflux_M_y_x_cd2^2+dflux_M_y_y_cd2^2+dflux_M_y_z_cd2^2)sqrt(cflux_M_y_x_cd2^2+cflux_M_y_y_cd2^2+cflux_M_y_z_cd2^2)sqrt(tflux_M_y_x_cd2^2+tflux_M_y_y_cd2^2+tflux_M_y_z_cd2^2)h*sqrt(beta_M_y_x_cd2^2+beta_M_y_y_cd2^2+beta_M_y_z_cd2^2)/Dm_M_y_cd2(Dxx_M_y_cd2*u_M_y_cd2^2+Dxy_M_y_cd2*u_M_y_cd2*v_M_y_cd2+Dxz_M_y_cd2*u_M_y_cd2*w_M_y_cd2+Dyx_M_y_cd2*v_M_y_cd2*u_M_y_cd2+Dyy_M_y_cd2*v_M_y_cd2^2+Dyz_M_y_cd2*v_M_y_cd2*w_M_y_cd2+Dzx_M_y_cd2*w_M_y_cd2*u_M_y_cd2+Dzy_M_y_cd2*w_M_y_cd2*v_M_y_cd2+Dzz_M_y_cd2*w_M_y_cd2^2)/(u_M_y_cd2^2+v_M_y_cd2^2+w_M_y_cd2^2+eps)-Dxx_M_y_cd2*M_yxx-Dxy_M_y_cd2*M_yxy-Dxz_M_y_cd2*M_yxz+M_yx*u_M_y_cd2-Dyx_M_y_cd2*M_yyx-Dyy_M_y_cd2*M_yyy-Dyz_M_y_cd2*M_yyz+M_yy*v_M_y_cd2-Dzx_M_y_cd2*M_yzx-Dzy_M_y_cd2*M_yzy-Dzz_M_y_cd2*M_yzz+M_yz*w_M_y_cd2-R_M_y_cd2M_yx*u_M_y_cd2+M_yy*v_M_y_cd2+M_yz*w_M_y_cd2-R_M_y_cd2Dts_M_y_cd2M_zx-Dxx_M_z_cd3*M_zx-Dxy_M_z_cd3*M_zy-Dxz_M_z_cd3*M_zzM_z*u_M_z_cd3dflux_M_z_x_cd3+cflux_M_z_x_cd3M_zy-Dyx_M_z_cd3*M_zx-Dyy_M_z_cd3*M_zy-Dyz_M_z_cd3*M_zzM_z*v_M_z_cd3dflux_M_z_y_cd3+cflux_M_z_y_cd3M_zz-Dzx_M_z_cd3*M_zx-Dzy_M_z_cd3*M_zy-Dzz_M_z_cd3*M_zzM_z*w_M_z_cd3dflux_M_z_z_cd3+cflux_M_z_z_cd3u_M_z_cd3v_M_z_cd3w_M_z_cd3sqrt(grad_M_z_x_cd3^2+grad_M_z_y_cd3^2+grad_M_z_z_cd3^2)sqrt(dflux_M_z_x_cd3^2+dflux_M_z_y_cd3^2+dflux_M_z_z_cd3^2)sqrt(cflux_M_z_x_cd3^2+cflux_M_z_y_cd3^2+cflux_M_z_z_cd3^2)sqrt(tflux_M_z_x_cd3^2+tflux_M_z_y_cd3^2+tflux_M_z_z_cd3^2)h*sqrt(beta_M_z_x_cd3^2+beta_M_z_y_cd3^2+beta_M_z_z_cd3^2)/Dm_M_z_cd3(Dxx_M_z_cd3*u_M_z_cd3^2+Dxy_M_z_cd3*u_M_z_cd3*v_M_z_cd3+Dxz_M_z_cd3*u_M_z_cd3*w_M_z_cd3+Dyx_M_z_cd3*v_M_z_cd3*u_M_z_cd3+Dyy_M_z_cd3*v_M_z_cd3^2+Dyz_M_z_cd3*v_M_z_cd3*w_M_z_cd3+Dzx_M_z_cd3*w_M_z_cd3*u_M_z_cd3+Dzy_M_z_cd3*w_M_z_cd3*v_M_z_cd3+Dzz_M_z_cd3*w_M_z_cd3^2)/(u_M_z_cd3^2+v_M_z_cd3^2+w_M_z_cd3^2+eps)-Dxx_M_z_cd3*M_zxx-Dxy_M_z_cd3*M_zxy-Dxz_M_z_cd3*M_zxz+M_zx*u_M_z_cd3-Dyx_M_z_cd3*M_zyx-Dyy_M_z_cd3*M_zyy-Dyz_M_z_cd3*M_zyz+M_zy*v_M_z_cd3-Dzx_M_z_cd3*M_zzx-Dzy_M_z_cd3*M_zzy-Dzz_M_z_cd3*M_zzz+M_zz*w_M_z_cd3-R_M_z_cd3M_zx*u_M_z_cd3+M_zy*v_M_z_cd3+M_zz*w_M_z_cd3-R_M_z_cd3Dts_M_z_cd3sqrt(avgvx^2+avgvy^2+avgvz^2)sqrt(ga9x^2+ga9y^2+ga9z^2)
0
0
x
0
0
y
0
0
z
0
0
detJ_emnc
muxx_emnc*Hx_emnc+muxy_emnc*Hy_emnc+muxz_emnc*Hz_emncmu0_emnc*(Hx_emnc+Mx_emnc)muyx_emnc*Hx_emnc+muyy_emnc*Hy_emnc+muyz_emnc*Hz_emncmu0_emnc*(Hy_emnc+My_emnc)muzx_emnc*Hx_emnc+muzy_emnc*Hy_emnc+muzz_emnc*Hz_emncmu0_emnc*(Hz_emnc+Mz_emnc)
mu0_emnc*mur_emnc
mu0_emnc*murxx_emnc
mu0_emnc*murxy_emnc
mu0_emnc*murxz_emnc
mu0_emnc*muryx_emnc
mu0_emnc*muryy_emnc
mu0_emnc*muryz_emnc
mu0_emnc*murzx_emnc
mu0_emnc*murzy_emnc
mu0_emnc*murzz_emnc
-Vmx
-Vmy
-Vmz
sqrt(abs(Bx_emnc)^2+abs(By_emnc)^2+abs(Bz_emnc)^2)
sqrt(abs(Mx_emnc)^2+abs(My_emnc)^2+abs(Mz_emnc)^2)
sqrt(abs(Hx_emnc)^2+abs(Hy_emnc)^2+abs(Hz_emnc)^2)
sqrt(abs(Brx_emnc)^2+abs(Bry_emnc)^2+abs(Brz_emnc)^2)
0.5*(Hx_emnc*Bx_emnc+Hy_emnc*By_emnc+Hz_emnc*Bz_emnc)0.5*(Hx_emnc*Bx_emnc+Hy_emnc*By_emnc+Hz_emnc*Bz_emnc+Mx_emnc*Bx_emnc+My_emnc*By_emnc+Mz_emnc*Bz_emnc)
dVol_emnc*Wm_emnc
0eta+zeta2*zeta*sy+FMx-2*zeta*sx+FMyFMz0.50.25sc0.3510.10Lagp2p1Lagp2p1-test(nojac(rho_ns)*(nojac(u)*ux+nojac(v)*uy+nojac(w)*uz)+px+if(gmg_level>0,0,-nojac(eta_ns)*(2*uxx+uyy+vxy+uzz+wxz)))*taum_ns*res_u_ns-test(nojac(rho_ns)*(nojac(u)*vx+nojac(v)*vy+nojac(w)*vz)+py+if(gmg_level>0,0,-nojac(eta_ns)*(vxx+uyx+2*vyy+vzz+wyz)))*taum_ns*res_v_ns-test(nojac(rho_ns)*(nojac(u)*wx+nojac(v)*wy+nojac(w)*wz)+pz+if(gmg_level>0,0,-nojac(eta_ns)*(wxx+uzx+wyy+vzy+2*wzz)))*taum_ns*res_w_ns-test(divU_ns)*tauc_ns*res_p_ns0(d(x,xi1)^2+d(x,xi2)^2+d(x,xi3)^2)^2+2*(d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2)+d(y,xi3)*d(x,xi3))^2+(d(y,xi1)^2+d(y,xi2)^2+d(y,xi3)^2)^2+2*(d(z,xi1)*d(x,xi1)+d(z,xi2)*d(x,xi2)+d(z,xi3)*d(x,xi3))^2+2*(d(z,xi1)*d(y,xi1)+d(z,xi2)*d(y,xi2)+d(z,xi3)*d(y,xi3))^2+(d(z,xi1)^2+d(z,xi2)^2+d(z,xi3)^2)^2U_nsd(x,xi1)^2+d(x,xi2)^2+d(x,xi3)^2d(y,xi1)*d(x,xi1)+d(y,xi2)*d(x,xi2)+d(y,xi3)*d(x,xi3)d(y,xi1)^2+d(y,xi2)^2+d(y,xi3)^2d(z,xi1)*d(x,xi1)+d(z,xi2)*d(x,xi2)+d(z,xi3)*d(x,xi3)d(z,xi1)*d(y,xi1)+d(z,xi2)*d(y,xi2)+d(z,xi3)*d(y,xi3)d(z,xi1)^2+d(z,xi2)^2+d(z,xi3)^2-nojac(0.5*min(ck_ns*sqrt((tauc_ns*res_p_ns/(nojac(rhoint_g1_ns/vol_g1_ns)*nojac(sqrt(u2int_g1_ns/vol_g1_ns))))^2+(taum_ns*res_u_ns)^2+(taum_ns*res_v_ns)^2+(taum_ns*res_w_ns)^2),U_ref_ns)*min(gijgij_ns^(-0.25),rho_ns*U_ref_ns/(48*eta_ns)))*rho_ns*(g11_ns*(ux*test(ux)+vx*test(vx)+wx*test(wx))+g21_ns*(uy*test(ux)+vy*test(vx)+wy*test(wx))+g31_ns*(uz*test(ux)+vz*test(vx)+wz*test(wx))+g21_ns*(ux*test(uy)+vx*test(vy)+wx*test(wy))+g22_ns*(uy*test(uy)+vy*test(vy)+wy*test(wy))+g32_ns*(uz*test(uy)+vz*test(vy)+wz*test(wy))+g31_ns*(ux*test(uz)+vx*test(vz)+wx*test(wz))+g32_ns*(uy*test(uz)+vy*test(vz)+wy*test(wz))+g33_ns*(uz*test(uz)+vz*test(vz)+wz*test(wz)))etaprimeetaprime000etaprime000etaprime1T+2*zeta*(vx-uy-2*s)00000000001uvw-s*M_y-(M_x-M_eqx)/omegatau00000000001uvws*M_x-(M_y-M_eqy)/omegatau11000100011uvw-(M_z-M_eqz)/omegatau
mu0_emnc*normH_emnc
dr_guess_emnc
R0_guess_emnc
0
0
0
1
0
0
0
0
0
0
Sdx_guess_emnc
Sdy_guess_emnc
Sdz_guess_emnc
S0x_guess_emnc
S0y_guess_emnc
S0z_guess_emnc
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
murxx_emnc
Bx_emnc/mu0_emnc-Hx_emncM_x0mu0_emnc*Mx_emncBy_emnc/mu0_emnc-Hy_emncM_y0mu0_emnc*My_emncBz_emnc/mu0_emnc-Hz_emncM_z0mu0_emnc*Mz_emnc
1
0
0
0
1
0
0
0
1
(normH_emnc>cut)*Ms-(normH_emnc<-cut)*Ms+(normH_emnc<=cut)*(normH_emnc>=-cut)*Xi*Hx(normH_emnc>cut)*Ms-(normH_emnc<-cut)*Ms+(normH_emnc<=cut)*(normH_emnc>=-cut)*Xi*Hy(normH_emnc>cut)*Ms-(normH_emnc<-cut)*Ms+(normH_emnc<=cut)*(normH_emnc>=-cut)*Xi*Hz
{0,0}
{0,0}
{1,2}
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{"u","v","w","p","s","M_x","M_y","M_z","avgv","Vm"}
eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)+nz_ns*(uz+wx))eta_ns*(2*nx_ns*ux+ny_ns*(uy+vx)+nz_ns*(uz+wx))-nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx)+nz_ns*eta_ns*(uz+wx)-nx_ns*p+2*nx_ns*eta_ns*ux+ny_ns*eta_ns*(uy+vx)+nz_ns*eta_ns*(uz+wx)eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy+nz_ns*(vz+wy))eta_ns*(nx_ns*(vx+uy)+2*ny_ns*vy+nz_ns*(vz+wy))-ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy+nz_ns*eta_ns*(vz+wy)-ny_ns*p+nx_ns*eta_ns*(vx+uy)+2*ny_ns*eta_ns*vy+nz_ns*eta_ns*(vz+wy)eta_ns*(nx_ns*(wx+uz)+ny_ns*(wy+vz)+2*nz_ns*wz)eta_ns*(nx_ns*(wx+uz)+ny_ns*(wy+vz)+2*nz_ns*wz)-nz_ns*p+nx_ns*eta_ns*(wx+uz)+ny_ns*eta_ns*(wy+vz)+2*nz_ns*eta_ns*wz-nz_ns*p+nx_ns*eta_ns*(wx+uz)+ny_ns*eta_ns*(wy+vz)+2*nz_ns*eta_ns*wznx_di*dflux_s_x_di+ny_di*dflux_s_y_di+nz_di*dflux_s_z_dinx_di*dflux_s_x_di+ny_di*dflux_s_y_di+nz_di*dflux_s_z_dinx_cd*dflux_M_x_x_cd+ny_cd*dflux_M_x_y_cd+nz_cd*dflux_M_x_z_cdnx_cd*dflux_M_x_x_cd+ny_cd*dflux_M_x_y_cd+nz_cd*dflux_M_x_z_cdnx_cd*cflux_M_x_x_cd+ny_cd*cflux_M_x_y_cd+nz_cd*cflux_M_x_z_cdnx_cd*cflux_M_x_x_cd+ny_cd*cflux_M_x_y_cd+nz_cd*cflux_M_x_z_cdnx_cd*tflux_M_x_x_cd+ny_cd*tflux_M_x_y_cd+nz_cd*tflux_M_x_z_cdnx_cd*tflux_M_x_x_cd+ny_cd*tflux_M_x_y_cd+nz_cd*tflux_M_x_z_cdnx_cd2*dflux_M_y_x_cd2+ny_cd2*dflux_M_y_y_cd2+nz_cd2*dflux_M_y_z_cd2nx_cd2*dflux_M_y_x_cd2+ny_cd2*dflux_M_y_y_cd2+nz_cd2*dflux_M_y_z_cd2nx_cd2*cflux_M_y_x_cd2+ny_cd2*cflux_M_y_y_cd2+nz_cd2*cflux_M_y_z_cd2nx_cd2*cflux_M_y_x_cd2+ny_cd2*cflux_M_y_y_cd2+nz_cd2*cflux_M_y_z_cd2nx_cd2*tflux_M_y_x_cd2+ny_cd2*tflux_M_y_y_cd2+nz_cd2*tflux_M_y_z_cd2nx_cd2*tflux_M_y_x_cd2+ny_cd2*tflux_M_y_y_cd2+nz_cd2*tflux_M_y_z_cd2nx_cd3*dflux_M_z_x_cd3+ny_cd3*dflux_M_z_y_cd3+nz_cd3*dflux_M_z_z_cd3nx_cd3*dflux_M_z_x_cd3+ny_cd3*dflux_M_z_y_cd3+nz_cd3*dflux_M_z_z_cd3nx_cd3*cflux_M_z_x_cd3+ny_cd3*cflux_M_z_y_cd3+nz_cd3*cflux_M_z_z_cd3nx_cd3*cflux_M_z_x_cd3+ny_cd3*cflux_M_z_y_cd3+nz_cd3*cflux_M_z_z_cd3nx_cd3*tflux_M_z_x_cd3+ny_cd3*tflux_M_z_y_cd3+nz_cd3*tflux_M_z_z_cd3nx_cd3*tflux_M_z_x_cd3+ny_cd3*tflux_M_z_y_cd3+nz_cd3*tflux_M_z_z_cd3
-VmTx
-VmTy
-VmTz
sqrt(abs(tHx_emnc)^2+abs(tHy_emnc)^2+abs(tHz_emnc)^2)
1
Bx_emnc*nx+By_emnc*ny+Bz_emnc*nz
-0.5*(up(Bx_emnc)*up(Hx_emnc)+up(By_emnc)*up(Hy_emnc)+up(Bz_emnc)*up(Hz_emnc))*dnx+(up(Hx_emnc)*dnx+up(Hy_emnc)*dny+up(Hz_emnc)*dnz)*up(Bx_emnc)
-0.5*(up(Bx_emnc)*up(Hx_emnc)+up(By_emnc)*up(Hy_emnc)+up(Bz_emnc)*up(Hz_emnc))*dny+(up(Hx_emnc)*dnx+up(Hy_emnc)*dny+up(Hz_emnc)*dnz)*up(By_emnc)
-0.5*(up(Bx_emnc)*up(Hx_emnc)+up(By_emnc)*up(Hy_emnc)+up(Bz_emnc)*up(Hz_emnc))*dnz+(up(Hx_emnc)*dnx+up(Hy_emnc)*dny+up(Hz_emnc)*dnz)*up(Bz_emnc)
-0.5*(down(Bx_emnc)*down(Hx_emnc)+down(By_emnc)*down(Hy_emnc)+down(Bz_emnc)*down(Hz_emnc))*unx+(down(Hx_emnc)*unx+down(Hy_emnc)*uny+down(Hz_emnc)*unz)*down(Bx_emnc)
-0.5*(down(Bx_emnc)*down(Hx_emnc)+down(By_emnc)*down(Hy_emnc)+down(Bz_emnc)*down(Hz_emnc))*uny+(down(Hx_emnc)*unx+down(Hy_emnc)*uny+down(Hz_emnc)*unz)*down(By_emnc)
-0.5*(down(Bx_emnc)*down(Hx_emnc)+down(By_emnc)*down(Hy_emnc)+down(Bz_emnc)*down(Hz_emnc))*unz+(down(Hx_emnc)*unx+down(Hy_emnc)*uny+down(Hz_emnc)*unz)*down(Bz_emnc)
00000000001100000000unxdnxunydnyunzdnz00000011unxdnxunydnyunzdnz000000000011unxdnxunydnyunzdnz00000011unxdnxunydnyunzdnz00000011unxdnxunydnyunzdnz000000unxdnxunydnyunzdnz
0
H0*(x*cos(t)+y*sin(t))*flc2hs(-1+t,0.05)
1
1
0
2
nx
ny
nz
0
0
0
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{1,1,1,1,2,3,3,2,1,1,2,3,1,3,2,1}
{"0","0","0","0","0","0","0","0","0","0"}{"0","0","0","0","0","0","0","0","0","0"}{"0","0","0","0","0","0","0","0","0","0"}{"0","0","0","0","0","0","0","0","0","0"}{"0","0","0","0","0","0","0","0","0","0"}{"0","0","0","0","0","0","0","0","0","0"}{"0","0","0","0","0","0","0","0","0","0"}{"0","0","0","0","0","0","0","0","0","0"}1234567891011111111111111111111111112111111111211111111121111111112111111{"","","","","","","","","",""}{"","","","","","","","","",""}{"","","","","","","","","",""}{"","","","","","","","","",""}
{"u","v","w","p","s","M_x","M_y","M_z","avgv","Vm"}
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}
{1,1,1,1,2,2,2,2,1,1,1,2,2,2,1,1,2,2,2,2,1,1,2,1}
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1
sqrt(x^2+y^2+z^2)
atan2(y,x)
atan2(z,x)
(theta<0.257)*(theta>-0.257)*(phi<0.257)*(phi>-0.257)*((Bmax*x/mu_r))+H0*(x*cos(t)+y*sin(t))*flc2hs(t-1,0.05)
thetaDifferent theta from spherical coordinates
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1022043
COMSOL 3.5.0.603
Ferrofluid in 3D Cylinder with rotating H field
Shahriar
MIT
EECS
1257979615171
1223349674938
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20
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off
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step
none
step
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0.01
0.01
0.01
Inf
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0.15
0.05
0.15
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1.3
0.5
none
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lines
khanforce_ns,emforce_emnc
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4*pi/3*1e-9
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{"0","0","0"}
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once
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stick
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0.001
off
{""}
{""}
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on
on
0.001
partt
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5
0.001
off
{"",""}
{"",""}
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on
on
0.001
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partt
off
5
off
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on
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{"U_ns"}
off
off
m/s
{"s"}
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off
1
on
off
on
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0
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none
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on
off
all
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off
off
on
on
on
{"u","v","w"}
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{"avgvx","avgvy","avgvz"}
{"","",""}
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1
0
stored
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moviefile
AVI
640
480
10
full
11
off
off
off
{"s"}
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1
0
0
stored
step
none
off
auto
4
on
{"s"}
off
m
0
0
stored
step
none
off
auto
4
on
{"U_ns"}
off
m^3/s
0
0
stored
step
none
off
auto
4
on
{"U_ns"}
off
m^4/s
0
0
stored
step
none
{"U_ns"}
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0.0
0.0
on
off
m/s
Rainbow
off
on
on
255,0,0
interp
fill
arc
off
{"U_ns"}
m/s
{"U_ns"}
m/s
off
{"s"}
on
off
1
arc
off
{"s"}
1
solid
cyclecolor
none
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off
255,0,0
Rainbow
off
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on
255,0,0
interp
fill
{"s"}
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1
off
{"s"}
1
solid
cyclecolor
none
off
off
255,0,0
255,0,0
0
0
stored
step
none
on
on
on
{"lin","lin"}
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on
4
0
6
on
{"U_ns"}
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0.0
0.002314587599750325
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off
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global
5
off
off
step
none
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off
on
on
255,0,0
interp
fill
off
{"FMx"}
off
A*mol/m^5
x
off
{"U_ns"}
m/s
solid
cyclecolor
none
off
off
255,0,0
Rainbow
off
on
on
255,0,0
interp
fill
200
{"-1","1","0","0","0","0"}
{"U_ns"}
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m/s
off
{"U_ns"}
m^4/s
solid
cyclecolor
none
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off
255,0,0
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none
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255,0,0
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0
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on
on
{"lin","lin"}
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1
{"s"}
off
1
element
2
{"s"}
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off
1
element
2
{"U_ns"}
off
off
m/s
element
2
{"U_ns"}
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off
m/s
10
off
10
off
10
off
step
none
step
none
step
none
element
2
0
0
stored
step
none
on
ptd
off
3
coorddata
off
off
on
0
0
stored
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none
step
none
step
none
{"U_ns"}
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m/s
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solid
cyclecolor
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off
255,0,0
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on
on
{"lin","lin"}
0
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192,192,192
on
on
0,0,0
on
off
128,128,128
on
on
0,0,0
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0,0,0
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all
1
random
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off
on
sr com.femlab.geom.Sphere���� xr com.femlab.geom.Ellipsoid�oy�D�: D aSemiD bSemiD cSemiL aSemiExprt !Lcom/femlab/geom/Geom$Expression;L bSemiExprq ~ )L cSemiExprq ~ )xr com.femlab.geom.Prim3�n.D��� D rot[ axist [D[ axisExprt "[Lcom/femlab/geom/Geom$Expression;[ posq ~ +[ posExprq ~ ,L rotExprq ~ )xr com.femlab.geom.Geom3]�(�.� xr com.femlab.geom.Geom�6��{ L geomAssoct Lcom/femlab/geom/GeomAssoc;L versionq ~ xpw q ~ w r�ur [B���T� xp r� G e o m 3 �����|�=-C��6? � ������������|�= � ���������|�= ��<