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Description
In this thesis I introduce a new direction to computing using nonlinear chaotic dynamics. The main idea is rich dynamics of a chaotic system enables us to (1) build better computers that have a flexible instruction set, and (2) carry out computation that conventional computers are not good at it. Here I start from the theory, explaining how one can build a computing logic block using a chaotic system, and then I introduce a new theoretical analysis for chaos computing. Specifically, I demonstrate how unstable periodic orbits and a model based on them explains and predicts how and how well a chaotic system can do computation. Furthermore, since unstable periodic orbits and their stability measures in terms of eigenvalues are extractable from experimental times series, I develop a time series technique for modeling and predicting chaos computing from a given time series of a chaotic system. After building a theoretical framework for chaos computing I proceed to architecture of these chaos-computing blocks to build a sophisticated computing system out of them. I describe how one can arrange and organize these chaos-based blocks to build a computer. I propose a brand new computer architecture using chaos computing, which shifts the limits of conventional computers by introducing flexible instruction set. Our new chaos based computer has a flexible instruction set, meaning that the user can load its desired instruction set to the computer to reconfigure the computer to be an implementation for the desired instruction set. Apart from direct application of chaos theory in generic computation, the application of chaos theory to speech processing is explained and a novel application for chaos theory in speech coding and synthesizing is introduced. More specifically it is demonstrated how a chaotic system can model the natural turbulent flow of the air in the human speech production system and how chaotic orbits can be used to excite a vocal tract model. Also as another approach to build computing system based on nonlinear system, the idea of Logical Stochastic Resonance is studied and adapted to an autoregulatory gene network in the bacteriophage λ.
ContributorsKia, Behnam (Author) / Ditto, William (Thesis advisor) / Huang, Liang (Committee member) / Lai, Ying-Cheng (Committee member) / Helms Tillery, Stephen (Committee member) / Arizona State University (Publisher)
Created2011
Description
What can classical chaos do to quantum systems is a fundamental issue highly relevant to a number of branches in physics. The field of quantum chaos has been active for three decades, where the focus was on non-relativistic quantumsystems described by the Schr¨odinger equation. By developing an efficient method to solve the Dirac equation in the setting where relativistic particles can tunnel between two symmetric cavities through a potential barrier, chaotic cavities are found to suppress the spread in the tunneling rate. Tunneling rate for any given energy assumes a wide range that increases with the energy for integrable classical dynamics. However, for chaotic underlying dynamics, the spread is greatly reduced. A remarkable feature, which is a consequence of Klein tunneling, arise only in relativistc quantum systems that substantial tunneling exists even for particle energy approaching zero. Similar results are found in graphene tunneling devices, implying high relevance of relativistic quantum chaos to the development of such devices. Wave propagation through random media occurs in many physical systems, where interesting phenomena such as branched, fracal-like wave patterns can arise. The generic origin of these wave structures is currently a matter of active debate. It is of fundamental interest to develop a minimal, paradigmaticmodel that can generate robust branched wave structures. In so doing, a general observation in all situations where branched structures emerge is non-Gaussian statistics of wave intensity with an algebraic tail in the probability density function. Thus, a universal algebraic wave-intensity distribution becomes the criterion for the validity of any minimal model of branched wave patterns. Coexistence of competing species in spatially extended ecosystems is key to biodiversity in nature. Understanding the dynamical mechanisms of coexistence is a fundamental problem of continuous interest not only in evolutionary biology but also in nonlinear science. A continuous model is proposed for cyclically competing species and the effect of the interplay between the interaction range and mobility on coexistence is investigated. A transition from coexistence to extinction is uncovered with a non-monotonic behavior in the coexistence probability and switches between spiral and plane-wave patterns arise. Strong mobility can either promote or hamper coexistence, while absent in lattice-based models, can be explained in terms of nonlinear partial differential equations.
ContributorsNi, Xuan (Author) / Lai, Ying-Cheng (Thesis advisor) / Huang, Liang (Committee member) / Yu, Hongbin (Committee member) / Akis, Richard (Committee member) / Arizona State University (Publisher)
Created2012
Description
Complex human controls is a topic of much interest in the fields of robotics, manufacturing, space exploration and many others. Even simple tasks that humans perform with ease can be extremely complicated when observed from a controls and complex systems perspective. One such simple task is that of a human carrying and moving a coffee cup. Though this may be a mundane task for humans, when this task is modelled and analyzed, the system may be quite chaotic in nature. Understanding such systems is key to the development robots and autonomous systems that can perform these tasks themselves.
The coffee cup system can be simplified and modeled by a cart-and-pendulum system. Bazzi et al. and Maurice et al. present two different cart-and-pendulum systems to represent the coffee cup system [1],[2]. The purpose of this project was to build upon these systems and to gain a better understanding of the coffee cup system and to determine where chaos existed within the system. The honors thesis team first worked with their senior design group to develop a mathematical model for the cart-and-pendulum system based on the Bazzi and Maurice papers [1],[2]. This system was analyzed and then built upon by the honors thesis team to build a cart-and-two-pendulum model to represent the coffee cup system more accurately.
Analysis of the single pendulum model showed that there exists a low frequency region where the pendulum and the cart remain in phase with each other and a high frequency region where the cart and pendulum have a π phase difference between them. The transition point of the low and high frequency region is determined by the resonant frequency of the pendulum. The analysis of the two-pendulum system also confirmed this result and revealed that differences in length between the pendulum cause the pendulums to transition to the high frequency regions at separate frequency. The pendulums have different resonance frequencies and transition into the high frequency region based on their own resonant frequency. This causes a range of frequencies where the pendulums are out of phase from each other. After both pendulums have transitioned, they remain in phase with each other and out of phase from the cart.
However, if the length of the pendulum is decreased too much, the system starts to exhibit chaotic behavior. The short pendulum starts to act in a chaotic manner and the phase relationship between the pendulums and the carts is no longer maintained. Since the pendulum length represents the distance between the particle of coffee and the top of the cup, this implies that coffee near the top of the cup would cause the system to act chaotically. Further analysis would be needed to determine the reason why the length affects the system in this way.
The coffee cup system can be simplified and modeled by a cart-and-pendulum system. Bazzi et al. and Maurice et al. present two different cart-and-pendulum systems to represent the coffee cup system [1],[2]. The purpose of this project was to build upon these systems and to gain a better understanding of the coffee cup system and to determine where chaos existed within the system. The honors thesis team first worked with their senior design group to develop a mathematical model for the cart-and-pendulum system based on the Bazzi and Maurice papers [1],[2]. This system was analyzed and then built upon by the honors thesis team to build a cart-and-two-pendulum model to represent the coffee cup system more accurately.
Analysis of the single pendulum model showed that there exists a low frequency region where the pendulum and the cart remain in phase with each other and a high frequency region where the cart and pendulum have a π phase difference between them. The transition point of the low and high frequency region is determined by the resonant frequency of the pendulum. The analysis of the two-pendulum system also confirmed this result and revealed that differences in length between the pendulum cause the pendulums to transition to the high frequency regions at separate frequency. The pendulums have different resonance frequencies and transition into the high frequency region based on their own resonant frequency. This causes a range of frequencies where the pendulums are out of phase from each other. After both pendulums have transitioned, they remain in phase with each other and out of phase from the cart.
However, if the length of the pendulum is decreased too much, the system starts to exhibit chaotic behavior. The short pendulum starts to act in a chaotic manner and the phase relationship between the pendulums and the carts is no longer maintained. Since the pendulum length represents the distance between the particle of coffee and the top of the cup, this implies that coffee near the top of the cup would cause the system to act chaotically. Further analysis would be needed to determine the reason why the length affects the system in this way.
ContributorsZindani, Abdul Rahman (Co-author) / Crane, Kari (Co-author) / Lai, Ying-Cheng (Thesis director) / Jiang, Junjie (Committee member) / Electrical Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-12
Description
A remarkable phenomenon in contemporary physics is quantum scarring in classically chaoticsystems, where the wave functions tend to concentrate on classical periodic orbits. Quantum
scarring has been studied for more than four decades, but the problem of efficiently detecting
quantum scars has remained to be challenging, relying mostly on human visualization of
wave function patterns. This paper develops a machine learning approach to detecting
quantum scars in an automated and highly efficient manner. In particular, this paper exploits Meta
learning. The first step is to construct a few-shot classification algorithm, under the
requirement that the one-shot classification accuracy be larger than 90%. Then propose a
scheme based on a combination of neural networks to improve the accuracy. This paper shows that
the machine learning scheme can find the correct quantum scars from thousands images of
wave functions, without any human intervention, regardless of the symmetry of the underlying
classical system. This will be the first application of Meta learning to quantum systems. Interacting spin networks are fundamental to quantum computing. Data-based tomography oftime-independent spin networks has been achieved, but an open challenge is to ascertain the
structures of time-dependent spin networks using time series measurements taken locally
from a small subset of the spins. Physically, the dynamical evolution of a spin network under
time-dependent driving or perturbation is described by the Heisenberg equation of motion.
Motivated by this basic fact, this paper articulates a physics-enhanced machine learning framework
whose core is Heisenberg neural networks. This paper demonstrates that, from local measurements, not only the local Hamiltonian can be recovered but the Hamiltonian reflecting the interacting structure of the whole system can
also be faithfully reconstructed. Using Heisenberg neural machine on spin networks of a
variety of structures. In the extreme case where measurements are taken from only one spin,
the achieved tomography fidelity values can reach about 90%. The developed machine
learning framework is applicable to any time-dependent systems whose quantum dynamical
evolution is governed by the Heisenberg equation of motion.
ContributorsHan, Chendi (Author) / Lai, Ying-Cheng (Thesis advisor) / Yu, Hongbin (Committee member) / Dasarathy, Gautam (Committee member) / Seo, Jae-Sun (Committee member) / Arizona State University (Publisher)
Created2022
Description
In this research, I surveyed existing methods of characterizing Epilepsy from Electroencephalogram (EEG) data, including the Random Forest algorithm, which was claimed by many researchers to be the most effective at detecting epileptic seizures [7]. I observed that although many papers claimed a detection of >99% using Random Forest, it was not specified “when” the detection was declared within the 23.6 second interval of the seizure event. In this research, I created a time-series procedure to detect the seizure as early as possible within the 23.6 second epileptic seizure window and found that the detection is effective (> 92%) as early as the first few seconds of the epileptic episode. I intend to use this research as a stepping stone towards my upcoming Masters thesis research where I plan to expand the time-series detection mechanism to the pre-ictal stage, which will require a different dataset.
ContributorsBou-Ghazale, Carine (Author) / Lai, Ying-Cheng (Thesis director) / Berisha, Visar (Committee member) / Barrett, The Honors College (Contributor) / Electrical Engineering Program (Contributor)
Created2022-05
Description
Conductance fluctuations associated with quantum transport through quantumdot systems are currently understood to depend on the nature of the corresponding classical dynamics, i.e., integrable or chaotic. There are a couple of interesting phenomena about conductance fluctuation and quantum tunneling related to geometrical shapes of graphene systems. Firstly, in graphene quantum-dot systems, when a magnetic field is present, as the Fermi energy or the magnetic flux is varied, both regular oscillations and random fluctuations in the conductance can occur, with alternating transitions between the two. Secondly, a scheme based on geometrical rotation of rectangular devices to effectively modulate the conductance fluctuations is presented. Thirdly, when graphene is placed on a substrate of heavy metal, Rashba spin-orbit interaction of substantial strength can occur. In an open system such as a quantum dot, the interaction can induce spin polarization. Finally, a problem using graphene systems with electron-electron interactions described by the Hubbard Hamiltonian in the setting of resonant tunneling is investigated.
Another interesting problem in quantum transport is the effect of disorder or random impurities since it is inevitable in real experiments. At first, for a twodimensional Dirac ring, as the disorder density is systematically increased, the persistent current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents, which cannot be discovered in normal metal and semiconductor rings. In addition, in a Floquet system with a ribbon structure, the conductance can be remarkably enhanced by onsite disorder.
Recent years have witnessed significant interest in nanoscale physical systems, such as semiconductor supperlattices and optomechanical systems, which can exhibit distinct collective dynamical behaviors. Firstly, a system of two optically coupled optomechanical cavities is considered and the phenomenon of synchronization transition associated with quantum entanglement transition is discovered. Another useful issue is nonlinear dynamics in semiconductor superlattices caused by its key potential application lies in generating radiation sources, amplifiers and detectors in the spectral range of terahertz. In such a system, transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt.
Another interesting problem in quantum transport is the effect of disorder or random impurities since it is inevitable in real experiments. At first, for a twodimensional Dirac ring, as the disorder density is systematically increased, the persistent current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents, which cannot be discovered in normal metal and semiconductor rings. In addition, in a Floquet system with a ribbon structure, the conductance can be remarkably enhanced by onsite disorder.
Recent years have witnessed significant interest in nanoscale physical systems, such as semiconductor supperlattices and optomechanical systems, which can exhibit distinct collective dynamical behaviors. Firstly, a system of two optically coupled optomechanical cavities is considered and the phenomenon of synchronization transition associated with quantum entanglement transition is discovered. Another useful issue is nonlinear dynamics in semiconductor superlattices caused by its key potential application lies in generating radiation sources, amplifiers and detectors in the spectral range of terahertz. In such a system, transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt.
ContributorsYing, Lei (Author) / Lai, Ying-Cheng (Thesis advisor) / Vasileska, Dragica (Committee member) / Chen, Tingyong (Committee member) / Yao, Yu (Committee member) / Arizona State University (Publisher)
Created2016
Description
This dissertation aims to study and understand the effect of nonlinear dynamics and quantum chaos in graphene, optomechanics, photonics and spintronics systems.
First, in graphene quantum dot systems, conductance fluctuations are investigated from the respects of Fano resonances and quantum chaos. The conventional semi-classical theory of quantum chaotic scattering used in this field depends on an invariant classical phase-space structure. I show that for systems without an invariant classical phase-space structure, the quantum pointer states can still be used to explain the conductance fluctuations. Another finding is that the chaotic geometry is demonstrated to have similar effects as the disorders in transportations.
Second, in optomechanics systems, I find rich nonlinear dynamics. Using the semi-classical Langevin equations, I demonstrate a quasi-periodic motion is favorable for the quantum entanglement between the optical mode and mechanical mode. Then I use the quantum trajectory theory to provide a new resolution for the breakdown of the classical-quantum correspondences in the chaotic regions.
Third, I investigate the analogs of the electrical band structures and effects in the non-electrical systems. In the photonic systems, I use an array of waveguides to simulate the transport of the massive relativistic particle in a non-Hermitian scenario. A new form of Zitterbewegung is discovered as well as its analytical explanation. In mechanical systems, I use springs and mass points systems to achieve a three band degenerate band structure with a new pair of spatially separated edge states in the Dice lattice. A new semi-metal phase with the intrinsic valley-Hall effect is found.
At last, I investigate the nonlinear dynamics in the spintronics systems, in which the topological insulator couples with a magnetization. Rich nonlinear dynamics are discovered in this systems, especially the multi-stability states.
First, in graphene quantum dot systems, conductance fluctuations are investigated from the respects of Fano resonances and quantum chaos. The conventional semi-classical theory of quantum chaotic scattering used in this field depends on an invariant classical phase-space structure. I show that for systems without an invariant classical phase-space structure, the quantum pointer states can still be used to explain the conductance fluctuations. Another finding is that the chaotic geometry is demonstrated to have similar effects as the disorders in transportations.
Second, in optomechanics systems, I find rich nonlinear dynamics. Using the semi-classical Langevin equations, I demonstrate a quasi-periodic motion is favorable for the quantum entanglement between the optical mode and mechanical mode. Then I use the quantum trajectory theory to provide a new resolution for the breakdown of the classical-quantum correspondences in the chaotic regions.
Third, I investigate the analogs of the electrical band structures and effects in the non-electrical systems. In the photonic systems, I use an array of waveguides to simulate the transport of the massive relativistic particle in a non-Hermitian scenario. A new form of Zitterbewegung is discovered as well as its analytical explanation. In mechanical systems, I use springs and mass points systems to achieve a three band degenerate band structure with a new pair of spatially separated edge states in the Dice lattice. A new semi-metal phase with the intrinsic valley-Hall effect is found.
At last, I investigate the nonlinear dynamics in the spintronics systems, in which the topological insulator couples with a magnetization. Rich nonlinear dynamics are discovered in this systems, especially the multi-stability states.
ContributorsWang, Guanglei (Author) / Lai, Ying-Cheng (Thesis advisor) / Vasileska, Dragica (Committee member) / Ning, Cun-Zheng (Committee member) / Zhao, Yuji (Committee member) / Arizona State University (Publisher)
Created2017
Description
This dissertation aims to study and understand relevant issues related to the electronic, spin and valley transport in two-dimensional Dirac systems for different given physical settings. In summary, four key findings are achieved.
First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system.
Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered.
Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies.
Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging.
First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system.
Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered.
Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies.
Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging.
ContributorsXu, Hongya (Author) / Lai, Ying-Cheng (Thesis advisor) / Bliss, Daniel (Committee member) / Yu, Hongbin (Committee member) / Chen, Tingyong (Committee member) / Arizona State University (Publisher)
Created2017
Description
The power of science lies in its ability to infer and predict the
existence of objects from which no direct information can be obtained
experimentally or observationally. A well known example is to
ascertain the existence of black holes of various masses in different
parts of the universe from indirect evidence, such as X-ray emissions.
In the field of complex networks, the problem of detecting
hidden nodes can be stated, as follows. Consider a network whose
topology is completely unknown but whose nodes consist of two types:
one accessible and another inaccessible from the outside world. The
accessible nodes can be observed or monitored, and it is assumed that time
series are available from each node in this group. The inaccessible
nodes are shielded from the outside and they are essentially
``hidden.'' The question is, based solely on the
available time series from the accessible nodes, can the existence and
locations of the hidden nodes be inferred? A completely data-driven,
compressive-sensing based method is developed to address this issue by utilizing
complex weighted networks of nonlinear oscillators, evolutionary game
and geospatial networks.
Both microbes and multicellular organisms actively regulate their cell
fate determination to cope with changing environments or to ensure
proper development. Here, the synthetic biology approaches are used to
engineer bistable gene networks to demonstrate that stochastic and
permanent cell fate determination can be achieved through initializing
gene regulatory networks (GRNs) at the boundary between dynamic
attractors. This is experimentally realized by linking a synthetic GRN
to a natural output of galactose metabolism regulation in yeast.
Combining mathematical modeling and flow cytometry, the
engineered systems are shown to be bistable and that inherent gene expression
stochasticity does not induce spontaneous state transitioning at
steady state. By interfacing rationally designed synthetic
GRNs with background gene regulation mechanisms, this work
investigates intricate properties of networks that illuminate possible
regulatory mechanisms for cell differentiation and development that
can be initiated from points of instability.
existence of objects from which no direct information can be obtained
experimentally or observationally. A well known example is to
ascertain the existence of black holes of various masses in different
parts of the universe from indirect evidence, such as X-ray emissions.
In the field of complex networks, the problem of detecting
hidden nodes can be stated, as follows. Consider a network whose
topology is completely unknown but whose nodes consist of two types:
one accessible and another inaccessible from the outside world. The
accessible nodes can be observed or monitored, and it is assumed that time
series are available from each node in this group. The inaccessible
nodes are shielded from the outside and they are essentially
``hidden.'' The question is, based solely on the
available time series from the accessible nodes, can the existence and
locations of the hidden nodes be inferred? A completely data-driven,
compressive-sensing based method is developed to address this issue by utilizing
complex weighted networks of nonlinear oscillators, evolutionary game
and geospatial networks.
Both microbes and multicellular organisms actively regulate their cell
fate determination to cope with changing environments or to ensure
proper development. Here, the synthetic biology approaches are used to
engineer bistable gene networks to demonstrate that stochastic and
permanent cell fate determination can be achieved through initializing
gene regulatory networks (GRNs) at the boundary between dynamic
attractors. This is experimentally realized by linking a synthetic GRN
to a natural output of galactose metabolism regulation in yeast.
Combining mathematical modeling and flow cytometry, the
engineered systems are shown to be bistable and that inherent gene expression
stochasticity does not induce spontaneous state transitioning at
steady state. By interfacing rationally designed synthetic
GRNs with background gene regulation mechanisms, this work
investigates intricate properties of networks that illuminate possible
regulatory mechanisms for cell differentiation and development that
can be initiated from points of instability.
ContributorsSu, Ri-Qi (Author) / Lai, Ying-Cheng (Thesis advisor) / Wang, Xiao (Thesis advisor) / Bliss, Daniel (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Arizona State University (Publisher)
Created2015