1,113 research outputs found
Linear stability analysis of capillary instabilities for concentric cylindrical shells
Motivated by complex multi-fluid geometries currently being explored in
fibre-device manufacturing, we study capillary instabilities in concentric
cylindrical flows of fluids with arbitrary viscosities, thicknesses,
densities, and surface tensions in both the Stokes regime and for the full
Navier--Stokes problem. Generalizing previous work by Tomotika (N=2), Stone &
Brenner (N=3, equal viscosities) and others, we present a full linear stability
analysis of the growth modes and rates, reducing the system to a linear
generalized eigenproblem in the Stokes case. Furthermore, we demonstrate by
Plateau-style geometrical arguments that only axisymmetric instabilities need
be considered. We show that the N=3 case is already sufficient to obtain
several interesting phenomena: limiting cases of thin shells or low shell
viscosity that reduce to N=2 problems, and a system with competing breakup
processes at very different length scales. The latter is demonstrated with full
3-dimensional Stokes-flow simulations. Many cases remain to be
explored, and as a first step we discuss two illustrative cases,
an alternating-layer structure and a geometry with a continuously varying
viscosity
Solving the Direction Field for Discrete Agent Motion
Models for pedestrian dynamics are often based on microscopic approaches
allowing for individual agent navigation. To reach a given destination, the
agent has to consider environmental obstacles. We propose a direction field
calculated on a regular grid with a Moore neighborhood, where obstacles are
represented by occupied cells. Our developed algorithm exactly reproduces the
shortest path with regard to the Euclidean metric.Comment: 8 pages, 4 figure
Extended Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries
In this article, we describe an approach for solving partial differential
equations with general boundary conditions imposed on arbitrarily shaped
boundaries. A continuous function, the domain parameter, is used to modify the
original differential equations such that the equations are solved in the
region where a domain parameter takes a specified value while boundary
conditions are imposed on the region where the value of the domain parameter
varies smoothly across a short distance. The mathematical derivations are
straightforward and generically applicable to a wide variety of partial
differential equations. To demonstrate the general applicability of the
approach, we provide four examples herein: (1) the diffusion equation with both
Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both
surface diffusion and reaction; (3) the mechanical equilibrium equation; and
(4) the equation for phase transformation with the presence of additional
boundaries. The solutions for several of these cases are validated against
corresponding analytical and semi-analytical solutions. The potential of the
approach is demonstrated with five applications: surface-reaction-diffusion
kinetics with a complex geometry, Kirkendall-effect-induced deformation,
thermal stress in a complex geometry, phase transformations affected by
substrate surfaces, and a self-propelled droplet.Comment: This document is the revised version of arXiv:0912.1288v
Analysis of an Inverse Problem Arising in Photolithography
We consider the inverse problem of determining an optical mask that produces
a desired circuit pattern in photolithography. We set the problem as a shape
design problem in which the unknown is a two-dimensional domain. The
relationship between the target shape and the unknown is modeled through
diffractive optics. We develop a variational formulation that is well-posed and
propose an approximation that can be shown to have convergence properties. The
approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur
Justifying and Explaining Disproportionality 1968—2008: A Critique of Underlying Views of Culture
This is the publisher's version, also found here: http://cec.metapress.com/content/e7835w1374x7g141/?p=0ee3fcac0688484aacb1d3c83c9c469c&pi=2Special education has made considerable advances in research, policy, and practice in its short history. However, students from historically underserved groups continue to be disproportionately identified as requiring special education. Support for color-blind practices and policies can justify racial disproportionality in special education and signal a retrenchment to deficit views about students from historically underserved groups. We respond to these emerging concerns through an analysis of arguments that justify disproportionality. We also identify explanations of the problem and critique the views of culture that underlie these explanations. We conclude with a brief discussion of implications and future directions
Relationships between a roller and a dynamic pressure distribution in circular hydraulic jumps
We investigated numerically the relation between a roller and the pressure
distribution to clarify the dynamics of the roller in circular hydraulic jumps.
We found that a roller which characterizes a type II jump is associated with
two high pressure regions after the jump, while a type I jump (without the
roller) is associated with only one high pressure region. Our numerical results
show that building up an appropriate pressure field is essential for a roller.Comment: 10 pages, 7 PS files. To appear in PR
A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery
In this paper, we will first introduce a novel multiscale representation
(MSR) for shapes. Based on the MSR, we will then design a surface inpainting
algorithm to recover 3D geometry of blood vessels. Because of the nature of
irregular morphology in vessels and organs, both phantom and real inpainting
scenarios were tested using our new algorithm. Successful vessel recoveries are
demonstrated with numerical estimation of the degree of arteriosclerosis and
vessel occlusion.Comment: 12 pages, 3 figure
Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition
This paper focuses on multi-scale approaches for variational methods and
corresponding gradient flows. Recently, for convex regularization functionals
such as total variation, new theory and algorithms for nonlinear eigenvalue
problems via nonlinear spectral decompositions have been developed. Those
methods open new directions for advanced image filtering. However, for an
effective use in image segmentation and shape decomposition, a clear
interpretation of the spectral response regarding size and intensity scales is
needed but lacking in current approaches. In this context, data
fidelities are particularly helpful due to their interesting multi-scale
properties such as contrast invariance. Hence, the novelty of this work is the
combination of -based multi-scale methods with nonlinear spectral
decompositions. We compare with scale-space methods in view of
spectral image representation and decomposition. We show that the contrast
invariant multi-scale behavior of promotes sparsity in the spectral
response providing more informative decompositions. We provide a numerical
method and analyze synthetic and biomedical images at which decomposition leads
to improved segmentation.Comment: 13 pages, 7 figures, conference SSVM 201
Level Set Approach to Reversible Epitaxial Growth
We generalize the level set approach to model epitaxial growth to include
thermal detachment of atoms from island edges. This means that islands do not
always grow and island dissociation can occur. We make no assumptions about a
critical nucleus. Excellent quantitative agreement is obtained with kinetic
Monte Carlo simulations for island densities and island size distributions in
the submonolayer regime.Comment: 7 pages, 9 figure
A new ghost cell/level set method for moving boundary problems:application to tumor growth
In this paper, we present a ghost cell/level set method for the evolution of interfaces whose normal velocity depend upon the solutions of linear and nonlinear quasi-steady reaction-diffusion equations with curvature-dependent boundary conditions. Our technique includes a ghost cell method that accurately discretizes normal derivative jump boundary conditions without smearing jumps in the tangential derivative; a new iterative method for solving linear and nonlinear quasi-steady reaction-diffusion equations; an adaptive discretization to compute the curvature and normal vectors; and a new discrete approximation to the Heaviside function. We present numerical examples that demonstrate better than 1.5-order convergence for problems where traditional ghost cell methods either fail to converge or attain at best sub-linear accuracy. We apply our techniques to a model of tumor growth in complex, heterogeneous tissues that consists of a nonlinear nutrient equation and a pressure equation with geometry-dependent jump boundary conditions. We simulate the growth of glioblastoma (an aggressive brain tumor) into a large, 1 cm square of brain tissue that includes heterogeneous nutrient delivery and varied biomechanical characteristics (white matter, gray matter, cerebrospinal fluid, and bone), and we observe growth morphologies that are highly dependent upon the variations of the tissue characteristics—an effect observed in real tumor growth
- …