Eulerian method for multiphase interactions of soft solid bodies in fluids

We introduce an Eulerian approach for problems involving one or more soft solids immersed in a fluid, which permits mechanical interactions between all phases. The reference map variable is exploited to simulate finite-deformation constitutive relations in the solid(s) on the same fixed grid as the fluid phase, which greatly simplifies the coupling between phases. Our coupling procedure, a key contribution in the current work, is shown to be computationally faster and more stable than an earlier approach, and admits the ability to simulate both fluid--solid and solid--solid interaction between submerged bodies. The interface treatment is demonstrated with multiple examples involving a weakly compressible Navier--Stokes fluid interacting with a neo-Hookean solid, and we verify the method's convergence. The solid contact method, which exploits distance-measures already existing on the grid, is demonstrated with two examples. A new, general routine for cross-interface extrapolation is introduced and used as part of the new interfacial treatment

A Nonlinear Computational Model of Floating Wind Turbines

The dynamic motion of floating wind turbines is studied using numerical simulations. Floating wind turbines in the deep ocean avoid many of the concerns with land-based wind turbines while allowing access to strong stable winds. The full three-dimensional Navier-Stokes equations are solved on a regular structured grid, using a level set method for the free surface and an immersed boundary method for the turbine platform. The tethers, the tower, the nacelle and the rotor weight are included using reduced order dynamic models, resulting in an efficient numerical approach which can handle nearly all the nonlinear wave forces on the platform, while imposing no limitation on the platform motion. Wind is modeled as a constant thrust force and rotor gyroscopic effects are accounted for. Other aerodynamic loadings and aero-elastic effects are not considered. Several tests, including comparison with other numerical, experimental and grid study tests, have been done to validate and verify the numerical approach. Also for further validation, a 100:1 scale model Tension Leg Platform (TLP) floating wind turbine has been simulated and the results are compared with water flume experiments conducted by our research group. The model has been extended to full scale systems and the response of the tension leg and spar buoy floating wind turbines has been studied. The tension leg platform response to different amplitude waves is examined and for large waves a nonlinear trend is seen. The nonlinearity limits the motion and shows that the linear assumption will lead to over prediction of the TLP response. Studying the flow field behind the TLP for moderate amplitude waves shows vortices during the transient response of the platform but not at the steady state, probably due to the small Keulegan-Carpenter number. The effects of changing the platform shape are considered and finally the nonlinear response of the platform to a large amplitude wave leading to slacking of the tethers is simulated. For the spar buoy floating wind turbine, the response to regular periodic waves is studied first. Then, the model is extended to irregular waves to study the interaction of the buoy with more realistic sea state. The results are presented for a harsh condition, in which waves over 17 m are generated, and linear models might not be accurate enough. The results are studied in both time and frequency domain without relying on any experimental data or linear assumption. Finally a design study has been conducted on the spar buoy platform to study the effects of tethers position, tethers stiffness, and platform aspect ratio, on the response of the floating wind turbine. It is shown that higher aspect ratio platforms generally lead to lower mean pitch and surge responses, but it may also lead to nonlinear trend in standard deviation in pitch and heave, and that the tether attachment points design near the platform center of gravity generally leads to a more stable platform in comparison with attachment points near the tank top or bottom of the platform

Modeling the Response of Premixed Flames to Flow Disturbances

Modeling the Response of Premixed Flames to Flow Disturbances Preetham 178 pages Directed by Dr. Tim Lieuwen Low emissions combustion systems for land based gas turbines rely on a premixed or partially premixed combustion process. These systems are exceptionally prone to combustion instabilities which are destructive to hardware and adversely affect performance and emissions. The success of dynamics prediction codes is critically dependent on the heat release model which couples the flame dynamics to the system acoustics. So the principal objective of the current research work is to predict the heat release response of premixed flames and to isolate the key non-dimensional parameters which characterize its linear and nonlinear dynamics. Explicit analytical solutions of the G- equation are derived in the linear and weakly nonlinear regime using the Small Perturbation Method (SPM). For the fully nonlinear case, the flame-flow interaction effects are captured by developing an unsteady, compressible, coupled Euler-G-equation solver with a Ghost Fluid Method (GFM) module for applying the jump conditions across the flame. The flame s nonlinear response is shown to exhibit two qualitatively different behaviors. Depending on the operating conditions and the disturbance field characteristics, it is shown that a combustor may exhibit supercritical bifurcations leading to a single stable limit cycle amplitude or exhibit sub-critical bifurcations wherein multiple stable solutions for the instability amplitude are possible. In addition, this study presents the first analytical model which captures the effects of unsteady flame stretch on the heat release response and thus extends the applicability of current models to high frequency instabilities, such as occurring during screech. It is shown that unsteady stretch effects, negligible at low frequencies (100 s of Hz) become significant at screeching frequencies (1000 s of Hz). Furthermore, the analysis also yields insight into the significant spatial dependence of the mean and perturbation velocity field induced by the coupling between the flame and the flow field. In order to meaningfully compare the heat release response across different flame configurations, this study has identified that the reference velocity (for defining the transfer function) should be based on the effective normal velocity perturbing the flame and the Strouhal number should be based on the effective residence time of the flame wrinkles.Ph.D.Committee Chair: Dr. Tim Lieuwen; Committee Member: Dr. Ben T. Zinn; Committee Member: Dr. Fei Han; Committee Member: Dr. L. Sankar; Committee Member: Dr. Suresh Meno

TOWARDS LARGE-SCALE SIMULATIONS OF TWO-PHASE FLOWS WITH MOVING CONTACT LINES IN COMPLEX GEOMETRIES

Predictive simulation of two-phase flows with moving contact lines is challenging due to their inherent multi-physics and multi-scale nature. Directly simulating such flows incurs an enormous computational cost due to the widely disparate scales at the contact line. Moreover, simulations of viscosity-dominated two-phase flows with moving contact lines are often reported to be mesh-dependent due to the diverging viscous stress at the contact point. This dissertation addresses the above simulation issues and by building a numerical framework to enable large-scale 3D simulations of two-phase flows in complex geometries. By analyzing the weak form of the Navier-Stokes equations for a control volume adjacent to a wall with moving contact line, two unclosed terms are identified: a sub-grid scale (SGS) surface tension force and an SGS viscous force. A closure for the SGS surface tension force is first proposed and tested in a numerical framework for simulating two-phase flows with contact lines. This framework combines a conservative level set method to capture the interface and a conservative cut-cell immersed boundary method to handle complex geometries. Detailed verification tests confirm that simulations using this framework are discretely conservative, accurate, and robust. Secondly, a physics-based closure is derived for the SGS viscous force. Simulations these two SGS models are verified to be mesh-independent and physically accurate across a number of viscosity-dominated two-phase flows, including drop spreading on a horizontal plane and drop sliding down an inclined plane. Finally, the present approach is applied in the study of drop-fiber interactions and jet-wall interactions

Extracting Diffusive States of Rho GTPase in Live Cells: Towards In Vivo Biochemistry

Resolving distinct biochemical interaction states when analyzing the trajectories of diffusing proteins in live cells on an individual basis remains challenging because of the limited statistics provided by the relatively short trajectories available experimentally. Here, we introduce a novel, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors which collectively result from distinct biochemical interactions. We validate the performance of pEM in silico and demonstrate that pEM is capable of uncovering the proper number of underlying diffusive states with an accurate characterization of their diffusion properties. We then apply pEM to experimental protein trajectories of Rho GTPases, an integral regulator of cytoskeletal dynamics and cellular homeostasis, in vivo via single particle tracking photo-activated localization microscopy. Remarkably, pEM uncovers 6 distinct diffusive states conserved across various Rho GTPase family members. The variability across family members in the propensities for each diffusive state reveals non-redundant roles in the activation states of RhoA and RhoC. In a resting cell, our results support a model where RhoA is constantly cycling between activation states, with an imbalance of rates favoring an inactive state. RhoC, on the other hand, remains predominantly inactive

Molecular Modeling of Bacterial Nanomachineries

Proteins have the ability to assemble in multimeric states to perform their specific biological function. Unfortunately, characterizing experimentally these structures at atomistic resolution is usually difficult. For this reason, in silico methodologies aiming at predicting how multiple protein copies arrange to forma multimeric complex would be desirable. We present Parallel OptimizationWorkbench (POW), a swarm intelligence based optimization framework able to deal, in principle, with any optimization problem. We show that POW can be applied to biologically relevant problems such as prediction of protein assemblies and the parameterization of a Coarse-Grained force field for proteins. By combining POW optimizations, Molecular Dynamics simulations, Poisson-Boltzmann calculations and a variety of experiments, we subsequently study two bacterial nanomachieries: Aeromonas hydrophila's pore-forming toxin aerolysin, and Yersinia enterocolitica injectisome. These structures are challenging both for their size, and for the timescales involved in their functioning. Aerolysin is a pore-forming toxin secreted as an hydrophilic monomer. By means of large conformational changes, the protein heptamerizes on the target cell's surface, and finally inserts β-barrel into its lipid bilayer, causing cell death. The main hurdle in the study of this structure is the complexity of the mode of action, which spans timescales currently unreachable by classical molecular dynamics. We show that aerolysin C-terminal region has the dual role of preventing premature oligomerization and helping the folding of tertiary structure, qualifying therefore as an intramolecular chaperone. We study the transmembrane β-barrel properties and compare them with those of the homologous protein α-hemolysin. We show that aerolysin's barrel is more rigid than α-hemolysin's, and should be anion selective. We present models for aerolysin heptamer both in prepore and, for the first time, in membrane-inserted conformation. Our results are validated experimentally, and are consistent with known biochemical and structural data. The injectisome is an example of a type III secretion system. Its most striking feature is probably its size: hundreds of proteins assemble in a unique structure spanning the Gram-negative bacterial double membrane, and protruding outside the cell as a needle for tenth of nanometers. Obtaining an atomistic representation of this massive structure, and therefore some insights about its mode of action, is one of the greatest challenges. We show that the final length of injectisome's needle is determined by the secondary structure content of a ruler protein located inside its cavity during assembly. Using POW, we also produce the first model for Yersinia injectisome's basal body, highlighting the flexibility of this region in adapting between the inner and outer membranes. As a whole, this work demonstrates that a synergy of dry and wet experiments can provide precious insights into macromolecular structure and function

Microcirculation and inflammation in a numerical simulation approach

Inflammation is the response of the organism to eradicate the agent of lesion or infection in order to achieve hemostasis. This response requires the migration of specific leukocyte populations from the blood circulation towards the inflamed area. Leukocyte recruitment constitutes a complex cellular process by which leukocytes are first recruited to the endothelial vascular wall of post-capillary venules across which they further extravasate into the interstitial tissue. Recruitment is mediated via cell-cell interactions between the leukocyte and the endothelium and occurs through a multi-step cascade: tethering, rolling, slow rolling, arrest, crawling, adhesion and transmigration. However, whether or not the leukocytes adhere to the endothelium depends not only on the chemical forces generated by adhesion molecules on leukocytes and endothelial cells, but also on the physical forces that act on those cells. It has been suggested that fluid shear stress resulting from blood flow also regulates leukocyte activity which makes the fluid dynamic environment of the circulation to be considered an important aspect for leukocyte recruitment and migration during the inflammatory response. Most of the studies on the inflammatory response and in particular on leukocyte recruitment are based on animal models and involve, among others, the quantification of inflammatory mediators and cellular players, and/or the analysis of the leukocyte-endothelial cell interactions by intravital microscopy. However, the contribution of hemodynamics for leukocyte recruitment has been seldom addressed in those studies. This is mostly due to the fact that the study of hemodynamics in in vivo animal models is not straightforward and moreover, that several hemodynamic parameters cannot be experimentally determined due to technical constraints. In this work, we reasoned that these limitations could be circumvented by the development and use of numerical simulations to describe leukocyte recruitment. Many of the processes, which take place in living organisms, can be expressed as mathematical equations. This applies to leukocyte recruitment, for which scarce numerical models existed before the beginning of this work. Importantly, these mathematical simulations were performed without considering simultaneously all the players in the process, namely the vessel, the blood flow and the leukocytes. Moreover, most of these studies were two dimensional, assumed blood as a Newtonian fluid with constant viscosity and did not take into account in vivo experimental data. Taken this, our major goal with this work was to understand the contribution of hemodynamics to leukocyte recruitment in inflammation. For such purpose, we aimed here at developing numerical simulations that more adequately reproduced this process. For such, we set up animal models of inflammation to obtain the experimental data required for the development of those numerical simulations. Finally, we used these models to investigate the role of hemodynamics in leukocyte recruitment in inflammation. First, we considered the simpler case of a numerical simulation that assumed leukocytes to be rigid spheres and blood, a non-Newtonian fluid. For such, we initially developed an animal model of inflammation in Wistar rats using a lipopolysaccharide (LPS) as an inflammatory agent. Blood samples were collected for determination of TNF-α levels to ensure the triggering of the inflammatory process. Importantly, the number of rolling and adherent leukocytes in post-capillary venules was monitored using an intravital microscopy approach. As expected, our results showed that there is an increase in TNF-α concentrations after 15 minutes of LPS administration and a significant increase in the number of rolling and adherent leukocytes. The recorded intravital microcopy images, along with other recorded parameters, were then used, in collaboration with a group of mathematicians, to develop a numerical model capable of describing leukocyte recruitment in the microcirculation. To evaluate the contribution of hemodynamics, the localized velocity fields and shear stresses on the surface of leukocytes and near the vessel wall contact points have been computed in two discrete situations, namely as a single leukocyte or when a cluster of them are recruited towards the vessel wall. In the first situation, our numerical results showed the presence of one region of maximum shear stress on the surface of the leuko- cyte close to the endothelial wall and of two regions of minimum shear stress on the op- posite side of the cell. The different areas of shear stress observed in the surface of the leukocyte may be important in directing it towards the endothelial wall during an inflammatory response. The identification of a region of maximum shear stress is consistent with the molecular mechanisms that govern leukocyte rolling because it may actually cor- respond to the area that supports the interaction with the endothelium. On the other hand, the relatively lower shear stress regions may correlate with leukocyte surface areas where binding to the endothelium is not occurring at the moment, thus enabling the roll- ing of the cell along the endothelium. It was also observed that the shear stress at the endothelium gets higher as a cluster of leukocytes moves in the main stream. This sug- gests that the presence of a cluster of leukocytes may potentiate leukocyte rolling, as the increase in the shear stress promoted by the recruited leukocytes may support the migra- tion and recruitment of additional cells. Despite closely simulating leukocyte recruitment, our initial numerical simulation consid- ered the simple case of leukocytes as rigid spheres. However, while circulating leukocytes maintain an approximately spherical shape, rolling leukocytes are known to deform. In order to account for the leukocyte deformability changes that occur during its recruit- ment in inflammation, we needed to assess the deformability profile of the leukocytes under flow and therefore, to “directly” observe them regardless of the other blood cells. For such, intravital microscopy was performed in the mouse cremaster of a transgenic mice strain (Lys-EGFP-ki) in which fluorescent neutrophils can be individually tracked. By using PAF as an inflammatory agent, the analysis of the leukocyte-endothelial cell interac- tions showed a continuous increase in the number of rolling and adherent neutrophils up to 4 hours after the introduction of the inflammatory stimuli, thus confirming the devel- opment of an inflammatory response. As the properties of the red blood cells modulate blood flow properties, erythrocyte deformability was also addressed in this model. A con- tinuous decrease of this parameter was observed throughout time. The decrease in the erythrocyte deformability will most probably lead to an increase in the blood viscosity and to the decrease of the blood flow velocity. These conditions should facilitate the mi- gration of leukocytes from the mainstream to the endothelial wall and promote leukocyte slow rolling and adhesion during the inflammatory response. Importantly, in the intravital microcopy images obtained with this latter model, we clearly observed the deformation of neutrophils along the endothelial wall during rolling, as well as the formation of tethers. As such, in these images, leukocyte trajectories were tracked and their velocities and diameters were measured and further applied to the numerical simulations. Using a recent validated mathematical model describing the coupled defor- mation-flow of an individual leukocyte and the respective experimental results, numerical simulations of the recruitment of an individual leukocyte and of two leukocytes under different velocities were performed, considering a constant blood viscosity. The mathe- matical models obtained showed that under conditions of increased velocity the cell movement is accelerated along the endothelial layer, favouring the dissociation of leuko- cyte-endothelium interactions at designated attraction points. These observations lead us to propose that, in order to attain an efficient inflammatory response, the blood flow ve- locity needs so as to decrease to facilitate slow rolling and subsequent adhesion. These results are corroborated by the decrease in the erythrocyte deformability observed in our animal model, which will ultimately have an impact on the blood flow velocity. Our results further showed that in the vicinity of an adherent leukocyte there is an early slight decel- eration of the rolling leukocyte when compared with the case of an individual leukocyte. As such, these observations strongly suggest that the presence of an adherent cell in the vicinity should decrease the velocity of another leukocyte that is being recruited, thus promoting its slow rolling, and contributing to its capture by the endothelial cells. Altogether, our experimental data and numerical simulations support our working hy- pothesis that the hemodynamic properties of the flow and of the cells in circulation should play an essential role in the margination and rolling of the leukocytes to the endo- thelial wall, which in turn will impact the success of the inflammatory response. In partic- ular, our results strongly suggest that changes in hemodynamic conditions, such as de- creased flow velocities and the increase of the shear stress, will contribute to target leu- kocytes to the endothelial wall. Given our results, we propose that any change in the he- modynamic properties will certainly influence the outcome of the inflammatory response. As such, the adherence of the leukocytes to the endothelium should depend not only on the relative magnitude of the chemical forces generated by the interaction of adhesion molecules between leukocytes and endothelial cells, but also on the physical forces that act on the leukocytes. In this respect, our results suggest that alterations in the blood flow, for example in the flow velocity, will occur during an inflammatory process, thus potentiating the recruitment of more leukocytes towards the inflamed area and contrib- uting to a successful inflammatory response. Overall, the numerical simulations allowed us to better understand the contribution of the hemodynamic properties of the flow to the progression of an inflammatory response and to deepen our knowledge on leukocyte recruitment in inflammation. Importantly, our work provided numerical tools that can be used for the subsequent study and modulation of the hemodynamic parameters involved in an inflammatory response. In particular, these numerical simulations will surely enable us, in the near future, to determine or es- timate a large set of parameters which are unlikely to be recoverable by in vivo experi- ments. Moreover, our methods will allow us to analyze how the parameters evolve over time. Altogether our results further reinforce the notion that the improvement and de- velopment of animal models and numerical tools will certainly provide the medical and biological community with useful tools to study leukocyte recruitment in inflammation. By closely reproducing the microcirculation and the inflammatory process, these tools will be critical for a better comprehension of the inflammatory process and of the mecha- nisms underlying a multitude of inflammatory pathological conditions

Coherent Label Placement for 3D Exploded View

The use of labels in images represents the basics of visual object presentations that we are all familiar with. However, few know that automatic label placement in 2D or 3D space belongs to the set of NP-complete and NP-hard problems. While state-of-the-art algorithms such as hedgehog labeling already produce incredible coherent results in real-time interactive applications, they were only designed for static and non-deformable objects. Therefore, their performance decreases when combined with the dynamic and model-deforming the 3D model presentation techniques such as exploded diagrams a.k.a. exploded views, which present the structure of 3D model by "exploding" their parts. We propose an extension of hedgehog labeling to work with exploded views by introducing clustering of model exploded parts and their labels. Clustered hedgehog labeling uses the explosion information to separate 3D space into sections belonging to individual label clusters, each running hedgehog labeling instances solely on the cluster members. The evaluation of the proposed solution and its Textplosion implementation was done by running a usability study enhanced with eye-tracking on a group of volunteers, where improvement of the original algorithm was detected. The need for 3D test models for experimentation resulted in the creation of a 3D Labeling dataset to be shared with the community in an attempt to fill the void of a missing standardized dataset for 3D labeling algorithms

MONOCULAR POSE ESTIMATION AND SHAPE RECONSTRUCTION OF QUASI-ARTICULATED OBJECTS WITH CONSUMER DEPTH CAMERA

Quasi-articulated objects, such as human beings, are among the most commonly seen objects in our daily lives. Extensive research have been dedicated to 3D shape reconstruction and motion analysis for this type of objects for decades. A major motivation is their wide applications, such as in entertainment, surveillance and health care. Most of existing studies relied on one or more regular video cameras. In recent years, commodity depth sensors have become more and more widely available. The geometric measurements delivered by the depth sensors provide significantly valuable information for these tasks. In this dissertation, we propose three algorithms for monocular pose estimation and shape reconstruction of quasi-articulated objects using a single commodity depth sensor. These three algorithms achieve shape reconstruction with increasing levels of granularity and personalization. We then further develop a method for highly detailed shape reconstruction based on our pose estimation techniques. Our first algorithm takes advantage of a motion database acquired with an active marker-based motion capture system. This method combines pose detection through nearest neighbor search with pose refinement via non-rigid point cloud registration. It is capable of accommodating different body sizes and achieves more than twice higher accuracy compared to a previous state of the art on a publicly available dataset. The above algorithm performs frame by frame estimation and therefore is less prone to tracking failure. Nonetheless, it does not guarantee temporal consistent of the both the skeletal structure and the shape and could be problematic for some applications. To address this problem, we develop a real-time model-based approach for quasi-articulated pose and 3D shape estimation based on Iterative Closest Point (ICP) principal with several novel constraints that are critical for monocular scenario. In this algorithm, we further propose a novel method for automatic body size estimation that enables its capability to accommodate different subjects. Due to the local search nature, the ICP-based method could be trapped to local minima in the case of some complex and fast motions. To address this issue, we explore the potential of using statistical model for soft point correspondences association. Towards this end, we propose a unified framework based on Gaussian Mixture Model for joint pose and shape estimation of quasi-articulated objects. This method achieves state-of-the-art performance on various publicly available datasets. Based on our pose estimation techniques, we then develop a novel framework that achieves highly detailed shape reconstruction by only requiring the user to move naturally in front of a single depth sensor. Our experiments demonstrate reconstructed shapes with rich geometric details for various subjects with different apparels. Last but not the least, we explore the applicability of our method on two real-world applications. First of all, we combine our ICP-base method with cloth simulation techniques for Virtual Try-on. Our system delivers the first promising 3D-based virtual clothing system. Secondly, we explore the possibility to extend our pose estimation algorithms to assist physical therapist to identify their patients’ movement dysfunctions that are related to injuries. Our preliminary experiments have demonstrated promising results by comparison with the gold standard active marker-based commercial system. Throughout the dissertation, we develop various state-of-the-art algorithms for pose estimation and shape reconstruction of quasi-articulated objects by leveraging the geometric information from depth sensors. We also demonstrate their great potentials for different real-world applications