An efficient step size control for continuation methods

In solving a nonlinear equation by the use of a continuation method one of the crucial problems is the choice of the step sizes. We present a model for the total computational cost of a standard numerical continuation process and solve the problem of optimal step size control for this model. Using the theoretical results as a basis, we develop an adaptive step size algorithm for Newton's method. This procedure is computationally inexpensive and it gives quite satisfactory results compared to some other numerical experiments found in the literature.     

Quasi-linearization and the Identification of Parameters in Partial Differential Equations

The method of quasi-linearization has been adapted to the problemof identifying parameters in partial differential equations.Convective and radiative heat transfer coefficients are obtainedfrom an equation that models the transient heating of a bedof spheres.     

Predictor-corrector Methods with Improved Absolute Stability Regions

Generalized predictor-corrector methods with an extended regionof absolute stability are studied. Choosing an extrapolation-predictorand a backward-differentiation-corrector, methods of ordersup to 6 are constructed. The real stability boundaries of thesemethods are of magnitude m², where m is the number of right-handside evaluations per integration step. The coefficients of themethods can be generated during the computation for arbitraryvalues of m. The storage requirements are limited and are independentof m.     

The change in phase behaviour and orientational order of solid N2 at high pressure under the influence of Ar: a simulation study

We have studied the influence of Ar atoms on the high-pressure phase behaviour of N₂ by a Monte Carlo study of Ar _x (N₂)_1-x mixed solids. The results were obtained on the N₂ rich side (0 ≤ x ≤ 0.25), in the region where the ? and δ phases exist in pure N₂. The ??—δ? transition shifts rapidly to lower temperatures with x: it has vanished for x ? 0.05. For x ? 0.12, a cubic orientationally ordered phase appears. The transition from this phase to the δ? phases shifts to higher temperatures with increasing x. The temperature of the onset as well as the completion of the cascade process, responsible for the δ?_loc—δ?_rot transition, is independent of composition. This transition disappears in the x-region where the ordered phase is present for all temperatures below the transition to the δ?_rot phase. Therefore, the influence of the isotropic diluents on the orientational behaviour of the N₂ molecules is threefold. In the δ?_loc phase, the vibron frequencies show a splitting that shifts as a function of x, which might be related to the occurrence of a tetragonal modification of this phase.     

Ethnic Preferences and Residential Segregation: Theoretical Explorations Beyond Detroit

We are strongly supportive of Fossett's theoretical approach and modeling methodology, which uses computational methods to perform thought experiments that generate compelling insights into the enigma of persistent residential segregation in the U.S. We also agree with his theoretical results, which challenge the prevailing view among demographers that institutional discrimination is the essential cause. However, we think he did not go far enough. Fossett limited his analysis to a narrow region of the parameter space that corresponded to conditions observed in one city at one time. This precludes generalization to other times and places and exploration of theoretically motivated “what if” scenarios that trespass beyond the Detroit city limits. When we extended the parameter space, we noticed two interesting results. First, Fossett's “paradox of weak minority preferences” requires qualification. Disproportionate in-group preferences among minorities are indeed segregation-promoting, not integration-promoting, but they generally have less impact on segregation than the in-group preferences of the majority. Second, not only are exclusionary practices and institutional discrimination not necessary for segregation (as Fossett demonstrates), we show that in certain regions of the parameter space they are not even sufficient.     

MARINE PROTECTED AREAS IN THE HIGH SEAS AND THEIR IMPACT ON INTERNATIONAL FISHING AGREEMENTS

Abstract Marine protected areas (MPAs) are gaining momentum as tools within fisheries management. Although many studies have been conducted to their use and potential, only few authors have considered their use in the High Seas. In this paper, we investigate the effects of fish growth enhancing MPAs on the formation of regional fisheries management organisations (RFMOs) for highly migratory fish stocks. We argue that in absence of enforcement MPAs constitute a weakest‐link public good, which can only be realized if everyone agrees. We combine this notion with a game theoretic model of RFMO formation to derive potentially stable RFMOs with and without MPAs. We find that MPAs generally increase the parameter range over which RFMOs are stable, and that they increase stability in a number of cases as compared to the case without MPAs. They do not necessarily induce a fully cooperative solution among all fishing nations. In summary, results of this paper suggest a positive role for MPAs in the High Seas.