Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes.

Time-Reversal Massive Multipath Effect and Bandwidth Heterogeneity

The proliferation of new mobile communication devices, such as smartphones and tablets, has led to an exponential growth in network traffic. The demand for supporting the fast-growing consumer data rates urges the wireless service providers and researchers to seek a new efficient radio access technology, which is the so-called 5G technology, beyond what current 4G LTE can provide. On the other hand, ubiquitous RFID tags, sensors, actuators, mobile phones and etc. cut across many areas of modern-day living, which offers the ability to measure, infer and understand the environmental indicators. The proliferation of these devices creates the term of the Internet of Things (IoT). For the researchers and engineers in the field of wireless communication, the exploration of new effective techniques to support 5G communication and the IoT becomes an urgent task, which not only leads to fruitful research but also enhance the quality of our everyday life. Massive MIMO, which has shown the great potential in improving the achievable rate with a very large number of antennas, has become a popular candidate. However, the requirement of deploying a large number of antennas at the base station may not be feasible in indoor scenarios. Does there exist a good alternative that can achieve similar system performance to massive MIMO for indoor environment? In this dissertation, we address this question by proposing the time-reversal technique as a counterpart of massive MIMO in indoor scenario with the massive multipath effect. It is well known that radio signals will experience many multipaths due to the reflection from various scatters, especially in indoor environments. The traditional TR waveform is able to create a focusing effect at the intended receiver with very low transmitter complexity in a severe multipath channel. TR's focusing effect is in essence a spatial-temporal resonance effect that brings all the multipaths to arrive at a particular location at a specific moment. We show that by using time-reversal signal processing, with a sufficiently large bandwidth, one can harvest the massive multipaths naturally existing in a rich-scattering environment to form a large number of virtual antennas and achieve the desired massive multipath effect with a single antenna. Further, we explore the optimal bandwidth for TR system to achieve maximal spectral efficiency. Through evaluating the spectral efficiency, the optimal bandwidth for TR system is found determined by the system parameters, e.g., the number of users and backoff factor, instead of the waveform types. Moreover, we investigate the tradeoff between complexity and performance through establishing a generalized relationship between the system performance and waveform quantization in a practical communication system. It is shown that a 4-bit quantized waveforms can be used to achieve the similar bit-error-rate compared to the TR system with perfect precision waveforms. Besides 5G technology, Internet of Things (IoT) is another terminology that recently attracts more and more attention from both academia and industry. In the second part of this dissertation, the heterogeneity issue within the IoT is explored. One of the significant heterogeneity considering the massive amount of devices in the IoT is the device heterogeneity, i.e., the heterogeneous bandwidths and associated radio-frequency (RF) components. The traditional middleware techniques result in the fragmentation of the whole network, hampering the objects interoperability and slowing down the development of a unified reference model for the IoT. We propose a novel TR-based heterogeneous system, which can address the bandwidth heterogeneity and maintain the benefit of TR at the same time. The increase of complexity in the proposed system lies in the digital processing at the access point (AP), instead of at the devices' ends, which can be easily handled with more powerful digital signal processor (DSP). Meanwhile, the complexity of the terminal devices stays low and therefore satisfies the low-complexity and scalability requirement of the IoT. Since there is no middleware in the proposed scheme and the additional physical layer complexity concentrates on the AP side, the proposed heterogeneous TR system better satisfies the low-complexity and energy-efficiency requirement for the terminal devices (TDs) compared with the middleware approach.

Probabilistic Imaging and Dynamic Modeling of Earthquake Source Processes

Investigation of large, destructive earthquakes is challenged by their infrequent occurrence and the remote nature of geophysical observations. This thesis sheds light on the source processes of large earthquakes from two perspectives: robust and quantitative observational constraints through Bayesian inference for earthquake source models, and physical insights on the interconnections of seismic and aseismic fault behavior from elastodynamic modeling of earthquake ruptures and aseismic processes.

To constrain the shallow deformation during megathrust events, we develop semi-analytical and numerical Bayesian approaches to explore the maximum resolution of the tsunami data, with a focus on incorporating the uncertainty in the forward modeling. These methodologies are then applied to invert for the coseismic seafloor displacement field in the 2011 Mw 9.0 Tohoku-Oki earthquake using near-field tsunami waveforms and for the coseismic fault slip models in the 2010 Mw 8.8 Maule earthquake with complementary tsunami and geodetic observations. From posterior estimates of model parameters and their uncertainties, we are able to quantitatively constrain the near-trench profiles of seafloor displacement and fault slip. Similar characteristic patterns emerge during both events, featuring the peak of uplift near the edge of the accretionary wedge with a decay toward the trench axis, with implications for fault failure and tsunamigenic mechanisms of megathrust earthquakes.

To understand the behavior of earthquakes at the base of the seismogenic zone on continental strike-slip faults, we simulate the interactions of dynamic earthquake rupture, aseismic slip, and heterogeneity in rate-and-state fault models coupled with shear heating. Our study explains the long-standing enigma of seismic quiescence on major fault segments known to have hosted large earthquakes by deeper penetration of large earthquakes below the seismogenic zone, where mature faults have well-localized creeping extensions. This conclusion is supported by the simulated relationship between seismicity and large earthquakes as well as by observations from recent large events. We also use the modeling to connect the geodetic observables of fault locking with the behavior of seismicity in numerical models, investigating how a combination of interseismic geodetic and seismological estimates could constrain the locked-creeping transition of faults and potentially their co- and post-seismic behavior.

Exploration of Ground Penetrating Radar and Time Domain Reflectometry Methods for the Determination of Pavement Dielectric Constant

Traditionally, densities of newly built roadways are checked by direct sampling (cores) or by nuclear density gauge measurements. For roadway engineers, density of asphalt pavement surfaces is essential to determine pavement quality. Unfortunately, field measurements of density by direct sampling or by nuclear measurement are slow processes. Therefore, I have explored the use of rapidly-deployed ground penetrating radar (GPR) as an alternative means of determining pavement quality. The dielectric constant of pavement surface may be a substructure parameter that correlates with pavement density, and can be used as a proxy when density of asphalt is not known from nuclear or destructive methods. The dielectric constant of the asphalt can be determined using ground penetrating radar (GPR). In order to use GPR for evaluation of road surface quality, the relationship between dielectric constants of asphalt and their densities must be established. Field measurements of GPR were taken at four highway sites in Houghton and Keweenaw Counties, Michigan, where density values were also obtained using nuclear methods in the field. Laboratory studies involved asphalt samples taken from the field sites and samples created in the laboratory. These were tested in various ways, including, density, thickness, and time domain reflectometry (TDR). In the field, GPR data was acquired using a 1000 MHz air-launched unit and a ground-coupled unit at 200 and 500 MHz. The equipment used was owned and operated by the Michigan Department of Transportation (MDOT) and available for this study for a total of four days during summer 2005 and spring 2006. The analysis of the reflected waveforms included “routine” processing for velocity using commercial software and direct evaluation of reflection coefficients to determine a dielectric constant. The dielectric constants computed from velocities do not agree well with those obtained from reflection coefficients. Perhaps due to the limited range of asphalt types studied, no correlation between density and dielectric constant was evident. Laboratory measurements were taken with samples removed from the field and samples created for this study. Samples from the field were studied using TDR, in order to obtain dielectric constant directly, and these correlated well with the estimates made from reflection coefficients. Samples created in the laboratory were measured using 1000 MHz air-launched GPR, and 400 MHz ground-coupled GPR, each under both wet and dry conditions. On the basis of these observations, I conclude that dielectric constant of asphalt can be reliably measured from waveform amplitude analysis of GJPR data, based on the consistent agreement with that obtained in the laboratory using TDR. Because of the uniformity of asphalts studied here, any correlation between dielectric constant and density is not yet apparent.

The effect of notch filtering on the waveform of the newborn auditory brainstem response

OBJECTIVE: To identify whether the use of a notch filter significantly affects the morphology or characteristics of the newborn auditory brainstem response (ABR) waveform and so inform future guidance for clinical practice. DESIGN: Waveforms with and without the application of a notch filter were recorded from babies undergoing routine ABR tests at 4000, 1000 and 500 Hz. Any change in response morphology was judged subjectively. Response latency, amplitude, and measurements of response quality and residual noise were noted. An ABR simulator was also used to assess the effect of notch filtering in conditions of low and high mains interference. RESULTS: The use of a notch filter changed waveform morphology for 500 Hz stimuli only in 15% of tests in newborns. Residual noise was lower when 4000 Hz stimuli were used. Response latency, amplitude, and quality were unaffected regardless of stimulus frequency. Tests with the ABR stimulator suggest that these findings can be extended to conditions of high level mains interference. CONCLUSIONS: A notch filter should be avoided when testing at 500 Hz, but at higher frequencies appears to carry no penalty.

Regulation of electrical transmission by protein kinase C in Aplysia bag cell neurons

Electrical synapses are composed of gap junctions, made from paired hemi-channels that allow for the transfer of current from one neuron to another. Gap junctions mediate electrical transmission in neurons, where they synchronize spiking and promote rapid transmission, thereby influencing the coordination, pattern, and frequency of firing. In the marine snail, Aplysia calfornica, two clusters of neuroendocrine bag cell neurons use electrical synapses to synchronize a 30-min burst of action potentials, known as the afterdischarge, which releases egg-laying hormone and induces reproduction. In culture, paired bag cell neurons present a junctional conductance that is non-rectifying and largely voltage-independent. During the afterdischarge, PKC is activated, which is known to increase voltage-gated Ca2+ current; yet, little is understood as to how this pathway impacts electrical transmission. The transfer of presynaptic spike-like waveforms (generated in voltage-clamp) to the postsynaptic cell (measured in current-clamp) was monitored with or without PKC activation. It was found that pretreatment with the PKC activator, phorbol-12-myristate-13-acetate (PMA), enhanced junctional conductance between bag cell neurons. Furthermore, in control, presynaptic action potential waveforms mainly evoked postsynaptic electrotonic potentials at both -60 and -40 mV. However, with PKC activation the presynaptic stimulus consistently elicited postsynaptic action potentials from resting potentials of -40 mV, and would occasionally result in firing from repetitive input at -60 mV. Moreover, to assess whether this enhanced electrical transmission genuinely reflects a greater junctional conductance or a change in postsynaptic responsiveness, a fast-phase junctional-like current was applied to single bag cell neurons. Neurons in PMA always fired action potentials in response to current injection as opposed to control, which were less likely to spike. This outcome did not change when the junctional-like current was artificially enhanced in control conditions. Also, in response to fast- and slow-phase electrotonic potential (ETP) waveforms, Ca2+ current was markedly larger in single PMA-treated neurons. These findings suggest that PKC activation may contribute to afterdischarge fidelity by recruiting postsynaptic Ca2+ current to promote synchronous network firing. Finally, Aplysia gap junction genes (innexins) were transfected into mouse N2A cells and characterized. This revealed a biophysical and pharmacological profile similar to native gap junctions.

Power Quality Evaluation of a Photovoltaic System on an Electric Grid

This paper focuses on tests of photovoltaic systems in order to address two case studies with silicon monocrystalline and silicon polycrystalline panels, respectively. The first case is an identification of the three parameters of the single-diode equivalent circuit for modelling photovoltaic systems with conclusion about the inevitably age degradation. A comparison between experimental observed and computed I-V and V-P characteristics curves is carried out at standard test conditions. The second case is an experimental observation on a photovoltaic system connected to an electric grid in what regards the quality of the energy injected into the grid. A measuring of the harmonic content in the voltage and in the current waveforms at the terminals of the photovoltaic system is carried out in order to conclude about the conformity with the Standard EN 50160 and the IEEE 519-1992, respectively.