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- Language: English
- Creators: Ira A. Fulton Schools of Engineering
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
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
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
Description
Energy efficient design and management of data centers has seen considerable interest in the recent years owing to its potential to reduce the overall energy consumption and thereby the costs associated with it. Therefore, it is of utmost importance that new methods for improved physical design of data centers, resource management schemes for efficient workload distribution and sustainable operation for improving the energy efficiency, be developed and tested before implementation on an actual data center. The BlueTool project, provides such a state-of-the-art platform, both software and hardware, to design and analyze energy efficiency of data centers. The software platform, namely GDCSim uses cyber-physical approach to study the physical behavior of the data center in response to the management decisions by taking into account the heat recirculation patterns in the data center room. Such an approach yields best possible energy savings owing to the characterization of cyber-physical interactions and the ability of the resource management to take decisions based on physical behavior of data centers. The GDCSim mainly uses two Computational Fluid Dynamics (CFD) based cyber-physical models namely, Heat Recirculation Matrix (HRM) and Transient Heat Distribution Model (THDM) for thermal predictions based on different management schemes. They are generated using a model generator namely BlueSim. To ensure the accuracy of the thermal predictions using the GDCSim, the models, HRM and THDM and the model generator, BlueSim need to be validated experimentally. For this purpose, the hardware platform of the BlueTool project, namely the BlueCenter, a mini data center, can be used. As a part of this thesis, the HRM and THDM were generated using the BlueSim and experimentally validated using the BlueCenter. An average error of 4.08% was observed for BlueSim, 5.84% for HRM and 4.24% for THDM. Further, a high initial error was observed for transient thermal prediction, which is due to the inability of BlueSim to account for the heat retained by server components.
ContributorsGilbert, Rose Robin (Author) / Gupta, Sandeep K.S (Thesis advisor) / Artemiadis, Panagiotis (Committee member) / Phelan, Patrick (Committee member) / Arizona State University (Publisher)
Created2012
Description
It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter.
ContributorsMunroe, Michael R (Author) / Phelan, Patrick (Thesis advisor) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2012
Description
The generation of walking motion is one of the most vital functions of the human body because it allows us to be mobile in our environment. Unfortunately, numerous individuals suffer from gait impairment as a result of debilitating conditions like stroke, resulting in a serious loss of mobility. Our understanding of human gait is limited by the amount of research we conduct in relation to human walking mechanisms and their characteristics. In order to better understand these characteristics and the systems involved in the generation of human gait, it is necessary to increase the depth and range of research pertaining to walking motion. Specifically, there has been a lack of investigation into a particular area of human gait research that could potentially yield interesting conclusions about gait rehabilitation, which is the effect of surface stiffness on human gait. In order to investigate this idea, a number of studies have been conducted using experimental devices that focus on changing surface stiffness; however, these systems lack certain functionality that would be useful in an experimental scenario. To solve this problem and to investigate the effect of surface stiffness further, a system has been developed called the Variable Stiffness Treadmill system (VST). This treadmill system is a unique investigative tool that allows for the active control of surface stiffness. What is novel about this system is its ability to change the stiffness of the surface quickly, accurately, during the gait cycle, and throughout a large range of possible stiffness values. This type of functionality in an experimental system has never been implemented and constitutes a tremendous opportunity for valuable gait research in regard to the influence of surface stiffness. In this work, the design, development, and implementation of the Variable Stiffness Treadmill system is presented and discussed along with preliminary experimentation. The results from characterization testing demonstrate highly accurate stiffness control and excellent response characteristics for specific configurations. Initial indications from human experimental trials in relation to quantifiable effects from surface stiffness variation using the Variable Stiffness Treadmill system are encouraging.
ContributorsBarkan, Andrew Robert (Author) / Artemiadis, Panagiotis (Thesis director) / Santello, Marco (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2015-05
Description
The ideal function of an upper limb prosthesis is to replace the human hand and arm, but a gulf in functionality between prostheses and biological arms still exists, in large part due the absence of the sense of touch. Tactile sensing of the human hand comprises a key component of a wide variety of interactions with the external environment; visual feedback alone is not always sufficient for the recreation of nuanced tasks. It is hoped that the results of this study can contribute to the advancement of prosthetics with a tactile feedback loop with the ultimate goal of replacing biological function. A three-fingered robot hand equipped with tactile sensing fingertips was used to biomimetically grasp a ball in order haptically explore the environment for a ball-in-hole task. The sensorized fingertips were used to measure the vibration, pressure, and skin deformation experienced by each fingertip. Vibration and pressure sensed by the fingertips were good indicators of changes in discrete phases of the exploratory motion such as contact with the lip of a hole. The most informative tactile cue was the skin deformation of the fingers. Upon encountering the lip of the test surface, the lagging digit experienced compression in the fingertip and radial distal region of the digit. The middle digit experienced decompression of the middle region of the finger and the lagging digit showed compression towards the middle digit and decompression in the distal-ulnar region. Larger holes caused an increase in pressure experienced by the fingertips while changes in stroke speed showed no effect on tactile data. Larger coefficients of friction between the ball and the test surface led to an increase in pressure and skin deformation of the finger. Unlike most tactile sensing studies that focus on tactile stimuli generated by direct contact between a fingertip and the environment, this preliminary study focused on tactile stimuli generated when a grasped object interacts with the environment. Findings from this study could be used to design experiments for functionally similar activities of daily living, such as the haptic search for a keyhole via a grasped key.
ContributorsLoges, Shea Remegio (Author) / Santos, Veronica (Thesis director) / Artemiadis, Panagiotis (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2014-05