Analytic expressions for the constitutive parameters of magnetoelectric metamaterials

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling. © 2010 The American Physical Society.

Cost Heterogeneity and the Potential Savings from Market-Based Policies

Policy makers and analysts are often faced with situations where it is unclear whether market-based instruments hold real promise of reducing costs, relative to conventional uniform standards. We develop analytic expressions that can be employed with modest amounts of information to estimate the potential cost savings associated with market-based policies, with an application to the environmental policy realm. These simple formulae can identify instruments that merit more detailed investigation. We illustrate the use of these results with an application to nitrogen oxides control by electric utilities in the United States.

Exact analytical expressions for the potential of electrical double layer interactions for a sphere-plate system.

Exact, closed-form analytical expressions are presented for evaluating the potential energy of electrical double layer (EDL) interactions between a sphere and an infinite flat plate for three different types of interactions: constant potential, constant charge, and an intermediate case as given by the linear superposition approximation (LSA). By taking advantage of the simpler sphere-plate geometry, simplifying assumptions used in the original Derjaguin approximation (DA) for sphere-sphere interaction are avoided, yielding expressions that are more accurate and applicable over the full range of κa. These analytical expressions are significant improvements over the existing equations in the literature that are valid only for large κa because the new equations facilitate the modeling of EDL interactions between nanoscale particles and surfaces over a wide range of ionic strength.

Analytic-domain lens design with proximate ray tracing.

We have developed an alternative approach to optical design which operates in the analytical domain so that an optical designer works directly with rays as analytical functions of system parameters rather than as discretely sampled polylines. This is made possible by a generalization of the proximate ray tracing technique which obtains the analytical dependence of the rays at the image surface (and ray path lengths at the exit pupil) on each system parameter. The resulting method provides an alternative direction from which to approach system optimization and supplies information which is not typically available to the system designer. In addition, we have further expanded the procedure to allow asymmetric systems and arbitrary order of approximation, and have illustrated the performance of the method through three lens design examples.

Experiences of Internalized and Enacted Stigma among Women with Obstetric Fistula in Tanzania

Background: Obstetric fistula is the development of a necrosis between the bladder and the vagina and/or the bladder and the rectum as a result of prolonged obstructed labor, resulting in urinary or fecal incontinence. In Tanzania surgical repair for obstetric fistula is provided freely by the government but it is estimated that there are over 25,000 women living with an untreated fistula. These women experience high degrees of psycho-social stresses exacerbated by the stigma surrounding their condition. There is a dire need to explore stigma within this population in order to better understand its impact, as stigma affects both treatment seeking behavior as well as long term recovery of those who access surgical repair.

Study Aims: This study aims to understand the experiences of stigma among women with obstetric fistulas by examining both internalized and enacted stigma, and by identifying pertinent correlates of internalized stigma.

Methods: This mixed-methods study utilized both quantitative and qualitative data collected in two related studies at a single hospital in Moshi, Tanzania. All study participants were women receiving surgical repair for an obstetric fistula. In the quantitative portion, cross-sectional survey data were collected from 52 patients. The primary outcome was fistula-related stigma, measured using an adaptation of the HASI-P stigma scale, which included constructs of both internalized and enacted stigma. In the qualitative portion, 45 patients participated in a semi-structured in-depth interview, which explored topics such as stressors caused by the fistula, coping mechanisms, and available support. The transcripts were analyzed using analytic memos and an iterative process of thematic coding using the framework of content analysis.

Results: Expressions of internalized stigma were common in the sample, with a median score of 2.1 on a scale of 0 – 3. Internalized was significantly correlated with negative religious coping, social participation, impact of incontinence and enacted stigma. Qualitative analysis was consistent and demonstrated widespread themes of shame and embarrassment. Experiences of enacted stigma were not as common (median score of 0), although some items, like those pertaining to mockery and blame, were endorsed by up to 25% of the study sample. Themes of anticipated stigma (isolation and non-disclosure due to the possibility of stigmatization) were also evident in the qualitative sample and may explain the low enacted stigma scores observed.

Conclusion: In this sample of women receiving surgical repair for an obstetric fistula, stigma was evident, with internalized stigma resulting in psychological impacts for patients. Experiences of both anticipated and enacted stigma were also observed. There is a need to explore interventions that would decrease stigma while also increasing support for these women, as stigma may be a barrier towards accessing surgical repair and reintegration following surgery.

Keywords: Tanzania, obstetric fistula, stigma, maternal health

Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics

The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion

and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense.