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This six-month progress report describes an ongoing program on the multiscale modeling of noncrystalline ceramics (glass) funded from the Directors Strategic Initiatives (DSIs) in support of the U.S. Army Research Laboratorys (ARL) Strategic Research Initiatives. The long-term research goal of the program is to develop a concurrent multiscale computational finite element code for optimizing or enhancing the performance of various glasses against shaped-charge jets; the initial work focuses on pure fused-silica (a-SiO2), and chemically varied a-SiO2 materials. As such, this objective falls squarely within the purview of the Weapons and Materials Research Directorate, since multiscale models are constitutive models (specific to a particular material) wherein time evolving short and intermediate range atomic structure, order, and microcrack initiation and growth, are fully coupled to the macroscale, a phenomenon that cannot be modeled or accounted for using classical homogenization methods. A more immediate research objective is to understand why certain chemically substituted a-SiO2 materials exhibit enhanced performance in the defeat of shaped-charge jets and other ballistic threats.

This six-month progress report describes an ongoing program on the multiscale modeling of noncrystalline ceramics (glass) funded from the Directors Strategic Initiatives (DSIs) in support of the U.S. Army Research Laboratorys (ARL) Strategic Research Initiatives. The long-term research goal of the program is to develop a concurrent multiscale computational finite element code for optimizing or enhancing the performance of various glasses against shaped-charge jets; the initial work focuses on pure fused-silica (a-SiO2), and chemically varied a-SiO2 materials. As such, this objective falls squarely within the purview of the Weapons and Materials Research Directorate, since multiscale models are constitutive models (specific to a particular material) wherein time evolving short and intermediate range atomic structure, order, and microcrack initiation and growth, are fully coupled to the macroscale, a phenomenon that cannot be modeled or accounted for using classical homogenization methods. A more immediate research objective is to understand why certain chemically substituted a-SiO2 materials exhibit enhanced performance in the defeat of shaped-charge jets and other ballistic threats.

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the Nernst-Planck (NP) equation to compute ion transport in the framework of the implicit-water electrolyte model. The difference is that the Poisson-Boltzmann theory is used in the Poisson-Nernst-Planck (PNP) approach, while the Local Equilibrium Monte Carlo (LEMC) method is used in the particle simulation approach (NP+LEMC) to relate the concentration profile to the electrochemical potential profile. Since we consider a bipolar pore which is short and narrow, we perform simulations using two-dimensional PNP. In addition, results of a non-linear version of PNP that takes crowding of ions into account are shown. We observe that the mean field approximation applied in PNP is appropriate to reproduce the basic behavior of the bipolar nanopore (e.g., rectification) for varying parameters of the system (voltage, surface charge, electrolyte concentration, and pore radius). We present current data that characterize the nanopore's behavior as a device, as well as concentration, electrical potential, and electrochemical potential profiles.

A first-principle multiscale modeling approach is presented, which is derived from the solution of the Ornstein-Zernike equation for the coarse-grained representation of polymer liquids. The approach is analytical, and for this reason is transferable. It is here applied to determine the structure of several polymeric systems, which have different parameter values, such as molecular length, monomeric structure, local flexibility, and thermodynamic conditions. When the pair distribution function obtained from this procedure is compared with the results from a full atomistic simulation, it shows quantitative agreement. Moreover, the multiscale procedure accurately captures both large and local scale properties while remaining computationally advantageous.

In this article, we report a theoretical analysis of a nanoelectromechanical shuttle based on a multiscale model that combines microscopic electronic structure data with macroscopic dynamics. The microscopic part utilizes a (static) density functional description to obtain the energy levels and orbitals of the shuttling particle together with the forces acting on the particle. The macroscopic part combines stochastic charge dynamics that incorporates the microscopically evaluated tunneling rates with a Newtonian dynamics. We have applied the multiscale model to describe the shuttling of a single copper atom between two gold-like jellium electrodes. We find that energy spectrum and particle surface interaction greatly influence shuttling dynamics; in the specific example that we studied the shuttling is found to involve only charge states Q=0 and Q=+e. The system is found to exhibit two quasi-stable shuttling modes, a fundamental one and an excited one with a larger amplitude of mechanical motion, with random transitions between them.

We employ a multiscale approach to model the translocation of biopolymers through nanometer size pores. Our computational scheme combines microscopic Molecular Dynamics (MD) with a mesoscopic Lattice Boltzmann (LB) method for the solvent dynamics, explicitly taking into account the interactions of the molecule with the surrounding fluid. We describe an efficient parallel implementation of the method which exhibits excellent scalability on the Blue Gene platform. We investigate both dynamical and statistical aspects of the translocation process by simulating polymers of various initial configurations and lengths. For a representative molecule size, we explore the effects of important parameters that enter in the simulation, paying particular attention to the strength of the molecule-solvent coupling and of the external electric field which drives the translocation process. Finally, we explore the connection between the generic polymers modeled in the simulation and DNA, for which interesting recent experimental results are available.

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.

Our long-term goal is to develop a multiscale nested modeling framework that simulates, with the finest resolution being sub-meter scale, surface mixed layer processes arising from the combined action of tides, winds, and mesoscale currents. We will focus on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves. We aim at understanding the impact of tidal, seasonal, and mesoscale variability of the internal wave field and how it influences the surface waves.

Multiscale mathematical modeling of flows containing particles is conducted in this study using computational fluid dynamics and molecular dynamics. The first study considered continuous media interaction of macro-scale fluid and micro-scale solid particles using computational fluid dynamics and rigid particle dynamics. This study investigates the potential enhancement of heat transfer properties of particulate fluid as well as the effect of injected particles on fluid profiles, and pressure on walls under different particle injection conditions. In the second part of this research, the molecular dynamics simulation was performed to simulate solid-liquid interaction at the molecular level (nanotechnology) to understand their behaviors. The results from two different scales were compared qualitatively.

An early detection and diagnosis of atrial fibrillation sets the course for timely intervention to prevent potentially occurring comorbidities. Electrocardiogram data resulting from electrophysiological cohort modeling and simulation can be a valuable data resource for improving automated atrial fibrillation risk stratification with machine learning techniques and thus, reduces the risk of stroke in affected patients.

We are developing a multiscale framework in computational modeling for the ultra high temperature ceramics (UHTC) ZrB2 and HfB2. These materials are characterized by high melting point, good strength, and reasonable oxidation resistance. They are candidate materials for a number of applications in extreme environments including sharp leading edges of hypersonic aircraft. In particular, we used a combination of ab initio methods, atomistic simulations and continuum computations to obtain insights into fundamental properties of these materials. Ab initio methods were used to compute basic structural, mechanical and thermal properties. From these results, a database was constructed to fit a Tersoff style interatomic potential suitable for atomistic simulations. These potentials were used to evaluate the lattice thermal conductivity of single crystals and the thermal resistance of simple grain boundaries. Finite element method (FEM) computations using atomistic results as inputs were performed with meshes constructed on SEM images thereby modeling the realistic microstructure. These continuum computations showed the reduction in thermal conductivity due to the grain boundary network.

This article is from PLoS Computational Biology , volume 9 . Abstract Influenza A viruses are respiratory pathogens that cause seasonal epidemics with up to 500,000 deaths each year. Yet there are currently only two classes of antivirals licensed for treatment and drug-resistant strains are on the rise. A major challenge for the discovery of new anti-influenza agents is the identification of drug targets that efficiently interfere with viral replication. To support this step, we developed a multiscale model of influenza A virus infection which comprises both the intracellular level where the virus synthesizes its proteins, replicates its genome, and assembles new virions and the extracellular level where it spreads to new host cells. This integrated modeling approach recapitulates a wide range of experimental data across both scales including the time course of all three viral RNA species inside an infected cell and the infection dynamics in a cell population. It also allowed us to systematically study how interfering with specific steps of the viral life cycle affects virus production. We find that inhibitors of viral transcription, replication, protein synthesis, nuclear export, and assembly/release are most effective in decreasing virus titers whereas targeting virus entry primarily delays infection. In addition, our results suggest that for some antivirals therapy success strongly depends on the lifespan of infected cells and, thus, on the dynamics of virus-induced apoptosis or the host's immune response. Hence, the proposed model provides a systems-level understanding of influenza A virus infection and therapy as well as an ideal platform to include further levels of complexity toward a comprehensive description of infectious diseases.

Integrated computational materials engineering (ICME) is a useful approach for tailoring the performance of a material. For fiber-reinforced composites, not only do the properties of the constituents of the composite affect the performance, but so does the architecture (or microstructure) of the constituents. The generalized method of cells is demonstrated to be a viable micromechanics tool for determining the effects of the microstructure on the performance of laminates. The micromechanics is used to predict the inputs for a macroscale model for a variety of different fiber volume fractions, and fiber architectures. Using this technique, the material performance can be tailored for specific applications by judicious selection of constituents, volume fraction, and architectural arrangement given a particular manufacturing scenario

A multiscale modeling strategy is developed to study grain boundary fracture in polycrystalline aluminum. Atomistic simulation is used to model fundamental nanoscale deformation and fracture mechanisms and to develop a constitutive relationship for separation along a grain boundary interface. The nanoscale constitutive relationship is then parameterized within a cohesive zone model to represent variations in grain boundary properties. These variations arise from the presence of vacancies, intersticies, and other defects in addition to deviations in grain boundary angle from the baseline configuration considered in the molecular dynamics simulation. The parameterized cohesive zone models are then used to model grain boundaries within finite element analyses of aluminum polycrystals.

Seminar given to the Redwood Center for Theoretical Neuroscience at UC-Berkeley on March 6, 2008. Speaker is Peter Robinson of the Brain Dynamics Center, Westmead Millenium Institute, Westmead Hospital and Faculty of Medicine, University of Sydney. Abstract: Neural activity in the brain has been observed for over a century and is widely used to probe brain function and disorders, through the electroencephalogram (EEG), functional MRI, and other measures. However, the connections between stimuli, physiology, processing, and measurements have been chiefly qualitative until recently, and most applications of EEG and fMRI have been based on phenomenological correlations. A quantitative model of brain activity is described that includes key features of physiology and anatomy from microscopic synapses to the whole brain. Its parameters measure quantities such as synaptic strengths, signal delays, cellular time constants, and neural ranges, and are all constrained by independent physiological measurements. The model successfully predicts a wide range of EEG and other phenomena, including time series, spectra, evoked responses to stimuli, seizure dynamics, visual gamma (40 Hz) correlations during perception, measurement effects, arousal dynamics, and pharmacological influences. Fitting to experimental data enables physiological parameters to be inferred in normal and abnormal conditions.

The climate change simulation community is moving toward use of global cloud resolving models (CRMs), however, current computational resources are not sufficient to run global CRMs over the hundreds of years necessary to produce climate change estimates. As an intermediate step between conventional general circulation models (GCMs) and global CRMs, many climate analysis centers are embedding a CRM in each grid cell of a conventional GCM. These Multiscale Modeling Frameworks (MMFs) represent a theoretical advance over the use of conventional GCM cloud and convection parameterizations, but have been shown to exhibit an overproduction of precipitation in the tropics during the northern hemisphere summer. In this study, simulations of clouds, precipitation, and radiation over the South China Sea using the CRM component of the NASA Goddard MMF are evaluated using retrievals derived from the instruments aboard the Tropical Rainfall Measuring Mission (TRMM) satellite platform for a 46-day time period that spans 5 May - 20 June 1998. The NASA Goddard Cumulus Ensemble (GCE) model is forced with observed largescale forcing derived from soundings taken during the intensive observing period of the South China Sea Monsoon Experiment. It is found that the GCE configuration used in the NASA Goddard MMF responds too vigorously to the imposed large-scale forcing, accumulating too much moisture and producing too much cloud cover during convective phases, and overdrying the atmosphere and suppressing clouds during monsoon break periods. Sensitivity experiments reveal that changes to ice cloud microphysical parameters have a relatively large effect on simulated clouds, precipitation, and radiation, while changes to grid spacing and domain length have little effect on simulation results. The results motivate a more detailed and quantitative exploration of the sources and magnitude of the uncertainty associated with specified cloud microphysical parameters in the CRM components of MMFs.

This paper has two goals related to the development of a physically-grounded methodology for modeling the initial stages of fatigue crack growth in an aluminum alloy. The aluminum alloy, AA 7075-T651, is susceptible to fatigue cracking that nucleates from cracked second phase iron-bearing particles. Thus, the first goal of the paper is to validate an existing framework for the prediction of the conditions under which the particles crack. The observed statistics of particle cracking (defined as incubation for this alloy) must be accurately predicted to simulate the stochastic nature of microstructurally small fatigue crack (MSFC) formation. Also, only by simulating incubation of damage in a statistically accurate manner can subsequent stages of crack growth be accurately predicted. To maintain fidelity and computational efficiency, a filtering procedure was developed to eliminate particles that were unlikely to crack. The particle filter considers the distributions of particle sizes and shapes, grain texture, and the configuration of the surrounding grains. This filter helps substantially reduce the number of particles that need to be included in the microstructural models and forms the basis of the future work on the subsequent stages of MSFC, crack nucleation and microstructurally small crack propagation. A physics-based approach to simulating fracture should ultimately begin at nanometer length scale, in which atomistic simulation is used to predict the fundamental damage mechanisms of MSFC. These mechanisms include dislocation formation and interaction, interstitial void formation, and atomic diffusion. However, atomistic simulations quickly become computationally intractable as the system size increases, especially when directly linking to the already large microstructural models. Therefore, the second goal of this paper is to propose a method that will incorporate atomistic simulation and small-scale experimental characterization into the existing multiscale framework. At the microscale, the nanoscale mechanics are represented within cohesive zones where appropriate, i.e. where the mechanics observed at the nanoscale can be represented as occurring on a plane such as at grain boundaries or slip planes at a crack front. Important advancements that are yet to be made include: 1. an increased fidelity in cohesive zone modeling; 2. a means to understand how atomistic simulation scales with time; 3. a new experimental methodology for generating empirical models for CZMs and emerging materials; and 4. a validation of simulations of the damage processes at the nano-micro scale. With ever-increasing computer power, the long-term ability to employ atomistic simulation for the prognosis of structural components will not be limited by computation power, but by our lack of knowledge in incorporating atomistic models into simulations of MSFC into a multiscale framework.

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification.

This article is from BMC Medical Informatics and Decision Making , volume 12 . Abstract Background: In this work, we propose a multilevel and multiparametric approach in order to model the growth and progression of oral squamous cell carcinoma (OSCC) after remission. OSCC constitutes the major neoplasm of the head and neck region, exhibiting a quite aggressive nature, often leading to unfavorable prognosis. Methods: We formulate a Decision Support System assembling a multitude of heterogeneous data sources (clinical, imaging tissue and blood genomic), aiming to capture all manifestations of the disease. Our primary aim is to identify the factors that dictate OSCC progression and subsequently predict potential relapses of the disease. The discrimination potential of each source of data is initially explored separately, and afterwards the individual predictions are combined to yield a consensus decision achieving complete discrimination between patients with and without a disease relapse. Moreover, we collect and analyze gene expression data from circulating blood cells throughout the follow-up period in consecutive time-slices, in order to model the temporal dimension of the disease. For this purpose a Dynamic Bayesian Network (DBN) is employed which is able to capture in a transparent manner the underlying mechanism dictating the disease evolvement, and employ it for monitoring the status and prognosis of the patients after remission. Results: By feeding as input to the DBN data from the baseline visit we achieve accuracy of 86%, which is further improved to complete discrimination when data from the first follow-up visit are also employed. Conclusions: Knowing in advance the progression of the disease, i.e. identifying groups of patients with higher/lower risk of reoccurrence, we are able to determine the subsequent treatment protocol in a more personalized manner.

Because of the relatively high specific mechanical properties of carbon fiber/epoxy composite materials, they are often used as structural components in aerospace applications. Graphene nanoplatelets (GNPs) can be added to the epoxy matrix to improve the overall mechanical properties of the composite. The resulting GNP/carbon fiber/epoxy hybrid composites have been studied using multiscale modeling to determine the influence of GNP volume fraction, epoxy crosslink density, and GNP dispersion on the mechanical performance. The hierarchical multiscale modeling approach developed herein includes Molecular Dynamics (MD) and micromechanical modeling, and it is validated with experimental testing of the same hybrid composite material system. The results indicate that the multiscale modeling approach is accurate and provides physical insight into the composite mechanical behavior. Also, the results quantify the substantial impact of GNP volume fraction and dispersion on the transverse mechanical properties of the hybrid composite while the effect on the axial properties is shown to be insignificant.

In this study the effective elastic modulus of cellulose nanocrystal CNC network is evaluated using multiscale method and micromechanical analysis. For this purpose, the elastic modulus of CNC water phases are randomly assigned to a two dimensional 2D checkerboard structure and the elastic response is evaluated. In addition, the effect of having a different number of phases CNC, water and interface is evaluated by assigning a discreet and continuous distribution of elastic modulus to checkerboard structure. When the number of phases increases dramatically, the distribution of phases is continuous and is defined with Weibull distribution. The results show that for two phase materials CNC and water when the microstructure has organized pattern the rule of the mixture and numerical model provide the same effective modulus, however when the microstructure is completely random, the self consistent micromechanical model should be used. Also, this study suggests 50 volume fraction as the percolation threshold for the CNC network with 10 GPa effective elastic modulus. The results from percolated multiphase network reveal that for microstructures with 4 phases and above, the percolated network converge to 35 GPa. By Mehrdad Bor | Jim Huang "Multiscale Modeling Approach for Prediction the Elastic Modulus of Percolated Cellulose Nanocrystal (CNC) Network" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26553.pdf Paper URL https://www.ijtsrd.com/engineering/mechanical-engineering/26553/multiscale-modeling-approach-for-prediction-the-elastic-modulus-of-percolated-cellulose-nanocrystal-cnc-network/mehrdad-bor

This paper examines the role of continuity of the basis in the computation of turbulent flows. We compare standard finite elements and NURBS (non-uniform rational B-splines) discretizations that are employed in Isogeometric Analysis. We make use of quadratic discretizations that are C0-continuous across element boundaries in standard finite elements, and C1-continuous in the case of NURBS. The variational multiscale residual-based method is employed as a turbulence modeling technique. We find that C1-continuous discretizations outperform their C0-continuous counterparts on a per-degree-of- freedom basis. We also find that the effect of continuity is greater for higher Reynolds number flows.

A multiscale modeling approach including molecular dynamics and computational fluid dynamics was carried out address the disparate time and length scales involved in modeling fluid flow and heat transfer. Molecular dynamics simulations were carried out to provide a molecular level understanding of the transport properties of surfactant aqueous solutions; the solvent effects on the solubility of the thermal decomposition reaction products of ammonium carbamate; and the temperature dependence of the accommodation coefficient of liquid octane. Computational fluid dynamics methods were used to investigate the heat transfer process in open-cell micro-foam with phase change material; enhancement of natural convection for fluid media in an enclosure; and thermal effects on vortex-induced vibrations.

This reports on the results of the MURI project on Engineering Microstructrual Complexity in Ferroelectric Devices.

In this article an upscaled model is presented, for complex networks with highly clustered regions exchanging some abstract quantities in both, microscale and macroscale level. Such an intricate system is approximated by a partitioned open map in $\mathbb{R}^{2}$ or $\mathbb{R}^{3}$. The behavior of the quantities is modeled as flowing in the map constructed and thus it is subject to be described by partial differential equations. We follow this approach using the Darcy Porous Media, saturated fluid flow model in mixed variational formulation.

The Colloquium and Workshop on Multiscale Coupled Modeling was held for the purpose of addressing modeling issues of importance to planning for the Cooperative Multiscale Experiment (CME). The colloquium presentations attempted to assess the current ability of numerical models to accurately simulate the development and evolution of mesoscale cloud and precipitation systems and their cycling of water substance, energy, and trace species. The primary purpose of the workshop was to make specific recommendations for the improvement of mesoscale models prior to the CME, their coupling with cloud, cumulus ensemble, hydrology, air chemistry models, and the observational requirements to initialize and verify these models.

A multiscale model was developed to link the hierarchies of human bone in different length scales. Bone has a unique structure displaying large stiffness with minimal weight. This is achieved through a hierarchy of complex geometries composed of only three materials: hydroxyapatite, collagen and water. The identifiable structures of bone are hydroxyapatite, tropocollagen, fibrils, fibers, lamellar layers, trabecular bone, cancellous bone and cortical bone. A spring model was used to evaluate the stiffness of collagen. A unit-cell based micromechanics model analyzed both the normal and shear properties of fibrils, fibers, and lamellar layers. A layered composite model assessed cortical and trabecular bone while a simple finite element model was used to evaluate cancellous bone. Modeling bone from nanoscale components to macroscale structures allows the influence of each structure to be assessed. It was found that the distribution of hydroxyapatite within the tropocollagen matrix at the fibril level influences the macroscale properties the most. Additionally, the model allows perturbations to the geometry of any hierarchy to be analyzed. With so little known about the detailed structure of nanoscale and microscale bone, a model comprising the complete hierarchy of bone can be used to help validate assumptions or hypotheses about structure.

A multiscale model was developed to link the hierarchies of human bone in different length scales. Bone has a unique structure displaying large stiffness with minimal weight. This is achieved through a hierarchy of complex geometries composed of only three materials: hydroxyapatite, collagen and water. The identifiable structures of bone are hydroxyapatite, tropocollagen, fibrils, fibers, lamellar layers, trabecular bone, cancellous bone and cortical bone. A spring model was used to evaluate the stiffness of collagen. A unit-cell based micromechanics model analyzed both the normal and shear properties of fibrils, fibers, and lamellar layers. A layered composite model assessed cortical and trabecular bone while a simple finite element model was used to evaluate cancellous bone. Modeling bone from nanoscale components to macroscale structures allows the influence of each structure to be assessed. It was found that the distribution of hydroxyapatite within the tropocollagen matrix at the fibril level influences the macroscale properties the most. Additionally, the model allows perturbations to the geometry of any hierarchy to be analyzed. With so little known about the detailed structure of nanoscale and microscale bone, a model comprising the complete hierarchy of bone can be used to help validate assumptions or hypotheses about structure.

This document summarizes research done during the period June 14, 1989 through December 14, 1991 on a project aimed at the development of advanced computational methods for modeling multiscale fluid-structure interaction phenomena. The major thrust of the work reported is the development of the component parts of a new family of computational schemes that could be used to study large-scale problems in fluid-structure interaction. The overall theme of the project was the optimization of the computational process through the development of new adaptive techniques, data structures, a posteriori error estimates, and high-order solvers. The premise behind studying these types of high-order methods is that, with proper data structures, they could lead to exponential rates of convergence and thereby allow one to numerically solve very large problems, with features covering many different physical scales, using many fewer degrees of freedom than that required by conventional methods. In this spirit, the project was an ambitious one for it involved developing not only new adaptive algorithms for simulating the motion of elastic structures, but also techniques for fluid structure interaction and for modeling various regimes of incompressible viscous flows. Presumably, these methods could also be used to model the transition to turbulence and ultimately turbulent boundary layers on compliant surfaces.

We discuss the implementation of a multiscale biophysico-chemical model able to cope with the main mechanisms underlying cumulative exocytosis in cells. The model is based on a diffusion equation in the presence of external forces that links calcium signaling and the biochemistry associated to the activity of cytoskeletal-based protein motors. This multiscale model offers an excellent quantitative spatio-temporal description of the cumulative exocytosis measured by means of fluorescence experiments. We also review pre-existing models reported in the literature on calcium waves, protein motor activation and dynamics, and intracellular directed transport of vesicles. As an example of the proposed model, we analyze the formation of the shield against polyspermy in the early events of fertilization in sea urchin eggs.

The surface of skin is lined with several thin layers of epithelial cells that are maintained throughout life time by a small population of stem cells. High dose radiation exposures could injure and deplete the underlying proliferative cells and induce cutaneous radiation syndrome. In this work we propose a multiscale computational model for skin epidermal dynamics that links phenomena occurring at the subcellular, cellular, and tissue levels of organization, to simulate the experimental data of the radiation response of swine epidermis, which is closely similar to human epidermis. Incorporating experimentally measured histological and cell kinetic parameters, we obtain results of population kinetics and proliferation indexes comparable to observations in unirradiated and acutely irradiated swine experiments. At the sub-cellular level, several recently published Wnt signaling controlled cell-cycle models are applied and the roles of key components and parameters are analyzed. Based on our simulation results, we demonstrate that a moderate increase of proliferation rate for the survival proliferative cells is sufficient to fully repopulate the area denuded by high dose radiation, as long as the integrity of underlying basement membrane is maintained. Our work highlights the importance of considering proliferation kinetics as well as the spatial organization of tissues when conducting in vivo investigations of radiation responses. This integrated model allow us to test the validity of several basic biological rules at the cellular level and sub-cellular mechanisms by qualitatively comparing simulation results with published research, and enhance our understanding of the pathophysiological effects of ionizing radiation on skin.

A mesh objective crack band model was implemented within the generalized method of cells micromechanics theory. This model was linked to a macroscale finite element model to predict post-peak strain softening in composite materials. Although a mesh objective theory was implemented at the microscale, it does not preclude pathological mesh dependence at the macroscale. To ensure mesh objectivity at both scales, the energy density and the energy release rate must be preserved identically across the two scales. This requires a consistent characteristic length or localization limiter. The effects of scaling (or not scaling) the dimensions of the microscale repeating unit cell (RUC), according to the macroscale element size, in a multiscale analysis was investigated using two examples. Additionally, the ramifications of the macroscale element shape, compared to the RUC, was studied.

To aid in the design of surfaces that prevent icing, a model and computational simulation of impact ice formation at the single droplet scale was implemented. The nucleation of a single supercooled droplet impacting on a substrate, in rime ice conditions, was simulated. Open source computational fluid dynamics (CFD) software was used for the simulation. To aid in the design of surfaces that prevent icing, a model of impact ice formation at the single droplet scale was proposed•No existing model simulates simultaneous impact and freezing of a single super-cooled water droplet•For the 10-week project, a low-fidelity feasibility study was the goal.

To aid in the design of surfaces that prevent icing, a model and computational simulation of impact ice formation at the single droplet scale was implemented. The nucleation of a single supercooled droplet impacting on a substrate, in rime ice conditions, was simulated. Open source computational fluid dynamics (CFD) software was used for the simulation. To aid in the design of surfaces that prevent icing, a model of impact ice formation at the single droplet scale was proposed•No existing model simulates simultaneous impact and freezing of a single super-cooled water droplet•For the 10-week project, a low-fidelity feasibility study was the goal.

To aid in the design of surfaces that prevent icing, a model and computational simulation of impact ice formation at the single droplet scale was implemented. The nucleation of a single supercooled droplet impacting on a substrate, in rime ice conditions, was simulated. Open source computational fluid dynamics (CFD) software was used for the simulation. To aid in the design of surfaces that prevent icing, a model of impact ice formation at the single droplet scale was proposed•No existing model simulates simultaneous impact and freezing of a single super-cooled water droplet•For the 10-week project, a low-fidelity feasibility study was the goal.

Multiscale mathematical modeling of flows containing particles is conducted in this study using computational fluid dynamics and molecular dynamics. The first study considered continuous media interaction of macro-scale fluid and micro-scale solid particles using computational fluid dynamics and rigid particle dynamics. This study investigates the potential enhancement of heat transfer properties of particulate fluid as well as the effect of injected particles on fluid profiles, and pressure on walls under different particle injection conditions. In the second part of this research, the molecular dynamics simulation was performed to simulate solid-liquid interaction at the molecular level (nanotechnology) to understand their behaviors. The results from two different scales were compared qualitatively.

An established multiscale model for materials is used as the basis for a failure model for fiber composites. The model’s computation is explained so that its results can be used to formulate the inputs to the failure model. The failure model proposed employs homogenization and disaggregation methods that are enabled by micro-scale modeling of the material’s constituents. This failure model is then used to define strength reductions in the composite at the micro-level. The strength reductions enable the definition of a progressive failure methodology for application to the micro-scale, and ultimately, the macro-scale composite. The failure model, the degradation model, and the multi-scale model they are based upon are combined in a computational program for inclusion in finite element software for efficient solving and prediction of intact and failed composite structural response. The model is then tested against existing experimental data as well as by experiments conducted by the author.

Both discrete and continuum models have been widely used to study rapid granular flow, discrete model is accurate but computationally expensive, whereas continuum model is computationally efficient but its accuracy is doubtful in many situations. Here we propose a hybrid discrete-continuum method to profit from the merits but discard the drawbacks of both discrete and continuum models. Continuum model is used in the regions where it is valid and discrete model is used in the regions where continuum description fails, they are coupled via dynamical exchange of parameters in the overlap regions. Simulation of granular channel flow demonstrates that the proposed hybrid discrete-continuum method is nearly as accurate as discrete model, with much less computational cost.

The purpose of the work funded by this grant was to study and model complex phenomena by using an approach that makes use of multiscale time sequences. The underlying idea is that a complex dynamical system can be better interpreted and modeled by taking into account how its dynamics behaves at different scales and how these scales relate to each other. This can be done by combining a set statistical fractal measures based on Hurst and Holder exponents, auto-regressive methods and Fourier and wavelet decomposition methods. The applications for this technology include mathematical algorithms to model and predict geophysical phenomena such as climate and weather patterns as well as biological/biomedical phenomena such as, for example, for the treatment of injured individuals.

We are developing a multiscale framework in computational modeling for the ultra high temperature ceramics (UHTC) ZrB2 and HfB2. These materials are characterized by high melting point, good strength, and reasonable oxidation resistance. They are candidate materials for a number of applications in extreme environments including sharp leading edges of hypersonic aircraft. In particular, we used a combination of ab initio methods, atomistic simulations and continuum computations to obtain insights into fundamental properties of these materials. Ab initio methods were used to compute basic structural, mechanical and thermal properties. From these results, a database was constructed to fit a Tersoff style interatomic potential suitable for atomistic simulations. These potentials were used to evaluate the lattice thermal conductivity of single crystals and the thermal resistance of simple grain boundaries. Finite element method (FEM) computations using atomistic results as inputs were performed with meshes constructed on SEM images thereby modeling the realistic microstructure. These continuum computations showed the reduction in thermal conductivity due to the grain boundary network.

Because of the relatively high specific mechanical properties of carbon fiber/epoxy composite materials, they are often used as structural components in aerospace applications. Graphene nanoplatelets (GNPs) can be added to the epoxy matrix to improve the overall mechanical properties of the composite. The resulting GNP/carbon fiber/epoxy hybrid composites have been studied using multiscale modeling to determine the influence of GNP volume fraction, epoxy crosslink density, and GNP dispersion on the mechanical performance. The hierarchical multiscale modeling approach developed herein includes Molecular Dynamics (MD) and micromechanical modeling, and it is validated with experimental testing of the same hybrid composite material system. The results indicate that the multiscale modeling approach is accurate and provides physical insight into the composite mechanical behavior. Also, the results quantify the substantial impact of GNP volume fraction and dispersion on the transverse mechanical properties of the hybrid composite, while the effect on the axial properties is shown to be insignificant.

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.

Talk by Ekaterina Brocke, KTH University, Stockholm, Sweden. Given to the Redwood Center for Theoretical Neuroscience at UC Berkeley. Abstract Multiscale modeling/simulations attracts an increasing number of neuroscientists to study how different levels of organization (networks of neurons, cellular/subcellular levels) interact with each other across multiple scales, space and time, to mediate different brain functions. Different scales are usually described by different physical and mathematical formalisms thus making it non trivial to perform the integration. In this talk, I will discuss key phenomena in Neuroscience that can be addressed using subcellular/cellular models, possible approaches to perform multiscale simulations in particular a co-simulation method. I will also introduce several multiscale "toy" models of cellular/subcellular levels that were developed with the aim to understand numerical and technical problems which might appear during the co-simulation. And finally, the first steps made towards multiscale co-simulation tool development will be presented during the talk.

A simulation framework was developed for studying the deformation behavior of metallic materials. Atomistic simulations were employed to study dislocation nucleation during nanoindentation and to correlate dislocation behavior and overall material response in thin-film crystals. An instrumented indenter was acquired to study the indentation behavior of metallic composites. Experimental and continuum- based modeling works on indentation of discontinuously reinforced metal matrix composites were also conducted. Detailed microscopic features were analyzed, which aided in our fundamental understanding of plastic deformation in these materials.

The development of the solidified microstructure in metal-matrix composites depends on complex interactions between non-planar solidification fronts and multiple particles. The problem is multiscale in nature; the motion of the particle (under the action of a nano-scale disjoining pressure force and a micro-scale viscous drag force) is dynamically coupled with the developing solidification front morphology, which is dependent on a variety of thermal conditions. Using computational techniques discussed in parts I and II, this paper seeks to describe the complicated nonlinear parametric dependencies of the phenomenon. The effects of four of the most important parameters in the particle-solidification front interaction are investigated, i.e. the Hamaker constant, the particle size, the thermal conductivity ratio of the particle to the melt, and the solid-liquid interfacial free energy. By performing simulations using the multiscale approach the dependencies of the critical velocity on these four parameters is clarified.

The development of protective and breathable clothing is a very important goal set for the Future Force. Recently, a new polymer membrane made of an ionic triblock (A-B-A) copolymer was developed at the U.S. Army Research Laboratory (ARL) that provides an excellent selective barrier for soldier s protective clothing. We have used multiscale modeling to gain an understanding of the static and dynamic properties of this polymer membrane at detailed atomistic and mesoscale levels. These simulations lead to the prediction of the architecture and morphology of the membrane. We have also studied mesoscale morphology of the copolymer constrained by a surface or the nanopore. Mechanical properties of copolymer were calculated using the self-consistent homogenization theory.

Multiscale modeling at small length scales (10(exp -9) to 10(exp -3) m) is discussed for aluminum matrices with embedded particles. A configuration containing one particle surrounded by about 50 grains and subjected to uniform tension and lateral constraint is considered. The analyses are performed to better understand the effects of material configuration on the initiation and progression of debonding of the particles from the surrounding aluminum matrix. Configurational parameters considered include particle aspect ratio and orientation within the surrounding matrix. Both configurational parameters are shown to have a significant effect on the behavior of the materials as a whole. For elliptical particles with the major axis perpendicular to the direction of loading, a particle with a 1:1 aspect ratio completely debonds from the surrounding matrix at higher loads than particles with higher aspect ratios. As the particle major axis is aligned with the direction of the applied load, increasing amounts of load are required to completely debond the particles.

Developed a method for multiscale analysis of genomic data. This method can be used to decompose high-throughput gene expression into natural clusters at different scales or resolution, thereby facilitating models that can interrogate disease using molecular profiling.

This grant was used to support the organization of the international conference Multiscale Materials Modeling: Mathematical and Computational Aspects at Rensselaer Polytechnic Institute, during the period June 10-12, 2014. The conference was organized under the auspices of the International Center for Applied Computational Mechanics (ICACM) and is the 8th meeting organized in this series. The conference brought together researchers from US, France and Canada working on various aspects of physics-based multiscale modeling of the mechanical behavior of materials. The details of the organization are presented in this report along with outcomes of the meeting relevant for the future directions in this field.