1,025 research outputs found
Relating phase field and sharp interface approaches to structural topology optimization
A phase field approach for structural topology optimization which allows for topology
changes and multiple materials is analyzed. First order optimality conditions are
rigorously derived and it is shown via formally matched asymptotic
expansions that these conditions converge to classical first order conditions obtained in
the context of shape calculus. We also discuss how to deal with triple junctions where
e.g. two materials and the void meet. Finally, we present several
numerical results for mean compliance problems and a cost involving the least square error
to a target displacement
Behavior of a net of fibers linked by viscous interactions: theory and mechanical properties
International audienceThis paper presents an investigation of the macroscopic mechanical behavior of highly concentrated fiber suspensions for which the mechanical behavior is governed by local fiber-fiber interactions. The problem is approached by considering the case of a net of rigid fibers of uniform length, linked by viscous point interactions of power-law type. Those interactions may result in local forces and moments located at the contacting point between two fibers, and respectively power-law functions of the local linear and angular velocity at this point. Assuming the existence of an elementary representative volume which size is small compared to the size of the whole structure, the fiber net is regarded as a periodic assembly of identical cells. Macroscopic equilibrium and constitutive equations of the equivalent continuum are then obtained by the discrete and periodic media homogenization method, based on the use of asymptotic expansions. Depending on the order of magnitude of local translational viscosities and rotational viscosities, three types of the equivalent continua are proved to be possible. One of them leads to an effective Cosserat medium, the other ones being usual Cauchy media. Lastly, formulations that enable an effective computation of constitutive equations are detailed. They show that the equivalent continuum behaves like an anisotropic power-law fluid
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments
In this paper we derive a pore-scale model for permeable biofilm formation in
a two-dimensional pore. The pore is divided in two phases: water and biofilm.
The biofilm is assumed to consist of four components: water, extracellular
polymeric substances (EPS), active bacteria, and dead bacteria. The flow of
water is modeled by the Stokes equation whereas a diffusion-convection equation
is involved for the transport of nutrients. At the water/biofilm interface,
nutrient transport and shear forces due to the water flux are considered. In
the biofilm, the Brinkman equation for the water flow, transport of nutrients
due to diffusion and convection, displacement of the biofilm components due to
reproduction/dead of bacteria, and production of EPS are considered. A
segregated finite element algorithm is used to solve the mathematical
equations. Numerical simulations are performed based on experimentally
determined parameters. The stress coefficient is fitted to the experimental
data. To identify the critical model parameters, a sensitivity analysis is
performed. The Sobol sensitivity indices of the input parameters are computed
based on uniform perturbation by of the nominal parameter values.
The sensitivity analysis confirms that the variability or uncertainty in none
of the parameters should be neglected
On the detection of several obstacles in 2D Stokes flow: topological sensitivity and combination with shape derivatives
International audienceWe consider the inverse problem of detecting the location and the shape of several obstacles immersed in a fluid flowing in a larger bounded domain Ω from partial boundary measurements in the two dimensional case. The fluid flow is governed by the steady-state Stokes equations. We use a topological sensitivity analysis for the Kohn-Vogelius functional in order to find the number and the qualitative location of the objects. Then we explore the numerical possibilities of this approach and also present a numerical method which combines the topological gradient algorithm with the classical geometric shape gradient algorithm; this blending method allows to find the number of objects, their relative location and their approximate shape
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