%0 Journal Article
%D 2014
%T Nonsingular Isogeometric Boundary Element Method for Stokes Flows in 3D
%A Luca Heltai
%A Marino Arroyo
%A Antonio DeSimone
%K Isogeometric Analysis
%X Isogeometric analysis (IGA) is emerging as a technology bridging Computer Aided Geometric Design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that de- scribe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of bound- ary integral equations, leading to Boundary Element Isogeometric Analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. [27] to IGA-BEM.
%I Elsevier
%G en
%U http://hdl.handle.net/1963/6326
%1 6250
%2 Mathematics
%4 1
%# MAT/08 ANALISI NUMERICA
%$ Submitted by Luca Heltai (heltai@sissa.it) on 2012-12-03T08:19:28Z
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%R 10.1016/j.cma.2013.09.017
%0 Journal Article
%D 2014
%T Shape control of active surfaces inspired by the movement of euglenids
%A Marino Arroyo
%A Antonio DeSimone
%X We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.
%I Elsevier
%G en
%U http://urania.sissa.it/xmlui/handle/1963/35118
%1 35375
%2 Mathematics
%4 1
%$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-12-03T09:19:38Z (GMT) No. of bitstreams: 0
%R 10.1016/j.jmps.2013.09.017
%0 Journal Article
%J Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879
%D 2012
%T Reverse engineering the euglenoid movement
%A Marino Arroyo
%A Luca Heltai
%A Daniel Millán
%A Antonio DeSimone
%K microswimmers
%X Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.
%B Proceedings of the National Academy of Sciences of the United States of America. Volume 109, Issue 44, 30 October 2012, Pages 17874-17879
%G en
%U http://hdl.handle.net/1963/6444
%1 6380
%2 Mathematics
%4 1
%# MAT/08 ANALISI NUMERICA
%$ Submitted by Luca Heltai (heltai@sissa.it) on 2013-02-01T17:29:31Z\\nNo. of bitstreams: 0
%R 10.1073/pnas.1213977109
%0 Report
%D 2010
%T The role of membrane viscosity in the dynamics of fluid membranes
%A Marino Arroyo
%A Antonio DeSimone
%A Luca Heltai
%X Fluid membranes made out of lipid bilayers are the fundamental separation structure in eukaryotic cells. Many physiological processes rely on dramatic shape and topological changes (e.g. fusion, fission) of fluid membrane systems. Fluidity is key to the versatility and constant reorganization of lipid bilayers. Here, we study the role of the membrane intrinsic viscosity, arising from the friction of the lipid molecules as they rearrange to accommodate shape changes, in the dynamics of morphological changes of fluid vesicles. In particular, we analyze the competition between the membrane viscosity and the viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative mechanism. We consider the relaxation dynamics of fluid vesicles put in an out-of-equilibrium state, but conclusions can be drawn regarding the kinetics or power consumption in regulated shape changes in the cell. On the basis of numerical calculations, we find that the dynamics arising from the membrane viscosity are qualitatively different from the dynamics arising from the bulk viscosity. When these two dissipation mechanisms are put in competition, we find that for small vesicles the membrane dissipation dominates, with a relaxation time that scales as the size of the vesicle to the power 2. For large vesicles, the bulk dissipation dominates, and the exponent in the relaxation time vs. size relation is 3.
%G en_US
%U http://hdl.handle.net/1963/3930
%1 471
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-29T11:13:35Z\\nNo. of bitstreams: 1\\nArroyo_55M.pdf: 4419667 bytes, checksum: ca8a9c175a457ad33996d46a08e85e44 (MD5)
%0 Journal Article
%J Phys. Rev. E 79 (2009) 031915
%D 2009
%T Relaxation dynamics of fluid membranes
%A Marino Arroyo
%A Antonio DeSimone
%X We study the effect of membrane viscosity in the dynamics of liquid membranes-possibly with free or internal boundaries-driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simplified geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.
%B Phys. Rev. E 79 (2009) 031915
%I American Physical Society
%G en_US
%U http://hdl.handle.net/1963/3618
%1 686
%2 Mathematics
%3 Functional Analysis and Applications
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%R 10.1103/PhysRevE.79.031915