Irrigation in Brookings County: Impacts of Credit and Commodity Price Levels

In this bulletin, the results of an investigation to determine the impacts of interest rates, leverage (the ratio of assets to liabilities), and crop prices on the organization and growth of a representative Brookings County irrigated farm are reported

Flux penetration in slab shaped Type-I superconductors

We study the problem of flux penetration into type--I superconductors with high demagnetization factor (slab geometry).Assuming that the interface between the normal and superconducting regions is sharp, that flux diffuses rapidly in the normal regions, and that thermal effects are negligible, we analyze the process by which flux invades the sample as the applied field is increased slowly from zero.We find that flux does not penetrate gradually.Rather there is an instability in the process and the flux penetrates from the boundary in a series of bursts, accompanied by the formation of isolated droplets of the normal phase, leading to a multiply connected flux domain structure similar to that seen in experiments.Comment: 4 pages, 2 figures, Fig 2.(b) available upon request from the authors, email - [email protected]

Adaptive Hierarchical Refinement of NURBS in Cohesive Fracture Analysis

Adaptive hierarchical refinement in isogeometric analysis is developed to model cohesive crack propagation along a prescribed interface. In the analysis, the crack is introduced by knot insertion in the NURBS basis, which yields math formula continuous basis functions. To capture the stress state smoothly ahead of the crack tip, the hierarchical refinement of the spline basis functions is used starting from a coarse initial mesh. A multi-level mesh is constructed, with a fine mesh used for quantifying the stresses ahead of the crack tip, and knot insertion, to insert the crack, and coarsening in the wake of the crack tip, since a lower resolution suffices there. This technique can be interpreted as a moving mesh around the crack tip. To ensure compatibility with existing finite element programs, an element-wise point of view is adopted using Bézier extraction. A detailed description is given how the approach can be implemented in a finite element data structure. The accuracy of the approach to cohesive fracture modelling is demonstrated by several numerical examples, including a double cantilever beam, an L-shaped specimen, and a fibre embedded in an epoxy matrix. This article is protected by copyright. All rights reserved

An immersed-boundary/isogeometric method for fluid–structure interaction involving thin shells

A computational framework is designed to accurately predict the elastic response of thin shells undergoing large displacements induced by local hydrodynamic forces, as well as to resolve the complex fluid pattern arising from its interaction with an incompressible fluid. Within the context of partitioned algorithms, two different approaches are employed for the fluid and structural domain. The fluid motion is resolved with a pressure projection method on a Cartesian structured grid. The immersed shell is modeled by means of a NURBS surface, and the elastic response is obtained from a displacement-based isogeometric analysis relying on the Kirchhoff–Love theory. The two solvers exchange data through a direct-forcing immersed-boundary approach, where the interpolation/spreading of the variables between Lagrangian and Eulerian grids is implemented with a Moving Least Squares approximation, which has proven to be very effective for moving boundaries. In this scenario, the isoparametric paradigm is exploited to perform an adaptive collocation of the Lagrangian markers, decoupling the local grid density of fluid and shell domains and reducing the computational expense. The accuracy of the method is verified by refinement analyses, segregating the Eulerian/Lagrangian refinement, which confirm the expected scheme accuracy in space and time. The effectiveness of the method is then validated against different test-cases of engineering and biologic inspiration, involving fundamentally different physical and numerical conditions, namely: (i) a flapping flag, (ii) an inverted flag, (iii) a clamped plate, (iv) a buoyant seaweed in a free stream. Both strong and loose coupling approaches are implemented to handle different fluid-to-structure density ratios, providing accurate results