/* vim: set ts=4 sts=4 sw=4 noet : */ #include #include "general.h" #include "energy.h" #include "vertex.h" #include #include /** @brief Wrapper that calculates energy of every vertex in vesicle * * Function calculated energy of every vertex in vesicle. It can be used in * initialization procedure or in recalculation of the energy after non-MCsweep * operations. However, when random move of vertex or flip of random bond occur * call to this function is not necessary nor recommended. * @param *vesicle is a pointer to vesicle. * @returns TS_SUCCESS on success. */ ts_bool mean_curvature_and_energy(ts_vesicle *vesicle){ ts_uint i; ts_vertex_list *vlist=vesicle->vlist; ts_vertex **vtx=vlist->vtx; for(i=0;in;i++){ energy_vertex(vtx[i]); } return TS_SUCCESS; } /** @brief Calculate energy of a bond (in models where energy is bond related) * * This function is experimental and currently only used in polymeres calculation (PEGs or polymeres inside the vesicle). * * @param *bond is a pointer to a bond between two vertices in polymere * @param *poly is a pointer to polymere in which we calculate te energy of the bond * @returns TS_SUCCESS on successful calculation */ inline ts_bool bond_energy(ts_bond *bond,ts_poly *poly){ //TODO: This value to be changed and implemented in data structure: ts_double d_relaxed=1.0; bond->energy=poly->k*pow(bond->bond_length-d_relaxed,2); return TS_SUCCESS; }; /** @brief Calculation of the bending energy of the vertex. * * Main function that calculates energy of the vertex \f$i\f$. Function returns \f$\frac{1}{2}(c_1+c_2-c)^2 s\f$, where \f$(c_1+c_2)/2\f$ is mean curvature, * \f$c/2\f$ is spontaneous curvature and \f$s\f$ is area per vertex \f$i\f$. * * Nearest neighbors (NN) must be ordered in counterclockwise direction for this function to work. * Firstly NNs that form two neighboring triangles are found (\f$j_m\f$, \f$j_p\f$ and common \f$j\f$). Later, the scalar product of vectors \f$x_1=(\mathbf{i}-\mathbf{j_p})\cdot (\mathbf{i}-\mathbf{j_p})(\mathbf{i}-\mathbf{j_p})\f$, \f$x_2=(\mathbf{j}-\mathbf{j_p})\cdot (\mathbf{j}-\mathbf{j_p})\f$ and \f$x_3=(\mathbf{j}-\mathbf{j_p})\cdot (\mathbf{i}-\mathbf{j_p})\f$ are calculated. From these three vectors the \f$c_{tp}=\frac{1}{\tan(\varphi_p)}\f$ is calculated, where \f$\varphi_p\f$ is the inner angle at vertex \f$j_p\f$. The procedure is repeated for \f$j_m\f$ instead of \f$j_p\f$ resulting in \f$c_{tn}\f$. * \begin{tikzpicture}{ \coordinate[label=below:$i$] (i) at (2,0); \coordinate[label=left:$j_m$] (jm) at (0,3.7); \coordinate[label=above:$j$] (j) at (2.5,6.4); \coordinate[label=right:$j_p$] (jp) at (4,2.7); \draw (i) -- (jm) -- (j) -- (jp) -- (i) -- (j); \begin{scope} \path[clip] (jm)--(i)--(j); \draw (jm) circle (0.8); \node[right] at (jm) {$\varphi_m$}; \end{scope} \begin{scope} \path[clip] (jp)--(i)--(j); \draw (jp) circle (0.8); \node[left] at (jp) {$\varphi_p$}; \end{scope} %%vertices \draw [fill=gray] (i) circle (0.1); \draw [fill=white] (j) circle (0.1); \draw [fill=white] (jp) circle (0.1); \draw [fill=white] (jm) circle (0.1); %\node[draw,circle,fill=white] at (i) {}; \end{tikzpicture} * The curvature is then calculated as \f$\mathbf{h}=\frac{1}{2}\Sigma_{k=0}^{\mathrm{neigh\_no}} c_{tp}^{(k)}+c_{tm}^{(k)} (\mathbf{j_k}-\mathbf{i})\f$, where \f$c_{tp}^{(k)}+c_{tm}^k=2\sigma^{(k)}\f$ (length in dual lattice?) and the previous equation can be written as \f$\mathbf{h}=\Sigma_{k=0}^{\mathrm{neigh\_no}}\sigma^{(k)}\cdot(\mathbf{j}-\mathbf{i})\f$ (See Kroll, p. 384, eq 70). * * From the curvature the enery is calculated by equation \f$E=\frac{1}{2}\mathbf{h}\cdot\mathbf{h}\f$. * @param *vtx is a pointer to vertex at which we want to calculate the energy * @returns TS_SUCCESS on successful calculation. */ inline ts_bool energy_vertex(ts_vertex *vtx){ ts_uint jj; ts_uint jjp,jjm; ts_vertex *j,*jp, *jm; ts_triangle *jt; ts_double s=0.0,xh=0.0,yh=0.0,zh=0.0,txn=0.0,tyn=0.0,tzn=0.0; ts_double x1,x2,x3,ctp,ctm,tot,xlen; ts_double h,ht; for(jj=1; jj<=vtx->neigh_no;jj++){ jjp=jj+1; if(jjp>vtx->neigh_no) jjp=1; jjm=jj-1; if(jjm<1) jjm=vtx->neigh_no; j=vtx->neigh[jj-1]; jp=vtx->neigh[jjp-1]; jm=vtx->neigh[jjm-1]; jt=vtx->tristar[jj-1]; x1=vtx_distance_sq(vtx,jp); //shouldn't be zero! x2=vtx_distance_sq(j,jp); // shouldn't be zero! x3=(j->x-jp->x)*(vtx->x-jp->x)+ (j->y-jp->y)*(vtx->y-jp->y)+ (j->z-jp->z)*(vtx->z-jp->z); #ifdef TS_DOUBLE_DOUBLE ctp=x3/sqrt(x1*x2-x3*x3); #endif #ifdef TS_DOUBLE_FLOAT ctp=x3/sqrtf(x1*x2-x3*x3); #endif #ifdef TS_DOUBLE_LONGDOUBLE ctp=x3/sqrtl(x1*x2-x3*x3); #endif x1=vtx_distance_sq(vtx,jm); x2=vtx_distance_sq(j,jm); x3=(j->x-jm->x)*(vtx->x-jm->x)+ (j->y-jm->y)*(vtx->y-jm->y)+ (j->z-jm->z)*(vtx->z-jm->z); #ifdef TS_DOUBLE_DOUBLE ctm=x3/sqrt(x1*x2-x3*x3); #endif #ifdef TS_DOUBLE_FLOAT ctm=x3/sqrtf(x1*x2-x3*x3); #endif #ifdef TS_DOUBLE_LONGDOUBLE ctm=x3/sqrtl(x1*x2-x3*x3); #endif tot=ctp+ctm; tot=0.5*tot; xlen=vtx_distance_sq(j,vtx); /* #ifdef TS_DOUBLE_DOUBLE vtx->bond[jj-1]->bond_length=sqrt(xlen); #endif #ifdef TS_DOUBLE_FLOAT vtx->bond[jj-1]->bond_length=sqrtf(xlen); #endif #ifdef TS_DOUBLE_LONGDOUBLE vtx->bond[jj-1]->bond_length=sqrtl(xlen); #endif vtx->bond[jj-1]->bond_length_dual=tot*vtx->bond[jj-1]->bond_length; */ s+=tot*xlen; xh+=tot*(j->x - vtx->x); yh+=tot*(j->y - vtx->y); zh+=tot*(j->z - vtx->z); txn+=jt->xnorm; tyn+=jt->ynorm; tzn+=jt->znorm; } h=xh*xh+yh*yh+zh*zh; ht=txn*xh+tyn*yh + tzn*zh; s=s/4.0; #ifdef TS_DOUBLE_DOUBLE if(ht>=0.0) { vtx->curvature=sqrt(h); } else { vtx->curvature=-sqrt(h); } #endif #ifdef TS_DOUBLE_FLOAT if(ht>=0.0) { vtx->curvature=sqrtf(h); } else { vtx->curvature=-sqrtf(h); } #endif #ifdef TS_DOUBLE_LONGDOUBLE if(ht>=0.0) { vtx->curvature=sqrtl(h); } else { vtx->curvature=-sqrtl(h); } #endif // c is forced curvature energy for each vertex. Should be set to zero for // normal circumstances. /* the following statement is an expression for $\frac{1}{2}\int(c_1+c_2-c_0^\prime)^2\mathrm{d}A$, where $c_0^\prime=2c_0$ (twice the spontaneous curvature) */ vtx->energy=0.5*s*(vtx->curvature/s-vtx->c)*(vtx->curvature/s-vtx->c); return TS_SUCCESS; } ts_bool sweep_attraction_bond_energy(ts_vesicle *vesicle){ int i; for(i=0;iblist->n;i++){ attraction_bond_energy(vesicle->blist->bond[i], vesicle->tape->w); } return TS_SUCCESS; } inline ts_bool attraction_bond_energy(ts_bond *bond, ts_double w){ if(fabs(bond->vtx1->c)>1e-16 && fabs(bond->vtx2->c)>1e-16){ bond->energy=-w; } else { bond->energy=0.0; } return TS_SUCCESS; } ts_double direct_force_energy(ts_vesicle *vesicle, ts_vertex *vtx, ts_vertex *vtx_old){ if(fabs(vtx->c)<1e-15) return 0.0; // printf("was here"); if(fabs(vesicle->tape->F)<1e-15) return 0.0; ts_double norml,ddp=0.0; ts_uint i; ts_double xnorm=0.0,ynorm=0.0,znorm=0.0; /*find normal of the vertex as sum of all the normals of the triangles surrounding it. */ for(i=0;itristar_no;i++){ xnorm+=vtx->tristar[i]->xnorm; ynorm+=vtx->tristar[i]->ynorm; znorm+=vtx->tristar[i]->znorm; } /*normalize*/ norml=sqrt(xnorm*xnorm+ynorm*ynorm+znorm*znorm); xnorm/=norml; ynorm/=norml; znorm/=norml; /*calculate ddp, perpendicular displacement*/ ddp=xnorm*(vtx->x-vtx_old->x)+ynorm*(vtx->y-vtx_old->y)+znorm*(vtx->z-vtx_old->z); /*calculate dE*/ // printf("ddp=%e",ddp); return vesicle->tape->F*ddp; } void stretchenergy(ts_vesicle *vesicle, ts_triangle *triangle){ triangle->energy=vesicle->tape->xkA0/2.0*pow((triangle->area/vesicle->tlist->a0-1.0),2); } ts_double stretchenergy2(ts_double current_area,ts_double tensionless_area){ return pow((current_area-tensionless_area),2)/tensionless_area; }