Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model
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...
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AIMS Press
2012-06-01
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| author | Antonio Fasano Marco Gabrielli Alberto Gandolfi |
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| description | 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: itincreases the minimal value of the surface tension needed for the existenceof the steady state, and, given $\gamma$, if (45) hasa solution this solution is greater than the solution of (35).However, since it is possible that the surface tension $\gamma$ has a monotonedependence on the yield stress $\tau_0$ (both these quantity have theirphysical origin in the intercellular adhesion bonds), a partialcompensation of the effect of the yield stress on the determination of $R$can be expected.For more information please click the 'Full Text' above. |
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| institution | Kabale University |
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| spelling | doaj-art-bd8f804d918a485e9a4f6ae7bde4abe82025-01-24T02:07:01ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-06-019369769710.3934/mbe.2012.9.697Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid modelAntonio Fasano0Marco Gabrielli1Alberto Gandolfi2Università degli Studi di Firenze, Dipartimento di Matematica, "Ulisse Dini", Viale Morgagni 67/A, I-50134, FirenzeUniversità degli Studi di Firenze, Dipartimento di Matematica, "Ulisse Dini", Viale Morgagni 67/A, I-50134, FirenzeUniversità degli Studi di Firenze, Dipartimento di Matematica, "Ulisse Dini", Viale Morgagni 67/A, I-50134, FirenzeIn 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: itincreases the minimal value of the surface tension needed for the existenceof the steady state, and, given $\gamma$, if (45) hasa solution this solution is greater than the solution of (35).However, since it is possible that the surface tension $\gamma$ has a monotonedependence on the yield stress $\tau_0$ (both these quantity have theirphysical origin in the intercellular adhesion bonds), a partialcompensation of the effect of the yield stress on the determination of $R$can be expected.For more information please click the 'Full Text' above.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.697 |
| spellingShingle | Antonio Fasano Marco Gabrielli Alberto Gandolfi Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model Mathematical Biosciences and Engineering |
| title | Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model |
| title_full | Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model |
| title_fullStr | Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model |
| title_full_unstemmed | Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model |
| title_short | Erratum to: Investigating the steady state ofmulticellular sheroids by revisiting the two-fluid model |
| title_sort | erratum to investigating the steady state ofmulticellular sheroids by revisiting the two fluid model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.697 |
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