Finding and verifying all solutions of a system of nonlinear equations using public domain software: Working paper series--02-14

Economic models are often stated as systems of nonlinear equations, for example general equilibrium models, game theory models, and macroeconomic models. The existence and uniqueness of solutions to the model are critical issues. Interval arithmetic is an arithmetic that operates on interval values rather than point values. It can be used to find all solutions of a system of nonlinear equations over a specified region and to determine if a solution is unique. We present arguments demonstrating that this arithmetic is capable of determining existence and uniqueness. We then use a public domain software package to find all roots of several simple economic example problems

Fano collective resonance as complex mode in a two dimensional planar metasurface of plasmonic nanoparticles

Fano resonances are features in transmissivity/reflectivity/absorption that owe their origin to the interaction between a bright resonance and a dark (i.e., sub-radiant) narrower resonance, and may emerge in the optical properties of planar two-dimensional (2D) periodic arrays (metasurfaces) of plasmonic nanoparticles. In this Letter, we provide a thorough assessment of their nature for the general case of normal and oblique plane wave incidence, highlighting when a Fano resonance is affected by the mutual coupling in an array and its capability to support free modal solutions. We analyze the representative case of a metasurface of plasmonic nanoshells at ultraviolet frequencies and compute its absorption under TE- and TM-polarized, oblique plane-wave incidence. In particular, we find that plasmonic metasurfaces display two distinct types of resonances observable as absorption peaks: one is related to the Mie, dipolar resonance of each nanoparticle; the other is due to the forced excitation of free modes with small attenuation constant, usually found at oblique incidence. The latter is thus an array-induced collective Fano resonance. This realization opens up to manifold flexible designs at optical frequencies mixing individual and collective resonances. We explain the physical origin of such Fano resonances using the modal analysis, which allows to calculate the free modes with complex wavenumber supported by the metasurface. We define equivalent array dipolar polarizabilities that are directly related to the absorption physics at oblique incidence and show a direct dependence between array modal phase and attenuation constant and Fano resonances. We thus provide a more complete picture of Fano resonances that may lead to the design of filters, energy-harvesting devices, photodetectors, and sensors at ultraviolet frequencies.Comment: 6 pages, 5 figure

Viscoelastic optical nonlocality of low-loss epsilon-near-zero nanofilms

Optical nonlocalities are elusive and hardly observable in traditional plasmonic materials like noble and alkali metals. Here we report experimental observation of viscoelastic nonlocalities in the infrared optical response of doped cadmium-oxide, epsilon-near-zero nanofilms. The nonlocality is detectable thanks to the low damping rate of conduction electrons and the virtual absence of interband transitions at infrared wavelengths. We describe the motion of conduction electrons using a hydrodynamic model for a viscoelastic fluid, and find excellent agreement with experimental results. The electrons elasticity blue-shifts the infrared plasmonic resonance associated with the main epsilon-near-zero mode, and triggers the onset of higher-order resonances due to the excitation of electron-pressure modes above the bulk plasma frequency. We also provide evidence of the existence of nonlocal damping, i.e., viscosity, in the motion of optically-excited conduction electrons using a combination of spectroscopic ellipsometry data and predictions based on the viscoelastic hydrodynamic model.Comment: 19 pages, 5 figure

Landscape-Scale Drivers of Resistance and Resilience to Bark Beetles: A Conceptual Susceptibility Model

Bark beetle (Dendroctonus spp.) outbreaks in the middle latitudes of western North America cause large amounts of tree mortality, outstripping wildfire by an order of magnitude. While temperatures play an important, and direct role in the population dynamics of ectothermic bark beetles, an equally important influence is the nature of the host substrate—the structure and composition of forested communities. For many of the dominant tree species in the western United States, “hazard” indices have been developed for specific bark beetles, which generally include three key variables—host tree size, absolute or relative density of the stand, and percentage of host composition. We provide a conceptual model to apply these three variables across forest ecosystems and bark beetles that shifts the thinking from a species–specific model to a model which focuses on the underlying ecological factors related to bark beetle outbreak susceptibility. We explored the use of our model across multiple scales using the Forest Inventory and Analysis database: Interior West, USA; the states of Colorado and Arizona; and specific national forests within Arizona that are implementing a large-scale restoration effort. We demonstrated that across the Interior West and Colorado, the vast majority of forests have moderate to high susceptibility to bark beetles. Our conceptual model maintains the simplicity of previous “hazard” models but acknowledges the need to consider scale when managing bark beetles. It also shifts the management approach from resistance thinking to the development of “associational resilience”, where the focus is not on any one individual stand or area but the longer-term perspective of forest persistence across the landscape

Water desalination by capacitive electrodialysis: Experiments and modelling

Electrodialysis-related technologies keep spreading in multiple fields, among which water desalination still plays a major role. A new technology that has not yet been thoroughly investigated is capacitive electrodialysis (CED), which couples the standard ED with capacitive electrodes. CED has a number of advantages such as removal of toxic products and system simplification. Little mention is made of this technology in the literature and, to the best of our knowledge, no modelling works have ever been presented. In this work, the CED process has been studied through experiments and modelling. A CED model is presented for the first time. With a simple calibration based on macroscopic membrane properties and the characterisation of electrode behaviour, the model is able to simulate the dynamics of simple as well as more complex layouts. An original experimental characterisation of electrodes is presented, showing how the collected data can be implemented into the model. After a successful validation with experimental data, dynamic simulations of a single pass CED unit have been performed with the aim of assessing the effect of different capacitive electrode properties on process performance. Results show how the impact of these properties is different depending on the number of cell pairs

Structural and Compositional Patterns in Forest Communities in the Intermountain West Across Multiple Scales

The United States Department of Agriculture (USDA) strives to use science-based research to both protect and enhance the management of natural resources. From this overarching goal, the USDA has a specific objective to protect the health and sustainability of forest and rangeland ecosystems. Based on this specific objective, an Advisory Board of natural resource scientists within the Quinney College of Natural Resources (QCNR) was awarded a National Institute of Food and Agricultural (NIFA) grant to train two PhD and two MS students. Their research would focus on managing for resilient forest ecosystem in the Intermountain West. With input from the advisory board and my PhD committee, my research focused on how to increase forest resilience at multiple scales. Locally, on the T.W. Daniel (TWD) Experimental Forest on the Logan Ranger District, three silvicultural trials were evaluated for resistance and resilience to the spruce beetle (partially funded by the TWD Forestry Fellowship). At the regional scale, a conceptual model was developed to classify forest communities based on structural features. The model was tested with data collected from 15 mountain ranges across the Intermountain West. Additionally, basic forest dynamics of limber pine (Pinus flexilis James.) were summarized across the Intermountain West. All three of these studies will aid in developing and implementing sound forest management practices to increase forest resilience

effect of calcipotriol on etanercept partial responder psoriasis vulgaris and psoriatic arthritis patients

Patients who respond only partially to etanercept may require additional treatments that act synergistically to improve their therapeutic response while at the same time reducing the dose required and the risk of side-effects. The aim of this study was to evaluate the effectiveness of topical calcipotriol in etanercept partial responder patients. We enrolled 120 patients affected by psoriasis vulgaris and psoriatic arthritis. A 50 mg dose of etanercept was administered twice weekly for the first 12 weeks, followed by a 25 mg dose twice weekly for an additional 12 weeks. At week 12, for 45 patients who had not achieved PASI 50, calcipotriol cream was also prescribed twice daily for 4 weeks and then once daily for a further 8 weeks. At week 24, of the 45 patients in the group treated with etanercept plus calcipotriol,14 (31.1%) had achieved PASI 75, and 23 PASI 50, while 8 (17.7%) had dropped out of therapy; of the 75 patients who continued etanercept in monotherapy with a 25 mg dose twice weekly for another 12 weeks, 71 (94.6%) had achieved PASI 50 and 57 (76.0%) PASI 75. The application of calcipotriol in etanercept partial responder patients had therefore helped 37 out of 120 patients (31 %) achieve at least PASI 50. This is the first report about the controlled combination of topical calcipotriol and etanercept in a large group of psoriatic patients. The efficacy and cost-effectiveness of the combined treatment is evidenced by the good response shown at week 24 by a group of etanercept low-responder patients using drugs sparingly and limiting likely toxicity

A three-dimensional approach to visualize pairwise morphological variation and its application to fragmentary palaeontological specimens

Classifying isolated vertebrate bones to a high level of taxonomic precision can be difficult. Many of Australia's Cretaceous terrestrial vertebrate fossil-bearing deposits, for example, produce large numbers of isolated bones and very few associated or articulated skeletons. Identifying these often fragmentary remains beyond high-level taxonomic ranks, such as Ornithopoda or Theropoda, is difficult and those classified to lower taxonomic levels are often debated. The ever-increasing accessibility to 3D-based comparative techniques has allowed palaeontologists to undertake a variety of shape analyses, such as geometric morphometrics, that although powerful and often ideal, require the recognition of diagnostic landmarks and the generation of sufficiently large data sets to detect clusters and accurately describe major components of morphological variation. As a result, such approaches are often outside the scope of basic palaeontological research that aims to simply identify fragmentary specimens. Herein we present a workflow in which pairwise comparisons between fragmentary fossils and better known exemplars are digitally achieved through three-dimensional mapping of their surface profiles and the iterative closest point (ICP) algorithm. To showcase this methodology, we compared a fragmentary theropod ungual (NMV P186153) from Victoria, Australia, identified as a neovenatorid, with the manual unguals of the megaraptoran Australovenator wintonensis (AODF604). We discovered that NMV P186153 was a near identical match to AODF604 manual ungual II-3, differing only in size, which, given their 10–15Ma age difference, suggests stasis in megaraptoran ungual morphology throughout this interval. Although useful, our approach is not free of subjectivity; care must be taken to eliminate the effects of broken and incomplete surfaces and identify the human errors incurred during scaling, such as through replication. Nevertheless, this approach will help to evaluate and identify fragmentary remains, adding a quantitative perspective to an otherwise qualitative endeavour

Non-Destructive Techniques in the Consolidation Works of the Church of S.M. of Itria in Piazza Armerina (Italy)

A real case of consolidation works is presented in which only field testing methods can reveal the causes of instability. This paper is an update of the one presented at the SAHC 2018 conference, concerning the study of the partial collapse of the Church of Itria in Piazza Armerina (Sicily, Italy). The previous paper beared hypotheses and design solutions based only on indirect investigations, theoretical formulations and checks with software. The consolidation works, started in November 2018 and still in progress, have made it possible to formulate new and documented hypotheses on the collapse and to integrate and partly modify the solutions hypothesized previously. In particular, the reconstruction techniques of the wall and chains have been confirmed. The new interventions have, instead, concerned the consolidation of the foundation soil which was found to be insubstantial,following electrical tomographic investigations, due to the presence of voids. At the same time, inspections were carried out on an old masonry sewage pipe which revealed several points of discontinuity through which large quantities of water entered under the walls of the church causing the removal of inconsistent elements from the ground. At first, the reconstruction of the collapsed wall was done and the restoration of the existing wall structures, to eliminate the causes of the collapse through the intervention on the sewage pipe and filling the voids under the foundations. The most important intervention, which required the use of innovative materials, forefront equipment and skilled labor, involved the filling the voids under the foundations through perforations every 50 cm, both on the inner and outer wire of the collapsed wall. Clamped canes were set in order to intercept the voids highlighted by the tomography. A 100% expansive mortar was injected at low pressure through the canes, filling one cane at a time and progressively raising the point of exit of the mortar until the higher far end. After this consolidation, the foundation and the wall were rebuilt with local limestone ashlars to have fair faced aspect as the original masonry. At the end of the work, further tomographic tests are planned to verify the validity of the interventions carried out