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36 results
  • We extend the two-dimensional model of drug use introduced in Behrens et al. [1999, 2000, 2002] by introducing two additional states that model in more detail newly initiated (“light”) users’ response to the drug experience. Those who dislike the drug quickly “quit” and briefly suppress initiation by others. Those who like the drug progress to ongoing (“moderate”) use, from which they may or may not escalate to “heavy” or dependent use. Initiation is spread contagiously by light and moderate users, but is moderated by the drug’s reputation, which is a function of the number of unhappy users (recent quitters + heavy users). The model reproduces recent prevalence data from the U.S. cocaine epidemic reasonably well, with one pronounced peak followed by decay toward a steady state. However, minor variation in parameter values yields both long-run periodicity with a period akin to the gap between the first U.S. cocaine epidemic (peak ~1910) and the current one (peak ~1980), as well as short-run periodicity akin to that observed in data on youthful use for a variety of substances. The combination of short- and long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman [2002]. The existence of such complex behavior including cycles, quasi periodic solutions, and chaos is proven by means of bifurcation analysis.
    Data Types:
    • Document
  • We extend the two-dimensional model of drug use introduced in Behrens et al. [1999, 2000, 2002] by introducing two additional states that model in more detail newly initiated (“light”) users’ response to the drug experience. Those who dislike the drug quickly “quit” and briefly suppress initiation by others. Those who like the drug progress to ongoing (“moderate”) use, from which they may or may not escalate to “heavy” or dependent use. Initiation is spread contagiously by light and moderate users, but is moderated by the drug’s reputation, which is a function of the number of unhappy users (recent quitters + heavy users). The model reproduces recent prevalence data from the U.S. cocaine epidemic reasonably well, with one pronounced peak followed by decay toward a steady state. However, minor variation in parameter values yields both long-run periodicity with a period akin to the gap between the first U.S. cocaine epidemic (peak ~1910) and the current one (peak ~1980), as well as short-run periodicity akin to that observed in data on youthful use for a variety of substances. The combination of short- and long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman [2002]. The existence of such complex behavior including cycles, quasi periodic solutions, and chaos is proven by means of bifurcation analysis.
    Data Types:
    • Document
  • We extend the two-dimensional model of drug use introduced in Behrens et al. [1999, 2000, 2002] by introducing two additional states that model in more detail newly initiated (“light”) users’ response to the drug experience. Those who dislike the drug quickly “quit” and briefly suppress initiation by others. Those who like the drug progress to ongoing (“moderate”) use, from which they may or may not escalate to “heavy” or dependent use. Initiation is spread contagiously by light and moderate users, but is moderated by the drug’s reputation, which is a function of the number of unhappy users (recent quitters + heavy users). The model reproduces recent prevalence data from the U.S. cocaine epidemic reasonably well, with one pronounced peak followed by decay toward a steady state. However, minor variation in parameter values yields both long-run periodicity with a period akin to the gap between the first U.S. cocaine epidemic (peak ~1910) and the current one (peak ~1980), as well as short-run periodicity akin to that observed in data on youthful use for a variety of substances. The combination of short- and long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman [2002]. The existence of such complex behavior including cycles, quasi periodic solutions, and chaos is proven by means of bifurcation analysis.
    Data Types:
    • Document
  • We extend the two-dimensional model of drug use introduced in Behrens et al. [1999, 2000, 2002] by introducing two additional states that model in more detail newly initiated (“light”) users’ response to the drug experience. Those who dislike the drug quickly “quit” and briefly suppress initiation by others. Those who like the drug progress to ongoing (“moderate”) use, from which they may or may not escalate to “heavy” or dependent use. Initiation is spread contagiously by light and moderate users, but is moderated by the drug’s reputation, which is a function of the number of unhappy users (recent quitters + heavy users). The model reproduces recent prevalence data from the U.S. cocaine epidemic reasonably well, with one pronounced peak followed by decay toward a steady state. However, minor variation in parameter values yields both long-run periodicity with a period akin to the gap between the first U.S. cocaine epidemic (peak ~1910) and the current one (peak ~1980), as well as short-run periodicity akin to that observed in data on youthful use for a variety of substances. The combination of short- and long-run periodicity is reminiscent of the elliptical burstors described by Rubin and Terman [2002]. The existence of such complex behavior including cycles, quasi periodic solutions, and chaos is proven by means of bifurcation analysis.
    Data Types:
    • Document
  • Synchronization plays an important role in neural signal processing and transmission. Many hypotheses have been proposed to explain the origin of neural synchronization. In recent years, correlated noise-induced synchronization has received support from many theoretical and experimental studies. However, many of these prior studies have assumed that neurons have identical biophysical properties and that their inputs are well modeled by white noise. In this context, we use colored noise to induce synchronization between oscillators with heterogeneity in both phase-response curves and frequencies. In the low noise limit, we derive novel analytical theory showing that the time constant of colored noise influences correlated noise-induced synchronization and that oscillator heterogeneity can limit synchronization. Surprisingly, however, heterogeneous oscillators may synchronize better than homogeneous oscillators given low input correlations. We also find resonance of oscillator synchronization to colored noise inputs when firing frequencies diverge. Collectively, these results prove robust for both relatively high noise regimes and when applied to biophysically realistic spiking neuron models, and further match experimental recordings from acute brain slices.
    Data Types:
    • Document
  • Synchronization plays an important role in neural signal processing and transmission. Many hypotheses have been proposed to explain the origin of neural synchronization. In recent years, correlated noise-induced synchronization has received support from many theoretical and experimental studies. However, many of these prior studies have assumed that neurons have identical biophysical properties and that their inputs are well modeled by white noise. In this context, we use colored noise to induce synchronization between oscillators with heterogeneity in both phase-response curves and frequencies. In the low noise limit, we derive novel analytical theory showing that the time constant of colored noise influences correlated noise-induced synchronization and that oscillator heterogeneity can limit synchronization. Surprisingly, however, heterogeneous oscillators may synchronize better than homogeneous oscillators given low input correlations. We also find resonance of oscillator synchronization to colored noise inputs when firing frequencies diverge. Collectively, these results prove robust for both relatively high noise regimes and when applied to biophysically realistic spiking neuron models, and further match experimental recordings from acute brain slices.
    Data Types:
    • Document
  • Microresonator layouts are synthesized such that their preferred mode of oscillation is well-separated from the higher order in-plane and out-of-plane modes. Building on our previous work, we have incorporated models for four out-of-plane modes. All these modes are modeled as springmass systems. The spring constants and the effective masses of these modes are analytically derived. Synthesis is accomplished by encoding a design quality metric as the design objective while simultaneously constraining the design to meet user specifications. These constraints require that the resonant frequency in the preferred direction is sufficiently lower than (and, hence, dominates over) the resonant frequency of other modes of vibration of the structure. The models are verified by comparison with 3D FEM simulations and also with experimental measurements on fabricated resonators. The usefulness of these models is illustrated by comparing the oscillation modes of layouts synthesized with and without these models. This exercise also shows that such mode-separation can be achieved only if the microresonators have a structural thickness larger than flexure width.
    Data Types:
    • Document
  • Microresonator layouts are synthesized such that their preferred mode of oscillation is well-separated from the higher order in-plane and out-of-plane modes. Building on our previous work, we have incorporated models for four out-of-plane modes. All these modes are modeled as springmass systems. The spring constants and the effective masses of these modes are analytically derived. Synthesis is accomplished by encoding a design quality metric as the design objective while simultaneously constraining the design to meet user specifications. These constraints require that the resonant frequency in the preferred direction is sufficiently lower than (and, hence, dominates over) the resonant frequency of other modes of vibration of the structure. The models are verified by comparison with 3D FEM simulations and also with experimental measurements on fabricated resonators. The usefulness of these models is illustrated by comparing the oscillation modes of layouts synthesized with and without these models. This exercise also shows that such mode-separation can be achieved only if the microresonators have a structural thickness larger than flexure width.
    Data Types:
    • Document
  • The growing demand for wireless communication systems is driving the integration of radio frequency (RF) front-ends on the same chip with multi-band functionality and higher spectral efficiency. Microelectromechanical systems (MEMS) have an overarching applicability to RF communications and are critical components in facilitating this integration process. Among a variety of RF MEMS devices, piezoelectric MEMS resonators have sparked significant research and commercial interest for use in oscillators, filters, and duplexers. Compared to their bulky quartz crystal and surface acoustic wave (SAW) counterparts, MEMS resonators exhibit impressive advantages of compact size, lower production cost, lower power consumption, and higher level of integration with CMOS fabrication processes. One of the promising piezoelectric MEMS resonator technologies is the aluminum nitride (AlN) contour mode resonator (CMR). On one hand, AlN is chemically stable and offers superior acoustic properties such as large stiffness and low loss. Furthermore, CMRs offer low motional resistance over a broad range of frequencies (few MHZ to GHz), which are lithographically-definable on the same silicon substrates. To date, RF MEMS resonators (include CMRs) have been extensively studied; however, one aspect that was not thoroughly investigated is how to modulate/tune their equivalent parameters to enhance their performance in oscillators and duplexers. The goal of this thesis is to investigate various modulation methods to improve the thermal stability of the resonator, its “effective” quality factor when used in an oscillator, and build completely novel non-reciprocal components. Broadly defined, modulation refers to the exertion of a modifying or controlling influence on something, herein specifically, the resonator admittance. In this thesis, three categories of modulation methods are investigated: thermal modulation, force modulation, and external electronic modulation. Firstly, the AlN CMR’s center frequency can be tunned by the applied thermal power to the resonator body. The resonator temperature is kept constant (for example, 90 °C) via a temperature sensor and feedback control such that the center frequency is stable over the whole operation temperature range of interest (e.g. –35 to 85 °C). The maximum power consumption to sustain the maximum temperature difference (120 ºC in this thesis) between resonator and ambient is reduced to a value as low as 353 μW – the lowest ever reported for any MEMS device. These results were attained while simultaneously maintaining a high quality factor (up to 4450 at 220 MHz device). The feedback control was implemented by either analog circuits or via a microprocessor. The analog feedback control, which innovatively utilized a dummy resistor to compensate for temperature gradients, resulted in a total power consumption of 3.8 mW and a frequency stability of 100 ppm over 120 ºC. As for the digital compensation, artificial neural network algorithm was employed to facilitate faster calibration of look-up tables for multiple frequencies. This method attained a frequency stability of 14 ppm over 120 ºC. The second modulation method explored in this thesis is based on the use of an effective external force to enhance the 3-dB quality factor of AlN CMRs and improve the phase noise performance of resonator-based oscillators. The force modulation method was embodied in a two-port device, where one of the two ports is used as a one-port resonator and the other is driven by an external signal to effectively apply an external force to the first port. Through this technique, the quality factor of the resonator was boosted by 140 times (up to 150,000) and the phase noise of the corresponding oscillator realized using the resonator was reduced by 10 dBc/Hz. Lastly, a novel magnetic-free electrical circulator topology that facilitates the development of in-band full duplexers (IBFD) for simultaneous transmit and receive (STAR) is proposed and modeled. Fundamentally, a linear time-invariant (LTI) filter network parametrically modulated via a switching matrix is used to break the reciprocity of the filter. The developed model accurately predicts the circulator behavior and shows very good agreement with the experimental results for a 21.4 MHz circulators built with MiniCircuit filter and switch components. Furthermore, a high frequency (1.1 GHz) circulator was synthesized based on AlN MEMS bandpass filters and CMOS RF switches, hence showing a compact approach that can be used in handheld devices. The modulation frequency and duty cycle are optimized so that the circulator can provide up to 15 dB of isolation over the filter bandwidth while good power transfer between the other two ports is maintained. The demonstrated device is expected to intrinsically offer low noise and high linearity. The combination of the first two modulation methods facilitates the implementation of monolithic, temperature-stable, ultra-low noise, multi-frequency oscillator banks. The third modulation technique that was investigated sets the path for the development of CMOS-compatible in-band full duplexers for simultaneous transmit and receive and thus facilitates the efficient utilization of the electromagnetic spectrum. With the aid of all these three modulation approaches, the author believes that a fully integrated, multi-frequency, spectrum-efficient transceiver is enabled for next-generation wireless communications.
    Data Types:
    • Document
  • The growing demand for wireless communication systems is driving the integration of radio frequency (RF) front-ends on the same chip with multi-band functionality and higher spectral efficiency. Microelectromechanical systems (MEMS) have an overarching applicability to RF communications and are critical components in facilitating this integration process. Among a variety of RF MEMS devices, piezoelectric MEMS resonators have sparked significant research and commercial interest for use in oscillators, filters, and duplexers. Compared to their bulky quartz crystal and surface acoustic wave (SAW) counterparts, MEMS resonators exhibit impressive advantages of compact size, lower production cost, lower power consumption, and higher level of integration with CMOS fabrication processes. One of the promising piezoelectric MEMS resonator technologies is the aluminum nitride (AlN) contour mode resonator (CMR). On one hand, AlN is chemically stable and offers superior acoustic properties such as large stiffness and low loss. Furthermore, CMRs offer low motional resistance over a broad range of frequencies (few MHZ to GHz), which are lithographically-definable on the same silicon substrates. To date, RF MEMS resonators (include CMRs) have been extensively studied; however, one aspect that was not thoroughly investigated is how to modulate/tune their equivalent parameters to enhance their performance in oscillators and duplexers. The goal of this thesis is to investigate various modulation methods to improve the thermal stability of the resonator, its “effective” quality factor when used in an oscillator, and build completely novel non-reciprocal components. Broadly defined, modulation refers to the exertion of a modifying or controlling influence on something, herein specifically, the resonator admittance. In this thesis, three categories of modulation methods are investigated: thermal modulation, force modulation, and external electronic modulation. Firstly, the AlN CMR’s center frequency can be tunned by the applied thermal power to the resonator body. The resonator temperature is kept constant (for example, 90 °C) via a temperature sensor and feedback control such that the center frequency is stable over the whole operation temperature range of interest (e.g. –35 to 85 °C). The maximum power consumption to sustain the maximum temperature difference (120 ºC in this thesis) between resonator and ambient is reduced to a value as low as 353 μW – the lowest ever reported for any MEMS device. These results were attained while simultaneously maintaining a high quality factor (up to 4450 at 220 MHz device). The feedback control was implemented by either analog circuits or via a microprocessor. The analog feedback control, which innovatively utilized a dummy resistor to compensate for temperature gradients, resulted in a total power consumption of 3.8 mW and a frequency stability of 100 ppm over 120 ºC. As for the digital compensation, artificial neural network algorithm was employed to facilitate faster calibration of look-up tables for multiple frequencies. This method attained a frequency stability of 14 ppm over 120 ºC. The second modulation method explored in this thesis is based on the use of an effective external force to enhance the 3-dB quality factor of AlN CMRs and improve the phase noise performance of resonator-based oscillators. The force modulation method was embodied in a two-port device, where one of the two ports is used as a one-port resonator and the other is driven by an external signal to effectively apply an external force to the first port. Through this technique, the quality factor of the resonator was boosted by 140 times (up to 150,000) and the phase noise of the corresponding oscillator realized using the resonator was reduced by 10 dBc/Hz. Lastly, a novel magnetic-free electrical circulator topology that facilitates the development of in-band full duplexers (IBFD) for simultaneous transmit and receive (STAR) is proposed and modeled. Fundamentally, a linear time-invariant (LTI) filter network parametrically modulated via a switching matrix is used to break the reciprocity of the filter. The developed model accurately predicts the circulator behavior and shows very good agreement with the experimental results for a 21.4 MHz circulators built with MiniCircuit filter and switch components. Furthermore, a high frequency (1.1 GHz) circulator was synthesized based on AlN MEMS bandpass filters and CMOS RF switches, hence showing a compact approach that can be used in handheld devices. The modulation frequency and duty cycle are optimized so that the circulator can provide up to 15 dB of isolation over the filter bandwidth while good power transfer between the other two ports is maintained. The demonstrated device is expected to intrinsically offer low noise and high linearity. The combination of the first two modulation methods facilitates the implementation of monolithic, temperature-stable, ultra-low noise, multi-frequency oscillator banks. The third modulation technique that was investigated sets the path for the development of CMOS-compatible in-band full duplexers for simultaneous transmit and receive and thus facilitates the efficient utilization of the electromagnetic spectrum. With the aid of all these three modulation approaches, the author believes that a fully integrated, multi-frequency, spectrum-efficient transceiver is enabled for next-generation wireless communications.
    Data Types:
    • Document