Theoretical studies of constrained membranes

Abstract : The present thesis is devoted to the study of constrained membranes with a focus on biological structures such as growing tissues and the cell membrane. It combines analytical and numerical approaches to investigate the interplay of geometry and mechanics. It also includes some experimental results albeit they are few in number and modest in size. After an introductory chapter, we explore three physical models addressed in three distinct chapters. In the first model, the deformations of growing soft tissues are treated as Gaussian point singularities in two dimensional surfaces. The equilibrium shapes are evaluated for two such defects forming a dipole. The predictions of the theory are also compared to tabletop experiments. The next chapter studies the invaginations of self-avoiding fluid membranes in constrained spaces. To this end, we developed a Finite Element code and performed extensive simulations to construct a geometric phase diagram for a fluid membrane vesicle in a spherical confinement. We also investigate the effects of the membrane's spontaneous curvature and the deformations of the container on the geometry of the invagination. In the fourth chapter of the manuscript, a tubular membrane composed of switchable components is proposed as a model to study conformations of intrinsically curved biological rods. We translated this system to a computational framework based on the Brownian Dynamics method and inquired how global shape emerges from local interactions
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Osman Kahraman. Theoretical studies of constrained membranes. Other [cond-mat.other]. Université de Lorraine, 2013. English. ⟨NNT : 2013LORR0109⟩. ⟨tel-01750097⟩

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