Erratum to: Investigating the steady state of
multicellular sheroids by revisiting the two-fluid model
-
1.
Università degli Studi di Firenze, Dipartimento di Matematica, "Ulisse Dini", Viale Morgagni 67/A, I-50134, Firenze
-
2.
Dipartimento di Matematica "U. Dini", Universita' di Firenze, Viale Morgagni 67/A, 50134 Firenze
-
3.
Istituto di Analisi dei Sistemi ed Informatica ''A. Ruberti", CNR, Viale Manzoni 30, 00185 Roma
-
Received:
01 July 2012
Accepted:
29 June 2018
Published:
01 July 2012
-
-
-
-
In our paper [1], equation (45) has been reported incorrectly. Its actual form is as follows:
\begin{align}\label{stresscont3}
\frac{2\gamma}{R}=&\frac{1}{\nu(1-\nu)}\frac{\chi R^2}{3K}\left\{\frac{R}
{\rho_D^{}}
\left[1-\left(\frac{\rho_P^{}}{R}\right)^3\right]-\frac{3}{2}\left[1-\left(
\frac{\rho_P^{}}{R}\right)^2\right]\right\}
\nonumber\\
+&\frac{4}{3}\eta_C\chi\left(\frac{R}{\rho_D^{}}\right)^3\left[1-\left(
\frac{\rho_P^{}}{R}\right)^3\right]
\nonumber\\
+&2\sqrt{3}\tau_0\left[\ln\frac{\rho_P^{}}{\rho_D^{}}+\frac{1}{3}\ln
\frac{\sqrt{2}(\frac{R}{\rho_P^{}})^3 + \sqrt{1+2(\frac{R}{\rho_P^{}})^6}}
{\sqrt{2}+\sqrt{3}}\right].
\end{align}
The comments that followed Eq. (45) then change accordingly.
It is immediate to realize that the presence of $\tau_0$ has two effects: it
increases the minimal value of the surface tension needed for the existence
of the steady state, and, given $\gamma$, if (45) has
a solution this solution is greater than the solution of (35).
However, since it is possible that the surface tension $\gamma$ has a monotone
dependence on the yield stress $\tau_0$ (both these quantity have their
physical origin in the intercellular adhesion bonds), a partial
compensation of the effect of the yield stress on the determination of $R$
can be expected.
For more information please click the "Full Text" above.
Citation: Antonio Fasano, Marco Gabrielli, Alberto Gandolfi. Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model[J]. Mathematical Biosciences and Engineering, 2012, 9(3): 697-697. doi: 10.3934/mbe.2012.9.697
-
Abstract
In our paper [1], equation (45) has been reported incorrectly. Its actual form is as follows:
\begin{align}\label{stresscont3}
\frac{2\gamma}{R}=&\frac{1}{\nu(1-\nu)}\frac{\chi R^2}{3K}\left\{\frac{R}
{\rho_D^{}}
\left[1-\left(\frac{\rho_P^{}}{R}\right)^3\right]-\frac{3}{2}\left[1-\left(
\frac{\rho_P^{}}{R}\right)^2\right]\right\}
\nonumber\\
+&\frac{4}{3}\eta_C\chi\left(\frac{R}{\rho_D^{}}\right)^3\left[1-\left(
\frac{\rho_P^{}}{R}\right)^3\right]
\nonumber\\
+&2\sqrt{3}\tau_0\left[\ln\frac{\rho_P^{}}{\rho_D^{}}+\frac{1}{3}\ln
\frac{\sqrt{2}(\frac{R}{\rho_P^{}})^3 + \sqrt{1+2(\frac{R}{\rho_P^{}})^6}}
{\sqrt{2}+\sqrt{3}}\right].
\end{align}
The comments that followed Eq. (45) then change accordingly.
It is immediate to realize that the presence of $\tau_0$ has two effects: it
increases the minimal value of the surface tension needed for the existence
of the steady state, and, given $\gamma$, if (45) has
a solution this solution is greater than the solution of (35).
However, since it is possible that the surface tension $\gamma$ has a monotone
dependence on the yield stress $\tau_0$ (both these quantity have their
physical origin in the intercellular adhesion bonds), a partial
compensation of the effect of the yield stress on the determination of $R$
can be expected.
For more information please click the "Full Text" above.
-
-
-
-
DownLoad: