231 research outputs found
Microstructure-based modeling of elastic functionally graded materials: One dimensional case
Functionally graded materials (FGMs) are two-phase composites with
continuously changing microstructure adapted to performance requirements.
Traditionally, the overall behavior of FGMs has been determined using local
averaging techniques or a given smooth variation of material properties.
Although these models are computationally efficient, their validity and
accuracy remain questionable, since a link with the underlying microstructure
(including its randomness) is not clear. In this paper, we propose a modeling
strategy for the linear elastic analysis of FGMs systematically based on a
realistic microstructural model. The overall response of FGMs is addressed in
the framework of stochastic Hashin-Shtrikman variational principles. To allow
for the analysis of finite bodies, recently introduced discretization schemes
based on the Finite Element Method and the Boundary Element Method are employed
to obtain statistics of local fields. Representative numerical examples are
presented to compare the performance and accuracy of both schemes. To gain
insight into similarities and differences between these methods and to minimize
technicalities, the analysis is performed in the one-dimensional setting.Comment: 33 pages, 14 figure
Stacking Characteristics of Composite Cardboard Boxes
This paper presents a simplified model and method for finding the deflection char acteristics of stacked cardboard boxes, provided the load-deflection characteristic of the box is known. A computer program, based on this model, allows the stability of stacked boxes to be investigated and to indicate the limits to the height of the stack and box parameters required to prevent stack toppling.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68424/2/10.1177_073168448300200302.pd
Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
A study of fermion nodes for spin-polarized states of a few-electron ions and
molecules with one-particle orbitals is presented. We find exact nodes
for some cases of two electron atomic and molecular states and also the first
exact node for the three-electron atomic system in state using
appropriate coordinate maps and wavefunction symmetries. We analyze the cases
of nodes for larger number of electrons in the Hartree-Fock approximation and
for some cases we find transformations for projecting the high-dimensional node
manifolds into 3D space. The node topologies and other properties are studied
using these projections. We also propose a general coordinate transformation as
an extension of Feynman-Cohen backflow coordinates to both simplify the nodal
description and as a new variational freedom for quantum Monte Carlo trial
wavefunctions.Comment: 7 pages, 7 figure
A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem
A wide variety of articles, starting with the famous paper (Gidas, Ni and
Nirenberg in Commun. Math. Phys. 68, 209-243 (1979)) is devoted to the
uniqueness question for the semilinear elliptic boundary value problem
-{\Delta}u={\lambda}u+u^p in {\Omega}, u>0 in {\Omega}, u=0 on the boundary of
{\Omega}, where {\lambda} ranges between 0 and the first Dirichlet Laplacian
eigenvalue. So far, this question was settled in the case of {\Omega} being a
ball and, for more general domains, in the case {\lambda}=0. In (McKenna et al.
in J. Differ. Equ. 247, 2140-2162 (2009)), we proposed a computer-assisted
approach to this uniqueness question, which indeed provided a proof in the case
{\Omega}=(0,1)x(0,1), and p=2. Due to the high numerical complexity, we were
not able in (McKenna et al. in J. Differ. Equ. 247, 2140-2162 (2009)) to treat
higher values of p. Here, by a significant reduction of the complexity, we will
prove uniqueness for the case p=3
Generalization of the Zlámal condition for simplicial finite elements in ℝ d
The famous Zlámal's minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method in 2d. In this paper we present and discuss its generalization to simplicial partitions in any space dimension
A computational framework for particle and whole cell tracking applied to a real biological dataset
Cell tracking is becoming increasingly important in cell biology as it provides a valuable tool for analysing
experimental data and hence furthering our understanding of dynamic cellular phenomena. The advent of high-throughput, high-resolution microscopy and imaging techniques means that a wealth of large data is routinely generated in many laboratories. Due to the sheer magnitude of the data involved manual tracking is often cumbersome and the development of computer algorithms for automated cell tracking is thus highly desirable.
In this work, we describe two approaches for automated cell tracking. Firstly, we consider particle tracking. We propose a few segmentation techniques for the detection of cells migrating in a non-uniform background, centroids of the segmented cells are then calculated and linked from frame to frame via a nearest-neighbour approach. Secondly, we consider the problem of whole cell tracking in which one wishes to reconstruct in time whole cell morphologies. Our approach is based on fitting a mathematical model to the experimental imaging data with the goal being that the physics encoded in the model is reflected in the reconstructed data. The resulting mathematical problem involves the optimal control of a phase-field formulation of a geometric evolution law. Efficient approximation of this challenging optimal control problem is achieved via advanced numerical methods for the solution of semilinear parabolic partial differential equations (PDEs) coupled with parallelisation and adaptive resolution techniques.
Along with a detailed description of our algorithms, a number of simulation results are reported on.
We focus on illustrating the effectivity of our approaches by applying the algorithms to the tracking of
migrating cells in a dataset which reflects many of the challenges typically encountered in
microscopy data
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