70,675 research outputs found
A model for the anisotropic response of fibrous soft tissues using six discrete fibre bundles
The development of accurate constitutive models of fibrous soft-tissues is a challenging problem. Many consider the tissue to be a collection of fibres with a continuous distribution function representing their orientations. A novel discrete fibre model is presented consisting of six weighted fibre bundles. Each bundle is oriented such that they pass through opposing vertices of a regular icosahedron. A novel aspect of the model is the use of simple analytical distribution functions to simulate the undulated collagen fibres. This approach yields a closed form analytical expression for the strain energy function for the collagen fibre bundle that avoids the sometimes costly numerical integration of some statistical distribution functions. The elastin fibres are characterized by a neo-Hookean strain energy function. The model accurately simulates the biaxial stretching of rabbit-skin (error-of-fit 8.7%), the uniaxial stretching of pig-skin (error-of-fit 7.6%), equibiaxial loading of aortic valve cusp (error-of-fit 0.8%), and the simple shear of rat septal myocardium (error-of-fit 9.1%). The proposed model compares favourably with previously published soft-tissue models and alternative methods of representing undulated collagen fibres. The stiffness of collagen fibres predicted by the model ranges from 8.0 MPa to 0.93 GPa. The stiffness of elastin fibres ranges from 2.5 kPa to 154.4 kPa. The anisotropy of model resulting from the representation of the fibre field with a discrete number of fibres is also explored
Worm Monte Carlo study of the honeycomb-lattice loop model
We present a Markov-chain Monte Carlo algorithm of "worm"type that correctly
simulates the O(n) loop model on any (finite and connected) bipartite cubic
graph, for any real n>0, and any edge weight, including the fully-packed limit
of infinite edge weight. Furthermore, we prove rigorously that the algorithm is
ergodic and has the correct stationary distribution. We emphasize that by using
known exact mappings when n=2, this algorithm can be used to simulate a number
of zero-temperature Potts antiferromagnets for which the Wang-Swendsen-Kotecky
cluster algorithm is non-ergodic, including the 3-state model on the
kagome-lattice and the 4-state model on the triangular-lattice. We then use
this worm algorithm to perform a systematic study of the honeycomb-lattice loop
model as a function of n<2, on the critical line and in the densely-packed and
fully-packed phases. By comparing our numerical results with Coulomb gas
theory, we identify the exact scaling exponents governing some fundamental
geometric and dynamic observables. In particular, we show that for all n<2, the
scaling of a certain return time in the worm dynamics is governed by the
magnetic dimension of the loop model, thus providing a concrete dynamical
interpretation of this exponent. The case n>2 is also considered, and we
confirm the existence of a phase transition in the 3-state Potts universality
class that was recently observed via numerical transfer matrix calculations.Comment: 33 pages, 12 figure
Maximum Likelihood Estimation of Triangular and Polygonal Distributions
Triangular distributions are a well-known class of distributions that are
often used as elementary example of a probability model. In the past,
enumeration and order statistic-based methods have been suggested for the
maximum likelihood (ML) estimation of such distributions. A novel
parametrization of triangular distributions is presented. The parametrization
allows for the construction of an MM (minorization--maximization) algorithm for
the ML estimation of triangular distributions. The algorithm is shown to both
monotonically increase the likelihood evaluations, and be globally convergent.
Using the parametrization is then applied to construct an MM algorithm for the
ML estimation of polygonal distributions. This algorithm is shown to have the
same numerical properties as that of the triangular distribution. Numerical
simulation are provided to demonstrate the performances of the new algorithms
against established enumeration and order statistics-based methods
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Flow field and Reynolds stress distribution in low turbulance natural convection in a triangular cavity
Triangular enclosures are typical configurations found in attic spaces of residential as well as industrial pitched-roof buildings. Previous studies on airflow within such spaces have focused on the laminar range. A numerical study has been carried out for time-dependent, two-dimensional low turbulence natural convection of air contained in the attic of a pitched roof of triangular cross-section. Two sets of boundary conditions have been considered: enclosure heated from the inclined walls and from the horizontal base wall, for aspect ratios (AR) of 0.33 ≤ AR ≤ 1.73 for Rayleigh number (Ra), 109 ≤ Ra ≤ 1011. In this paper, the flow field and Reynolds stress distribution are presented for the isothermal and isoflux cases
Robust nonparametric detection of objects in noisy images
We propose a novel statistical hypothesis testing method for detection of
objects in noisy images. The method uses results from percolation theory and
random graph theory. We present an algorithm that allows to detect objects of
unknown shapes in the presence of nonparametric noise of unknown level and of
unknown distribution. No boundary shape constraints are imposed on the object,
only a weak bulk condition for the object's interior is required. The algorithm
has linear complexity and exponential accuracy and is appropriate for real-time
systems. In this paper, we develop further the mathematical formalism of our
method and explore important connections to the mathematical theory of
percolation and statistical physics. We prove results on consistency and
algorithmic complexity of our testing procedure. In addition, we address not
only an asymptotic behavior of the method, but also a finite sample performance
of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049.
Link to the abstract at EURANDOM repository:
http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at
EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd
Acoustic modeling using the digital waveguide mesh
The digital waveguide mesh has been an active area of music acoustics research for over ten years. Although founded in 1-D digital waveguide modeling, the principles on which it is based are not new to researchers grounded in numerical simulation, FDTD methods, electromagnetic simulation, etc. This article has attempted to provide a considerable review of how the DWM has been applied to acoustic modeling and sound synthesis problems, including new 2-D object synthesis and an overview of recent research activities in articulatory vocal tract modeling, RIR synthesis, and reverberation simulation. The extensive, although not by any means exhaustive, list of references indicates that though the DWM may have parallels in other disciplines, it still offers something new in the field of acoustic simulation and sound synth
Deep D-Bar: Real-Time Electrical Impedance Tomography Imaging With Deep Neural Networks
The mathematical problem for electrical impedance tomography (EIT) is a highly nonlinear ill-posed inverse problem requiring carefully designed reconstruction procedures to ensure reliable image generation. D-bar methods are based on a rigorous mathematical analysis and provide robust direct reconstructions by using a low-pass filtering of the associated nonlinear Fourier data. Similarly to low-pass filtering of linear Fourier data, only using low frequencies in the image recovery process results in blurred images lacking sharp features, such as clear organ boundaries. Convolutional neural networks provide a powerful framework for post-processing such convolved direct reconstructions. In this paper, we demonstrate that these CNN techniques lead to sharp and reliable reconstructions even for the highly nonlinear inverse problem of EIT. The network is trained on data sets of simulated examples and then applied to experimental data without the need to perform an additional transfer training. Results for absolute EIT images are presented using experimental EIT data from the ACT4 and KIT4 EIT systems
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