function [R,navg1,navg2] = twomolmodelanalytic_integrate_hyperbolic(td) %[R,navg1,navg2] = twomolmodelanalytic_integrate_hyperbolic(td) %100325 %100616 s1=1; J1=1.5e21; n01=2.6e18; tau1=7.2e-4; f1=1.7e24; V1=3.8e-29; sigma1=4.95e-21; s2=1; J2=1.5e19/2; n02=1.1e18; tau2=.00009; f2=f1; V2=6e-28; sigma2=2.3e-18; kd1=s1*J1/n01+1/tau1+sigma1*f1; kr1=s1*J1/n01+1/tau1; kd2=s2*J2/n02+1/tau2+sigma2*f2; kr2=s2*J2/n02+1/tau2; kc1=s1*J1/n02; kc2=s2*J2/n01; nr1=(s1*J1*kr2-s2*J2*kc1)/(kr1*kr2-kc1*kc2); nr2=(s2*J2*kr1-s1*J1*kc2)/(kr1*kr2-kc1*kc2); nd1=(s1*J1*kd2-s2*J2*kc1)/(kd1*kd2-kc1*kc2); nd2=(s2*J2*kd1-s1*J1*kc2)/(kd1*kd2-kc1*kc2); Dn1=nr1-nd1; Dn2=nr2-nd2; kappa=sqrt((kd1-kd2)^2/4+kc1*kc2); kda=(kd1+kd2)/2; N1=((kda-kd1)*Dn1-kc1*Dn2)/kappa; N2=((kda-kd2)*Dn2-kc2*Dn1)/kappa; for i=1:max(size(td)) navg1(i)=quad(@integrnd, 0, td(i))/td(i); navg2(i)=quad(@integrnd2, 0, td(i))/td(i); %ntilde1(i)=navg1(i)/n01; %ntilde2(i)=navg2(i)/n02; R1(i)=V1*sigma1*f1*navg1(i); R2(i)=V2*sigma2*f2*navg2(i); R(i)=R1(i)+R2(i); end function n1=integrnd(ta) %n1=X(1)*exp(r1*ta)+X(2)*exp(r2*ta)+nd1; %n1=nd1+exp(-kda*ta).*(Dn1*cosh(kappa*ta)+N1*sinh(kappa*ta)); n1=nd1+.5*((Dn1+N1)*exp((kappa-kda)*ta)+(Dn1-N1)*exp((-kappa-kda)*ta)); end function n2=integrnd2(ta) %n2=X(3)*exp(r1*ta)+X(4)*exp(r2*ta)+nd2; %n2=nd2+exp(-kda*ta).*(Dn2*cosh(kappa*ta)+N2*sinh(kappa*ta)); n2=nd2+.5*((Dn2+N2)*exp((kappa-kda)*ta)+(Dn2-N2)*exp((-kappa-kda)*ta)); end end