A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.     

Miscibility of bisphenol-A polycarbonate with poly(methyl methacrylate)

The miscibility of bisphenol-A polycarbonate (PC) with poly(methyl methacrylate) (PMMA) has been reexamined using differential scanning calorimetry (DSC) and optical indications for phase separation on heating, i.e., lower critical solution temperature (LCST) behavior. Various methods have been used to prepare the blends including methylene chloride (CH₂Cl₂) and tetrahydrofuran (THF) solution casting, melt mixing, and precipitation of PC and PMMA simultaneously from THF solution by using the nonsolvents methanol and heptane. It is shown that the resulting phase behavior for PC/PMMA blends is strongly affected by the blend preparation method. However, these blends are miscible over the whole blend composition range (unambiguous single composition-dependent T_g's and LCST behavior) when prepared by precipitation from solution using heptane as the nonsolvent. To the contrary, solution-cast and melt-mixed PC/PMMA blends were all phase separated, which may be attributed to the “solvent” effect and LCST behavior, respectively, not discovered in previous reports. Methanol precipitation does not lead to fully mixed blends, which demonstrates the importance of the choice of nonsolvent when using the precipitation method.     

High-temperature expansions to fifteenth order

High-temperature series expansions of the susceptibility and second moment to 15th order are calculated for zero external field on the linear chain (LC), plane square (PSQ), simple cubic (SC), and body-centered cubic (BCC) lattices. Checks for specific models against pertinent work in the literature are detailed.     

Semi‐analytical integration of the 8‐node plane element stiffness matrix using symbolic computation

The semi‐analytical integration of an 8‐node plane strain finite element stiffness matrix is presented in this work. The element is assumed to be super‐parametric, having straight sides. Before carrying out the integration, the integral expressions are classified into several groups, thus avoiding duplication of calculations. Symbolic manipulation and integration is used to obtain the basic formulae to evaluate the stiffness matrix. Then, the resulting expressions are postprocessed, optimized, and simplified in order to reduce the computation time. Maple symbolic‐manipulation software was used to generate the closed expressions and to develop the corresponding Fortran code. Comparisons between semi‐analytical integration and numerical integration were made. It was demonstrated that semi‐analytical integration required less CPU time than conventional numerical integration (using Gaussian‐Legendre quadrature) to obtain the stiffness matrix. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Co-Segregation Effects on Boundary Migration

We analyze the effect of co-segregation on the mobility of grain boundaries within the framework of the impurity drag theory originally proposed by Cahn and Lücke and Stüwe for an ideal solution. The new derivation extends this model to the case where there are two types of impurities (or three components in the alloy). Since the resultant expression for the boundary mobility is complicated, numerical solutions were obtained for several cases to show how co-segregation affects the boundary mobility. Depending on the relative diffusivities of the two impurities which are both attracted to the boundary, the mobility may either increase or decrease with increasing concentration of one of the impurities. When one of the impurities is attracted to the boundary and the other repelled from the boundary, increasing the concentration of the attractive impurity can lead to a sharp decrease in the boundary mobility.     

Nonlinear Theory of Spectra of Thermally Stimulated Currents in Complex Crystals with Hydrogen Bonds

The nonlinear theory of thermally stimulated depolarization currents is developed. The theory explains the processes of hetero- and homocharge relaxation in complex crystals with hydrogen bonds and allows the relaxation oscillator parameters to be calculated using the quadratic approximation for the external electric field.     

Time delay as a key to apoptosis induction in the p53 network

A feedback mechanism that involves the proteins p53 and mdm2, induces cell death as a controlled response to severe DNA damage. A minimal model for this mechanism demonstrates that the response may be dynamic and connected with the time needed to translate the mdm2 protein. The response takes place if the dissociation constant k between p53 and mdm2 varies from its normal value. Although it is widely believed that it is an increase in k that triggers the response, we show that the experimental behaviour is better described by a decrease in the dissociation constant. The response is quite robust upon changes in the parameters of the system, as required by any control mechanism, except for few weak points, which could be connected with the onset of cancer. Received 8 May 2002 / Received in final form 9 July 2002 Published online 17 September 2002     

Analytic Properties of the Transition Admittance of an Infinite Plate in a medium and the Regularization of Boundary-Contact Integrals in Acoustics

A condition for regularization of boundary-contact integrals in two-dimensional problems of acoustics is considered. With an example of the simplest boundary-contact problem of acoustics, it is shown that a known sufficient condition for regularization is also a necessary one. The study of analytic properties of the transition admittance of an infinite plate that is in contact with a medium is conducted in order to obtain this statement. The considerations are carried out in general terms. The results obtained may be used in arbitrary models of plate theory, and they also may be adapted to boundary-contact problems of another physical nature. Bibliography: 9 titles.     

Segregation in the Falicov--Kimball Model

The Falicov–Kimball model is a simple quantum lattice model that describes light and heavy electrons interacting with an on-site repulsion; alternatively, it is a model of itinerant electrons and fixed nuclei. It can be seen as a simplification of the Hubbard model; by neglecting the kinetic (hopping) energy of the spin up particles, one gets the Falicov–Kimball model. We show that away from half-filling, i.e. if the sum of the densities of both kinds of particles differs from 1, the particles segregate at zero temperature and for large enough repulsion. In the language of the Hubbard model, this means creating two regions with a positive and a negative magnetization. Our key mathematical results are lower and upper bounds for the sum of the lowest eigenvalues of the discrete Laplace operator in an arbitrary domain, with Dirichlet boundary conditions. The lower bound consists of a bulk term, independent of the shape of the domain, and of a term proportional to the boundary. Therefore, one lowers the kinetic energy of the itinerant particles by choosing a domain with a small boundary. For the Falicov- Kimball model, this corresponds to having a single “compact” domain that has no heavy particles. Received: 21 June 2001 / Accepted: 4 January 2002     

High energy asymptotics of the scattering amplitude for the Schrödinger equation

We find an explicit function approximating at high energies the kernel of the scattering matrix with arbitrary accuracy. Moreover, the same function gives all diagonal singularities of the kernel of the scattering matrix in the angular variables. This paper is dedicated to Jean-Michel Combes on the occasion of his sixtieth birthday.