A Preconditioned Iterative Method for the Solution of the Biharmonic Problem

The numerical solution of the first biharmonic problem on polygonalplane domains is considered. A method is derived, which allowsan arbitrary degree of finite-element approximation and thediscretized system is solved by a fast iterative procedure.Theoretical estimates for the computational complexity are derivedand a number of test examples are examined.     

OPTIMAL HARVEST FEEDBACK RULE ACCOUNTING FOR THE FISHING‐UP EFFECT AND SIZE‐DEPENDENT PRICING

Abstract Fishing leads to truncation of a population's age and size structure. However, large‐sized fish are usually more valuable per unit weight than small ones. Nevertheless, these size‐related factors have mostly been ignored in bioeconomic modeling. Here, we present a simple extension to the Gordon–Schaefer model that accounts for variations in mean individual catch weight, and derive the feedback rule for optimal harvest in this setting. As the Gordon–Schaefer model has no population structure, size effects have to be accounted for indirectly. Here we assume a simple negative relationship between fishing effort and mean individual weight, and a positive relationship between mean catch weight and price. The aim is to emulate alterations of size structure in fish populations due to fishing and the influence of size on price per weight unit and eventually, net revenues. This demonstrates, on a general level, how such size‐dependent effects change the patterns of optimal harvest paths and sustainable revenue in single fish stocks. The model shows clear shifts toward lower levels of optimal effort and yield compared to classical models without size effects. This suggests that ignoring body size could lead to misleading assumptions and policies, potentially causing rent dissipation and suboptimal utilization of renewable resources.     

WHY INCREASED UNCERTAINTY MAY LEAD TO MORE RISKY BEHAVIOR

The purpose of this article is to investigate circumstances under which it may be optimal to deliberately harvest a fish stock to extinction applying a stochastic surplus growth model. It is known from the literature that deliberate extinction may result when there is critical depensation or when the discount rate is high compared to the intrinsic growth rate. Here it is shown that deliberate extinction may also be optimal when the degree of stochasticitry is high even with zero discounting. A high degree of stochasticity may have the same effect as critical depensation even though it is not present in the biological model. In other words, high uncertainty, instead of leading to more conservative harvesting as is usually expected, in this model result in more aggressive harvesting and more risky behavior. The main message is therefore always to try to keep the stock well above any critical limit.     

MODELLING OF RELEASE OF GAS FROM HIGH-PRESSURE PIPELINES

The problem investigated is the break of a high-pressure pipeline carrying natural single-phase gas which may condensate (retrograde) when the pressure drops. Single-phase non-ideal gas is assumed using a general- ized equation of state. Taking advantage of the choked massflow condition, the break is split into a pipe flow problem and a dispersion flow problem, both solved using a finite difference control volume scheme. The transient flow field from the pipeline break location is expanded analytically, using an approximation of the governing equations, until ambient pressure is reached and matched to the corresponding gas dispersion flow field using as subgrid model a jet box with a time-varying equivalent nozzle area as an internal boundary of the dispersion domain. The turbulence models used for the pipe and dispersion flow fields are an empirical model of Reichard and the k–ϵ model for buoyant flow respectively. The pipe flow simulations indicate that the flow from the pipeline might include dispersed condensate which will affect quantitatively the mass flow rate from the pipeline and qualitatively the gas dispersion if the condensate rains out. The transient dispersion simulation shows that an entrainment flow field develops and mixes supersaturated gas with ambient warmer air to an unsaturated mixture. Because of the inertia of the ambient air, it takes time to develop the entrainment flow field. As a consequence of this and the decay of the mass flow with time, the lower flammability limit of the gas–air mixture reaches its most remote downstream position relatively early in the simulation (about 15 s) and withdraws closer to the break location.     

INFERRING A BIOPOLITICAL CONSENSUS VIEW OF STOCHASTIC DYNAMICS FOR MANAGEMENT OF A TRANSBOUNDARY FISHERY

ABSTRACT. Management of trans‐boundary fisheries is a complicated problem with biological, legal, economic and political implications. We propose a simple stochastic differential‐equation model to describe a biopolitical consensus view of fish stock dynamics. Estimates of the drift and diffusion terms of three stochastic differential equations are obtained using data from the southern bluefin tuna (SBT) fishery with a method based on the Kolmogorov‐Smirnov statistic. We refer to these estimated equations as alternative biopolitical consensus views of SBT stock dynamics. Each of these is used to generate a time series of optimal harvest that achieves the objective of maximizing the present value of expected fishery returns. These time series of optimal harvests are then compared to actual harvests for the period 1981 1997.