Space averaging of vibration level differences measured in lightweight building structures

This paper examines space averaging methods applied to structural level differences measured in lightweight building structures (two beam junction and single plate and beam junction). The methods studied include the averaging assuming a constant input force, the averaging based on a constant vibration level across the source element, and the arithmetic averaging of level differences. Tests indicate that a fairly steady input force can be easily produced when using an impulsive source such as a hammer; the constant input force method is then appropriate and can be used to space average level differences (the two beam structure showing a standard deviation of 0.1 dB from the averaging based on levels normalised to the force). On the other hand, acceleration levels can exhibit significant variations with position due to the low mode count and modal overlap of some lightweight elements such as timber beams. Variations in the vibration level across the source element can then be responsible for large inaccuracies in the level difference calculated from the constant level assumption, the two beams’ results showing errors greater than 5 dB at several 1/3 octave band frequencies. The latter averaging method is then inappropriate and should not be used.     

ECONOMICALLY OPTIMAL MARINE RESERVES WITHOUT SPATIAL HETEROGENEITY IN A SIMPLE TWO‐PATCH MODEL

Bioeconomic analyses of spatial fishery models have established that marine reserves can be economically optimal (i.e., maximize sustainable profit) when there is some type of spatial heterogeneity in the system. Analyses of spatially continuous models and models with more than two discrete patches have also demonstrated that marine reserves can be economically optimal even when the system is spatially homogeneous. In this note we analyze a spatially homogeneous two‐patch model and show that marine reserves can be economically optimal in this case as well. The model we study includes the possibility that fishing can damage habitat. In this model, marine reserves are necessary to maximize sustainable profit when dispersal between the patches is sufficiently high and habitat is especially vulnerable to damage.     

Optimal control systems with state variable jump discontinuities

Consideration is given to continuous-time, parameter-dependent optimal control problems with state-variable jump discontinuities atN variable interior times. A maximum principle involving known costate jump conditions is stated and is proved by transforming the problem into a standard Mayer control problem. An illustrative example for fisheries management is included.This work was partially supported by a grant from Control Data. The authors are grateful to Professor T. L. Vincent for drawing their attention to Refs. 4–6 listed below.     

OPTIMAL FISH HARVESTING FOR A POPULATION MODELED BY A NONLINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATION

As the human population continues to grow, there is a need for better management of our natural resources in order for our planet to be able to produce enough to sustain us. One important resource we must consider is marine fish populations. We use the tool of optimal control to investigate harvesting strategies for maximizing yield of a fish population in a heterogeneous, finite domain. We determine whether these solutions include no‐take marine reserves as part of the optimal solution. The fishery stock is modeled using a nonlinear, parabolic partial differential equation with logistic growth, movement by diffusion and advection, and with Robin boundary conditions. The objective for the problem is to find the harvest rate that maximizes the discounted yield. Optimal harvesting strategies are found numerically.     

Acoustics of a Bubbly Liquid with a Weak Chemical Reaction in the Gaseous Phase

The influence of the composition and thermophysical properties of gas-liquid bubbly systems with a dissociating component in the gaseous phase on the laws of small-disturbance propagation and attenuation is investigated. It is found that the reacting gas component in the bubbles significantly affects the sonic-wave attenuation coefficient in the bubbly liquid. This follows from the fact that when a gas bubble is compressed isothermally, a recombination reaction occurs which prevents pressure growth in the bubble.Small-disturbance propagation in bubbly liquids was investigated in a number of publications discussed in review [1]. The acoustics of a bubbly liquid with a gas phase containing active admixtures are of both methodical and practical interest. The dynamics of such multicomponent bubbles were investigated in [2].     

Interaction between Low and High-Frequency Modes in a Nonlinear System: Gas-Filled Cylinder Covered by a Movable Piston

A simple mechanical system containing a low-frequency vibration mode andset of high-frequency acoustic modes is considered. The frequencyresponse is calculated. Nonlinear behaviour and interaction betweenmodes is described by system of functional equations. Two types ofnonlinearities are taken into account. The first one is caused by thefinite displacement of a movable boundary, and the second one is thevolume nonlinearity of gas. New mathematical models based on nonlinearequations are suggested. Some examples of nonlinear phenomena arediscussed on the base of derived solutions.     

The unknown object problem in a sea with sloping bottom

This article considers the acoustic unknown object problem for a shallow ocean with a sloping seabed. The incident waves are sent from point sources along a s raight line parallel to the sea surface, and the corresponding scattered fields are measured from a line above the unknown object. We prove a uniqueness theorem for the inverse problem,and describe a generalizeddual space indicator method for numerical solution.Numerical results are given in Section 4.     

MULTISPECIES AND SINGLE‐SPECIES MODELS OF FISH POPULATION DYNAMICS: COMPARING PARAMETER ESTIMATES

Abstract Population features inferred from single‐species, age‐structured models are compared to those inferred from a multispecies, age‐structured model that includes predator‐prey interactions among three commercially harvested fish species—walleye pollock, Atka mackerel, and Pacific cod—on the Aleutian Shelf, Alaska. The multispecies framework treats the single‐species models and data as a special case of the multispecies model and data. The same data from fisheries and surveys are used to estimate model parameters for both single‐species and multispecies configurations of the model. Additionally, data from stomach samples and predator rations are used to estimate the parameters of the multispecies model. One form of the feeding functional response, predator pre‐emption, was selected using AIC from seven alternative models for how the predation rate changes with the densities of prey and possibly other predators. Differences in estimated population dynamics and productivity between the multispecies and single‐species models were observed. The multispecies model estimated lower mackerel population sizes from 1964–2003 than the single‐species model, while the spawning biomass of pollock was estimated to have declined more than three times faster since 1964 by the multispecies model. The variances around the estimates of spawning biomass were smaller for mackerel and larger for pollock in the multispecies model compared to the single‐species model.     

RANDOM PENALTIES AND RENEWABLE RESOURCES: A MECHANISM TO REACH OPTIMAL LANDINGS IN FISHERIES

Abstract Recent literature considers illegal landings a moral hazard problem that arises because individual landings are unobservable. The literature proposes incentive schemes to solve the information problem. However, most of the proposed schemes raise huge information requirements and social budget balance is not secured. In this paper, we suggest a random penalty mechanism that reduces the information requirements and secures budget balance in the case of a given number of licensed vessels. In the random penalty mechanism, aggregate landings are measured through stock sizes and the natural growth function. If aggregate landings are below optimal landings, each fisherman receives a subsidy. If aggregate catches are above optimal landings, the mechanism works such that either the fisherman is randomly selected and pays a fine or the fisherman is not selected and receives a subsidy. The fine and subsidy can be designed such that budget balance is secured. Provided risk aversion is sufficiently large and the fine is high enough, the random penalty mechanism will generate optimal individual landings. The budget balance combined with risk aversion drives the result for this advanced tax/subsidy system that does not exhaust the resource rents. The budget balance creates interdependence between fishermen that secure optimality.