A diagrammatic method to compute the effective Hamiltonian of driven nonlinear oscillators

In this work, we present a new method, based on Feynman-like diagrams, for computing the effective Hamiltonian of driven nonlinear oscillators. The pictorial structure associated with each diagram corresponds directly to a Hamiltonian term, the prefactor of which involves a simple counting of topologically equivalent diagrams. We also leverage the algorithmic simplicity of our scheme in a readily available computer program that generates the effective Hamiltonian to arbitrary order. At the heart of our diagrammatic method is a novel canonical perturbation expansion developed in phase space to capture the quantum nonlinear dynamics. A merit of this expansion is that it reduces to classical harmonic balance in the limit of $\hbar\rightarrow0$. Our method establishes the foundation of the dynamic control of quantum systems with the precision needed for future quantum machines. We demonstrate its value by treating five examples from the field of superconducting circuits. These examples involve an experimental proposal for the Hamiltonian stabilization of a three-legged Schr\"odinger cat, modeling of energy renormalization phenomena in superconducting circuits experiments, a comprehensive characterization of multiphoton resonances in a driven transmon, a proposal for an novel inductively shunted transmon circuit, and a characterization of classical ultra-subharmonic bifurcation in driven oscillators. Lastly, we benchmark the performance of our method by comparing it with experimental data and exact Floquet numerical diagonalization

A Metastable Modular Structure Approach for Shape Morphing, Property Tuning and Wave Propagation Tailoring

The emerging concept of reconfigurable mechanical metamaterials has received increasing attention for realizing future advanced multifunctional adaptive structural systems partially due to their advantages over conventional bulk materials that are beneficial and desirable in many engineering applications. However, some of the critical challenges remain unaddressed before the concept can effectively and efficiently achieve real-world impacts. For instance, in the state-of-art, modules of mechanical metamaterials only reconfigure collectively to achieve global topology adaptation. As a result, the structure merely exhibits limited number of configurations that are discretely different from each other, which greatly undermines the benefits and impact of the reconfiguration effect. Additionally, most of the metamaterials investigations are focusing on the “materials” characteristics assuming infinite domain without considering the “structure” aspect of the systems. The effects of having finite domains and boundary conditions will generate new research issues and phenomena that are critical to real-world systems. To address the challenges and fundamentally advance the state of the art of multifunctional adaptive structures, this dissertation seeks to create a paradigm shift by exploiting and harnessing metastable modular mechanics and dynamics. Through developing new analysis and synthesis methodologies and conducting rigorous analytical, numerical, and experimental investigations, this research creates a new class of reconfigurable metastructure that can achieve mechanical property and topology adaptation as well as adaptive non-reciprocal vibration/wave transmission. The intellectual merit of this dissertation lies in introducing metastable modules that can be synergistically assembled and individually tuned to realize near continuous topology and mechanical property adaptation and elucidating the intricate nonlinear dynamics afforded by the metastructure. This research reveals different kinds of nonlinear instabilities that are able to facilitate the onset of supratransmission, a bandgap transmission phenomenon pertained to nonlinear periodic metastructure. In addition, utilizing this novel phenomenon, supratransmission, together with inherent spatial asymmetry of strategically configured constituents, the proposed metastructure is shown to be able to facilitate unprecedented broadband non-reciprocal vibration and wave transmission and on-demand adaptation. Since the proposed approach depends primarily on scale-independent principles, the broader impact of this dissertation is that the proposed metastructure could foster a new generation of reconfigurable structural and material systems with unprecedented adaptation and unconventional vibration control and wave transmission characteristics that are applicable to vastly different length scales for a wide spectrum of applications.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147525/1/wuzhen_1.pd

References, Appendices & All Parts Merged

Includes: Appendix MA: Selected Mathematical Formulas; Appendix CA: Selected Physical Constants; References; EGP merged file (all parts, appendices, and references)https://commons.library.stonybrook.edu/egp/1007/thumbnail.jp

An experimental investigation of cavity flow

Of particular interest are the flow structure and dynamics associated with open shallow rectangular cavities at low Mach numbers for various length-to-depth ratios. At the Reynolds number investigated, it is the presence of convective instabilities through the process of feedback disturbance that gives rise to a globally unstable flowfield. Using an instrumental wing model with a cut-out an experimental investigation of a cavity flowfield exhibiting ‘fluid-dynamic’ phenomenon has been completed. A post-processing module for the PIV image data was constructed which optimised the data fidelity and accuracy while improving upon velocity spatial resolution. These improvements were necessary to capture the flow scales of interest and minimise the measurement error for the presentation of velocity, velocity-derivative and turbulent statistics. It is shown that the hydrodynamics that is intrinsic to the cavity flowfield at these inflow conditions organises the oscillation of small- and large-scale vortical structures. The impingent scenario at the downstream edge is seen to be crucially important to the cavity oscillation and during the mass addition phase a jet-edge is seen to form over the rear bulkhead and floor. In some instances this jet-like flow is observed to traverse the total internal perimeter of the cavity and interact with the shear layer at the leading edge of the cavity, this disturbs the normal growth of the shear layer and instigates an increase in fluctuation. The coexistence and interplay between a lower frequency mode dominant within the cavity zone and the shear layer mode is seen to shed large-scale eddies from the cavity. This modulation imposes a modification to the feedback signal strength such that two distinct states of the shear layer are noted. Concepts for the passive reduction of internal cavity fluctuation are successful although modifications to the shear layer unsteadiness are encountered; an increase in drag is implied

Dynamical systems : mechatronics and life sciences

Proceedings of the 13th Conference „Dynamical Systems - Theory and Applications" summarize 164 and the Springer Proceedings summarize 60 best papers of university teachers and students, researchers and engineers from whole the world. The papers were chosen by the International Scientific Committee from 315 papers submitted to the conference. The reader thus obtains an overview of the recent developments of dynamical systems and can study the most progressive tendencies in this field of science

Nonlinear Dynamics

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students

Hadron models and related New Energy issues

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena. The authors explored some new approaches to describe novel phenomena in particle physics. M Pitkanen introduces his nuclear string hypothesis derived from his Topological Geometrodynamics theory, while E. Goldfain discusses a number of nonlinear dynamics methods, including bifurcation, pattern formation (complex GinzburgLandau equation) to describe elementary particle masses. Fu Yuhua discusses a plausible method for prediction of phenomena related to New Energy development. F. Smarandache discusses his unmatter hypothesis, and A. Yefremov et al. discuss Yang-Mills field from Quaternion Space Geometry. Diego Rapoport discusses theoretical link between Torsion fields and Hadronic Mechanic. A.H. Phillips discusses semiconductor nanodevices, while V. and A. Boju discuss Digital Discrete and Combinatorial methods and their likely implications in New Energy research. Pavel Pintr et al. describe planetary orbit distance from modified Schrödinger equation, and M. Pereira discusses his new Hypergeometrical description of Standard Model of elementary particles. The present volume will be suitable for researchers interested in New Energy issues, in particular their link with alternative hadron models and interpretation

Out-of-Equilibrium Carrier Dynamics in Graphene and Graphene-based Devices for High-Performance Electronics

[ES]Con los límites tecnológicos de las tecnologías de semiconductores tradicionales alcanzando los límites de escalado y integración en chip, el descubrimiento del grafeno y sus impresionantes propiedades supuso una prometedora alternativa para el futuro de la electrónica. Para contextualizar adecuadamente las posibilidades del grafeno, la investigación de las propiedades micrsocópicas del transporte electrónico es una tarea crucial. Con este objetivo, se ha desarrollado un simulador Monte Carlo para grafeno, que incluye la dinámica de electrones y huecos, con espacial atención a fenómenos de portadores calientes, como fonones fuera de equilibrio, procesos Auger o generación/recombinación asistida por fonones. El análisis del transporte electrónico a campos altos permitió cuantificar el impacto relativo del autocalentamiento y los fonones calientes sobre la velocidad de deriva en condiciones estacionarias y la temperatura del material. Además se observó un comportamiento lineal de la corriente debida a la ionización por impacto. Se ha estudiado la fenomenología relacionada con fluctuaciones empleando diversos métodos numéricos orientados a condiciones transitorias particulares (saltos abruptos de campo o señales AC). La temperatura del ruido dependiente de la frecuencia se obtuvo a partir de la difusividad y movilidad diferencial los portadores, y la viabilidad de la generación de armónicos de orden alto en grafeno se presenta en términos del ancho de banda límite para su detección. El potencial del grafeno para aplicaciones optoelectrónicas precisa de una comprensión detallada de los procesos de relajación ultrarrápida que sufren los portadores fotoexcitados con longitudes de onda apropiadas. Llevamos a cabo un examen exhaustivo de este proceso, con especial atención a las condiciones iniciales de fotoexcitación, el papel de los fonones calientes, y el efecto del sustrato. Finalmente presentamos una versión inicial de simulador para dispositivos electrónicos basados en materiales 2D, que cimentará las líneas futuras de investigación en el campo del modelado Monte Carlo de estos dispositivos.[EN] With traditional semiconductor technology approaching the limits of scaling and chip integration, the discovery of graphene and its astonishing properties stood as a promising alternative for future electronics. In order to adequately put into context the possibilities of graphene, it is critical to investigate the microscopic properties of electronic transport in this material. With this objective, a Monte Carlo simulator for graphene that includes the dynamics of electrons and holes, with especial focus on hot carrier phenomena, like hot phonons, Auger processes, and phonon-assisted generation and recombination mechanisms has been developed. The analysis of electronic transport at high fields allowed to quantify the relative impact that self heating and hot phonons have in the steady state drift velocity of the carriers and temperature. Linear sheet current behavior at high fields was found to be the result of free charge carriers created through impact ionization collisions. Velocity fluctuation phenomena in graphene were studied employing various numerical methods aimed at the analysis of specific transient dynamics (under the application of switching or AC electric fields). The frequency-dependent noise temperature was obtained from the diffusivity an differential mobility, and the feasibility of generating high-order harmonics in graphene, was presented in terms of the detection bandwidth. The potential of graphene for optoelectronic applications requires also a deep understanding of the ultrafast relaxation processes that carriers undergo after being exposed to light with an adequate wavelength. A thorough exploration of this process, with particular focus on the initial photoexcitation conditions, the effect of out-of-equilibrium phonons and the influence of an underlying substrate is presented, together with an experimental pump and probe differential transmission spectroscopy approach. An initial version of a simulator of 2D material-based devices is presented, which allows to set the basis for future research in the field of Monte Carlo modeling of this kind of electronic devices

Josephson Tunneling at the Atomic Scale:The Josephson Effect as a Local Probe

The aim of this thesis is to characterize the properties of a Josephson junction in a Scanning Tunneling Microscope (STM) at millikelvin temperatures and to implement Josephson STM (JSTM) as a versatile probe at the atomic scale. To this end we investigate the I(V) tunneling characteristics of the Josephson junction in our STM at a base temperature of 15 mK by means of current-biased and voltage-biased experiments. We find that in the tunneling regime, the Josephson junction is operated in the dynamical Coulomb blockade (DCB) regime in which the sequential tunneling of Cooper pairs dominates the tunneling current. Employing P(E)-theory allows us to model experimental I(V) characteristics from voltage-biased experiments and determine experimental values of the Josephson critical current in agreement to theory. Moreover, we observe a breakdown of P(E)-theory for experiments at large values of the tunneling conductance on the order of the quantum of conductance, which could indicate that the coherent tunneling of Cooper pairs strongly contributes to the tunneling current in this limit. We also observe that the Josephson junction in an STM at temperatures well below 100 mK is highly sensitive to its electromagnetic environment that results from its tiny junction capacitance of a few femtofarads. The combination of the experimental results with numerical simulations reveals that the immediate environment of the Josephson junction in an STM is frequency-dependent and, additionally, that a typical STM geometry shares the electromagnetic properties of a monopole antenna with the STM tip acting as the antenna. Comparing the I(V) curves of voltage-biased and current-biased experiments, we observe that the time evolution of the phase is strongly effected by dissipation due to quasiparticle excitations. From investigations on the retrapping current we show first that the temporal evolution of the junction phase in our STM satisfies a classical equation of motion. Second, we can determine two different channels for energy dissipation of the junction phase. For tunneling resistance values RN< 150 k­Ohm the junction dissipates via Andreev reflections whereas for larger values of RN <150 k­Ohm the energy dissipation is dominated by lifetime effects of Cooper pairs. Moreover, from comparing both experiments we also observe that the quantum-mechanical nature of the junction phase manifests itself in quantum-mechanical phenomena, such as phase tunneling, which strongly alter our experimental I(V) characteristics for GN<=G0. To conclude, within this thesis we characterized the properties of a Josephson junction in an STM that is operated at millikelvin temperatures. Hence, this work represents necessary and fundamental steps that allows us to employ the Josephson effect as a versatile probe on the atomic scale

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...