47,580 research outputs found
Systematic numerical investigation of the role of hierarchy in heterogeneous bio-inspired materials
It is well known that hierarchical structure is an important feature in biological materials to optimise various properties, including mechanical ones. It is however still unclear how these hierarchical architectures can improve material characteristics, for example strength. Also, the transposition of these structures from natural to artificial bioinspired materials remains to be perfected. In this paper, we introduce a numerical method to evaluate the strength of fibre-based heterogeneous biological materials and systematically investigate the role of hierarchy. Results show that hierarchy indeed plays an important role and that it is possible to “tune” the strength of bio-inspired materials in a wide range of values, in some cases improving the strength of non-hierarchical structures considerably
Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method
The complexity and heterogeneity of bone tissue require a multiscale
modelling to understand its mechanical behaviour and its remodelling
mechanisms. In this paper, a novel multiscale hierarchical approach including
microfibril scale based on hybrid neural network computation and homogenisation
equations was developed to link nanoscopic and macroscopic scales to estimate
the elastic properties of human cortical bone. The multiscale model is divided
into three main phases: (i) in step 0, the elastic constants of collagen-water
and mineral-water composites are calculated by averaging the upper and lower
Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril
are computed using a trained neural network simulation. Finite element (FE)
calculation is performed at nanoscopic levels to provide a database to train an
in-house neural network program; (iii) in steps 2 to 10 from fibril to
continuum cortical bone tissue, homogenisation equations are used to perform
the computation at the higher scales. The neural network outputs (elastic
properties of the microfibril) are used as inputs for the homogenisation
computation to determine the properties of mineralised collagen fibril. The
mechanical and geometrical properties of bone constituents (mineral, collagen
and cross-links) as well as the porosity were taken in consideration. This
paper aims to predict analytically the effective elastic constants of cortical
bone by modelling its elastic response at these different scales, ranging from
the nanostructural to mesostructural levels. Our findings of the lowest scale's
output were well integrated with the other higher levels and serve as inputs
for the next higher scale modelling. Good agreement was obtained between our
predicted results and literature data.Comment: 2
An adaptive hierarchical domain decomposition method for parallel contact dynamics simulations of granular materials
A fully parallel version of the contact dynamics (CD) method is presented in
this paper. For large enough systems, 100% efficiency has been demonstrated for
up to 256 processors using a hierarchical domain decomposition with dynamic
load balancing. The iterative scheme to calculate the contact forces is left
domain-wise sequential, with data exchange after each iteration step, which
ensures its stability. The number of additional iterations required for
convergence by the partially parallel updates at the domain boundaries becomes
negligible with increasing number of particles, which allows for an effective
parallelization. Compared to the sequential implementation, we found no
influence of the parallelization on simulation results.Comment: 19 pages, 15 figures, published in Journal of Computational Physics
(2011
Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms
We present a mathematical framework for constructing and analyzing parallel
algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting
algorithms have the capacity to simulate a wide range of spatio-temporal scales
in spatially distributed, non-equilibrium physiochemical processes with complex
chemistry and transport micro-mechanisms. The algorithms can be tailored to
specific hierarchical parallel architectures such as multi-core processors or
clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms
are controlled-error approximations of kinetic Monte Carlo algorithms,
departing from the predominant paradigm of creating parallel KMC algorithms
with exactly the same master equation as the serial one.
Our methodology relies on a spatial decomposition of the Markov operator
underlying the KMC algorithm into a hierarchy of operators corresponding to the
processors' structure in the parallel architecture. Based on this operator
decomposition, we formulate Fractional Step Approximation schemes by employing
the Trotter Theorem and its random variants; these schemes, (a) determine the
communication schedule} between processors, and (b) are run independently on
each processor through a serial KMC simulation, called a kernel, on each
fractional step time-window.
Furthermore, the proposed mathematical framework allows us to rigorously
justify the numerical and statistical consistency of the proposed algorithms,
showing the convergence of our approximating schemes to the original serial
KMC. The approach also provides a systematic evaluation of different processor
communicating schedules.Comment: 34 pages, 9 figure
Joint estimation of multiple related biological networks
Graphical models are widely used to make inferences concerning interplay in
multivariate systems. In many applications, data are collected from multiple
related but nonidentical units whose underlying networks may differ but are
likely to share features. Here we present a hierarchical Bayesian formulation
for joint estimation of multiple networks in this nonidentically distributed
setting. The approach is general: given a suitable class of graphical models,
it uses an exchangeability assumption on networks to provide a corresponding
joint formulation. Motivated by emerging experimental designs in molecular
biology, we focus on time-course data with interventions, using dynamic
Bayesian networks as the graphical models. We introduce a computationally
efficient, deterministic algorithm for exact joint inference in this setting.
We provide an upper bound on the gains that joint estimation offers relative to
separate estimation for each network and empirical results that support and
extend the theory, including an extensive simulation study and an application
to proteomic data from human cancer cell lines. Finally, we describe
approximations that are still more computationally efficient than the exact
algorithm and that also demonstrate good empirical performance.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS761 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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