Window scaling in one-dimensional maps

We describe both the internal structure and the width of the periodic windows in one-dimensional maps, by considering a universal local submap. Both features are found to depend only on the order of the extremum of this submap. Moreover, we discuss how the windows are grouped in accumulating families, and we calculate the scaling of the widths within these families

Implications of Spatially Variable Costs and Habitat Conversion Risk in Landscape-Scale Conservation Planning

‘‘Strategic habitat conservation’’ refers to a process used by the U.S. Fish and Wildlife Service to develop cost-efficient strategies for conserving wildlife populations and their habitats. Strategic habitat conservation focuses on resolving uncertainties surrounding habitat conservation to meet specific wildlife population objectives (i.e., targets) and developing tools to guide where conservation actions should be focused on the landscape. Although there are examples of using optimization models to highlight where conservation should be delivered, such methods often do not explicitly account for spatial variation in the costs of conservation actions. Furthermore, many planning approaches assume that habitat protection is a preferred option, but they do not assess its value relative to other actions, such as restoration. We developed a case study to assess the implications of accounting for and ignoring spatial variation in conservation costs in optimizing conservation targets. We included assumptions about habitat loss to determine the extent to which protection or restoration would be necessary to meet an established population target. Our case study focused on optimal placement of grassland protection or restoration actions to influence bobolink Dolichonyx oryzivorus populations in the tallgrass prairie ecoregion of the north central United States. Our results show that not accounting for spatially variable costs doubled or tripled the cost of meeting the population target. Furthermore, our results suggest that one should not assume that protecting existing habitat is always a preferred option. Rather, our results show that the balance between protection and restoration can be influenced by a combination of desired targets, assumptions about habitat loss, and the relative cost of the two actions. Our analysis also points out how difficult it may be to reach targets, given the expense to meet them. We suggest that a full accounting of expected costs and benefits will help to guide development of viable management actions and meaningful conservation plans

The squeeze effect in non-integrable Hamiltonian systems

In non-integrable Hamiltonian systems (represented by mappings of the plane) the stable island around an elliptic fixed point is generally squeezed into the fixed point by three saddle points, when the rotation number ρ of the motion at the fixed point approaches 1/3. At ρ=1/3 the island is reduced to one single point.\ud A detailed investigation of this squeeze effect, and some of its global implications, is presented by means of a typical two-dimensional area-preserving map. In particular, it turns out that the squeeze effect occurs in any mapping for which the Taylor expansion around the fixed point contains a quadratic term, whereas it does not occur if the first non-linear term is cubic. We illustrate this with two physical examples: a compass needle in an oscillating field, showing the squeeze effect, and a ball which bounces on a vibrating plane, for which the squeeze effect does not occur

Bifurcations in two-dimensional reversible maps

We give a treatment of the non-resonant bifurcations involving asymmetric fixed points with Jacobian J≠1 in reversible mappings of the plane. These bifurcations include the saddle-node bifurcation not in the neighbourhood of a fixed point with J≠1, as well as the so-called transcritical bifurcations and generalized Rimmer bifurcations taking place at a fixed point with Jacobian J≠1. The bifurcations are illustrated by some simple examples of model maps. The Rimmer type of bifurcation, with e.g. a center point with J≠1 changing into a saddle with Jacobian J≠1, an attractor and a repeller, occurs under more general conditions, i.e. also in non-reversible mappings if only a certain order of local reversibility is satisfied. These Rimmer bifurcations are important in connection with the emergence of dissipative features in non-measure-preserving reversible dynamical systems

FE calculations on a three stage metal forming process of Sandvik Nanoflex

Sandvik NanoflexTM combines good corrosion resistance with high strength. This steel has good deformability in\ud austenitic conditions. It belongs to the group of metastable austenites, which means that during deformation a strain-induced\ud transformation into martensite takes place. After deformation, transformation continues as a result of internal stresses. Both\ud transformations are stress-state and temperature dependent. A constitutive model for this steel has been formulated, based\ud on the macroscopic material behaviour measured by inductive measurements. Both the stress-assisted and the strain-induced\ud transformation into martensite have been incorporated in this model. Path-dependent work hardening has also been taken\ud into account. This article describes how the model is implemented in an internal Philips FE code called CRYSTAL, which is\ud a dedicated robust and accurate finite element solver. The implementation is based on lookup tables in combination with\ud feed-forward neural networks. The radial return method is used to determine the material state during and after plastic\ud flow, however, it has been extended to cope with the stiff character of the partial differential equation that describes the\ud transformation behaviour

Shift rostering using decomposition: assign weekend shifts first

This paper introduces a shift rostering problem that surprisingly has not been studied in literature: the weekend shift rostering problem. It is motivated by our experience that employees’ shift preferences predominantly focus on the weekends, since many social activities happen during weekends. The Weekend Rostering Problem (WRP) addresses the rostering of weekend shifts, for which we design a problem specific heuristic. We consider the WRP as the first phase of the shift rostering problem. To complete the shift roster, the second phase assigns the weekday shifts using an existing algorithm. We discuss effects of this two-phase approach both on the weekend shift roster and on the roster as a whole. We demonstrate that our first-phase heuristic is effective both on generated instances and real-life instances. For situations where the weekend shift roster is one of the key determinants of the quality of the complete roster, our two-phase approach shows to be effective when incorporated in a commercially implemented algorithm