Designing three-dimensional transformation optical media using quasiconformal coordinate transformations.

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasiconformal mapping approach. The generalized quasiconformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional carpet ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices.

Adapting Arthur: The transformations and adaptations of Wirnt von Graffenberg's Wigalois

The stories of King Arthur and his noble knights have fascinated audiences for many centuries and continue to being retold and fashioned to attract modern audiences. Amongst these stories is the tale of Wigalois, the son of the reputable Gawain. This dissertation traces the story of Wigalois across different languages, cultures, and media in order to show how this is a shared German-Yiddish narrative. Furthermore, this dissertations challenges traditional understanding of adaptation within a diachronic and teleological framework by uncovering dialogical and dynamic processes inherent in this narrative tradition. Using the theoretical framework of a combined Adaptation Studies and Medieval Literature Studies’ notions of unstable texts my argumentation focuses on eight specific examples: Wirnt von Grafenberg’s Wigalois (1st half 13th ct.), Italian murals from the fourteenth century, Wigoleis von dem Rade (1483/93), Viduvilt (Yiddish, 16th ct.), Johann Christoph Wagenseil’s Belehrung der Jüdisch-Teutschen Red- und Schreibart (Yiddish and German, 1715), Gabein (Yiddish, 1789), the illustrations by Ludwig Richter (before 1851), and Die phantastischen Abenteuer der Glücksritters Wigalois (Comic, German, 2011).

The Islamic commercial crisis: Institutional roots of economic underdevelopment in the Middle East

During the second millennium, the Middle East's commerce with Western Europe fell increasingly under European domination. Two factors played critical roles. First, the Islamic inheritance system, by raising the costs of dissolving a partnership following a partner's death, kept Middle Eastern commercial enterprises small and ephemeral. Second, certain European inheritance systems facilitated large and durable partnerships by reducing the likelihood of premature dissolution. The upshot is that European enterprises grew larger than those of the Islamic world. Moreover, while ever larger enterprises propelled further organizational transformations in Europe, persistently small enterprises inhibited economic modernization in the Middle East.

Enhancing imaging systems using transformation optics.

We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.

Fluid flow control with transformation media.

We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations-for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium-we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The proposed fluid flow cloak eliminates downstream wake and compensates viscous drag, hinting at the possibility of novel propulsion techniques.

Four-decade responses of soil trace elements to an aggrading old-field forest: B, Mn, Zn, Cu, and Fe.

In the ancient and acidic Ultisol soils of the Southern Piedmont, USA, we studied changes in trace element biogeochemistry over four decades, a period during which formerly cultivated cotton fields were planted with pine seedlings that grew into mature forest stands. In 16 permanent plots, we estimated 40-year accumulations of trace elements in forest biomass and O horizons (between 1957 and 1997), and changes in bioavailable soil fractions indexed by extractions of 0.05 mol/L HCl and 0.2 mol/L acid ammonium oxalate (AAO). Element accumulations in 40-year tree biomass plus O horizons totaled 0.9, 2.9, 4.8, 49.6, and 501.3 kg/ha for Cu, B, Zn, Mn, and Fe, respectively. In response to this forest development, samples of the upper 0.6-m of mineral soil archived in 1962 and 1997 followed one of three patterns. (1) Extractable B and Mn were significantly depleted, by -4.1 and -57.7 kg/ha with AAO, depletions comparable to accumulations in biomass plus O horizons, 2.9 and 49.6 kg/ha, respectively. Tree uptake of B and Mn from mineral soil greatly outpaced resupplies from atmospheric deposition, mineral weathering, and deep-root uptake. (2) Extractable Zn and Cu changed little during forest growth, indicating that nutrient resupplies kept pace with accumulations by the aggrading forest. (3) Oxalate-extractable Fe increased substantially during forest growth, by 275.8 kg/ha, about 10-fold more than accumulations in tree biomass (28.7 kg/ha). The large increases in AAO-extractable Fe in surficial 0.35-m mineral soils were accompanied by substantial accretions of Fe in the forest's O horizon, by 473 kg/ha, amounts that dwarfed inputs via litterfall and canopy throughfall, indicating that forest Fe cycling is qualitatively different from that of other macro- and micronutrients. Bioturbation of surficial forest soil layers cannot account for these fractions and transformations of Fe, and we hypothesize that the secondary forest's large inputs of organic additions over four decades has fundamentally altered soil Fe oxides, potentially altering the bioavailability and retention of macro- and micronutrients, contaminants, and organic matter itself. The wide range of responses among the ecosystem's trace elements illustrates the great dynamics of the soil system over time scales of decades.

Construction of invisibility cloaks of arbitrary shape and size using planar layers of metamaterials

Transformation optics (TO) is a powerful tool for the design of electromagnetic and optical devices with novel functionality derived from the unusual properties of the transformation media. In general, the fabrication of TO media is challenging, requiring spatially varying material properties with both anisotropic electric and magnetic responses. Though metamaterials have been proposed as a path for achieving such complex media, the required properties arising from the most general transformations remain elusive, and cannot implemented by state-of-the-art fabrication techniques. Here, we propose faceted approximations of TO media of arbitrary shape in which the volume of the TO device is divided into flat metamaterial layers. These layers can be readily implemented by standard fabrication and stacking techniques. We illustrate our approximation approach for the specific example of a two-dimensional, omnidirectional "invisibility cloak", and quantify its performance using the total scattering cross section as a practical figure of merit. © 2012 American Institute of Physics.

Three-dimensional broadband omnidirectional acoustic ground cloak.

The control of sound propagation and reflection has always been the goal of engineers involved in the design of acoustic systems. A recent design approach based on coordinate transformations, which is applicable to many physical systems, together with the development of a new class of engineered materials called metamaterials, has opened the road to the unconstrained control of sound. However, the ideal material parameters prescribed by this methodology are complex and challenging to obtain experimentally, even using metamaterial design approaches. Not surprisingly, experimental demonstration of devices obtained using transformation acoustics is difficult, and has been implemented only in two-dimensional configurations. Here, we demonstrate the design and experimental characterization of an almost perfect three-dimensional, broadband, and, most importantly, omnidirectional acoustic device that renders a region of space three wavelengths in diameter invisible to sound.

Assessing the homogenization of urban land management with an application to US residential lawn care.

Changes in land use, land cover, and land management present some of the greatest potential global environmental challenges of the 21st century. Urbanization, one of the principal drivers of these transformations, is commonly thought to be generating land changes that are increasingly similar. An implication of this multiscale homogenization hypothesis is that the ecosystem structure and function and human behaviors associated with urbanization should be more similar in certain kinds of urbanized locations across biogeophysical gradients than across urbanization gradients in places with similar biogeophysical characteristics. This paper introduces an analytical framework for testing this hypothesis, and applies the framework to the case of residential lawn care. This set of land management behaviors are often assumed--not demonstrated--to exhibit homogeneity. Multivariate analyses are conducted on telephone survey responses from a geographically stratified random sample of homeowners (n = 9,480), equally distributed across six US metropolitan areas. Two behaviors are examined: lawn fertilizing and irrigating. Limited support for strong homogenization is found at two scales (i.e., multi- and single-city; 2 of 36 cases), but significant support is found for homogenization at only one scale (22 cases) or at neither scale (12 cases). These results suggest that US lawn care behaviors are more differentiated in practice than in theory. Thus, even if the biophysical outcomes of urbanization are homogenizing, managing the associated sustainability implications may require a multiscale, differentiated approach because the underlying social practices appear relatively varied. The analytical approach introduced here should also be productive for other facets of urban-ecological homogenization.

Global value chains in a post-Washington Consensus world

Contemporary globalization has been marked by significant shifts in the organization and governance of global industries. In the 1970s and 1980s, one such shift was characterized by the emergence of buyer-driven and producer-driven commodity chains. In the early 2000s, a more differentiated typology of governance structures was introduced, which focused on new types of coordination in global value chains (GVCs). Today the organization of the global economy is entering another phase, with transformations that are reshaping the governance structures of both GVCs and global capitalism at various levels: (1) the end of the Washington Consensus and the rise of contending centers of economic and political power; (2) a combination of geographic consolidation and value chain concentration in the global supply base, which, in some cases, is shifting bargaining power from lead firms in GVCs to large suppliers in developing economies; (3) new patterns of strategic coordination among value chain actors; (4) a shift in the end markets of many GVCs accelerated by the economic crisis of 2008-09, which is redefining regional geographies of investment and trade; and (5) a diffusion of the GVC approach to major international donor agencies, which is prompting a reformulation of established development paradigms. © 2013 © 2013 Taylor & Francis.

Similar prevalence and magnitude of auditory-evoked and visually evoked activity in the frontal eye fields: implications for multisensory motor control.

Saccadic eye movements can be elicited by more than one type of sensory stimulus. This implies substantial transformations of signals originating in different sense organs as they reach a common motor output pathway. In this study, we compared the prevalence and magnitude of auditory- and visually evoked activity in a structure implicated in oculomotor processing, the primate frontal eye fields (FEF). We recorded from 324 single neurons while 2 monkeys performed delayed saccades to visual or auditory targets. We found that 64% of FEF neurons were active on presentation of auditory targets and 87% were active during auditory-guided saccades, compared with 75 and 84% for visual targets and saccades. As saccade onset approached, the average level of population activity in the FEF became indistinguishable on visual and auditory trials. FEF activity was better correlated with the movement vector than with the target location for both modalities. In summary, the large proportion of auditory-responsive neurons in the FEF, the similarity between visual and auditory activity levels at the time of the saccade, and the strong correlation between the activity and the saccade vector suggest that auditory signals undergo tailoring to match roughly the strength of visual signals present in the FEF, facilitating accessing of a common motor output pathway.

Neural network evidence for the coupling of presaccadic visual remapping to predictive eye position updating

As we look around a scene, we perceive it as continuous and stable even though each saccadic eye movement changes the visual input to the retinas. How the brain achieves this perceptual stabilization is unknown, but a major hypothesis is that it relies on presaccadic remapping, a process in which neurons shift their visual sensitivity to a new location in the scene just before each saccade. This hypothesis is difficult to test in vivo because complete, selective inactivation of remapping is currently intractable. We tested it in silico with a hierarchical, sheet-based neural network model of the visual and oculomotor system. The model generated saccadic commands to move a video camera abruptly. Visual input from the camera and internal copies of the saccadic movement commands, or corollary discharge, converged at a map-level simulation of the frontal eye field (FEF), a primate brain area known to receive such inputs. FEF output was combined with eye position signals to yield a suitable coordinate frame for guiding arm movements of a robot. Our operational definition of perceptual stability was "useful stability,” quantified as continuously accurate pointing to a visual object despite camera saccades. During training, the emergence of useful stability was correlated tightly with the emergence of presaccadic remapping in the FEF. Remapping depended on corollary discharge but its timing was synchronized to the updating of eye position. When coupled to predictive eye position signals, remapping served to stabilize the target representation for continuously accurate pointing. Graded inactivations of pathways in the model replicated, and helped to interpret, previous in vivo experiments. The results support the hypothesis that visual stability requires presaccadic remapping, provide explanations for the function and timing of remapping, and offer testable hypotheses for in vivo studies. We conclude that remapping allows for seamless coordinate frame transformations and quick actions despite visual afferent lags. With visual remapping in place for behavior, it may be exploited for perceptual continuity.