COLLECTIONS

Documents published in Scipedia

• Confined bilayers passively regulate shape and stress

  M. Staykova, M. Arroyo, M. Rahimi, H. Stone

  Physical review letters (2013). Vol. 110 (2), pp. 1-5 (Preprint)

  
  

  Abstract

  Lipid membranes are commonly confined to adjacent subcellular structures or to artificial substrates and particles. We develop an experimental and theoretical framework to investigate the mechanics of confined membranes, including the influence of adhesion, strain, and osmotic pressure. We find that supported lipid bilayers respond to stress by nucleating and evolving spherical and tubular protrusions. In cells, such transformations are generally attributed to proteins. Our results offer insights into the mechanics of cell membranes and can further extend the applications of supported bilayers.

  Abstract
  Lipid membranes are commonly confined to adjacent subcellular structures or to artificial substrates and particles. We develop an experimental and theoretical framework to [...]

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• An atomistic-based foliation model for multilayer graphene materials and nanotubes

  M. Arroyo

  Journal of the Mechanics and Physics of Solids (2013). Vol. 61 (1), pp. 235-253 (preprint)

  
  

  Abstract

  We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model to multilayer graphene materials, including multi-walled carbon nanotubes (MWCNTs). We view the material as a foliation, partitioning of space into a continuous stack of leaves, thus loosing track of the location of the individual graphene layers. The constitutive model for the bulk is derived from the atomistic interactions by appropriate kinematic assumptions, adapted to the foliation structure and mechanics. In particular, the elastic energy along the leaves of the foliation results from the bonded interactions, while the interaction energy between the walls, resulting from van der Waals forces, is parametrized with a stretch transversal to the foliation. The resulting theory is distinct from conventional anisotropic models, and can be readily discretized with finite elements. The discretization is not tied to the individual walls and allows us to coarse-grain the system in all directions. Furthermore, the evaluation of the non-bonded interactions becomes local. We test the accuracy of the foliation model against a previously proposed atomistic-based continuum model that explicitly describes each and every wall. We find that the new model is very efficient and accurate. Furthermore, it allows us to rationalize the rippling deformation modes characteristic of thick MWCNTs, highlighting the role of the van der Waals forces and the sliding between the walls. By exercising the model with very large systems of hollow MWCNTs and suspended multilayer graphene, containing up to 109 atoms, we find new complex post-buckling deformation patterns.

  Abstract
  We present a three-dimensional continuum model for layered crystalline materials made out of weakly interacting two-dimensional crystalline sheets. We specialize the model [...]

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• Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

  B. Hashemian, D. Millán, M. Arroyo

  Journal of chemical physics (2013). Vol. 139, pp. 214101/214101-12

  
  

  Abstract

  Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

  Abstract
  Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes [...]

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• Nonlinear manifold learning for model reduction in finite elastodynamics

  D. Zurita, M. Arroyo

  Comput. Methods Appl. Mech. Engrg., (2013). Vol. 261-262, pp. 118-131 (preprint)

  
  

  Abstract

  Model reduction in computational mechanics is generally addressed with linear dimensionality reduction methods such as Principal Components Analysis (PCA). Hypothesizing that in many applications of interest the essential dynamics evolve on a nonlinear manifold, we explore here reduced order modeling based on nonlinear dimen- sionality reduction methods. Such methods are gaining popularity in diverse fields of science and technology, such as machine perception or molecular simulation. We consider finite deformation elastodynamics as a model problem, and identify the manifold where the dynamics essentially take place –the slow manifold– by nonlinear dimensionality reduction methods applied to a database of snapshots. Contrary to linear dimensionality reduction, the smooth parametrization of the slow manifold needs special techniques, and we use local maximum entropy approximants. We then formulate the Lagrangian mechanics on these data-based generalized coordinates, and de- velop variational time-integrators. Our proof-of-concept example shows that a few nonlinear collective variables provide similar accuracy to tens of PCA modes, suggesting that the proposed method may be very attractive in control or optimization applications. Furthermore, the reduced number of variables brings insight into the me- chanics of the system under scrutiny. Our simulations also highlight the need of modeling the net e ¿ ect of the disregarded degrees of freedom on the reduced dynamics at long times.

  Abstract
  Model reduction in computational mechanics is generally addressed with linear dimensionality reduction methods such as Principal Components Analysis (PCA). Hypothesizing that [...]

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• Reverse engineering the euglenoid movement

  M. Arroyo, L. Heltai, D. Millán, A. DeSimone

  Proceedings of the National Academy of Sciences of the United States of America (2012). Vol. 109 (44), pp. 17874-17879

  
  

  Abstract

  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.

  Abstract
  Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid [...]

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• Shape dynamics, lipid hydrodynamics, and the complex viscoelasticity of bilayer membranes

  M. Rahimi, M. Arroyo

  Physical review E: statistical, nonlinear and soft matter physics (2012). Vol. 86 (1), pp. 1-15

  
  

  Abstract

  Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. Even the dynamics of plain lipid membranes in experimental model systems are very complex due to the tight interplay between the bilayer architecture, the shape dynamics, and the rearrangement of the lipid molecules. We formulate and numerically implement a continuum model of the shape dynamics and lipid hydrodynamics, which describes the bilayer by its midsurface and by a lipid density field for each monolayer. The viscoelastic response of bilayers is determined by the stretching and curvature elasticity, and by the inter-monolayer friction and the membrane interfacial shear viscosity. While the bilayer equilibria are well understood theoretically, dynamical calculations have relied on simplified continuum approaches of uncertain transferability, or on molecular simulations reaching very limited length and time scales. Our approach incorporates the main physics, is fully nonlinear, does not assume predefined shapes, and can access a wide range of time and length scales. We validate it with the well understood tether extension. We investigate the tubular lipid transport between cells, the dynamics of bud absorption by a planar membrane, and the fate of a localized lipid density asymmetry in vesicles. These axisymmetric examples bear biological relevance and highlight the diversity of dynamical regimes that bilayers can experience.

  Abstract
  Biological membranes are continuously brought out of equilibrium, as they shape organelles, package and transport cargo, or respond to external actions. Even the dynamics [...]

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• Thin-shell theory based analysis of radially pressurized multiwall carbon nanotubes

  H. Shima, M. Arroyo, K. Iiboshi, M. Sato

  Computational Materials Science (2012). Vol. 52 (1), pp. 90-94

  
  

  Abstract

  The radial deformation of multiwall carbon nanotubes (MWNTs) under hydrostatic pressure is investi gated within the continuum elastic approximation. A thin shell theory, with accurate elastic constants and interwall couplings, allows us to estimate the critical pressure above which the original circular cross section transforms into radially corrugated ones. The emphasis is placed on the rigorous formula tion of the van der Waals interaction between adjacent walls, which we analyze using two different approaches. Possible consequences of the radial corrugation in the physical properties of pressurized MWNTs are also discussed.

  Abstract
  The radial deformation of multiwall carbon nanotubes (MWNTs) under hydrostatic pressure is investi gated within the continuum elastic approximation. A thin shell theory, with [...]

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• Thin shell analysis from scattered points with maximum-entropy approximants

  D. Milan, A. Rosolen, M. Arroyo

  Int. J. Numer. Meth. Engng. (2011). Vol. 85 (6), pp. 723-751

  
  

  Abstract

  We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of any genus. It combines three ingredients: (1) the automatic detection of the local geometric structure of the manifold by statistical learning methods; (2) the local parameterization of the surface using smooth meshfree (here maximum-entropy) approximants; and (3) patching together the local representations by means of a partition of unity. Mesh-based methods can deal with surfaces of complex topology, since they rely on the element-level parameterizations, but cannot handle high-dimensional manifolds, whereas previous meshfree methods for thin shells consider a global parametric domain, which seriously limits the kinds of surfaces that can be treated. We present the implementation of the method in the context of Kirchhoff–Love shells, but it is applicable to other calculations on manifolds in any dimension. With the smooth approximants, this fourth-order partial differential equation is treated directly. We show the good performance of the method on the basis of the classical obstacle course. Additional calculations exemplify the flexibility of the proposed approach in treating surfaces of complex topology and geometry.

  Abstract
  We present a method to process embedded smooth manifolds using sets of points alone. This method avoids any global parameterization and hence is applicable to surfaces of [...]

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• On the optimum support size in meshfree methods: a variational adaptivity approach with maximum-entropy approximants

  D. Millán, A. Rosolen, M. Arroyo

  Int. J. Numer. Meth. Engng. (2010). Vol. 82 (7), pp. 868-895

  
  

  Abstract

  We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions.

  Abstract
  We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming [...]

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• Diverse corrugation pattern in radially shrinking carbon nanotubes

  H. Shima, M. Sato, K. Iiboshi, S. Ghosh, M. Arroyo

  Physical review B: condensed matter and material physics (2010). Vol. 82 (8), pp. 085401

  
  

  Abstract

  Stable cross sections of multiwalled carbon nanotubes subjected to electron-beam irradiation are investigated in the realm of the continuum mechanics approximation. The self-healing nature of sp2 graphitic sheets implies that selective irradiation of the outermost walls causes their radial shrinkage with the remaining inner walls undamaged. The shrinking walls exert high pressure on the interior part of nanotubes, yielding a wide variety of radial-corrugation patterns (i.e. circumferentially wrinkling structures) in the cross section. All corrugation patterns can be classified into two deformation phases for which the corrugation amplitudes of the innermost wall differ significantly.

  Abstract
  Stable cross sections of multiwalled carbon nanotubes subjected to electron-beam irradiation are investigated in the realm of the continuum mechanics approximation. The self-healing [...]

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