Experimental Verification of a Depth Controller using Model Predictive Control with Constraints onboard a Thruster Actuated AUV

In this work a depth and pitch controller for an autonomous underwater vehicle (AUV) is developed. This controller uses the model predictive control method to manoeuvre the vehicle whilst operating within the defined constraints of the AUV actuators. Experimental results are given for the AUV performing a step change in depth whilst maintaining zero pitch

Soil phosphorus testing on alkaline calcareous soils

Soil phosphorus testing made great strides with multiple chemical tests proposed and implemented that have been used for fertilizer management programs for crop production during the previous century. In the latter part of the previous century, the environmental impact of excess nonpoint phosphorus loading from the landscape (e.g. agricultural lands) to waterbodies became an issue of increased concern and soil phosphorus testing came to the forefront of management and monitoring. This article will provide a general overview of the usage of phosphorus testing for agronomic purposes in the United States

Evaluation of soil test phosphorus extractants in Idaho soils

Evaluation of soil-phosphorus (P) tests is critical to ensure the accuracy of fertilizer recommendations to optimize crop yield while minimizing negative environmental consequences. Olsen-P is the most commonly used soil-P test for alkaline calcareous soils found in Idaho and the Western United States. The Bray-1 test is commonly used in the Pacific Northwest (PNW) on neutral to acidic soils but underestimates P in alkaline calcareous soils. Mehlich-3 has been evaluated throughout various regions in the United States. Little data evaluating the test exists on soils in the Western United States. Additionally, the comparatively newly developed H3A test, a component of the soil health tool, has not been widely evaluated on alkaline calcareous soils. Soil samples from the 0- to 30-cm depth were collected from agricultural fields throughout Idaho and analyzed using Bray-1, H3A, Mehlich-3, and Olsen P extractants. Results suggested that Olsen P was strongly correlated with Mehlich-3, while Bray-1 and H3A were not correlated with Olsen P. Both the Bray-1 and H3A test underestimated extractable P when compared with the Olsen P test, whereas the Mehlich-3 overestimated. A threshold point in calcium carbonate (i.e., inorganic carbon (IC)) of 6.7 and 5.1 mg kg-1 for the Bray-1 and H3A was obtained, respectively, that indicated inorganic carbon concentrations at or above these levels result in underestimation of extractable soil P. Thus, Mehlich-3 was very strongly correlated to Olsen P and could be evaluated for use in alkaline calcareous soils whereas Bray-1 and H3A have notable issues that would limit their applicability

Evaluation of a microplate spectrophotometer for soil organic carbon determination in south-central Idaho

Soil organic carbon (SOC) is traditionally measured through dry combustion of soil but is inaccurate in soils recently limed or containing carbonates. Soils of south central Idaho contain carbonates therefore 3 alternative methods are typically used. Walkley-Black titration (WBTIT) has an extensive history but generates a large volume of hazardous waste for each sample analyzed. Low temperature loss on ignition (LOI360°C) may be utilized but requires frequent sample manipulation and is therefore prone to human error. A pressure calcimeter (Pcal) may be used, however the sample container may leak leading to inaccurate results. Therefore, a new method of SOC determination (WBSPEC) utilizing a microplate spectrophotometer was compared to LOI360°C, Pcal, and WBTIT in 75 south central Idaho soils and 10 standard soils. First, it was confirmed that soils of south central Idaho contain carbonates leading to inaccurate SOC determination by dry combustion. During the alternative method comparison, the WBSPEC method reduced waste production over the traditional WBTIT method by 89% while reducing sample handling over LOI360°C. The LOI360°C and WBTIT methods were most similar, however, the WBSPEC method performed adequately; the Pcal method often overestimated SOC compared to each other method. As the low SOC soils of south central Idaho were of particular interest, the methods were compared a second time on low SOC (<13.11 g kg-1) soils. Here, SOC determination was challenging however the WBSPEC method followed other methods well. It was determined that WBSPEC allows for accurate SOC determination in low SOC soils containing carbonates while reducing hazardous waste production and sample handling

Monitoring and evaluation of spatially managed areas: a generic framework and its application

The application of an ecosystem approach to management of the sea requires both integrated and strategic frameworks such as Integrated Coastal Zone Management (ICZM) and the use of marine spatial planning (MSP) to minimize spatial use conflicts and environmental degradation. Such an integrated management promotes sustainable development based on achieving a balance of environmental, social and economic objectives. Here we introduce a first draft of a generic framework which is developed in the EU FP7 project MESMA that gives guidance on how to assess the effectiveness of an existing management within a spatially defined area. More precisely, we define spatially managed areas as geographical entities where a marine planning framework is or will be used to manage multiple human activities in space and time while aiming to maintain ecosystem integrity. The framework consists of seven steps and comprises practical guidance on the selection of operational objectives and related criteria (step 1), the collation and integration of information (steps 2, 3 and 4), performance assessment (step 5), and feedback processes (steps 6 and 7). In the course of the MESMA project, this generic framework will be applied and tested in nine case studies, representing all European seas. Here we highlight the processes and practical tasks involved in each of the framework steps, reflect on the first attempts to implement this framework and identify the requirements for practical tools such as standardized methods to map human activities and assess their cumulative impacts

Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the pp-Adics-Quantum Group Connection

We establish a previously conjectured connection between $p$-adics and quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra and its generalizations, the conceptual basis for the Macdonald polynomials, which ``interpolate'' between the zonal spherical functions of related real and $p$\--adic symmetric spaces. The elliptic quantum algebras underlie the $Z_n$\--Baxter models. We show that in the n \air \infty limit, the Jost function for the scattering of {\em first} level excitations in the $Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function constructed from the Macdonald polynomials associated to the root system $A_1$. The partition function of the $Z_2$\--Baxter model itself is also expressed in terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less simple way. We relate the two parameters $q$ and $t$ of the Macdonald polynomials to the anisotropy and modular parameters of the Baxter model. In particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond to a discrete sequence of XXZ models. We also discuss the possibility of ``$q$\--deforming'' Euler products.Comment: 25 page

Cloud microphysical effects of turbulent mixing and entrainment

Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence time scales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.Comment: 17 pages, 10 Postscript figures (figures 3,4,6,7,8 and 10 are in reduced quality), to appear in Theoretical Computational Fluid Dynamic

Comparison of nutrient management recommendations and soil health indicators in southern Idaho

Advanced soil tests are being developed to help improve the estimation of plant available nutrients in order to better match fertilizer additions with plant needs as well as provide a measure of soil health, in some instances. The Soil Health Tool (SHT) has been developed with both goals in mind, yet it has not been tested for use in semi-arid regions such as southern Idaho. In the present study, we compared the use of the SHT for making fertilizer recommendations vs. using the standard regional method as well as evaluated the SHT soil health score (SHS) relative to crop yields and quality. The SHT was designed to analyze samples for 0-15 cm depth and regional guidelines call for deeper soil sampling (0-30 cm or 0-60 cm). In order to determine N fertilizer applications, use of the tool without accounting for depth, would recommend greater N application (~138 kg/ha) than the current regional methodology. However, it does appear that by accounting for depth in the SHT can provide similar available N estimates for the top 30 cm of soil. While N mineralization was not well predicted utilizing the method included in the SHT or from the regional methodology, the average estimated available N for these soils (47 kg/ha) was similar to the N mineralization value used in the current regional methodology (50 kg/ha). The P fertilizer recommendations were more similar between the two methodologies with the SHT recommending, on average 4.7 kg/ha less P than the regional method. The lower P recommendation are likely due to a lack of accounting for the effects of high calcium carbonate levels on the P availability from fertilizers in this region. The SHS was highly correlated with measures of soil C but was not positively correlated to crop yield. In some instances, increasing SHS resulted in decreases in crop quality as the addition of manure increased soil C but also created other potential problems such as high salt contents and release of late season N. With modification to more accurately represent irrigation conditions and including sampling to greater soil depths, this test may be tailored to better estimate soil nutrient status and provide better fertilizer recommendations for the region

Dilogarithm Identities in Conformal Field Theory and Group Homology

Recently, Rogers' dilogarithm identities have attracted much attention in the setting of conformal field theory as well as lattice model calculations. One of the connecting threads is an identity of Richmond-Szekeres that appeared in the computation of central charges in conformal field theory. We show that the Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be interpreted as a lift of a generator of the third integral homology of a finite cyclic subgroup sitting inside the projective special linear group of all $2 \times 2$ real matrices viewed as a {\it discrete} group. This connection allows us to clarify a few of the assertions and conjectures stated in the work of Nahm-Recknagel-Terhoven concerning the role of algebraic $K$-theory and Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related to hyperbolic 3-manifolds as suggested but is more appropriately related to the group manifold of the universal covering group of the projective special linear group of all $2 \times 2$ real matrices viewed as a topological group. This also resolves the weaker version of the conjecture as formulated by Kirillov. We end with the summary of a number of open conjectures on the mathematical side.Comment: 20 pages, 2 figures not include

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.Comment: 43 pages, amste