Homogenisation applied to thermal radiation in porous media

Heat transport in granular and porous media occurs through conduction in the solid and radiation through the voids. By exploiting the separation of length scales between the small typical particles or voids and the large size of whole region, the method of multiple scales can be applied. For a purely diffusive system, this yields a problem on the macroscale with an effective conductivity, deduced by solving a ‘cell problem’ on the microscale. Here, we apply the method when radiation and conduction are both present; however, care must be taken to correctly handle the integral nature of the radiative boundary condition. Again, an effective conductivity is found by solving a ‘cell problem’ which, because of the non-linearity of radiative transfer, to be solved for each temperature value. We also incorporate modifications to the basic theory of multiple scales in order to deal with the non-local nature of the radiative boundary condition. We derive the multiple scales formulation of the problem and report on numerical comparisons between the homogenised problem and direct solution of the problem. We also compare the effective conductivity to that derived using Maxwell models and effective medium theory.

Homogenization of quadratic convolution energies in periodically perforated domains

We prove a homogenization theorem for quadratic convolution energies defined in perforated domains. The corresponding limit is a Dirichlet-type quadratic energy, whose integrand is defined by a non-local cell-problem formula. The proof relies on an extension theorem from perforated domains belonging to a wide class containing compact periodic perforations.

HOMOGENIZATION OF TRANSPORT PROCESSES AND HYDRATION PHENOMENA IN FRESH CONCRETE

The problem of hydration and transport processes in fresh concrete is strongly coupled and non- inear, and therefore, very difficult for a numerical modelling. Physically accurate results can be obtained using fine-scale simulations, which are, however, extremely time consuming. Therefore, there is an interest in developing new physically accurate and computationally effective models. In this paper, a new fully coupled two-scale (meso-macro) homogenization framework for modelling of simultaneous heat transfer, moisture flows, and hydration phenomena in fresh concrete is proposed. A modified mesoscalemodelisfirstintroduced. Inthismodel, concreteisassumedasacompositematerialwithtwo periodically distributed mesoscale components, cement paste and aggregates. A homogenized model is then derived by an upscaling method from the mesoscale model. The coefficients for the homogenized model are obtained from the solution of a periodic cell problem. For solving the periodic cell problem, two approaches are used – a standard finite element method and a simplified closed-form approximation taken from literature. The homogenization framework is then implemented in MATLAB environment and finally employed for illustrative numerical experiments, which verify that the homogenized model provides physically accurate results comparable with the results obtained by the mesoscale model. Moreover, it is verified that, using the homogenization framework with a closed-form approach to the periodic cell problem, significant computational cost savings can be achieved.

Apprehending the effects of mechanical deformations in cardiac electrophysiology: A homogenization approach

We follow a formal homogenization approach to investigate the effects of mechanical deformations in electrophysiology models relying on a bidomain description of ionic motion at the microscopic level. To that purpose, we extend these microscopic equations to take into account the mechanical deformations, and proceed by recasting the problem in the framework of classical two-scale homogenization in periodic media, and identifying the equations satisfied by the first coefficients in the formal expansions. The homogenized equations reveal some interesting effects related to the microstructure — and associated with a specific cell problem to be solved to obtain the macroscopic conductivity tensors — in which mechanical deformations play a nontrivial role, i.e. they do not simply lead to a standard bidomain problem posed in the deformed configuration. We then present detailed numerical illustrations of the homogenized model with coupled cardiac electrical–mechanical simulations — all the way to ECG simulations — albeit without taking into account the abundantly-investigated effect of mechanical deformations in ionic models, in order to focus here on other effects. And in fact our numerical results indicate that these other effects are numerically of a comparable order, and therefore cannot be disregarded.

Comparison of HNN and Ga Based Hybrid Algorithm for Standard Cell Placement in VLSI Design

This research contracts with the notion of hybridization and reports use of hybridizing on GA and HNN. GA and HNN were individually applied to resolve the SCP [3, 4, 5]. In first section we used GA and HNN independently to solve Standard Cell Problem. In the second section we present a new hybrid of GA and HNN. In the last section of the paper we compare the results of hybrid system of GA and HNN with independent result of GA and HNN in respect of wire length and CPU time.