1,189 research outputs found
The Semi Implicit Gradient Augmented Level Set Method
Here a semi-implicit formulation of the gradient augmented level set method
is presented. By tracking both the level set and it's gradient accurate subgrid
information is provided,leading to highly accurate descriptions of a moving
interface. The result is a hybrid Lagrangian-Eulerian method that may be easily
applied in two or three dimensions. The new approach allows for the
investigation of interfaces evolving by mean curvature and by the intrinsic
Laplacian of the curvature. In this work the algorithm, convergence and
accuracy results are presented. Several numerical experiments in both two and
three dimensions demonstrate the stability of the scheme.Comment: 19 Pages, 14 Figure
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
Dewetting-controlled binding of ligands to hydrophobic pockets
We report on a combined atomistic molecular dynamics simulation and implicit
solvent analysis of a generic hydrophobic pocket-ligand (host-guest) system.
The approaching ligand induces complex wetting/dewetting transitions in the
weakly solvated pocket. The transitions lead to bimodal solvent fluctuations
which govern magnitude and range of the pocket-ligand attraction. A recently
developed implicit water model, based on the minimization of a geometric
functional, captures the sensitive aqueous interface response to the
concave-convex pocket-ligand configuration semi-quantitatively
Some flows in shape optimization
Geometric flows related to shape optimization problems of Bernoulli type are
investigated. The evolution law is the sum of a curvature term and a nonlocal
term of Hele-Shaw type. We introduce generalized set solutions, the definition
of which is widely inspired by viscosity solutions. The main result is an
inclusion preservation principle for generalized solutions. As a consequence,
we obtain existence, uniqueness and stability of solutions. Asymptotic behavior
for the flow is discussed: we prove that the solutions converge to a
generalized Bernoulli exterior free boundary problem
Characterizing Width Uniformity by Wave Propagation
This work describes a novel image analysis approach to characterize the
uniformity of objects in agglomerates by using the propagation of normal
wavefronts. The problem of width uniformity is discussed and its importance for
the characterization of composite structures normally found in physics and
biology highlighted. The methodology involves identifying each cluster (i.e.
connected component) of interest, which can correspond to objects or voids, and
estimating the respective medial axes by using a recently proposed wavefront
propagation approach, which is briefly reviewed. The distance values along such
axes are identified and their mean and standard deviation values obtained. As
illustrated with respect to synthetic and real objects (in vitro cultures of
neuronal cells), the combined use of these two features provide a powerful
description of the uniformity of the separation between the objects, presenting
potential for several applications in material sciences and biology.Comment: 14 pages, 23 figures, 1 table, 1 referenc
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
A Replica Inference Approach to Unsupervised Multi-Scale Image Segmentation
We apply a replica inference based Potts model method to unsupervised image
segmentation on multiple scales. This approach was inspired by the statistical
mechanics problem of "community detection" and its phase diagram. Specifically,
the problem is cast as identifying tightly bound clusters ("communities" or
"solutes") against a background or "solvent". Within our multiresolution
approach, we compute information theory based correlations among multiple
solutions ("replicas") of the same graph over a range of resolutions.
Significant multiresolution structures are identified by replica correlations
as manifest in information theory overlaps. With the aid of these correlations
as well as thermodynamic measures, the phase diagram of the corresponding Potts
model is analyzed both at zero and finite temperatures. Optimal parameters
corresponding to a sensible unsupervised segmentation correspond to the "easy
phase" of the Potts model. Our algorithm is fast and shown to be at least as
accurate as the best algorithms to date and to be especially suited to the
detection of camouflaged images.Comment: 26 pages, 22 figure
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