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- Creators: Ira A. Fulton Schools of Engineering
- Language: English
Description
Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates solitary waves, or even leads to singular solutions. This dissertation studies the global behavior of finite energy solutions to the $d$-dimensional focusing NLS equation, $i partial _t u+Delta u+ |u|^{p-1}u=0, $ with initial data $u_0in H^1,; x in Rn$; the nonlinearity power $p$ and the dimension $d$ are chosen so that the scaling index $s=frac{d}{2}-frac{2}{p-1}$ is between 0 and 1, thus, the NLS is mass-supercritical $(s>0)$ and energy-subcritical $(s<1).$ For solutions with $ME[u_0]<1$ ($ME[u_0]$ stands for an invariant and conserved quantity in terms of the mass and energy of $u_0$), a sharp threshold for scattering and blowup is given. Namely, if the renormalized gradient $g_u$ of a solution $u$ to NLS is initially less than 1, i.e., $g_u(0)<1,$ then the solution exists globally in time and scatters in $H^1$ (approaches some linear Schr"odinger evolution as $ttopminfty$); if the renormalized gradient $g_u(0)>1,$ then the solution exhibits a blowup behavior, that is, either a finite time blowup occurs, or there is a divergence of $H^1$ norm in infinite time. This work generalizes the results for the 3d cubic NLS obtained in a series of papers by Holmer-Roudenko and Duyckaerts-Holmer-Roudenko with the key ingredients, the concentration compactness and localized variance, developed in the context of the energy-critical NLS and Nonlinear Wave equations by Kenig and Merle. One of the difficulties is fractional powers of nonlinearities which are overcome by considering Besov-Strichartz estimates and various fractional differentiation rules.
ContributorsGuevara, Cristi Darley (Author) / Roudenko, Svetlana (Thesis advisor) / Castillo_Chavez, Carlos (Committee member) / Jones, Donald (Committee member) / Mahalov, Alex (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2011
Description
Advanced composites are being widely used in aerospace applications due to their high stiffness, strength and energy absorption capabilities. However, the assurance of structural reliability is a critical issue because a damage event will compromise the integrity of composite structures and lead to ultimate failure. In this dissertation a novel homogenization based multiscale modeling framework using semi-analytical micromechanics is presented to simulate the response of textile composites. The novelty of this approach lies in the three scale homogenization/localization framework bridging between the constituent (micro), the fiber tow scale (meso), weave scale (macro), and the global response. The multiscale framework, named Multiscale Generalized Method of Cells (MSGMC), continuously bridges between the micro to the global scale as opposed to approaches that are top-down and bottom-up. This framework is fully generalized and capable of modeling several different weave and braids without reformulation. Particular emphasis in this dissertation is placed on modeling the nonlinearity and failure of both polymer matrix and ceramic matrix composites.
ContributorsLiu, Guang (Author) / Chattopadhyay, Aditi (Thesis advisor) / Mignolet, Marc (Committee member) / Jiang, Hanqing (Committee member) / Li, Jian (Committee member) / Rajadas, John (Committee member) / Arizona State University (Publisher)
Created2011
Description
This thesis focuses on the continued extension, validation, and application of combined thermal-structural reduced order models for nonlinear geometric problems. The first part of the thesis focuses on the determination of the temperature distribution and structural response induced by an oscillating flux on the top surface of a flat panel. This flux is introduced here as a simplified representation of the thermal effects of an oscillating shock on a panel of a supersonic/hypersonic vehicle. Accordingly, a random acoustic excitation is also considered to act on the panel and the level of the thermo-acoustic excitation is assumed to be large enough to induce a nonlinear geometric response of the panel. Both temperature distribution and structural response are determined using recently proposed reduced order models and a complete one way, thermal-structural, coupling is enforced. A steady-state analysis of the thermal problem is first carried out that is then utilized in the structural reduced order model governing equations with and without the acoustic excitation. A detailed validation of the reduced order models is carried out by comparison with a few full finite element (Nastran) computations. The computational expedience of the reduced order models allows a detailed parametric study of the response as a function of the frequency of the oscillating flux. The nature of the corresponding structural ROM equations is seen to be of a Mathieu-type with Duffing nonlinearity (originating from the nonlinear geometric effects) with external harmonic excitation (associated with the thermal moments terms on the panel). A dominant resonance is observed and explained. The second part of the thesis is focused on extending the formulation of the combined thermal-structural reduced order modeling method to include temperature dependent structural properties, more specifically of the elasticity tensor and the coefficient of thermal expansion. These properties were assumed to vary linearly with local temperature and it was found that the linear stiffness coefficients and the "thermal moment" terms then are cubic functions of the temperature generalized coordinates while the quadratic and cubic stiffness coefficients were only linear functions of these coordinates. A first validation of this reduced order modeling strategy was successfully carried out.
ContributorsMatney, Andrew (Author) / Mignolet, Marc (Thesis advisor) / Jiang, Hanqing (Committee member) / Spottswood, Stephen (Committee member) / Arizona State University (Publisher)
Created2011
Description
As robots are increasingly migrating out of factories and research laboratories and into our everyday lives, they should move and act in environments designed for humans. For this reason, the need of anthropomorphic movements is of utmost importance. The objective of this thesis is to solve the inverse kinematics problem of redundant robot arms that results to anthropomorphic configurations. The swivel angle of the elbow was used as a human arm motion parameter for the robot arm to mimic. The swivel angle is defined as the rotation angle of the plane defined by the upper and lower arm around a virtual axis that connects the shoulder and wrist joints. Using kinematic data recorded from human subjects during every-day life tasks, the linear sensorimotor transformation model was validated and used to estimate the swivel angle, given the desired end-effector position. Defining the desired swivel angle simplifies the kinematic redundancy of the robot arm. The proposed method was tested with an anthropomorphic redundant robot arm and the computed motion profiles were compared to the ones of the human subjects. This thesis shows that the method computes anthropomorphic configurations for the robot arm, even if the robot arm has different link lengths than the human arm and starts its motion at random configurations.
ContributorsWang, Yuting (Author) / Artemiadis, Panagiotis (Thesis advisor) / Mignolet, Marc (Committee member) / Santos, Veronica J (Committee member) / Arizona State University (Publisher)
Created2013
Description
Electromyogram (EMG)-based control interfaces are increasingly used in robot teleoperation, prosthetic devices control and also in controlling robotic exoskeletons. Over the last two decades researchers have come up with a plethora of decoding functions to map myoelectric signals to robot motions. However, this requires a lot of training and validation data sets, while the parameters of the decoding function are specific for each subject. In this thesis we propose a new methodology that doesn't require training and is not user-specific. The main idea is to supplement the decoding functional error with the human ability to learn inverse model of an arbitrary mapping function. We have shown that the subjects gradually learned the control strategy and their learning rates improved. We also worked on identifying an optimized control scheme that would be even more effective and easy to learn for the subjects. Optimization was done by taking into account that muscles act in synergies while performing a motion task. The low-dimensional representation of the neural activity was used to control a two-dimensional task. Results showed that in the case of reduced dimensionality mapping, the subjects were able to learn to control the device in a slower pace, however they were able to reach and retain the same level of controllability. To summarize, we were able to build an EMG-based controller for robot devices that would work for any subject, without any training or decoding function, suggesting human-embedded controllers for robotic devices.
ContributorsAntuvan, Chris Wilson (Author) / Artemiadis, Panagiotis (Thesis advisor) / Muthuswamy, Jitendran (Committee member) / Santos, Veronica J (Committee member) / Arizona State University (Publisher)
Created2013
Description
Humans have an inherent capability of performing highly dexterous and skillful tasks with their arms, involving maintaining posture, movement and interacting with the environment. The latter requires for them to control the dynamic characteristics of the upper limb musculoskeletal system. Inertia, damping and stiffness, a measure of mechanical impedance, gives a strong representation of these characteristics. Many previous studies have shown that the arm posture is a dominant factor for determining the end point impedance in a horizontal plane (transverse plane). The objective of this thesis is to characterize end point impedance of the human arm in the three dimensional (3D) space. Moreover, it investigates and models the control of the arm impedance due to increasing levels of muscle co-contraction. The characterization is done through experimental trials where human subjects maintained arm posture, while perturbed by a robot arm. Moreover, the subjects were asked to control the level of their arm muscles' co-contraction, using visual feedback of their muscles' activation, in order to investigate the effect of the muscle co-contraction on the arm impedance. The results of this study showed a very interesting, anisotropic increase of the arm stiffness due to muscle co-contraction. This can lead to very useful conclusions about the arm biomechanics as well as many implications for human motor control and more specifically the control of arm impedance through muscle co-contraction. The study finds implications for the EMG-based control of robots that physically interact with humans.
ContributorsPatel, Harshil Naresh (Author) / Artemiadis, Panagiotis (Thesis advisor) / Berman, Spring (Committee member) / Helms Tillery, Stephen (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis outlines the development of a vector retrieval technique, based on data assimilation, for a coherent Doppler LIDAR (Light Detection and Ranging). A detailed analysis of the Optimal Interpolation (OI) technique for vector retrieval is presented. Through several modifications to the OI technique, it is shown that the modified technique results in significant improvement in velocity retrieval accuracy. These modifications include changes to innovation covariance portioning, covariance binning, and analysis increment calculation. It is observed that the modified technique is able to make retrievals with better accuracy, preserves local information better, and compares well with tower measurements. In order to study the error of representativeness and vector retrieval error, a lidar simulator was constructed. Using the lidar simulator a thorough sensitivity analysis of the lidar measurement process and vector retrieval is carried out. The error of representativeness as a function of scales of motion and sensitivity of vector retrieval to look angle is quantified. Using the modified OI technique, study of nocturnal flow in Owens' Valley, CA was carried out to identify and understand uncharacteristic events on the night of March 27th 2006. Observations from 1030 UTC to 1230 UTC (0230 hr local time to 0430 hr local time) on March 27 2006 are presented. Lidar observations show complex and uncharacteristic flows such as sudden bursts of westerly cross-valley wind mixing with the dominant up-valley wind. Model results from Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS®) and other in-situ instrumentations are used to corroborate and complement these observations. The modified OI technique is used to identify uncharacteristic and extreme flow events at a wind development site. Estimates of turbulence and shear from this technique are compared to tower measurements. A formulation for equivalent wind speed in the presence of variations in wind speed and direction, combined with shear is developed and used to determine wind energy content in presence of turbulence.
ContributorsChoukulkar, Aditya (Author) / Calhoun, Ronald (Thesis advisor) / Mahalov, Alex (Committee member) / Kostelich, Eric (Committee member) / Huang, Huei-Ping (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2013
Description
Shock loading is a complex phenomenon that can lead to failure mechanisms such as strain localization, void nucleation and growth, and eventually spall fracture. Studying incipient stages of spall damage is of paramount importance to accurately determine initiation sites in the material microstructure where damage will nucleate and grow and to formulate continuum models that account for the variability of the damage process due to microstructural heterogeneity. The length scale of damage with respect to that of the surrounding microstructure has proven to be a key aspect in determining sites of failure initiation. Correlations have been found between the damage sites and the surrounding microstructure to determine the preferred sites of spall damage, since it tends to localize at and around the regions of intrinsic defects such as grain boundaries and triple points. However, considerable amount of work still has to be done in this regard to determine the physics driving the damage at these intrinsic weak sites in the microstructure. The main focus of this research work is to understand the physical mechanisms behind the damage localization at these preferred sites. A crystal plasticity constitutive model is implemented with different damage criteria to study the effects of stress concentration and strain localization at the grain boundaries. A cohesive zone modeling technique is used to include the intrinsic strength of the grain boundaries in the simulations. The constitutive model is verified using single elements tests, calibrated using single crystal impact experiments and validated using bicrystal and multicrystal impact experiments. The results indicate that strain localization is the predominant driving force for damage initiation and evolution. The microstructural effects on theses damage sites are studied to attribute the extent of damage to microstructural features such as grain orientation, misorientation, Taylor factor and the grain boundary planes. The finite element simulations show good correlation with the experimental results and can be used as the preliminary step in developing accurate probabilistic models for damage nucleation.
ContributorsKrishnan, Kapil (Author) / Peralta, Pedro (Thesis advisor) / Mignolet, Marc (Committee member) / Sieradzki, Karl (Committee member) / Jiang, Hanqing (Committee member) / Oswald, Jay (Committee member) / Arizona State University (Publisher)
Created2013
Description
The focus of this investigation includes three aspects. First, the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting "large" deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology, successfully validated in recent years on simpler panel structures, by developing a novel identification strategy of the reduced order model parameters, that enables the consideration of the large number of modes needed for complex structures, and by extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. These novel developments are successfully validated on the nonlinear static and dynamic responses of a 9-bay panel structure modeled within Nastran. In addition, a multi-scale approach based on Component Mode Synthesis methods is explored. Second, an assessment of the predictive capabilities of nonlinear reduced order models for the prediction of the large displacement and stress fields of panels that have a geometric discontinuity; a flat panel with a notch was used for this assessment. It is demonstrated that the reduced order models of both virgin and notched panels provide a close match of the displacement field obtained from full finite element analyses of the notched panel for moderately large static and dynamic responses. In regards to stresses, it is found that the notched panel reduced order model leads to a close prediction of the stress distribution obtained on the notched panel as computed by the finite element model. Two enrichment techniques, based on superposition of the notch effects on the virgin panel stress field, are proposed to permit a close prediction of the stress distribution of the notched panel from the reduced order model of the virgin one. A very good prediction of the full finite element results is achieved with both enrichments for static and dynamic responses. Finally, computational challenges associated with the solution of the reduced order model equations are discussed. Two alternatives to reduce the computational time for the solution of these problems are explored.
ContributorsPerez, Ricardo Angel (Author) / Mignolet, Marc (Thesis advisor) / Oswald, Jay (Committee member) / Spottswood, Stephen (Committee member) / Peralta, Pedro (Committee member) / Jiang, Hanqing (Committee member) / Arizona State University (Publisher)
Created2012
Description
Humans' ability to perform fine object and tool manipulation is a defining feature of their sensorimotor repertoire. How the central nervous system builds and maintains internal representations of such skilled hand-object interactions has attracted significant attention over the past three decades. Nevertheless, two major gaps exist: a) how digit positions and forces are coordinated during natural manipulation tasks, and b) what mechanisms underlie the formation and retention of internal representations of dexterous manipulation. This dissertation addresses these two questions through five experiments that are based on novel grip devices and experimental protocols. It was found that high-level representation of manipulation tasks can be learned in an effector-independent fashion. Specifically, when challenged by trial-to-trial variability in finger positions or using digits that were not previously engaged in learning the task, subjects could adjust finger forces to compensate for this variability, thus leading to consistent task performance. The results from a follow-up experiment conducted in a virtual reality environment indicate that haptic feedback is sufficient to implement the above coordination between digit position and forces. However, it was also found that the generalizability of a learned manipulation is limited across tasks. Specifically, when subjects learned to manipulate the same object across different contexts that require different motor output, interference was found at the time of switching contexts. Data from additional studies provide evidence for parallel learning processes, which are characterized by different rates of decay and learning. These experiments have provided important insight into the neural mechanisms underlying learning and control of object manipulation. The present findings have potential biomedical applications including brain-machine interfaces, rehabilitation of hand function, and prosthetics.
ContributorsFu, Qiushi (Author) / Santello, Marco (Thesis advisor) / Helms Tillery, Stephen (Committee member) / Buneo, Christopher (Committee member) / Santos, Veronica (Committee member) / Artemiadis, Panagiotis (Committee member) / Arizona State University (Publisher)
Created2013