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Chapter
A Theory and Challenges for Coarsening in Microstructure
Cellular networks are ubiquitous in nature. Most engineered materials are polycrystalline microstructures composed of a myriad of small grains separated by grain boundaries, thus comprising cellular networks. ...
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Article
An Approach to the Mesoscale Simulation of Grain Growth
The simulation of curvature driven growth in grain boundary systems is becoming an important tool in understanding the behavior of microstructure evolution and there is much distinguished work in this subject....
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Protocol
BioLogic: A Mathematical Modeling Framework for Immunologists
The immune response to pathogens is a result of complex interactions among many cell types and a large number of molecular processes. As such it poses numerous challenges for modeling, simulation, and analysis...
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Article
Multiplex Assessment of Serum Biomarker Concentrations in Well-Appearing Children With Inflicted Traumatic Brain Injury
Proper diagnosis of mild inflicted traumatic brain injury (ITBI) is difficult; children often present without a history of trauma and with nonspecific symptoms, such as vomiting. Previous studies suggest that ...
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Article
New insights into mathematical modeling of the immune system
In order to understand the integrated behavior of the immune system, there is no alternative to mathematical modeling. In addition, the advent of experimental tools such as gene arrays and proteomics poses new...
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Article
Evaluating spatial constraints in cellular assembly processes using a Monte Carlo approach
Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the ce...
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Chapter and Conference Paper
Remarks on a Multiscale Approach to Grain Growth in Polycrystals
Nearly all technologically useful materials are polycrystalline. Their ability to meet system level specifications of performance and reliability is influenced by the types of grain boundaries present and thei...
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Article
Grain Boundary Properties and Grain Growth: Al Foils, Al Films
Relative grain boundary energy as a function of misorientation angle has been measured in cube-oriented, i.e., <100> fiber-textured, 120 µm-thick Al foil using orientation imaging microscopy and a statistical ...
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Chapter and Conference Paper
Bridging Micro and Macro Scales in Fluids
This paper presents coarse-graining methodologies for the passage from Molecular Dynamics (MD) models of fluids to the Navier-Stokes equations via an intermediate scale model. The microscopic and macroscopic d...
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Chapter and Conference Paper
An Optimization Algorithm for the Meteorological Data Assimilation Problem
The aim of this paper is to present an efficient optimization algorithm for solving the meteorological data assimilation problem. In our study this inverse problem is formulated as a constrained optimization p...
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Chapter and Conference Paper
Numerical Simulation and Coarse-Graining of Large Particle Systems
We discuss the use of combined analysis and simulation to tackle the problem of bridging between the scales in large systems of interacting particles (agents). On the microscopic level we consider several mode...
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Chapter and Conference Paper
From Molecular Dynamics to Navier-Stokes and Beyond
In this paper we outline numerical techniques for the ‘derivation’ of macroscopic equations from microscopic models. The main tool is regression analysis applied to certain coloring schemes whose role is to tr...
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Chapter and Conference Paper
From Molecular Dynamics to Continuum Models
This paper discusses the problem of deriving macroscopic behavior from molecular models using analysis combined with MD simulations. The goal is twofold, to understand the large scale dynamics of many particle...
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Article
Fourier-Laplace analysis of the multigrid waveform relaxation method for hyperbolic equations
The multigrid waveform relaxation (WR) algorithm has been fairly studied and implemented for parabolic equations. It has been found that the performance of the multigrid WR method for a parabolic equation is p...
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Chapter and Conference Paper
Shape Optimization in One Shot
The multigrid one shot method for optimal shape design problems, governed by elliptic systems, is introduced for the infinite dimensional design space. In this case the design variable is a function whose disc...
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Chapter and Conference Paper
Shape optimization governed by the quasi 1D Euler equations using an adjoint method
In this paper we discuss a numerical approach for the treatment of optimal shape problems governed by the quasi one-dimensional Euler equations. In particular, we focus on flows with embedded shocks. We introd...
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Chapter
Large Discretization Step (LDS) Methods For Evolution Equations
A new method for the acceleration of linear time dependent calculations is presented. It solves an extended system of equations on coarse spatial grids using large time steps yielding very accurate solutions. ...
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Chapter
Optimal Multigrid Method for Inviscid Flows
In this paper we describe a novel approach for the solution of in-viscid flow problems both for incompressible and subsonic compressible cases. The approach is based on canonical forms of the equations in whic...
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Chapter
Improved Finite Difference Method for Long Distance Propagation of Waves
Evaluation of aging aircraft involves inspection of large areas of plates, including lap joints, bonded material and other complex geometries. These inspections need to be done within a reasonable time in orde...
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Article
Multigrid method for stability problems
The problem of calculating the stability of steady state solutions of differential equations is treated. Leading eigenvalues (i.e., having maximal real part) of large matrices that arise from discretization ar...
