September 12-15, 2012
A Variational Perspective on Cloaking by Anomalous Localized Resonance
A body of literature has developed concerning “cloaking by anomalous localized resonance”. The mathematical heart of the matter involves the behavior of a divergence-form elliptic equation in the plane, ∇ · (a(x)∇u(x)) = f(x). The complex-valued coefficient has a matrix-shell-core geometry, with real part equal to 1 in the matrix and the core, and -1 in the shell; one is interested in understanding the resonant behavior of the solution as the imaginary part of a(x) decreases to zero (so that ellipticity is lost). Most analytical work in this area has relied on separation of variables, and has therefore been restricted to radial geometries.
We introduce a new approach based on a pair of dual variational principles, and apply it to some non-radial examples. In our examples, as in the radial setting, the spatial location of the source f plays a crucial role in determining whether or not resonance occurs.(joint work with Robert V. Kohn, Benjamin Schweizer and Michael I. Weinstein)
Panel Discussion 1: Large Scale Modeling and Industrial Challenges
The panel will address the modeling challenges encountered in industry. Within the MGI perspective, these may range from materials design and experiment, through mathematical modeling, large scale computing, model validation and managing large sets of data.
Virtual Testing of Composite Materials
The qualification of new materials and certification of new structures is a major hurdle in the deployment of new material systems. Virtual testing may provide a way to decrease the long lead time associated with maturing new materials. This area is a problem rich field, including effect of defects, variability of the material and structure, load control/testing apparatus, and many more.
Integrated Computational Materials Science and Engineering: An Air
Advanced materials are both enablers and limiting factors for high-performance technologies. The massive overall investment to bring a new material system to bear inhibits the integration of new material solutions and thus slows technological growth. Through processes such as Integrated Computational Materials Science and Engineering, the Air Force is attacking the problem of rapid design AND deployment of materials. This presentation will discuss the mission of the Materials & Manufacturing Directorate of the Air Force Research Laboratory, how it is attacking the problem of design and maturation of new materials, and will conclude with information about outreach programs to unite academic, industrial, and government research teams.
Panel Discussion 3: MGI and Education
The MGI focuses on restructuring, coordinating and, in some degree, reinventing the multiple stages of materials research, by focusing in the underlying science and mathematics. One question the panel will discuss is how these efforts may help improve education, with a goal of optimally preparing students for high tech jobs. Panel participants will bring different perspectives (high school, community college, undergraduate and graduate institutions). Panelists from industries and national labs can help identify what works and how to improve the current programs, and also new resources to be implemented.
Mathematical Modeling of The Interstitial Space
The interstitial space is the region that surrounds the cells of a given tissue.
It plays an important role in the control of fluid volume
in the human body. The interstitial space contains about one sixth
of total fluid volume in the body. The goal of this
project is to provide mathematical insights into the fluid distribution of the interstitial space.
Also with S. Lyu
Electrochemical Energy Storage Devices for Electrified Vehicles
Keywords of the presentation: batteries, lithium-ion, energy storage, modeling, materials, automotive
A brief historical review of various chemistries that have been used in batteries for automotive applications will be provided. This will be followed by an overview of Ford’s electrification strategy and our research and advanced engineering efforts. Next, the material components of lithium-ion cells and modeling of these electrochemical energy storage devices will be discussed. Finally, the challenges in this field and potential opportunities for interdisciplinary research to meet our goals will be highlighted with specific examples from our present collaborations.
A Dynamic Model of Polyelectrolyte Gels
Volume phase transition is a very important phenomenon of many polyelectrolyte gels. It is widely used in artificial devices, however, mathematically not much has been studied yet. In this poster, we give a dynamic model of polyelectrolyte gels, including governing equations and boundary conditions at the interface, which satisfies free energy dissipation identity. We analyze the 1-D linear stability for nonionic case and two ionic cases. We also show numerical simulations for the nonionic model. When using backward Euler method, there is a certain way that a discretized version of free energy dissipation identity can hold.
The Quest for Descriptors in Materials Development: A Rational
Use of aflowlib.org through examples.
While extremely helpful and important, databases are intrinsically sterile repositories of information, unless rational descriptors are implemented for rapid identification of the materials genomics. In this talk we will give examples of descriptors (i.e. scintillation, photovoltaics, thermoelectricity, piezoelectricity, supermagnets, spintronics, catalysis, phase stability), and will introduce the concept of AFLOW genetic-daemons: the tools for automatic
discovery of materials without human intervention
Multiscale Modeling of Defects in Ionic and Polarizable Solids
Ionic conductors are central to modern batteries, fuel cells, and other energy-related technologies. In these materials, functionality is entirely driven by the behavior of defects, namely the motion of charged point defects. Next-generation devices will potentially exploit nanostructuring and other strategies to improve performance by orders of magnitude. Predicting the behavior and response of defects to the complex electric fields and complex geometries in these settings presents a multiscale challenge: it requires resolution of both defect cores as well as device-scale features, in material systems where ions and electrons have both short-range as well as long-range Coulombic interactions. I will present our development of a multiscale numerical method to compute defect structure and response to field in these settings.
Algorithms for critical nucleation, microstructure evolution and materials design
Keywords of the presentation: critical nucleation, materials design, microstructure, algorithms
To improve materials design, it is important to understand the influence of
microstructure on the physical properties of a material. Very often, it is the
nucleation process that dictates the microstructure. We present some recent
joint works with colleagues at Penn State on the computational studies of critical
nuclei morphology, growth and coarsening of microstructures as well as
stability of interacting particle systems.Read More...
Multiscale computational modeling of complex materials systems
This poster gives an overview of the computational issues underpinning
mathematical modeling of polycrystalline materials on multiple spatial
and temporal scales and calculation of phase diagrams for advancing
materials design and engineering. There is a number of challenges to
be faced, including the development of fast yet reliable simulation
techniques for prediction of microcracking and irreversible damage in
by environmental factors, as well as the design of efficient methods
for analyzing vast
amounts of 3-d imaging data recently made available by advances in
Multiscale Computational Modeling of Complex Materials Systems
This talk gives an overview of the computational and analytical issues
underpinning mathematical modeling of polycrystalline materials on multiple spatial and temporal scales for advancing materials design and engineering.
There is a number of challenges to be faced, including the development
of fast yet reliable simulation techniques for prediction of microcracking and irreversible damage in materials caused by environmental factors, as well as the design of efficient methods for analyzing vast amounts of data recently made available by advances in experimental design and instrumentation.
Charged Kinetic transport for full electronic bands: novel applications
Keywords of the presentation: charged transport, semiconductors, Boltzmann Poisson system, solar fuel cells modeling, inverse problems in nanoscale heterogeneous materials
We will discuss a deterministic approximation for charged transport model of Boltzmann Poisson type along electronic bands. This is a kinetic model of hot electron flow in a graph given by computed energy bands and the scattering mechanisms for the collisional structure such as Fermi's golden rule for symmetric bands or full scattering forms for general numerical bands structure.
Simulations of semiconductor models will be shown and well as applications to an inverse problem for doping profile reconstruction for nano scale semiconductor devices and electron-hole transport for semiconductor/electrolyte interface reaction problem as a prototype modeling of solar/fuel cells.
Ginzburg-Landau-Type Model for Carbon Nanotubes
The structure of a Ginzburg-Landau (GL) model originally introduced to model superconductivity can be extended to describe a variety of other physical phenomena that involve ordered systems. The GL theory is particularly useful for understanding the behavior of structural defects - the regions of disorder that appear, e.g., for topological reasons. In my talk, I will discuss a macroscopic level GL-type model that arises in continuum mechanics of carbon nanotubes. The focus will be on establishing a connection between the coarse-grained
model and its atomistic counterpart.
Compressive sensing: A new paradigm for model
Using Compressive Sensing to Uncover the Alloy Genome with
High-Throughput Model Building
First-principles codes can nowadays provide hundreds of high-fidelity enthalpies on thousands of alloy systems with a modest investment of a few tens of millions of CPU hours. But a mere database of enthalpies provides only the starting point for uncovering the "alloy genome." What one needs to fundamentally change alloy discovery and design are complete searches over candidate structures (not just hundreds of known experimental phases) and models that can be used to simulate both kinetics and thermodynamics. Despite more than a decade of effort by many groups, developing robust models for these simulations is still a human-time-intensive endeavor. We have developed an new
approach for alloy model building that is faster and more robust that conventional approaches. We extract cluster expansion-based models from a large database (www.aflowlib.org) of alloy enthalpies. Our framework will uncover, in a general way across the periodic table, the important components of such models and reveal the underlying "genome" of alloy physics.
A weak compatibility condition of Widmanstatten structure: the 'Materials Genome' of Sb2Te3 in PbTe
We propose a weak condition of compatibility between phases applicable to cases exhibiting full or partial coherence and Widmanstatten microstructure. The condition is applied to the study of Sb2Te3 precipitates in a PbTe matrix in a thermoelectric alloy. The weak condition of compatibility predicts elongated precipitates lying on a cone determined by a transformation stretch tensor. Comparison of this cone with the long directions of precipitates revealing by FIB/SEM shows good agreement between theory and experiment.
New and unique materials from dewetting of pulsed-laser melted, multilayer metallic films at the nanoscale: experiments and modeling
Self-organized nanoparticle arrays from pulsed laser-induced
dewetting of ultra-thin (< 20 nm), multilayer metallic films can be
used to manufacture complex multifunctional surfaces that can be
applied to existing technologies such as surface Raman sensing or
magnetic data storage devices, but can also enable a host of new
applications that are generally based on sensing, detecting or
manipulating charge, electromagnetic signals, and magnetization.
This poster describes the basic nonlinear PDE model of self-organization
in bilayer films. In experiments, pulsed irradiation by
thousands of pulses with pulse width around 10 ns results in film
dewetting into nanoparticle arrays with well-defined length scales,
composition, and intricate morphologies. We used stability analyses
and computations of film height dynamics to determine dependencies
of these quantities on physical and process parameters. The combined
experimental/theoretical exploration is a step toward predictively
manufacture scalable multifunctional surfaces in new systems.
New and Unique Materials from Dewetting of Pulsed-laser Melted, Multilayer Metallic Films at the Nanoscale: Experiments and Modeling
Self-organized nanoparticle arrays from pulsed laser-induced dewetting of ultra-thin (< 20 nm), multilayer metallic films can be used to manufacture complex multifunctional surfaces that can be applied to existing technologies such as surface Raman sensing or magnetic data storage devices, but can also enable a host of new applications that are generally based on sensing, detecting or manipulating charge, electromagnetic signals, and magnetization.
This presentation and accompanying poster will attempt to describe key features of pulsed laser processing at the nanoscale, outline recent progress in experiments, and formulate challenges to quantitative modeling. It will also introduce the basic nonlinear PDE model of self-organization in bilayer films. In experiments, pulsed irradiation by thousands of pulses with pulse width around 10 ns results in film dewetting into nanoparticle arrays with well-defined length scales, composition, and intricate morphologies. We used stability analyses and computations of film height dynamics to determine dependencies of these quantities on physical and process parameters. The combined experimental/theoretical exploration is a step toward predictively manufacture scalable multifunctional surfaces in new systems.
Closed-form solutions to the effective properties of
Magnetoelectric coupling is of interest for a variety of applications,
but is weak in natural materials. Strain-coupled fibrous composites of
piezoelectric and piezomagnetic materials are an attractive way of
obtaining enhanced effective magnetoelectricity. This paper studies the effective magnetoelectric behaviors of two-phase multiferroic composites with periodic array of inhomogeneities. For a class of microstructures called periodic E-inclusions, we obtain a rigorous closed-form formula of the
effective magnetoelectric coupling coefficient in terms of the shape
matrix and volume fraction of the periodic E-inclusion. Based on the closed form formula, we find the optimal volume fractions of the fiber phase for maximum magnetoelectric coupling and correlate the maximum magnetoelectric
coupling with the material properties of the constituent phases. Based
on these results, useful design principles are proposed for
engineering magnetoelectric composites.
A Continuum Theory of Thermoelectric Bodies and Proposed Large-scale Application in Energy Conversion
We develop a continuum theory for thermoelectric bodies following the framework of continuum mechanics and conforming to general principles of thermodynamics. For steady states, the governing equations for local fields are intrinsically nonlinear. However, under conditions of small variations of electrochemical potential, temperature and their gradients, the governing equations may be reduced to a linear elliptic system, which can be conveniently solved to determine behaviors of thermoelectric bodies. The linear theory is further applied to predict effective properties of thermoelectric composites. In particular, explicit formula of e ffective properties are obtained for simple
microstructures of laminates and periodic E-inclusions, which implies useful design principles for engineering thermoelectric composites. We also discuss feasibility of large scale power generation by thermoelectric materials.
Space and Time Coarse-graining for Genomics-Based Materials Design and
New theoretical, algorithmic, and computational tools are needed to
overcome the space and time scale challenges presented by
genomics-based materials design and manufacturing. I will discuss
several approaches to the coarse-graining of space and time needed to
achieve the predictive and efficient simulation of materials with
optimized properties — accelerated dynamics, atomistic-to-continuum
coupling, and microstructure coarse-graining. I will also present the
need for theory-driven method verification and benchmarking with some
Crystal Facets in Materials Surface
Relaxation: A two-scale perspective
I will discuss recent progress and open
challenges in connecting the dynamics
of line defects to the large-scale evolution of
facets, which give rise to free boundaries,
on macroscopic crystal surfaces. At the microscale,
a large number of differential equations is invoked
for the positions of defects. At the macroscale, the surface
evolution is plausibly described by a Partial Differential
Equation (PDE) for the surface height profile. A goal is to
derive boundary conditions for the PDE consistent with
the motion of defects. I will address the (simplified) case of an
evaporation-condensation process in a radial geometry,
which provides some generic features of the
more general problem.
Micromechanics Based Second Gradient Continuum Mechanics Theory for Cohesive Granular Materials
Cohesive granular materials are known for their pressure-dependent strain softening behavior that is intimately linked to their microstructure and grain interactions. To understand the relationship of mechanical properties, composition and structure of these materials, we have been developing continuum theories utilizing higher displacement gradients and micromechanics [1-5]. In this presentation, we will first describe the second gradient continuum theory using the principal of virtual work to establish the governing equations and the boundary conditions. We will then describe the derivation of constitutive equations for this theory using a granular micromechanics approach. The model predictions will be shown to have both quantitative and qualitative consistency with the observed behavior of cohesive granular material obtained in experiments and through ab initio atomistic simulations. We expect that the proposed approach can be used to correlate measured mechanical properties at micro/nano-meter scales with truly atomic-scale information for systems that possess complex structures at atomic and micro-scales.
Use of the String Method to Find Minimal Energy Paths and Energy Barriers of Droplets on Superhydrophobic Surfaces
Interest in superhydrophobic surfaces has increased due to a number of interesting advances in science and engineering. Here we use a diffuse interface model for droplets on topographically and chemically patterned surfaces in the regime where gravity is negligible. We then apply the constrained string method to examine the transition of droplets between different metastable/stable states. The string method finds the minimal energy paths (MEPs) which correspond to the most probable transition pathways between the metastable/stable states in the configuration space. In the case of a hydrophobic surface with posts of variable height and separation, we determine the MEP corresponding to the transition between the Cassie-Baxter and Wenzel states. Additionally, we realize critical droplet morphologies along the MEP associated with saddle points of the free-energy potential and the energy barrier of the free energy. We analyze and compare the MEPs and free-energy barriers for a variety of surface geometries, droplets sizes, and static contact angles ranging from partial wetting to complete wetting. We also introduce an unbiased double well potential in the diffuse interface model by introducing a chemical potential that is fixed for a given simulation. We find that the energy barrier shifts toward the Wenzel state along the MEP as the height of the pillars increases in the topographically patterned case while a shorter energy barrier exists and is more centered along the MEP for pillars of shorter height. More importantly, we demonstrate the string method as a useful tool in the study of droplets on superhydrophobic surfaces by presenting a numerical study that finds MEPs in configuration space, critical droplet morphologies and free-energy barriers which in turn give us a greater understanding of the free-energy landscape.
Network Formation and Ionic Conduction in Polymer Electrolyte Materials
We present a novel energy formulation for the microstructured networks that develop when functionalized polymers interact with solvent. Such materials
find widespread use in energy conversion and storage devices: PEM fuel cells, Dye-sensitized solar cells, Lithium-ion batteries. The formulation balances the favorable electrostatic interaction of tethered charges with solvent against entropic and elastic energy.
Toward in-silico Design of Polycrystalline Materials
Keywords of the presentation: polycrystalline materials, in-silicon design, optimization, high energy diffraction microscopy, large deviation theory, gradient flows with non-convex energies
Grand challenges in materials science include the accelerated design of materials with exceptional properties for use in applications that span from microelectronics to large structures used in airplanes. Examples of desired properties include high-strength and high-formability, resistance to creep, fatigue, radiation, and high-thermal loading. The design of materials that meet such properties requires integration of experiment, modeling, simulation and analysis across multiple scales: from DFT to macroscopic levels. Moreover, it requires the assembling of teams with expertise spanning multiple engineering, physics and mathematical fields. We discuss an example of such integration that may result in enabling technologies for in-silico design of polycrystalline materials. Infrastructure in terms human resources, hardware, software and experimentation is needed to meet the challenge.
Mesoscale Description of Defected Materials
A quantitative description of defected materials at the mesoscale
is emerging that is based on traditional order parameter descriptions of
the material, coupled with appropriate kinetic equations. We summarize
the salient aspects of the methodology, including static and dynamic
properties of grain boundaries, and the introduction of reversible degrees
of freedom in mesophases. In the latter case, we outline applications to
block copolymer processing.