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With the rapid development of microtechnology, the low-dimensional materials are fabricated with nontrivial topological structures, and then the action of geometric properties on the effective dynamics receives increasing attention. It is an effective theory that the quantum mechanics of low-dimensional curved systems can be given by using the thin-layer quantization approach, in which the geometric potential and the geometric momentum have been demonstrated experimentally. In the present paper, the thin-layer quantization formalism is first recalled, its fundamental calculation framework is first clarified, and the geometric quantum effects result from the diffeomorphism transformation and the rotation transformation connecting the local frames of different points. The results are helpful to understand the gravitational gauge and emerging gauge, and to image the geometries implied in the artificial gauge. In the particular quantum systems, the novel physical phenomena are briefly recalled that are induced by geometry, such as resonation tunneling, quantum block, quantum Hall effect, quantum Hall viscosity, quantum spin Hall effect, effective monopole magnetic field and so on. The results will shed light from a different angle on the relationships between the geometry and the novel physical phenomenon. [ABSTRACT FROM AUTHOR]

In order to determine the quantization level of sensors in quantized measurements, a new filter with allowable quantization level as low as possible was designed for given constraints of variance. The condition of the stability of error covariance matrix and a LMI method for current-estimation-type steady filter were presented. It means that, on the premise of meeting the system estimation variance, the designers can choose the sensors with lower resolution. A numerical example shows the usefulness and flexibility of the proposed approach. [ABSTRACT FROM AUTHOR]

System level analysis and design of a single-loop fourth-order sigma-delta (ΣΔ) accelerometer is presented to reduce quantization noise and enhance resolution of the micromachined accelerometer. Stability of the system is analyzed by root locus method based on the linear model established in this work. Theoretical analysis indicates that the forth-order ΣΔ micromachined accelerometer has good performance in noise, dead zone and idle tone. Based on the analysis and discussion of the system level, the transistor level design of the interface circuit is implemented, the circuit is fabricated in 0. 5 µm two poly two metal CMOS process, and the tested results indicate that the sensitivity is 1.2 V/g, nonlinearity is 0.2% , open-loop noise density is 12 µg/Hz1/2, closed-loop noise density is 80 u/Hz1/2 and the power dissipation is 40 mW. [ABSTRACT FROM AUTHOR]

With the assistant study of Twin-T circuit and memristor based chaotic circuit (MCC),bifurcation and chaos in several typical digitally controlled power electronic circuits were discussed. Additionally, chaos was then applied to power electronic circuits for the sake of improving the system performance. Twin-T circuit is widely used in oscillators and notch filter design due to its outstanding frequency-selecting ability. A new chaotic Twin-T circuit was designed by connecting a light-emitting diode to the junction of two capacitors in the original circuit topology. The bifurcation diagrams were drawn, which shows clearly that the output voltage evolved to chaos through period-adding bifurcation as the control signal strength coefficient increases. Memristor is regarded as the forth basic element except for resistor, capacitor and inductor. By replacing the nonlinear element in Chua's circuit with memristor, MCC system was obtained. Bifurcation behavior and double-scroll strange attractor were studied by means of numerical methods such as bifurcation diagram, the largest Lyapunov exponent, power spectrum, etc. A chaos controller which includes a Twin-T notch filter and a voltage-current interface circuit was designed to adjust MCC from chaos to period in this dissertation. By modifying MCC system with an inductor and a negative conductance, a new four order hyperchaotic circuit was achieved. It has been validated that bifurcation and chaos are common phenomena in power electronic converters. However, the bifurcation phenomena in digitally controlled converter involving with time delay and quantization error is rarely concerned. The bifurcation phenomenon of a digitally proportional-integral (PI) controlled synchronous buck converter (SBC) was investigated by making use of z-domain small signal model. In addition, the limit cycle was estimated by taking into account the dynamic gain caused by quantization effect on the basis of describing function. Switched reluctance drive (SRD) can also be regarded as a converter circuit including a particular moving component. Based on the assumption that phase inductance is independent of phase current, the comparison of bifurcation behaviors between analogly and digitally controlled SRD were presented. Additionally, a new nonlinear model on the basis of exponential function was designed and brought to analyze the bifurcate and chaotic behaviors in SRD system by the aid of bifurcation diagram and power spectrum. In many cases, the topology as well as mathematic describing equations of a circuit is of impossibility to characterize by reason of the complex. A time series sampled from MCC was used to testify the validation of phase space reconstruction technique. Additionally, a fuzzy controlled SRD simulation model was built based on MATLAB SIMULINK environment. The calculation results of fractal dimension and the largest Lyapunov exponent demonstrate that in a wide parameter region, digitally controlled SRD behaves in chaotic oscillation. MCC was introduced as signal source to carry out the chaotic frequency spreading strategy for digitally controlled SBC. In accordance with the conclusion that fuzzy controlled SRD system can operate in a wide region chaotically, a chaotic frequency spreading strategy was designed by taking feedback acceleration as chaotic signal. In addition, the frequency spectrum of filter capacitor in SRD operated under the condition that different single phase faults come forth in the converter was analyzed. Single fault diagnosis of converter in SRD system is implemented on the strength of chaotic invariant extracted from detailed filter capacitor voltage. [ABSTRACT FROM AUTHOR]