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We study the time evolution of driven quantum systems using analytic, algebraic, and numerical methods. First, we obtain analytic solutions for driven free and oscillator systems by shifting the coordinate and phase of the undriven wave function. We also factorize the quantum evolution operator using the generators of the Lie algebra comprising the Hamiltonian. We obtain coupled ODE's for the time evolution of the Lie algebra parameters. These parameters allow us to find physical properties of oscillator dynamics. In particular we find phase-space trajectories and transition probabilities. We then search for chaotic behavior in the Lie algebra parameters as a signature for dynamical chaos in the quantum system. We plot the trajectories, transition probabilities, and Lyapunov exponents for a wide range of the following physical parameters: strength and duration of the driving force, frequency difference, and anharmonicity of the oscillator. We identify conditions for the appearance of chaos in the system.

We investigated the antiferromagnetic phase transition in the frustrated and multiferroic hexagonal manganites h-YMnO3 (YMO) and h-(Y0.98Eu0.02)MnO3 (YEMO). Elastic neutron scattering was used to study, in detail, the phase transition in YMO and YEMO under zero pressure and in YMO under a hydrostatic pressure of 1.5 GPa. Under conditions of zero pressure, we found critical temperatures of TN = 71.3(1) K and 72.11(5) K and the critical exponent 0.22(2) and b = 0.206(3), for YMO and YEMO, respectively. This is in agreement with earlier work by Roessli et al. Under an applied hydrostatic pressure of 1.5 GPa, the ordering temperature increased to TN = 75.2(5) K, in agreement with earlier reports, while b was unchanged. Inelastic neutron scattering was used to determine the size of the anisotropy spin wave gap close to the phase transition. From spin wave theory, the gap is expected to close with a critical exponent, b0, identical to the order parameter b. Our results indicate that the gap in YEMO indeed closes at TN = 72.4(3) K with b0 = 0.24(2), while the in-pressure gap in YMO closes at 75.2(5) K with an exponent of b0 = 0.19(3). In addition, the low temperature anisotropy gap was found to have a slightly higher absolute value under pressure. The consistent values obtained for b in the two systems support the likelihood of a new universality class for triangular, frustrated antiferromagnets.

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No description available.

To identify the long-term trend of particle size variation, we analyzed aerosol optical depth (AOD, τ) separated as dust (τD) and coarse-(τPC) and fine-pollution particles (τPF) depending on emission sources and size. Ångström exponent values are also identified separately as total and fine-mode particles (αT and αPF). We checked these trends in various ways; (1) first-order linear regression analysis of the annual average values, (2) percent variation using the slope of linear regression method, and (3) a reliability analysis using the Mann–Kendall (MK) test. We selected 17 AERONET sun/sky radiometer sites classified into six regions, i.e., Europe, North Africa, the Middle East, India, Southeast Asia, and Northeast Asia. Although there were regional differences, τ decreased in Europe and Asian regions and increased in the Middle East, India, and North Africa. Values of τPC and τPF, show that aerosol loading caused by non-dust aerosols decreased in Europe and Asia and increased in India. In particular, τPF considerably decreased in Europe and Northeast Asia (95% confidential levels in MK-test), and τPC decreased in Northeast Asia (Z-values for Seoul and Osaka are −2.955 and −2.306, respectively, statistically significant if |z| ≥ 1.96). The decrease in τPC seems to be because of the reduction of primary and anthropogenic emissions from regulation by air quality policies. The meaningful result in this paper is that the particle size became smaller, as seen by values of αT that decreased by −3.30 to −30.47% in Europe, North Africa, and the Middle East because αT provides information on the particle size. Particle size on average became smaller over India and Asian regions considered in our study due to the decrease in coarse particles. In particular, an increase of αPF in most areas shows the probability that the average particle size of fine-mode aerosols became smaller in recent years. We presumed the cause of the increase in αT is because relatively large-sized fine-mode particles were eliminated due to air quality policies.

Fluid mixing is a challenging problem in laminar flow systems. Chaotic advection can play an important role in enhancing mixing in such flow. In this thesis, different approaches are used to enhance fluid mixing in two laminar flow systems. In the first system, chaos is generated in a flow between two closely spaced parallel circular plates by pulsed operation of fluid extraction and reinjection through singularities in the domain. A singularity through which fluid is injected (or extracted) is called a source (or a sink). In a bounded domain, one source and one sink with equal strength operate together as a source-sink pair to conserve the fluid volume. Fluid flow between two closely spaced parallel plates is modeled as Hele-Shaw flow with the depth averaged velocity proportional to the gradient of the pressure. So, with the depth-averaged velocity, the flow between the parallel plates can effectively be modeled as two-dimensional potential flow. This thesis discusses pulsed source-sink systems with two source-sink pairs operating alternately to generate zig-zag trajectories of fluid particles in the domain. For reinjection purpose, fluid extracted through a sink-type singularity can either be relocated to a source-type one, or the same sink-type singularity can be activated as a source to reinject it without relocation. Relocation of fluid can be accomplished using either "first out first in" or "last out first in" scheme. Both relocation methods add delay to the pulse time of the system. This thesis analyzes mixing in pulsed source-sink systems both with and without fluid relocation. It is shown that a pulsed source-sink system with "first out first in" scheme generates comparatively complex fluid flow than pulsed source-sink systems with "last out first in" scheme. It is also shown that a pulsed source-sink system without fluid relocation can generate complex fluid flow. In the second system, mixing and transport is analyzed in a two-dimensional Stokes flow system. Appropriate periodic motions of three rods or periodic points in a two-dimensional flow are determined using the Thurston-Nielsen Classification Theorem (TNCT), which also predicts a lower bound on the complexity generated in the fluid flow. This thesis extends the TNCT -based framework by demonstrating that, in a perturbed system with no lower order fixed points, almost invariant sets are natural objects on which to apply the TNCT. In addition, a method is presented to compute line stretching by tracking appropriate motion of finite size rods. This method accounts for the effect of the rod size in computing the complexity generated in the fluid flow. The last section verifies the existence of almost invariant sets in a two-dimensional flow at finite Reynolds number. The almost invariant set structures move with appropriate periodic motion validating the application of the TNCT to predict a lower bound on the complexity generated in the fluid flow. / Ph. D.

Tire-pavement interaction is a dominant noise source for passenger cars and trucks above 25 mph (40 km/h) and 43 mph (70 km/h), respectively. For the same pavement, tires with different tread pattern and construction generate noise of different levels and frequencies. In the present study, forty-two different tires were tested over a range of speeds (45-65 mph, i.e., 72-105 km/h) on a non-porous asphalt pavement (a section of U.S. Route 460, both eastbound and westbound). An On-Board Sound Intensity (OBSI) system was instrumented on the test vehicle to collect the tire noise data at both the leading and trailing edge of the tire contact patch. An optical sensor recording the once-per-revolution signal of the wheel was also installed to monitor the vehicle speed and, more importantly, to provide the data needed to perform the order tracking analysis in order to break down the tire noise into two components. These two components are: the tread pattern and the non-tread pattern noise. Based on the experimental noise data collected, two artificial neural networks (ANN) were developed to predict the tread pattern (ANN1) and the non-tread pattern noise (ANN2) components, separately. The inputs of ANN1 are the coherent tread profile spectrum and the air volume velocity spectrum calculated from the digitized 3D tread pattern. The inputs of ANN2 are the tire size and tread rubber hardness. The vehicle speed is also included as input for the two ANN's. The optimized ANN's are able to predict the tire-pavement interaction noise well for different tires on the pavement tested. Another outcome of this work is the complete literature review on Tire-Pavement Interaction Noise (TPIN), as an appendix of this dissertation and covering ~1000 references, which might be the most comprehensive compilation of this topic. / PHD

Kapaciteter kan vara till stor nytta, bland annat då partiella differentialekvationer ska lösas. Kapaciteter är dock i många fall väldigt svåra att beräkna exakt, speciellt i viktade rum. Vad som istället kan göras är att försöka uppskatta kapaciteterna, vilket för ringar runt en fix punkt kan utföras med hjälp av fyra olika exponentmängder, \underline{Q}_0, \underline{S}_0, \overline{S}_0 och \overline{Q}_0, som beskriver hur vikten beter sig i närheten av denna punkt och i viss mån ger rummets lokala dimension. För att kunna dra nytta av exponentmängderna är det bra att veta vilka kombinationer av dessa som kan förekomma. För att få fram nya kombinationer använder vi olika sätt att mäta volym av klot med varierande radier. Dessa mått är definierade genom olika vikter. Det har tidigare funnits ett fåtal exempel på hur olika kombinationer av exponentmängderna kan se ut. Variationerna består av hur avstånden är i förhållande till varandra och om ändpunkterna tillhör mängderna eller inte. I denna rapport har vi tagit fram ytterligare fem nya kombinationer av mängderna, bland annat en där \underline{Q}_0 är öppen. / Capacities can be of great benefit, for instance when solving partial differential equations. In most cases, capacities can be difficult to calculate exactly, in particular on weighted spaces. In these cases, it can be sufficient with an estimation of the capacity instead. For annuli around a given point, the estimation can be done using four exponent sets \underline{Q}_0, \underline{S}_0, \overline{S}_0 and \overline{Q}_0, which describe how the weight behaves in a neighbourhood of that point and in some sense define the local dimension of the space. To be able to use the exponent sets, it is useful to know which combinations of them can exist. For this we use various measures, which are a way to measure volumes of balls with varying radii in Rn. These measures are defined by different weights. Earlier, there existed a few examples giving different combinations of exponent sets. The variations consist in their relationship to each other and if their endpoints belong to the set or not. In this thesis we present five new combinations of the exponent sets, amongst them one where \underline{Q}_0 is open.

This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value.