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.     

Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (C_ω)_ωεΩ in a real Hilbert space H, one wants to find a point that belongs to C_ω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point     

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.     

Enhanced multi‐objective optimization of a dimpled channel through evolutionary algorithms and multiple surrogate methods

Using a multi‐objective evolutionary algorithm (MOEA) and enhanced surrogate approximations, the present study demonstrates the numerical analysis and optimization of staggered‐dimple channels. Two surrogates, the response surface approximation (RSA) model and the Kriging (KRG) model, are applied in light of the surrogate fidelity of the approximate analysis. An enhanced Pareto‐optimal front is obtained by performing local resampling of the Pareto‐optimal front, which provides relatively more accurate Pareto‐optimal solutions in the design space for each surrogate model. Three dimensionless design variables are selected, which are related to geometric parameters, namely, the channel height, dimple print diameter, dimple spacing, and dimple depth. Two objective functions are selected that are related to the heat transfer and pressure loss, respectively. The objective‐function values are numerically evaluated through Reynolds‐averaged Navier–Stokes analysis at the design points that are selected through the Latin hypercube sampling method. Using these numerical simulations two surrogates, viz, the RSA and Kriging models, are constructed for each objective function and a hybrid MOEA is applied to obtain the Pareto‐optimal front. For the particular implementation of surrogate models, it is observed that Pareto‐optimal predictions of the RSA model are better than those of the KRG model, whereas the KRG model predicts equally well at the off‐Pareto‐region (region away from the Pareto‐optimal solutions), which is not the case with the RSA model. The local resampling of the Pareto‐optimal front increases the fidelity of the approximate solutions near the Pareto‐optimal region. The ratios of the channel height to the dimple print diameter and of the dimple print diameter to the dimple pitch are found to be more sensitive along the Pareto‐optimal front than the ratio of the dimple depth to the print diameter. The decrease of the ratio of the channel height to the dimple diameter and the increase of the ratio of the dimple print diameter to the pitch lead to greater heat transfer at the expense of the pressure loss, whereas the ratio of the dimple depth to the print diameter is rather insensitive to Pareto‐optimal solutions. Pareto‐optimal solutions at higher values of the Nusselt number are associated with higher values of the pressure loss due to the increased recirculation, mixing of fluid and vorticity generation. Copyright © 2010 John Wiley & Sons, Ltd.     

Modified characteristic finite difference fractional step method for moving boundary value problem of percolation coupled system

For the coupled system with moving boundary values of multilayer dynamicsof fluids in porous media,a characteristic finite difference fractional step scheme appli-cable to the parallel arithmetic is put forward.Some techniques,such as the change ofregions,the calculus of variations,the piecewise threefold quadratic interpolation,themultiplicative commutation rule of difference operators,the decomposition of high orderdifference operators,and the prior estimates,are adopted.The optimal order estimatesin the l2norm are derived to determine the error in the approximate solution.This nu-merical method has been successfully used to simulate the flow of migration-accumulationof the multilayer percolation coupled system.Some numerical results are well illustratedin this paper.     

Optimal control for reinitialization in finite element level set methods

A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first‐order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE‐based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Scheme for the implementation of 1→3 optimal phase-covariant quantum cloning in ion-trap systems

This paper proposes a scheme for the implementation of 1→ 3 optimal phase-covariant quantum cloning with trapped ions. In the present protocol, the required time for the whole procedure is short due to the resonant interaction, which is important in view of decoherence. Furthermore, the scheme is feasible based on current technologies.     

Enhanced nonlinearity in photonic crystal fiber by germanium doping in the core region

Germanium doping in silica can be used as a method for nonlinearity enhancement.Properties of the enhanced nonlinearity in photonic crystal fiber(PCF)with a GeO2-doped core are investigated theoretically by using all-vector finite element method.Numerical result shows that the nonlinear coefficient of PCF is greatly enhanced with increasing doping concentration,furthermore,optimal radius of the doped region should be considered for the desired operating wavelength.     

Alpha decay energies and half-lives for possibly synthesized superheavy elements

We investigate the ground state properties of some superheavy nuclei, which may be synthesized in future experiments. Special emphases are placed on the alpha decay energies and half-lives. The alpha decay energies and half-lives from different theoretical models are compared and discussed comprehensively. Through these calculations and comparisons, the optimal superheavy elements to be synthesized in future experiments are proposed theoretically.     

父代种群参与竞争遗传算法几乎必然收敛

熟知,标准遗传算法如不采用“杰出者记录策略”则必不收敛。本文发现：允许父代种群参与竞争是标准遗传算法几乎必然收敛的条件。特别地,我们运用鞅收敛定理证明：允许父代种群参与竞争型遗传算法能以概率1确保在限步内达到全局最优解,且收敛与种群规模无关。所获结果对该类遗传算法的应用奠定了可靠基础。