Approximations of energy minimization in cell­induced phase transitions of fibrous biomaterials: ­ convergence analysis Γ

[1]  Marina Vannucci,et al.  Bayesian statistics and modelling , 2021, Nature Reviews Methods Primers.

[2]  Albert Y. Zomaya,et al.  Partial Differential Equations , 2007, Explorations in Numerical Analysis.

[3]  P. Rosakis,et al.  Cells exploit a phase transition to establish interconnections in fibrous extracellular matrices , 2019, 1905.11246.

[4]  Oliver Fest,et al.  Measure theory , 2019, A Tool Kit for Groupoid 𝐶*-Algebras.

[5]  William Gropp,et al.  PETSc Users Manual: Revision 3.11 , 2019 .

[6]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[7]  Ricardo H. Nochetto,et al.  Bilayer Plates: Model Reduction, Γ‐Convergent Finite Element Approximation, and Discrete Gradient Flow , 2015, 1506.03335.

[8]  P. Rosakis,et al.  Microbuckling of fibrin provides a mechanism for cell mechanosensing , 2014, Journal of The Royal Society Interface.

[9]  Chris H. Rycroft,et al.  Rapid disorganization of mechanically interacting systems of mammary acini , 2013, Proceedings of the National Academy of Sciences.

[10]  Charalambos Makridakis,et al.  On Atomistic-to-Continuum Couplings without Ghost Forces in Three Dimensions , 2012, 1211.7158.

[11]  A. Ern,et al.  Mathematical Aspects of Discontinuous Galerkin Methods , 2011 .

[12]  Lisandro Dalcin,et al.  Parallel distributed computing using Python , 2011 .

[13]  H. Brezis.  Functional Analysis, Sobolev Spaces and Partial Differential Equations , 2010 .

[14]  A. Ern,et al.  Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations , 2010, Mathematics of Computation.

[15]  A. Buffa,et al.  Compact embeddings of broken Sobolev spaces and applications , 2009 .

[16]  G. Sweers.  A survey on boundary conditions for the biharmonic , 2009 .

[17]  Amy Henderson Squilacote.  The Paraview Guide , 2008 .

[18]  R. Eymard,et al.  Discretisation of heterogeneous and anisotropic diffusion problems on general non-conforming meshes. SUSHI: a scheme using stabilisation and hybrid interfaces , 2008, 0801.1430.

[19]  Ohannes A. Karakashian,et al.  Convergence of Adaptive Discontinuous Galerkin Approximations of Second-Order Elliptic Problems , 2007, SIAM J. Numer. Anal..

[20]  Endre Süli,et al.  Poincaré-type inequalities for broken Sobolev spaces , 2003 .

[21]  Ohannes A. Karakashian,et al.  A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems , 2003, SIAM J. Numer. Anal..

[22]  F. Brezzi,et al.  Discontinuous Galerkin approximations for elliptic problems , 2000 .

[23]  S. Rebay,et al.  A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations , 1997 .

[24]  Mitchell Luskin,et al.  On the computation of crystalline microstructure , 1996, Acta Numerica.

[25]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[26]  A K Harris,et al.  Connective tissue morphogenesis by fibroblast traction. I. Tissue culture observations. , 1982, Developmental biology.

[27]  Albert K. Harris,et al.  Fibroblast traction as a mechanism for collagen morphogenesis , 1981, Nature.

[28]  C. S. Hönig.  Real Analysis , 1972 .

[29]  Antje Baer,et al.  Direct Methods In The Calculus Of Variations , 2016 .

[30]  Rohan Abeyaratne,et al.  Lecture Notes on The Mechanics of Elastic Solids Volume I: A Brief Review of Some Mathematical , 2006 .

[31]  Susanne C. Brenner,et al.  C0 Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal Domains , 2005, J. Sci. Comput..

[32]  Gerald Teschl,et al.  Functional Analysis , 2023, Texts and Readings in Mathematics.

[33]  M. Ortiz,et al.  Optimal BV estimates for a discontinuous Galerkin method for linear elasticity , 2004 .

[34]  Andrea Braides.  Γ-convergence for beginners , 2002 .

[35]  Eric Jones,et al.  SciPy: Open Source Scientific Tools for Python , 2001 .

[36]  Jim Fischer,et al.  Introduction to the Calculus of Variations , 1999 .

[37]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[38]  J. Graver,et al.  Graduate studies in mathematics , 1993 .

[39]  G. D. Maso,et al.  An Introduction to-convergence , 1993 .

[40]  L. Evans.  Measure theory and fine properties of functions , 1992 .

[41]  M. Rao,et al.  Theory of Orlicz spaces , 1991 .

[42]  Neil S. Trudinger,et al.  On Imbeddings into Orlicz Spaces and Some Applications , 1967 .