Analysis of guided and leaky modes of circular waveguides and realization of mechanical tunable metamaterial and devices

The guided and leaky mode characteristics for planar dielectric structures are relatively well known, due to its various kind of applications. However, the investigation to the modes characteristics for a circular rod structure is relatively rare, especially for the leaky modes, despite the rod structure is very simple and useful. Accordingly, in the first part of the thesis, we analyze the guided and leaky modes for a circular dielectric rod in detail. The analysis is carried out in several steps. First, by considering the field distributions outside the rod, the modes are well defined and classified based on their physical meanings. The relations for the mode solutions using different types of special functions and Riemann sheets are figured out. Further, completed forms of characteristic equations used to solve different modes are presented explicitly. Second, in order to solve this nonlinear characteristic equation efficiently and accurately, we employ iterative methods and spent lots of efforts in deriving the initial guess expression in a simply but efficient form. Through using the asymptotic expansion method and employing the Lambert W function, we derive the initial guesses around the cutoff frequency, low frequency limit and high frequency limit for both TM and TE cases. Finally, the numerical results are presented for the complex transverse propagation constants of proper and two types of improper modes for both cases. Some of the improper modes have not been shown in literatures. Next, we extend the analysis to the circular rod with negative permittivity and permeability (double negative material (DNG)). Following the same analysis procedure for the conventional dielectric circular rod, first, we derive the characteristic equation for the DNG case and de fine different types of modes. Second, we expand the characteristic equation asymptotically and then find the initial guess expression for different types of modes around the cutoff, high frequency limit and low frequency limit. Finally, using these initial guesses we solve the char acteristic equation with iterative methods and find the dispersion curves. xi The electromagnetic (EM) material property of simultaneous negative permittivity and per meability we use for the DNG rod analysis actually can not be found in nature so far. The method in generating material with DNG property is using metamaterials. In the second part of the thesis we introduce metamaterials, and discuss our work of realizing tunable metamate rials in detail. This type of tunable property allows the metamaterial device to overcome the drawback of fixed and limited bandwidth from the conventional metamaterials. We start it from presenting a novel tunable and flexible SRR-based meta-atom capable of tuning its EM response characteristics over a broad frequency range by simple mechanical stretching. First, we design and simulate a meta-atom with a liquid metal as the resonator material. The liquid metal is patterned to be a SRR structure and embedded inside a highly stretchable silicone elastomer. Due to its liquid nature, the liquid metal-based SRR could flow in response to an applied strain, and compliant to change from the encasing elastomer as the meta-atom being stretched and twisted. Therefore, through simple mechanical stretching, the shape of the SRR is changed. Correspondingly, the equivalent capacitance and inductance of the SRR are adjusted, thus tuning the resonance frequency of the meta-atom. The shifting trend of the resonance frequency with different stretching orientations is predicted by a simple circuit mode, and verified from the experiment. Next, we extend the idea of meta-atom to the meta-skin, which is composed of an array of meta-atoms. This meta-skin performed as a tunable selective surface with a wide resonance frequency tuning range when being stretched. Further, due to its flexibility, this meta-skin can function as a flexible “cloaking” surface in suppressing the scattering from the dielectric ob ject. As examples, we demonstrate frequency selective responses of multilayer meta-skins with different stretching ratio in the planar direction. Also, we investigate scattering suppression effect of the meta-skin coated on a finite-length dielectric rod in free space. Benefit from the liquid metal and highly stretchable elastomer, we design and realize a directivity reconfigurable two-arm spiral antenna. This new device has the ability to reconfig urate the radiation pattern along the main lobe direction by control the shape of the antenna, as the radiation pattern becomes sharper, directivity is optimized. Finally, the directivity, efficiency, and axial ratio with different dome height, operating frequencies are presented

The structure of TeV-bright shell-type supernova remnants

Aims. Two-dimensional MHD simulations are used to model the emission properties of TeV-bright shell-type supernova remnants (SNRs) and to explore their nature. Methods. In the leptonic scenario for the TeV emission, the $\gamma$-ray emission is produced via Inverse Compton scattering of background soft photons by high-energy electrons accelerated by the shocks of the SNRs. The TeV emissivity is proportional to the magnetic field energy density and MHD simulations can be used to model the TeV structure of such remnants directly. 2D MHD simulations for SNRs are then performed under the assumption that the ambient interstellar medium is turbulent with the magnetic field and density fluctuations following a Kolmogorov-like power-law spectrum. Results. (1) As expected, these simulations confirm early 1D and 2D modelings of these sources, namely the hydrodynamical evolution of the shock waves and amplification of magnetic field by Rayleigh-Taylor convective flows and by shocks propagating in a turbulent medium; (2) We reproduce rather complex morphological structure for $\gamma$-rays, suggesting intrinsic variations of the source morphology not related to the structure of the progenitor and environment; (3)The observed radial profile of several remnants are well reproduced with an ambient medium density of $0.1-1$ cm$^{-3}$. An even lower ambient density leads to a sharper drop of the TeV brightness with radius than what is observed near the outer edge of these remnants. Conclusions. In a turbulent background medium, we can reproduce the observed characteristics of several shell-type TeV SNRs with reasonable parameters except for a higher ambient density than that inferred from X-ray observations.Comment: 7pages,12figures,Accepted for publication in A&A. arXiv admin note: text overlap with arXiv:1306.439

Fermi Large Area Telescope observations of the supernova remnant HESS J1731-347

Context: HESS J1731-347 has been identified as one of the few TeV-bright shell-type supernova remnants (SNRs). These remnants are dominated by nonthermal emission, and the nature of TeV emission has been continuously debated for nearly a decade. Aims: We carry out the detailed modeling of the radio to gamma-ray spectrum of HESS J1731-347 to constrain the magnetic field and energetic particles sources, which we compare with those of the other TeV-bright shell-type SNRs explored before. Methods: Four years of data from Fermi Large Area Telescope (LAT) observations for regions around this remnant are analyzed, leading to no detection correlated with the source discovered in the TeV band. The Markov Chain Monte Carlo method is used to constrain parameters of one-zone models for the overall emission spectrum. Results: Based on the 99.9% upper limits of fluxes in the GeV range, one-zone hadronic models with an energetic proton spectral slope greater than 1.8 can be ruled out, which favors a leptonic origin for the gamma-ray emission, making this remnant a sibling of the brightest TeV SNR RX J1713.7-3946, the Vela Junior SNR RX J0852.0-4622, and RCW 86. The best-fit leptonic model has an electron spectral slope of 1.8 and a magnetic field of about 30 muG, which is at least a factor of 2 higher than those of RX J1713.7-3946 and RX J0852.0-4622, posing a challenge to the distance estimate and/or the energy equipartition between energetic electrons and the magnetic field of this source. A measurement of the shock speed will address this challenge and has implications on the magnetic field evolution and electron acceleration driven by shocks of SNRs.Comment: 7 pages, 3 fogures, A&A in pres

Essays in Law and Economics

This dissertation consists of three papers relating to the field of Law and Economics. The first two papers examine the impact of increased judicial discretion on both racial disparities and inter-judge disparities in the federal criminal justice system. The third paper analyzes the effects of OSHA programs on workplace safety, wages, and employment. The common thread throughout this work is a focus on how legal actors and institutions affect substantive outcomes of individuals.Economic

Free at Last? Judicial Discretion and Racial Disparities in Federal Sentencing

The Federal Sentencing Guidelines were created to reduce unwarranted sentencing disparities among similar defendants. This paper explores the impact of increased judicial discretion on racial disparities in sentencing after the Guidelines were struck down in United States v. Booker (2005). Using data on the universe of federal defendants, I find that black defendants are sentenced to almost two months more in prison compared to their white counterparts after Booker, a 4% increase in average sentence length. To identify the sources of racial disparities, I construct a dataset linking judges to over 400,000 defendants. Exploiting the random assignment of cases to judges, I find that racial disparities are greater among judges appointed after Booker, suggesting acculturation to the Guidelines by judges with experience sentencing under a mandatory regime. Prosecutors also respond to increased judicial discretion by charging black defendants with longer mandatory minimums.Harvard Law School 2013 Student Writing Prize: John M. Olin Law and Economics Priz

Comparative Metabolomics of Early Development of the Parasitic Plants Phelipanche aegyptiaca and Triphysaria versicolor.

Parasitic weeds of the family Orobanchaceae attach to the roots of host plants via haustoria capable of drawing nutrients from host vascular tissue. The connection of the haustorium to the host marks a shift in parasite metabolism from autotrophy to at least partial heterotrophy, depending on the level of parasite dependence. Species within the family Orobanchaceae span the spectrum of host nutrient dependency, yet the diversity of parasitic plant metabolism remains poorly understood, particularly during the key metabolic shift surrounding haustorial attachment. Comparative profiling of major metabolites in the obligate holoparasite Phelipanche aegyptiaca and the facultative hemiparasite Triphysaria versicolor before and after attachment to the hosts revealed several metabolic shifts implicating remodeling of energy and amino acid metabolism. After attachment, both parasites showed metabolite profiles that were different from their respective hosts. In P. aegyptiaca, prominent changes in metabolite profiles were also associated with transitioning between different tissue types before and after attachment, with aspartate levels increasing significantly after the attachment. Based on the results from 15N labeling experiments, asparagine and/or aspartate-rich proteins were enriched in host-derived nitrogen in T. versicolor. These results point to the importance of aspartate and/or asparagine in the early stages of attachment in these plant parasites and provide a rationale for targeting aspartate-family amino acid biosynthesis for disrupting the growth of parasitic weeds

Addressing the Accuracy-Cost Tradeoff in Material Property Prediction: A Teacher-Student Strategy

Deep learning has revolutionized the process of new material discovery, with state-of-the-art models now able to predict material properties based solely on chemical compositions, thus eliminating the necessity for material structures. However, this cost-effective method has led to a trade-off in model accuracy. Specifically, the accuracy of Chemical Composition-based Property Prediction Models (CPMs) significantly lags behind that of Structure-based Property Prediction Models (SPMs). To tackle this challenge, we propose an innovative Teacher-Student (T-S) strategy, where a pre-trained SPM serves as the 'teacher' to enhance the accuracy of the CPM. Leveraging the T-S strategy, T-S CrabNet has risen to become the most accurate model among current CPMs. Initially, we demonstrated the universality of this strategy. On the Materials Project (MP) and Jarvis datasets, we validated the effectiveness of the T-S strategy in boosting the accuracy of CPMs with two distinct network structures, namely CrabNet and Roost. This led to CrabNet, under the guidance of the T-S strategy, emerging as the most accurate model among the current CPMs. Moreover, this strategy shows remarkable efficacy in small datasets. When predicting the formation energy on a small MP dataset comprising merely 5% of the samples, the T-S strategy boosted CrabNet's accuracy by 37.1%, exceeding the enhancement effect of the T-S strategy on the whole dataset