Browsing by Author "DeSimone, Antonio"

Now showing 1 - 11 of 11
  • Thumbnail Image
    Item
    Attainment results for nematic elastomers
    (SISSA, 2013-10-10) Agostiniani, Virginia; Dal Maso, Gianni; DeSimone, Antonio; Mathematics
    We consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.
  • Thumbnail Image
    Item
    A fully nonlinear potential model for ship hydrodynamics directly interfaced with CAD data structures
    (SISSA, 2014-03) Mola, Andrea; Heltai, Luca; DeSimone, Antonio; Mathematics
    We present a model for ship hydrodynamics simulations currently under development at SISSA. The model employs potential flow theory and fully nonlinear free surface boundary conditions. The spatial discretization of the equations is performed by means of a collocation BEM. This gives rise to a Differential Algbraic Equations (DAE) system, solved using an implicit BDF scheme to time advance the solution. The model has been implemented into a C++ software able to automatically generate the computational grids from the CAD geometry of the hull. Numerical results on Kriso KCS and KVLCC2 hulls are presented and discussed.
  • Thumbnail Image
    Item
    Motility of a Model Bristle-Bot: a Theoretical Analysis.
    (SISSA, 2014) Cicconofri, Giancarlo; DeSimone, Antonio
    Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.
  • Thumbnail Image
    Item
    A new model for contact angle hysteresis
    (2006-07-26T09:50:37Z) DeSimone, Antonio; Gruenewald, Natalie; Otto, Felix; Mathematics; Functional Analysis and Applications
    We present a model which explains several experimental observations relating contact angle hysteresis with surface roughness. The model is based on the balance between released energy and dissipation, and it describes the stick-slip behavior of drops on a rough surface using ideas similar to those employed in dry friction, elasto-plasticity and fracture mechanics. The main results of our analysis are formulas giving the interval of stable contact angles as a function of the surface roughness. These formulas show that the difference between advancing and receding angles is much larger for a drop in complete contact with the substrate (Wenzel drop) than for one whose cavities are filled with air (Cassie-Baxter drop). This fact is used as the key tool to interpret the experimental evidence.
  • Thumbnail Image
    Item
    Optimally swimming Stokesian Robots
    (2010-07-29T11:02:56Z) Alouges, Francois; DeSimone, Antonio; Heltai, Luca; Lefebvre, Aline; Merlet, Benoit; Mathematics; Functional Analysis and Applications
    We study self propelled stokesian robots composed of assemblies of balls, in dimen- sions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow's theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically the analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.
  • Thumbnail Image
    Item
    The role of membrane viscosity in the dynamics of fluid membranes
    (2010-07-29T11:13:36Z) Arroyo, Marino; DeSimone, Antonio; Heltai, Luca; Mathematics; Functional Analysis and Applications
    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.
  • Thumbnail Image
    Item
    Soft elasticity and microstructure in smectic C elastomers
    (2006-04-12T09:42:25Z) DeSimone, Antonio; Adams, James; Conti, Sergio; Mathematics; Functional Analysis and Applications
    Smectic C elastomers are layered materials exhibiting a solid-like elastic response along the layer normal and a rubbery one in the plane. The set of strains minimizing the elastic energy contains a one-parameter family of simple stretches associated with an internal degree of freedom, coming from the in-plane component of the director. We investigate soft elasticity and the corresponding microstructure by determining the quasiconvex hull of the set , and use this to propose experimental tests that should make the predicted soft response observable.
  • Thumbnail Image
    Item
    A stable and adaptive semi-Lagrangian potential model for unsteady and nonlinear ship-wave interactions
    (SISSA, 2012-03) Mola, Andrea; Heltai, Luca; DeSimone, Antonio; Mathematics; Functional Analysis and Applications
    We present an innovative numerical discretization of the equations of inviscid potential flow for the simulation of three dimensional unsteady and nonlinear water waves generated by a ship hull advancing in water. The equations of motion are written in a semi-Lagrangian framework, and the resulting integro-diff erential equations are discretized in space via an adaptive iso-parametric collocation Boundary Element Method, and in time via adaptive implicit Backward Di erentiation Formulas (BDF) with variable step and variable order. When the velocity of the advancing ship hull is non-negligible, the semi-Lagrangian formulation (also known as Arbitrary Lagrangian Eulerian formulation, or ALE) of the free surface equations contains dominant transport terms which are stabilized with a Streamwise Upwind Petrov-Galerkin (SUPG) method. The SUPG stabilization allows automatic and robust adaptation of the spatial discretization with unstructured quadrilateral grids. Preliminary results are presented where we compare our numerical model with experimental results on the case of a Wigley hull advancing in calm water with fi xed sink and trim.
  • Thumbnail Image
    Item
    Stratos: a code for 3D free surface flows with floating constraints
    (2009-07-30T14:37:02Z) DeSimone, Antonio; Bianchi, B.; Heltai, Luca; Mathematics; Functional Analysis and Applications
    This report presents a brief discussion of the theoretical aspects and practical implementation of STRATOS . STRATOS is a 3D code for the simulation of hydrodynamic flows for incompressible fluids, in the presence of a free surface, capable of simulating the interaction between the free surface and a floating object via Lagrange multipliers......
  • Thumbnail Image
    Item
    Time-dependent systems of generalized Young measures
    (2005) Dal Maso, Gianni; DeSimone, Antonio; Mora, Maria Giovanna; Morini, Massimiliano; Mathematics; Functional Analysis and Applications
    In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.
  • Thumbnail Image
    Item
    Tools for the Solution of PDEs Defined on Curved Manifolds with deal.II
    (2009-07-30T14:20:03Z) DeSimone, Antonio; Heltai, Luca; Manigrasso, Cataldo; Mathematics; Functional Analysis and Applications
    The deal.II finite element library was originally designed to solve partial differential equations defined on one, two or three space dimensions, mostly via the Finite Element Method. In its versions prior to version 6.2, the user could not solve problems defined on curved manifolds embedded in two or three spacial dimensions. This infrastructure is needed if one wants to solve, for example, Boundary Integral Equations.