@@ -73,25 +73,25 @@ namespace aspect
7373
7474 if (mmm == -1 )
7575 {
76- alpha=-gammma*(pow (R2,3 )-pow (R1,3 ))/(pow (R2,3 )*log (R1)-pow (R1,3 )*log (R2));
77- beta=-3 *gammma*(log (R2)-log (R1))/(pow (R1,3 )*log (R2)-pow (R2,3 )*log (R1)) ;
76+ alpha=-gammma*(std:: pow (R2,3 )-std:: pow (R1,3 ))/(std:: pow (R2,3 )*std:: log (R1)-std:: pow (R1,3 )*std:: log (R2));
77+ beta=-3 *gammma*(std:: log (R2)-std:: log (R1))/(std:: pow (R1,3 )*std:: log (R2)-std:: pow (R2,3 )*std:: log (R1)) ;
7878 fr=alpha/(r*r)+beta*r;
79- gr=-2 /(r*r)*(alpha*log (r)+beta/3 *pow (r,3 )+gammma);
79+ gr=-2 /(r*r)*(alpha*std:: log (r)+beta/3 *std:: pow (r,3 )+gammma);
8080 }
8181 else
8282 {
83- alpha=gammma*(mmm+1 )*(pow (R1,-3 )-pow (R2,-3 ))/(pow (R1,-mmm-4 )-pow (R2,-mmm-4 ));
84- beta=-3 *gammma*(pow (R1,mmm+1 )-pow (R2,mmm+1 ))/(pow (R1,mmm+4 )-pow (R2,mmm+4 ));
85- fr=alpha/pow (r,mmm+3 )+beta*r;
86- gr=-2 /(r*r)*(-alpha/(mmm+1 )*pow (r,-mmm-1 )+beta/3 *pow (r,3 )+gammma);
83+ alpha=gammma*(mmm+1 )*(std:: pow (R1,-3 )-std:: pow (R2,-3 ))/(std:: pow (R1,-mmm-4 )-std:: pow (R2,-mmm-4 ));
84+ beta=-3 *gammma*(std:: pow (R1,mmm+1 )-std:: pow (R2,mmm+1 ))/(std:: pow (R1,mmm+4 )-std:: pow (R2,mmm+4 ));
85+ fr=alpha/std:: pow (r,mmm+3 )+beta*r;
86+ gr=-2 /(r*r)*(-alpha/(mmm+1 )*std:: pow (r,-mmm-1 )+beta/3 *std:: pow (r,3 )+gammma);
8787 }
8888
89- const double v_r =gr*cos (theta);
90- const double v_theta=fr*sin (theta);
91- const double v_phi =fr*sin (theta);
92- const double v_x=sin (theta)*cos (phi)*v_r + cos (theta)*cos (phi)*v_theta-sin (phi)*v_phi;
93- const double v_y=sin (theta)*sin (phi)*v_r + cos (theta)*sin (phi)*v_theta+cos (phi)*v_phi;
94- const double v_z=cos (theta)*v_r - sin (theta)*v_theta;
89+ const double v_r =gr*std:: cos (theta);
90+ const double v_theta=fr*std:: sin (theta);
91+ const double v_phi =fr*std:: sin (theta);
92+ const double v_x=std:: sin (theta)*std:: cos (phi)*v_r + std:: cos (theta)*std:: cos (phi)*v_theta-std:: sin (phi)*v_phi;
93+ const double v_y=std:: sin (theta)*std:: sin (phi)*v_r + std:: cos (theta)*std:: sin (phi)*v_theta+std:: cos (phi)*v_phi;
94+ const double v_z=std:: cos (theta)*v_r - std:: sin (theta)*v_theta;
9595
9696 // create a Point<3> (because it has a constructor that takes
9797 // three doubles) and return it (it automatically converts to
@@ -115,21 +115,21 @@ namespace aspect
115115 if (mmm == -1 )
116116 {
117117 mur=mu0;
118- alpha=-gammma*(pow (R2,3 )-pow (R1,3 ))/(pow (R2,3 )*log (R1)-pow (R1,3 )*log (R2));
119- beta=-3 *gammma*(log (R2)-log (R1))/(pow (R1,3 )*log (R2)-pow (R2,3 )*log (R1)) ;
120- gr=-2 /(r*r)*(alpha*log (r)+beta/3 *pow (r,3 )+gammma);
118+ alpha=-gammma*(std:: pow (R2,3 )-std:: pow (R1,3 ))/(std:: pow (R2,3 )*std:: log (R1)-std:: pow (R1,3 )*std:: log (R2));
119+ beta=-3 *gammma*(std:: log (R2)-std:: log (R1))/(std:: pow (R1,3 )*std:: log (R2)-std:: pow (R2,3 )*std:: log (R1)) ;
120+ gr=-2 /(r*r)*(alpha*std:: log (r)+beta/3 *std:: pow (r,3 )+gammma);
121121 hr=2 /r*gr*mur;
122122 }
123123 else
124124 {
125- mur=mu0*pow (r,mmm+1 );
126- alpha=gammma*(mmm+1 )*(pow (R1,-3 )-pow (R2,-3 ))/(pow (R1,-mmm-4 )-pow (R2,-mmm-4 ));
127- beta=-3 *gammma*(pow (R1,mmm+1 )-pow (R2,mmm+1 ))/(pow (R1,mmm+4 )-pow (R2,mmm+4 ));
128- gr=-2 /(r*r)*(-alpha/(mmm+1 )*pow (r,-mmm-1 )+beta/3 *pow (r,3 )+gammma);
125+ mur=mu0*std:: pow (r,mmm+1 );
126+ alpha=gammma*(mmm+1 )*(std:: pow (R1,-3 )-std:: pow (R2,-3 ))/(std:: pow (R1,-mmm-4 )-std:: pow (R2,-mmm-4 ));
127+ beta=-3 *gammma*(std:: pow (R1,mmm+1 )-std:: pow (R2,mmm+1 ))/(std:: pow (R1,mmm+4 )-std:: pow (R2,mmm+4 ));
128+ gr=-2 /(r*r)*(-alpha/(mmm+1 )*std:: pow (r,-mmm-1 )+beta/3 *std:: pow (r,3 )+gammma);
129129 hr=(mmm+3 )/r*gr*mur;
130130 }
131131
132- return hr*cos (theta) + rho_0 * gravity * (R2 - r);
132+ return hr*std:: cos (theta) + rho_0 * gravity * (R2 - r);
133133 }
134134
135135 template <int dim>
@@ -147,20 +147,20 @@ namespace aspect
147147
148148 if (mmm == -1 )
149149 {
150- alpha=-gammma*(pow (R2,3 )-pow (R1,3 ))/(pow (R2,3 )*log (R1)-pow (R1,3 )*log (R2));
151- beta=-3 *gammma*(log (R2)-log (R1))/(pow (R1,3 )*log (R2)-pow (R2,3 )*log (R1)) ;
150+ alpha=-gammma*(std:: pow (R2,3 )-std:: pow (R1,3 ))/(std:: pow (R2,3 )*std:: log (R1)-std:: pow (R1,3 )*std:: log (R2));
151+ beta=-3 *gammma*(std:: log (R2)-std:: log (R1))/(std:: pow (R1,3 )*std:: log (R2)-std:: pow (R2,3 )*std:: log (R1)) ;
152152 fr=alpha/(r*r)+beta*r;
153- gr=-2 /(r*r)*(alpha*log (r)+beta/3 *pow (r,3 )+gammma);
153+ gr=-2 /(r*r)*(alpha*std:: log (r)+beta/3 *std:: pow (r,3 )+gammma);
154154 }
155155 else
156156 {
157- alpha=gammma*(mmm+1 )*(pow (R1,-3 )-pow (R2,-3 ))/(pow (R1,-mmm-4 )-pow (R2,-mmm-4 ));
158- beta=-3 *gammma*(pow (R1,mmm+1 )-pow (R2,mmm+1 ))/(pow (R1,mmm+4 )-pow (R2,mmm+4 ));
159- fr=alpha/pow (r,mmm+3 )+beta*r;
160- gr=-2 /(r*r)*(-alpha/(mmm+1 )*pow (r,-mmm-1 )+beta/3 *pow (r,3 )+gammma);
157+ alpha=gammma*(mmm+1 )*(std:: pow (R1,-3 )-std:: pow (R2,-3 ))/(std:: pow (R1,-mmm-4 )-std:: pow (R2,-mmm-4 ));
158+ beta=-3 *gammma*(std:: pow (R1,mmm+1 )-std:: pow (R2,mmm+1 ))/(std:: pow (R1,mmm+4 )-std:: pow (R2,mmm+4 ));
159+ fr=alpha/std:: pow (r,mmm+3 )+beta*r;
160+ gr=-2 /(r*r)*(-alpha/(mmm+1 )*std:: pow (r,-mmm-1 )+beta/3 *std:: pow (r,3 )+gammma);
161161 }
162162
163- return -(6 .*gr + 4 .*fr) * cos (theta) * mu0 / r;
163+ return -(6 .*gr + 4 .*fr) * std:: cos (theta) * mu0 / r;
164164 }
165165
166166
@@ -366,7 +366,7 @@ namespace aspect
366366 const Point<dim> &pos = in.position [i];
367367 const std::array<double ,dim> spos = aspect::Utilities::Coordinates::cartesian_to_spherical_coordinates (pos);
368368 const double r = spos[0 ];
369- const double mu = pow (r,mmm+1 );
369+ const double mu = std:: pow (r,mmm+1 );
370370 out.viscosities [i] = mu;
371371
372372 const double theta=spos[2 ];
@@ -380,15 +380,15 @@ namespace aspect
380380
381381 if (mmm == -1 )
382382 {
383- alpha = -gammma*(pow (R2,3 )-pow (R1,3 ))/(pow (R2,3 )*log (R1)-pow (R1,3 )*log (R2));
384- beta = -3 *gammma*(log (R2)-log (R1))/(pow (R1,3 )*log (R2)-pow (R2,3 )*log (R1)) ;
385- rho = -(alpha/pow (r,4 )*(8 *log (r)-6 ) + 8 ./3 .*beta/r+8 *gammma/pow (r,4 ))*cos (theta) + rho_0;
383+ alpha = -gammma*(std:: pow (R2,3 )-std:: pow (R1,3 ))/(std:: pow (R2,3 )*std:: log (R1)-std:: pow (R1,3 )*std:: log (R2));
384+ beta = -3 *gammma*(std:: log (R2)-std:: log (R1))/(std:: pow (R1,3 )*std:: log (R2)-std:: pow (R2,3 )*std:: log (R1)) ;
385+ rho = -(alpha/std:: pow (r,4 )*(8 *std:: log (r)-6 ) + 8 ./3 .*beta/r+8 *gammma/std:: pow (r,4 ))*std:: cos (theta) + rho_0;
386386 }
387387 else
388388 {
389- alpha=gammma*(mmm+1 )*(pow (R1,-3 )-pow (R2,-3 ))/(pow (R1,-mmm-4 )-pow (R2,-mmm-4 ));
390- beta=-3 *gammma*(pow (R1,mmm+1 )-pow (R2,mmm+1 ))/(pow (R1,mmm+4 )-pow (R2,mmm+4 ));
391- rho= -(2 *alpha*pow (r,-4 )*(mmm+3 )/(mmm+1 )*(mmm-1 )-2 *beta/3 *(mmm-1 )*(mmm+3 )*pow (r,mmm)-mmm*(mmm+5 )*2 *gammma*pow (r,mmm-3 ) )*cos (theta) + rho_0;
389+ alpha=gammma*(mmm+1 )*(std:: pow (R1,-3 )-std:: pow (R2,-3 ))/(std:: pow (R1,-mmm-4 )-std:: pow (R2,-mmm-4 ));
390+ beta=-3 *gammma*(std:: pow (R1,mmm+1 )-std:: pow (R2,mmm+1 ))/(std:: pow (R1,mmm+4 )-std:: pow (R2,mmm+4 ));
391+ rho= -(2 *alpha*std:: pow (r,-4 )*(mmm+3 )/(mmm+1 )*(mmm-1 )-2 *beta/3 *(mmm-1 )*(mmm+3 )*std:: pow (r,mmm)-mmm*(mmm+5 )*2 *gammma*std:: pow (r,mmm-3 ) )*std:: cos (theta) + rho_0;
392392 }
393393
394394 out.densities [i] = rho;
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