In dieser Arbeit wird für Strukturen, die im makroskopischen aufgrund unterschiedlicher Materialeigenschaften oder komplexer Geometrien eine hohe Netzfeinheit für Finite-Elemente-Berechnungen benötigen, eine neue Möglichkeit zur Berechnung effektiver Materialkennwerte vorgestellt. Durch einen modalen Ansatz, bei dem, je nach Struktur analytisch oder numerisch, mit Hilfe der modalen Kennwerte die Formänderungsenergie eines repräsentativen Volumens der Originalstruktur mit der Formänderungsenergie eines äquivalenten homogen Vergleichsvolumens verglichen wird, können effektive Materialkennwerte ermittelt und daran anschließend eine Finite-Elemente-Berechnung mit einem im Vergleich zum Originalmodell sehr viel gröberen Netz durchgeführt werden, was eine enorme Zeiteinsparung mit sich bringt. Weiterhin enthält die vorgestellte Methode die Möglichkeit, unsichere Eingabeparameter wie Geometrieabmessungen oder Materialkennwerte mit Hilfe der polynomialen Chaos Expansion zu approximieren, um Möglichkeiten zur Aussage bzgl. der daraus resultierenden Verteilungen modaler Kenngrößen auf eine schnelle und effektive Weise zu gewinnen.

Druj Aeterni is a large chamber ensemble piece for flute, clarinet, French horn, two trumpets, piano, two percussionists, string quintet, and electric bass. My composition integrates three intellectual pursuits and interests, ancient mythology, cosmology, and mathematics. The title of the piece uses Latin and the language of the Avesta, the holy book of Zoroastrianism, and comments upon a philosophical perspective based in string theory. I abstract the cosmological implications of string theory, apply them to the terminology and theology of Zoroastrianism, and then structure the composition in consideration of a possible reconciliation. The analysis that follows incorporates analytical techniques similar to David Cope’s style of Vectoral Analysis.

Chaotic systems have been studied for the past few decades because of its complex behaviour given simple governing ordinary differential equations. In the field of cryptology, several methods have been proposed for the use of chaos in cryptosystems. In this work, a method for harnessing the beneficial behaviour of chaos was proposed for use in RFID authentication and encryption. In order to make an accurate estimation of necessary hardware resources required, a complete hardware implementation was designed using a Xilinx Virtex 6 FPGA. The results showed that only 470 Xilinx Virtex slices were required, which is significantly less than other RFID authentication methods based on AES block cipher. The total number of clock cycles required per encryption of a 288-bit plaintext was 57 clock cycles. This efficiency level is many times higher than other AES methods for RFID application. Based on a carrier frequency of 13.56Mhz, which is the standard frequency of common encryption enabled passive RFID tags such as ISO-15693, a data throughput of 5.538Kb/s was achieved. As the strength of the proposed RFID authentication and encryption scheme is based on the problem of predicting chaotic systems, it was important to ensure that chaotic behaviour is maintained in this discretized version of Lorenz dynamical system. As a result, key boundaries and fourth order Runge Kutta approximation time step values that are unique for this new mean of chaos utilization were discovered. The result is a computationally efficient and cryptographically complex new RFID authentication scheme that can be readily adopted in current RFID standards such as ISO-14443 and ISO-15693. A proof of security by the analysis of time series data obtained from the hardware FPGA design is also presented. This is to ensure that my proposed method does not exhibit short periodic cycles, has an even probabilistic distribution and builds on the beneficial chaotic properties of the continuous version of Lorenz dynamical system.

Accurate prediction and control pervades domains such as engineering, physics, chemistry, and biology. Often, it is discovered that the systems under consideration cannot be well represented by linear, periodic nor random data. It has been shown that these systems exhibit deterministic chaos behavior. Deterministic chaos describes systems which are governed by deterministic rules but whose data appear to be random or quasi-periodic distributions. Deterministically chaotic systems characteristically exhibit sensitive dependence upon initial conditions manifested through rapid divergence of states initially close to one another. Due to this characterization, it has been deemed impossible to accurately predict future states of these systems for longer time scales. Fortunately, the deterministic nature of these systems allows for accurate short term predictions, given the dynamics of the system are well understood. This fact has been exploited in the research community and has resulted in various algorithms for short term predictions. Detection of normality in deterministically chaotic systems is critical in understanding the system sufficiently to able to predict future states. Due to the sensitivity to initial conditions, the detection of normal operational states for a deterministically chaotic system can be challenging. The addition of small perturbations to the system, which may result in bifurcation of the normal states, further complicates the problem. The detection of anomalies and prediction of future states of the chaotic system allows for greater understanding of these systems. The goal of this research is to produce methodologies for determining states of normality for deterministically chaotic systems, detection of anomalous behavior, and the more accurate prediction of future states of the system. Additionally, the ability to detect subtle system state changes is discussed. The dissertation addresses these goals by proposing new representational techniques and novel prediction methodologies. The value and efficiency of these methods are explored in various case studies. Presented is an overview of chaotic systems with examples taken from the real world. A representation schema for rapid understanding of the various states of deterministically chaotic systems is presented. This schema is then used to detect anomalies and system state changes. Additionally, a novel prediction methodology which utilizes Lyapunov exponents to facilitate longer term prediction accuracy is presented and compared with other nonlinear prediction methodologies. These novel methodologies are then demonstrated on applications such as wind energy, cyber security and classification of social networks.

In the last few decades, the study of many-body quantum systems far from equilibrium has risen to prominence, with exciting developments on both experimental and theoretical physics fronts. In this dissertation, we will focus particularly on the adiabatic gauge potential (AGP), which is the generator of adiabatic deformations between quantum eigenstates and also related to "fidelity susceptibility", as our lens into the general phenomenon. In the first two projects, the AGP is studied in the context of counter-diabatic driving protocols which present a way of generating adiabatic dynamics at an arbitrary pace. This is quite useful as adiabatic evolution, which is a common strategy for manipulating quantum states, is inherently a slow process and is, therefore, susceptible to noise and decoherence from the environment. However, obtaining and implementing the AGP in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be systematically built up as a series of nested commutators, remaining well-defined in the thermodynamic limit. Furthermore, the resulting counter-diabatic driving protocols can be realized up to arbitrary order without leaving the available control space using tools from periodically-driven (Floquet) systems. In the first project, this driving protocol was successfully implemented on the electronic spin of a nitrogen vacancy in diamond as a proof of concept and in the second project, it was extended to many-body systems, where it was shown the resulting Floquet protocols significantly suppress dissipation and provide a drastic increase in fidelity. In the third project, the AGP is studied in the context of quantum chaos wherein it is found to be an extremely sensitive probe. We are able to detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability-breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size. This work paves the way for further studies in various areas such as quantum computation, quantum state preparation and quantum chaos.

This thesis presents a novel work on hardware realization of symmetric image encryption utilizing chaos based continuous systems as pseudo random number generators. Digital implementation of chaotic systems results in serious degradations in the dynamics of the system. Such defects are illuminated through a new technique of generalized post proceeding with very low hardware cost. The thesis further discusses two encryption algorithms designed and implemented as a block cipher and a stream cipher. The security of both systems is thoroughly analyzed and the performance is compared with other reported systems showing a superior results. Both systems are realized on Xilinx Vetrix-4 FPGA with a hardware and throughput performance surpassing known encryption systems.

This diploma project is showen possibilities in classification of genomic sequences with CGR and FCGR methods in pictures. From this picture is computed classificator with BCM. Next here is written about the programme and its opportunities for classification. In the end is compared many of sequences computed in different options of programme.

This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed design is then enhanced to increase the operating speed using the divide- and-conquer concept. Such enhancement, did not only make the AES algorithm more secure, but also enabled the AES to be faster, as it can now operate on higher frequencies, and more area-efficient.

Thulium (Tm) based high repetition rate compact optical frequency comb sources operating in the 2 µm regime with femtosecond pulse durations enable a wide range of applications such as precise micro-machining, spectroscopy and metrology. Applications such as metrology and spectroscopy rely on the stability of mode-locked lasers (MLLs) which provide extreme precision, yet, the complex dynamics of such highly nonlinear systems result in unstable events which could hinder the normal operation of a MLL. MLL as a nonlinear system inherently exists a wide variety of complex attractors, which are sets of states that the system tends to evolve toward, exhibiting unique behaviors. Complex phenomena including pulsating solitons, chaotic solitons, period-doubling, soliton explosion, etc., have been predicted theoretically and observed experimentally in the past decade. However, most experimental observations rely on conventional characterization methods, which are limited to the scanning speed of the spectrometer and the electronic speed of photodetector and digitizer, so that the details of the non-repetitive events can be buried. In recent years, a technique called dispersive Fourier transform (DFT) has been developed and allows consecutive recordings of the pulse-to-pulse spectral evolution of a femtosecond pulse train, opening a whole new world of nonlinear dynamics in MLL. In this dissertation, we first demonstrate the ability of scaling the repetition rate of a Tm MLL to repetition rate as high as 1.25 GHz through miniaturizing the cavity. Our approach of maintaining comparable pulse energies while scaling the repetition rates allows a high-quality femtosecond mode-locking performance with low noise performance in Tm soliton lasers. Then we experimentally study the transition dynamics between consecutive multi-pulsing states through adjusting pump power with a constant rate in an erbium-doped fiber laser, specifically the build-up and annihilation of soliton pulses between a double pulsing and a three-pulse state utilizing DFT. To investigate real-time laser dynamics in Tm based laser systems, we propose and develop a DFT system that up-converts the signal to the 1 µm regime via second harmonics generation (SHG) and stretches the signal in a long spool of single-mode fiber to realize DFT. This approach overcomes the limitation of bandwidth of 2 µm photodetector and high intrinsic absorption of 2 µm light in fused silica fibers. The SHG-DFT system is used to study dynamics of both explosions in a chaotic state between stable single-pulsing and double-pulsing state, and explosions induced by soliton collision in a dual-wavelength vector soliton state. We also study dynamics of transient regimes in a Tm-doped fiber ring laser that can be switched between conventional soliton and dissipative soliton, revealing how spectral filtering plays a role in obtaining stable stationary states. / 2022-11-23T00:00:00Z

No description available.