Two multiscale continuum models for simulating protein dynamics are developed which allow for resolution of protein peptide planes in a beam-like finite element. A curvature and strain based finite element formulation is utilized. This formulation is advantageous in simulating proteins since amino acid chains may be described by a single element, even when the protein segment considered exhibits large curvature and twist such as the alpha-helical shapes prominent in many proteins. Specifically, concurrent and hierarchical multiscale models are developed for the curvature and strain based beam formulation. The hierarchical multiscale continuum model utilizes a novel shooting method to calculate the deformed configuration of the protein. An optimization algorithm determines the requisite stiffness parameters by varying the beam stiffness used in the shooting method until deformed configurations of test cases correspond to those produced by the LAMMPS molecular dynamics software. Additionally, a concurrent multiscale method is detailed for evaluating protein inter-atomic potential parameters from the curvature and strain degrees of freedom employed in the model. This allows internal forces and moments to be calculated using nonlinear protein potentials. Proof of concept testing and model verification for both models includes comparing the multiscale techniques to all-atom molecular dynamics solutions. Specifically, the models are verified by simulating a polypeptide in a vacuum and comparing the predicted results to those computed using LAMMPS.

The analysis of wave propagation in solids with complex microstructures, and local heterogeneities finds extensive applications in areas such as material characterization, structural health monitoring (SHM), and metamaterial design. Within continuum mechanics, sources of heterogeneities are typically associated to localized defects in structural components, or to periodic microstructures in phononic crystals and acoustic metamaterials. Numerical analysis often requires computational meshes which are refined enough to resolve the wavelengths of deformation and to properly capture the fine geometrical features of the heterogeneities. It is common for the size of the microstructure to be small compared to the dimensions of the structural component under investigation, which suggests multiscale analysis as an effective approach to minimize computational costs while retaining predictive accuracy. This research proposes a multiscale framework for the efficient analysis of the dynamic behavior of heterogeneous solids. The developed methodology, called Geometric Multiscale Finite Element Method (GMsFEM), is based on the formulation of multi-node elements with numerically computed shape functions. Such shape functions are capable to explicitly model the geometry of heterogeneities at sub-elemental length scales, and are computed to automatically satisfy compatibility of the solution across the boundaries of adjacent elements. Numerical examples illustrate the approach and validate it through comparison with available analytical and numerical solutions. The developed methodology is then applied to the analysis of periodic media, structural lattices, and phononic crystal structures. Finally, GMsFEM is exploited to study the interaction of guided elastic waves and defects in plate structures.

International Telemetering Conference Proceedings / October 25-28, 1999 / Riviera Hotel and Convention Center, Las Vegas, Nevada / In this paper, we extended the matched filter bound (MFB) of time-discrete multipath Rayleigh fading channels derived in [1,2] for multiscale wavelet signaling communication.

Single ventricle heart defects are present in two of every 1000 live births in the US. In this condition the systemic and pulmonary blood flow mix in the functioning ventricle, resulting in insufficient blood oxygenation to sustain life. As part of the palliation of these defects, the staged surgical procedure, known as the Fontan procedure, is performed. Here, the venous returns are directed to the pulmonary arteries, bypassing the right heart and forming the Total Cavopulmonary Connection (TCPC). Even though the palliation improves life expectancy, there are numerous long-term complications that become more prevalent as patients reach adulthood. Many of these complications have been related to the function of the single ventricle circulation, especially to the abnormal TCPC hemodynamics, for which this has been the focus of research throughout the years. Recent progress has been made with the availability of improved medical imaging techniques and computational modeling tools; however, there is limited information on how these evolve in time. In order to improve the Fontan palliation, image-based surgical planning has been used in the most complex cases to prospectively design the TCPC, aiming to improve the hemodynamics. Even though this paradigm has shown promising results, improvement is needed to provide more realistic predictions of the post-operative outcomes. To address this, in this thesis we have developed a novel surgical planning framework that allows us to: (i) model the interaction of the TCPC and global circulation hemodynamics, and (ii) assess the robustness of the surgical option proposed. Here, the single ventricle circulation is modeled using a lumped parameter model, coupled to a computational fluid solver to describe the local TCPC hemodynamics. With this framework, we can predict the immediate post-operative state, model various physiological scenarios, and assess the impact on the local hemodynamics and global circulation. This will allow us to provide information on the effect on the global hemodynamics to the clinical team. In addition to the surgical planning advancements obtained in this thesis, we have performed the largest longitudinal Fontan study to date in which we have evaluated the evolution of the Fontan physiology in time and the effect it has on the energy efficiency of the TCPC. In this thesis, we have studied the short and long-term effects that geometrical and physiological changes have on the Fontan hemodynamics. With this, we have improved the understanding of the Fontan physiology in terms of the short-term effects of Fontan palliation and the long-term deterioration of the changing single ventricle physiology.

Modeling of engineering objects with complex heterogeneous material structure at nanoscale level has emerged as an important research problem. In this research, we are interested in multiscale modeling and analysis of mechanical properties of the polymer structures created in the Step and Flash Imprint Lithography (SFIL) process. SFIL is a novel imprint lithography process designed to transfer circuit patterns for fabricating microchips in low-pressure and room-temperature environments. Since the smallest features in SFIL are only a few molecules across, approximating them as a continuum is not completely accurate. Previous research in this subject has dealt with coupling discrete models with continuum hyperelasticity models. The modeling of the post-polymerization step in SFIL involves computing solutions of large nonlinear energy minimization problems with fast spatial variation in material properties. An equilibrium configuration is found by minimizing the energy of this heterogeneous polymeric lattice. Numerical solution of such a molecular statics base model, which is assumed to describe the microstructure completely, is computationally very expensive. This is due to the problem size – on the order of millions of degrees of freedom (DOFs). Rapid variation in material properties, ill-conditioning, nonlinearity, and non-convexity make this problem even more challenging to solve. We devise a method for efficient approximation of the solution. Combining numerical homogenization, adaptive finite element meshes, and goaloriented error estimation, we develop a black-box method for efficient solution of problems with multiple spatial scales. The purpose of this homogenization method is to reduce the number of DOFs, find locally optimal effective material properties, and do goal-oriented mesh refinement. In addition, it smoothes the energy landscape. Traditionally, a finite element mesh is designed after obtaining material properties in different regions. The mesh has to resolve material discontinuities and rapid variations. In our approach, however, we generate a sequence of coarse meshes (possibly 1-irregular), and homogenize material properties on each coarse mesh element using a locally posed constrained convex quadratic optimization problem. This upscaling is done using Moore-Penrose pseudoinverse of the linearized fine-scale element stiffness matrices, and a material independent interpolation operator. This requires solution of a continuous-time Lyapunov equation on each element. Using the adjoint solution, we compute local error estimates in the quantity of interest. The error estimates also drive the automatic mesh adaptivity algorithm. The results show that this method uses orders of magnitude fewer degrees of freedom to give fast and approximate solutions of the original fine-scale problem. Critical to the computational speed of local homogenization is computing Moore-Penrose pseudoinverse of rank-deficient matrices without using Singular Value Decomposition. To this end, we use four algorithms, each having different desirable features. The algorithms are based on Tikhonov regularization, sparse QR factorization, a priori knowledge of the null-space of the matrix, and iterative methods based on proper splittings of matrices. These algorithms can exploit sparsity and thus are fast. Although the homogenization method is designed with a specific molecular statics problem in mind, it is a general method applicable for problems with a given fine mesh that sufficiently resolves the fine-scale material properties. We verify the method using a conductivity problem in 2-D, with chessboard like thermal conductivity pattern, which has a known homogenized conductivity. We analyze other aspects of the homogenization method, for example the choice of norm in which we measure local error, optimum coarse mesh element size for homogenizing SFIL lattices, and the effect of the method chosen for computing the pseudoinverse. / text

Receptor tyrosine kinases (RTKs) are a major class of cell surface receptors, important in cell signalling events associated with a variety of functions. High-throughput (HTP), coarse-grained molecular dynamics (CG-MD) simulations have been used to investigate the dimerization of the transmembrane (TM) domain of selected RTKs, including epidermal growth factor receptor (EGFR) and muscle-specific kinase (MuSK). EGFR activation requires not only a specific TM dimer interface, but also a proper orientation of its juxtamembrane (JM) domain. Phosphatidylinositol 4,5-bisphosphate (PIP₂) is known to abolish EGFR phosphorylation through interaction with basic residues within the JM domain. Here, a multiscale approach was used to investigate anionic lipid clustering around the TM-JM junction and how such clustering is modulated by the mutation of basic residues. The simulations demonstrated that PIP₂ may help stabilize the JM-A antiparallel dimer, which may in turn help stabilize TM domain helix packing of the N-terminal dimerization motif. A proximal TM domain residue has been implicated in the inhibition of ganglioside GM3 in phase-separated membranes. Here, CG simulations were used to explore the dynamic behaviour of the EGFR TM domain dimer in GM3-containing and GM3-depleted bilayers designed to resemble lipid-disordered (Ld) and phase-separated (Ld/Lo) membranes. The simulations suggest that the presence of GM3 in Ld/Lo bilayers can disrupt and destabilize the TM dimer, which helps to explain why GM3 may favour monomeric EGFR in vivo. To gain insights into the dynamic nature of the intact EGFR, a nearly complete EGFR dimer was modelled using available structural data and embedded in an asymmetric compositional complex bilayer, which resembles the mammalian plasma membrane. The results demonstrated the dynamic nature of the EGFR ectodomain and its predicted interactions with lipids in the local bilayer. Strong protein-lipid interactions, as well as lipid-lipid interactions, affect the local clustering of lipids and the diffusion of lipids in the vicinity of the protein on both leaflets.

Multiscale (analytical and computational) models have been developed based on a thermodynamic variational principle (TVP) to model sintering and eventual mudcracking in thermal barrier coatings (TBCs) made using the electron beam physical vapour deposition (EB-PVD) process. It is assumed that the sintering occurs by interfacial diffusion at local contacts between columns and driven by changes in interface free energy and elastic stored energy of the coating. The models link diffusional processes at the scale of contacting feathery columns with the macroscopic deformation and sintering response. In service, the columns can come into contact and sinter together. As sintering progresses there is a build up of strain energy in the system which reduces the driving force for sintering and leads to either complete or incomplete sintering of the TBC depending on the magnitude of effective modulus (E) of the coating. By seeding the coating with initial imperfections, different types of behaviour are observed depending on the value of E and the spacing between imperfections. For compliant coatings, the response is insensitive to the presence of imperfections and the coating fully sinters. At higher values of E, strain energy is released by the development of intercolumnar cracks in the coating, which can propagate to the interface with the TGO (thermally grown oxide), deflect into the interface and propagate, leading to spallation of regions of the coating and loss of thermal protection. It is observed that cracks develop at initial imperfections in the structure. The greater the spacing between imperfections the faster the development of cracks at these locations. If a TBC contains a distribution of imperfections there is progressive formation of cracks, with the average spacing decreasing with time, after an initial incubation period. The crack density eventually saturates to a constant value, which depends on the mechanical properties of the TBC. Initially, a crack spacing, CS, in the range 1.5H ≤ CS ≤ 3H has been predicted based on trapezoidal contact models. Here H is the thickness of the coating. Crack spacing predicted using this model is consistent in the lower range of experimentally observed crack spacing. However, axisymmetric contact models predict a crack spacing, CS, in the range 4H ≤ CS ≤ 8H, which is in good agreement with experimentally observed crack spacing range 3H ≤ CS ≤ 10H reported in the literature. Compared to the trapezoidal contact models, axisymmetric contact models more accurately predict the sintering response.

<p>Domain decomposition method provides a solution for the very large electromagnetic</p><p>system which are impossible for single domain methods. Discontinuous Galerkin</p><p>(DG) method can be viewed as an extreme version of the domain decomposition,</p><p>i.e., each element is regarded as one subdomain. The whole system is solved element</p><p>by element, thus the inversion of the large global system matrix is no longer necessary,</p><p>and much larger system can be solved with the DG method compared to the</p><p>continuous Galerkin (CG) method.</p><p>In this work, the DG method is implemented on a subdomain level, that is, each subdomain contains multiple elements. The numerical flux only applies on the</p><p>interfaces between adjacent subdomains. The subodmain level DG method divides</p><p>the original large global system into a few smaller ones, which are easier to solve,</p><p>and it also provides the possibility of parallelization. Compared to the conventional</p><p>element level DG method, the subdomain level DG has the advantage of less total</p><p>DoFs and fexibility in interface choice. In addition, the implicit time stepping is </p><p>relatively much easier for the subdomain level DG, and the total CPU time can be</p><p>much less for the electrically small or multiscale problems.</p><p>The hybrid of elements are employed to reduce the total DoF of the system.</p><p>Low-order tetrahedrons are used to catch the geometry ne parts and high-order</p><p>hexahedrons are used to discretize the homogeneous and/or geometry coarse parts.</p><p>In addition, the non-conformal mesh not only allow dierent kinds of elements but</p><p>also sharp change of the element size, therefore the DoF can be further decreased.</p><p>The DGTD method in this research is based on the EB scheme to replace the</p><p>previous EH scheme. Dierent from the requirement of mixed order basis functions</p><p>for the led variables E and H in the EH scheme, the EB scheme can suppress the</p><p>spurious modes with same order of basis functions for E and B. One order lower in</p><p>the basis functions in B brings great benets because the DoFs can be signicantly</p><p>reduced, especially for the tetrahedrons parts.</p><p>With the basis functions for both E and B, the EB scheme upwind </p><p>ux and</p><p>EB scheme Maxwellian PML, the eigen-analysis and numerical results shows the</p><p>eectiveness of the proposed DGTD method, and multiscale problems are solved</p><p>eciently combined with the implicit-explicit hybrid time stepping scheme and multiple</p><p>kinds of elements.</p><p>The EB scheme DGTD method is further developed to allow arbitrary anisotropic</p><p>media via new anisotropic EB scheme upwind </p><p>ux and anisotropic EB scheme</p><p>Maxwellian PML. The anisotropic M-PML is long time stable and absorb the outgoing</p><p>wave eectively. A new TF/SF boundary condition is brought forward to</p><p>simulate the half space case. The negative refraction in YVO4 bicrystal is simulated</p><p>with the anisotropic DGTD and half space TF/SF condition for the rst time with</p><p>numerical methods.</p> / Dissertation

Flexible pipes are essential components in the subsea oil and gas industry, where they are used to convey fluids under conditions of extreme external pressure and (often) axial load, while retaining low bending stiffness. This is made possible by their complex internal structure, consisting of unbonded components that are, to a certain extent, free to move internally relative to each other. Due to the product's high value and high cost of testing facilities, much e ort has been invested in the development of analytical and numerical models for simulating flexible pipe behaviour, which includes bulk response to various loading actions, calculation of component stresses and use of this data for component fatigue calculations. In this work, it is proposed that the multi-scale methods currently in widespread use for the modelling of composite materials can be applied to the modelling of flexible pipe. This allows the large-scale dynamics of an installed pipe (often several kilometers in length) to be related to the behaviour of its internal components (with characteristic lengths in millimeters). To do this, a formal framework is developed for an extension of the computational homogenisation procedure that allows multiscale models to be constructed in which models at both the large and small scales are composed of different structural elements. Within this framework, a large-scale flexible pipe model is created, using a two-dimensional corotational beam formulation with a constitutive model representative of flexible pipe bulk behaviour, which was obtained by further development of a recently proposed formulation inspired by the analogy between the flexible pipe structural behaviour and that of plastic materials with non-associative flow rules. A three-dimensional corotational formulation is also developed. The model is shown to perform adequately for practical analyses. Next, a detailed finite element (FE) model of a flexible pipe was created, using shell finite elements, generalised periodic boundary conditions and an implicit solution method. This model is tested against two analytical flexible pipe models for several basic load cases. Finally, the two models are used to carry out a sequential multi-scale analysis, in which a set of simulations using the detailed FE model is carried out in order to find the most appropriate coefficients for the large-scale model.

Pas de résumé / Fluidized beds are a particular hydrodynamic configuration in which a pack (either dense or loose) of particles laid inside a container is re-suspended as a result of an upward oriented imposed flow at the bottom of the pack. This kind of system is widely used in the chemical engineering industry where catalytic cracking or polymerization processes involve chemical reactions between the catalyst particles and the surrounding fluid and fluidizing the bed is admittedly beneficial to the efficiency of the process. Due to the wide range of spatial scales and complex features of solid/solid and solid/fluid interactions in a dense fluidized bed, the system can be studied at different length scales, namely micro, meso and macro. In this work we focus on micro/meso simulations of fluidized beds. The workflow we use is based on home made high-fidelity numerical tools: GRAINS3D (Pow. Tech., 224:374-389, 2012) for granular dynamics of convex particles and PeliGRIFF (Parallel Efficient LIbrary for GRains In Fluid Flows, Comp. Fluids, 38(8):1608-1628,2009) for reactive fluid/solid flows. The objectives of our micro/meso simulations of such systems are two-fold: (i) to understand the multi-scale features of the system from a hydrodynamic standpoint and (ii) to analyze the performance of our meso-scale numerical model and to improve it accordingly. To this end, we first perform Particle Resolved Simulations (PRS) of liquid/solid and gas/solid fluidization of a 2000 particle system. The accuracy of the numerical results is examined by assessing the space convergence of the computed solution in order to guarantee that our PRS results can be reliably considered as a reference solution for this problem. The computational challenge for our PRS is a combination of a fine mesh to properly resolve all flow length scales to a long enough physical simulation time in order to extract time converged statistics. For that task, High Performance Computing and highly parallel codes as GRAINS3D/PeliGRIFF are extremely helpful. Second, we carry out a detailed cross-comparison of PRS results with those of locally averaged Euler- Lagrange simulations. Results show an acceptable agreement between the micro- and meso-scale predictions on the integral measures as pressure drop, bed height, etc. However, particles fluctuations are remarkably underpredicted by the meso-scale model, especially in the direction transverse to the main flow. We explore different directions in the improvement of the meso-scale model, such as (a) improving the inter-phase coupling scheme and (b) introducing a stochastic formulation for the drag law derived from the PRS results. We show that both improvements (a) and (b) are required to yield a satisfactory match of meso-scale results with PRS results. The new stochastic drag law, which incorporates information on the first and second-order moments of the PRS results, shows promises to recover the appropriate level of particles fluctuations. It now deserves to be validated on a wider range of flow regimes.