3,030 research outputs found
Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization
The distribution of forces on the surface of complex, deforming geometries is
an invaluable output of flow simulations. One particular example of such
geometries involves self-propelled swimmers. Surface forces can provide
significant information about the flow field sensed by the swimmers, and are
difficult to obtain experimentally. At the same time, simulations of flow
around complex, deforming shapes can be computationally prohibitive when
body-fitted grids are used. Alternatively, such simulations may employ
penalization techniques. Penalization methods rely on simple Cartesian grids to
discretize the governing equations, which are enhanced by a penalty term to
account for the boundary conditions. They have been shown to provide a robust
estimation of mean quantities, such as drag and propulsion velocity, but the
computation of surface force distribution remains a challenge. We present a
method for determining flow- induced forces on the surface of both rigid and
deforming bodies, in simulations using re-meshed vortex methods and Brinkman
penalization. The pressure field is recovered from the velocity by solving a
Poisson's equation using the Green's function approach, augmented with a fast
multipole expansion and a tree- code algorithm. The viscous forces are
determined by evaluating the strain-rate tensor on the surface of deforming
bodies, and on a 'lifted' surface in simulations involving rigid objects. We
present results for benchmark flows demonstrating that we can obtain an
accurate distribution of flow-induced surface-forces. The capabilities of our
method are demonstrated using simulations of self-propelled swimmers, where we
obtain the pressure and shear distribution on their deforming surfaces
An isogeometric finite element formulation for phase transitions on deforming surfaces
This paper presents a general theory and isogeometric finite element
implementation for studying mass conserving phase transitions on deforming
surfaces. The mathematical problem is governed by two coupled fourth-order
nonlinear partial differential equations (PDEs) that live on an evolving
two-dimensional manifold. For the phase transitions, the PDE is the
Cahn-Hilliard equation for curved surfaces, which can be derived from surface
mass balance in the framework of irreversible thermodynamics. For the surface
deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation.
Both PDEs can be efficiently discretized using -continuous interpolations
without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured
spline spaces with pointwise -continuity are utilized for these
interpolations. The resulting finite element formulation is discretized in time
by the generalized- scheme with adaptive time-stepping, and it is fully
linearized within a monolithic Newton-Raphson approach. A curvilinear surface
parameterization is used throughout the formulation to admit general surface
shapes and deformations. The behavior of the coupled system is illustrated by
several numerical examples exhibiting phase transitions on deforming spheres,
tori and double-tori.Comment: fixed typos, extended literature review, added clarifying notes to
the text, added supplementary movie file
Non-Commutative Tools for Topological Insulators
This paper reviews several analytic tools for the field of topological
insulators, developed with the aid of non-commutative calculus and geometry.
The set of tools includes bulk topological invariants defined directly in the
thermodynamic limit and in the presence of disorder, whose robustness is shown
to have non-trivial physical consequences for the bulk states. The set of tools
also includes a general relation between the current of an observable and its
edge index, relation that can be used to investigate the robustness of the edge
states against disorder. The paper focuses on the motivations behind creating
such tools and on how to use them.Comment: Final version (some arguments were corrected
Arbitrary Lagrangian-Eulerian form of flowfield dependent variation (ALE-FDV) method for moving boundary problems
Flowfield Dependent Variation (FDV) method is a mixed explicit-implicit numerical
scheme that was originally developed to solve complex flow problems through the use
of so-called implicitness parameters. These parameters determine the implicitness of
FDV method by evaluating local gradients of physical flow parameters, hence vary
across the computational domain. The method has been used successfully in solving
wide range of flow problems. However it has only been applied to problems where the
objects or obstacles are static relative to the flow. Since FDV method has been proved
to be able to solve many complex flow problems, there is a need to extend FDV
method into the application of moving boundary problems where an object
experiences motion and deformation in the flow. With the main objective to develop a
robust numerical scheme that is applicable for wide range of flow problems involving
moving boundaries, in this study, FDV method was combined with a body
interpolation technique called Arbitrary Lagrangian-Eulerian (ALE) method. The
ALE method is a technique that combines Lagrangian and Eulerian descriptions of a
continuum in one numerical scheme, which then enables a computational mesh to
follow the moving structures in an arbitrary movement while the fluid is still seen in a
Eulerian manner. The new scheme, which is named as ALE-FDV method, is
formulated using finite volume method in order to give flexibility in dealing with
complicated geometries and freedom of choice of either structured or unstructured
mesh. The method is found to be conditionally stable because its stability is dependent
on the FDV parameters. The formulation yields a sparse matrix that can be solved by
using any iterative algorithm. Several benchmark stationary and moving body
problems in one, two and three-dimensional inviscid and viscous flows have been
selected to validate the method. Good agreement with available experimental and
numerical results from the published literature has been obtained. This shows that the
ALE-FDV has great potential for solving a wide range of complex flow problems
involving moving bodies
Fast Non-Rigid Radiance Fields from Monocularized Data
3D reconstruction and novel view synthesis of dynamic scenes from collectionsof single views recently gained increased attention. Existing work showsimpressive results for synthetic setups and forward-facing real-world data, butis severely limited in the training speed and angular range for generatingnovel views. This paper addresses these limitations and proposes a new methodfor full 360{\deg} novel view synthesis of non-rigidly deforming scenes. At thecore of our method are: 1) An efficient deformation module that decouples theprocessing of spatial and temporal information for acceleration at training andinference time; and 2) A static module representing the canonical scene as afast hash-encoded neural radiance field. We evaluate the proposed approach onthe established synthetic D-NeRF benchmark, that enables efficientreconstruction from a single monocular view per time-frame randomly sampledfrom a full hemisphere. We refer to this form of inputs as monocularized data.To prove its practicality for real-world scenarios, we recorded twelvechallenging sequences with human actors by sampling single frames from asynchronized multi-view rig. In both cases, our method is trained significantlyfaster than previous methods (minutes instead of days) while achieving highervisual accuracy for generated novel views. Our source code and data isavailable at our project pagehttps://graphics.tu-bs.de/publications/kappel2022fast.<br
Robust interactive cutting based on an adaptive octree simulation mesh
We present an adaptive octree based approach for interactive cutting of deformable objects. Our technique relies on efficient refine- and node split-operations. These are sufficient to robustly represent cuts in the mechanical simulation mesh. A high-resolution surface embedded into the octree is employed to represent a cut visually. Model modification is performed in the rest state of the object, which is accomplished by back-transformation of the blade geometry. This results in an improved robustness of our approach. Further, an efficient update of the correspondences between simulation elements and surface vertices is proposed. The robustness and efficiency of our approach is underlined in test examples as well as by integrating it into a prototype surgical simulato
Simulations of propelling and energy harvesting articulated bodies via vortex particle-mesh methods
The emergence and understanding of new design paradigms that exploit flow
induced mechanical instabilities for propulsion or energy harvesting demands
robust and accurate flow structure interaction numerical models. In this
context, we develop a novel two dimensional algorithm that combines a Vortex
Particle-Mesh (VPM) method and a Multi-Body System (MBS) solver for the
simulation of passive and actuated structures in fluids. The hydrodynamic
forces and torques are recovered through an innovative approach which crucially
complements and extends the projection and penalization approach of Coquerelle
et al. and Gazzola et al. The resulting method avoids time consuming
computation of the stresses at the wall to recover the force distribution on
the surface of complex deforming shapes. This feature distinguishes the
proposed approach from other VPM formulations. The methodology was verified
against a number of benchmark results ranging from the sedimentation of a 2D
cylinder to a passive three segmented structure in the wake of a cylinder. We
then showcase the capabilities of this method through the study of an energy
harvesting structure where the stocking process is modeled by the use of
damping elements
Sculpting multi-dimensional nested structures
Special Issue: Shape Modeling International (SMI) Conference 2013International audienceSolid shape is typically segmented into surface regions to define the appearance and function of parts of the shape; these regions in turn use curve networks to represent boundaries and creases, and feature points to mark corners and other shape landmarks. Conceptual modeling requires these multi-dimensional nested structures to persist throughout the modeling process, an aspect not supported, up to now, in free-form sculpting systems. We present the first shape sculpting framework that preserves and controls the evolution of such nested shape features. We propose a range of geometric and topological behaviors (such as rigidity or mutability) applied hierarchically to points, curves or surfaces in response to a set of typical free-form sculpting operations, such as stretch, shrink, split or merge. Our method is illustrated within a free-form sculpting system for self-adaptive quasi-uniform polygon meshes, where geometric and topology changes resulting from sculpting operations are applied to points, edges and triangular facets. We thus facilitate, for example, the persistence of sharp features that automatically split or merge with variable rigidity, even when the shape changes genus. Sculpting nested structures expands the capabilities of most conceptual design workflows, as exhibited by a suite of models created by our system
Shaping Giant Membrane Vesicles in 3D-Printed Protein Hydrogel Cages
Giant unilamellar phospholipid vesicles are attractive starting points for constructing minimal living cells from the bottom-up. Their membranes are compatible with many physiologically functional modules and act as selective barriers, while retaining a high morphological flexibility. However, their spherical shape renders them rather inappropriate to study phenomena that are based on distinct cell shape and polarity, such as cell division. Here, a microscale device based on 3D printed protein hydrogel is introduced to induce pH-stimulated reversible shape changes in trapped vesicles without compromising their free-standing membranes. Deformations of spheres to at least twice their aspect ratio, but also toward unusual quadratic or triangular shapes can be accomplished. Mechanical force induced by the cages to phase-separated membrane vesicles can lead to spontaneous shape deformations, from the recurrent formation of dumbbells with curved necks between domains to full budding of membrane domains as separate vesicles. Moreover, shape-tunable vesicles are particularly desirable when reconstituting geometry-sensitive protein networks, such as reaction-diffusion systems. In particular, vesicle shape changes allow to switch between different modes of self-organized protein oscillations within, and thus, to influence reaction networks directly by external mechanical cues
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