OPTIMAL HARVESTING WITH DENSITY DEPENDENT RANDOM EFFECTS

We consider the effect of sudden large, randomly occurring density dependent disasters on the optimal harvest policy and optimal expected return for an exploited population. The population is assumed to grow logistically with disasters occurring on a time scale very short compared to the natural growth scale. The case of a density dependent disaster frequency is also treated. Stochastic dynamic programming is used in the optimization. For a set of realistic field data it is found that random effects typically have a significant effect on both optimal return and optimal effort levels. The effect of density dependence is far more pronounced for optimal return than for optimal effort levels.     

Nonlinear Stability of Baroclinic Fronts in a Channel with Variable Topography

The governing equations describing baroclinic bottom-trapped fronts in a channel with variable bottom topography are shown to be a noncanonical Hamiltonian system. The Hamiltonian formalism is exploited to derive a variational principle for arbitrary steady solutions based on an appropriately constrained energy functional. The variational principle is exploited to obtain formal and nonlinear stability conditions. In the infinitesimal amplitude limit, these stability conditions reduce to previously obtained normal mode results for the transverse gradient of the mean frontal potential vorticity.     

Optimization of Discrete-Continuous Dynamic Systems Based on Disjunctive Programming

In this contribution, a novel approach for the modeling and optimization of discrete-continuous dynamic systems based on a disjunctive problem formulation is proposed. It will be shown that a disjunctive model representation, which constitutes an alternative to mixed-integer model formulations, provides a very flexible and intuitive way to formulate discrete-continuous dynamic optimization problems. Moreover, the structure and properties of the disjunctive process models can be exploited for an efficient and robust numerical solution by applying generalized disjunctive programming techniques. The proposed modeling and optimization approach will be illustrated by means of an optimal control problem that embeds a linear discretecontinuous dynamic system. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Application of PID Control Unit for System Stabilization in Process-integrated Powder Coating by Radial Axial Rolling of Rings

The process integrated powder coating by radial axial rolling of rings represents a new hybrid production technique in order to apply the functional layers on ring-shaped work pieces. Since the layer is produced in a powder metallurgical way [1], the ring volume decreases during the compaction of the layer material. In conventional ring rolling processes an isochoric plastic deformation of the ring is exploited in order to control the process. However this is not true any more for a ring exhibiting a compressible layer [2]. Consequently different control mechanisms have to be developed for the new considered process. One major aspect is the stability of the process which is governed by a stable position of the ring as well as the roundness of the ring. Therefore the finite element (FE) model has been coupled with a PID-controller unit and it will be shown that a stable process can be reached in this way. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal design of robust piezoelectric unimorph microgrippers

Topology optimization can be used to design piezoelectric actuators by simultaneous design of host structure and polarization profile. Subsequent micro-scale fabrication leads us to overcome important manufacturing limitations: difficulties in placing a piezoelectric layer on both top and bottom of the host layer. Unsymmetrical layer placement makes the actuator bend, spoiling the predicted performance of the device. The aim of this work is to maximize the in-plane displacement of a microgripper-type actuator while out-of-plane displacement at some points of interest is suppressed. This last issue is the main novelty introduced in this work, and the emphasis is placed on the modelling and its applicability rather than numerical methods. In addition, a robust formulation of the problem has been used in order to ensure minimum length scale in the optimal designs, which it is crucial from the manufacturability point of view.     

The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets

Flow induced in a viscoelastic fluid by a linearly stretched sheet is investigated assuming that the fluid is Maxwellian and the sheet is subjected to a transverse magnetic field. The objective is to investigate the effects of parameters such as elasticity number, magnetic number, radiative heat transfer, Prandtl number, and Eckert number on the temperature field above the sheet. To do this, boundary layer theory will be used to simplify energy and momentum equations assuming that fluid physical/rheological properties remain constant. A suitable similarity transformation will be used to transform boundary layer equations from PDEs into ODEs. Homotopy analysis method (HAM) will be invoked to find an analytical solution for the temperature field above the sheet knowing the velocity profiles (see Alizadeh-Pahlavan et al. [Alizadeh-Pahlavan A, Aliakbar V, Vakili-Farahani F, Sadeghy K. MHD flows of UCM fluids above porous stretching sheets using two-auxiliary parameter homotopy analysis method. Commun. Nonlinear Sci Numer Simulat, in press]). The importance of manipulating the transverse velocity component, v, will be discussed on the temperature field above the sheet.     

用时变雷诺方程模型模拟孤立波与半圆型防波堤的相互作用

以时变雷诺方程为控制方程,用k-ε模型封闭该方程,采用体积函数(VOF)方法来跟踪波动自由表面,建立了二维垂向波浪数学模型,并用已有的实验资料进行了验证．随后用该模型模拟了半圆型防波堤与孤立波在淹没、平顶水位、完全露顶且不越浪3种典型工况下的相互作用过程．得到了半圆堤附近的流场、压强场和波面的变形过程．结果表明,在淹没状态下,半圆堤背浪面的底部会产生涡旋;平顶水位时,由于越浪的冲击作用,在半圆堤的背浪面将逐渐形成一对较大的涡旋,而半圆堤背浪面的底部,速度始终相对较小;而在露顶不越浪时,半圆堤的迎浪面会出现波浪的二次爬升的现象．为进一步研究结构物附近的污染物的输移扩散和泥沙运动提供基础．     

A Numerical Treatment of One-dimensional Models of Radiative Heat Transfer in Co-current Tube Furnaces

A model of a top-fired furnace, such as is used in chemicalindustrial plants, is described. The model gives rise to a systemof first-order differential equations, with boundary conditionsat both the top and bottom of the furnace. This also involvesa non-linear coupling of the radiation field to the energy ofthe gases flowing. Published accounts of this problem make useof shooting methods which converge extremely slowly. An alternativemethod will be described in which the radiative field equationsare solved by an algorithm of Grant and, to deal with the non-linearitiesof the system, a generalized Newton-Raphson method is employed.     

Behavioral optimal insurance

The present work studies the optimal insurance policy offered by an insurer adopting a proportional premium principle to an insured whose decision-making behavior is modeled by Kahneman and Tversky’s Cumulative Prospect Theory with convex probability distortions. We show that, under a fixed premium rate, the optimal insurance policy is a generalized insurance layer (that is, either an insurance layer or a stop–loss insurance). This optimal insurance decision problem is resolved by first converting it into three different sub-problems similar to those in Jin and Zhou (2008); however, as we now demand a more regular optimal solution, a completely different approach has been developed to tackle them. When the premium is regarded as a decision variable and there is no risk loading, the optimal indemnity schedule in this form has no deductibles but a cap; further results also suggests that the deductible amount will be reduced if the risk loading is decreased. As a whole, our paper provides a theoretical explanation for the popularity of limited coverage insurance policies in the market as observed by many socio-economists, which serves as a mathematical bridge between behavioral finance and actuarial science.     

On optimal operating conditions for a data processing system: A stochastic approach

In this paper, we consider the problem of determining optimal operating conditions for a data processing system. The system is burned‐in for a fixed burn‐in time before it is put into field operation and, in field operation, it has a work size and follows an age‐replacement policy. Assuming that the underlying lifetime distribution of the system has a bathtub‐shaped failure rate function, the properties of optimal burn‐in time, optimal work size and optimal age‐replacement policy will be derived. It can be seen that this model is a generalization of those considered in the previous works, and it yields a better optimal operating conditions. This paper presents an analytical method for three‐dimensional optimization problem. An algorithm for determining optimal operating conditions is also given. Copyright © 2007 John Wiley & Sons, Ltd.     

Self-Similarity and the Evaluation of Long-Time Nonhydrostatic Effects in Compositionally Driven Gravity Flows in Deep Surroundings

In the study of compositionally driven gravity currents involving one or more homogeneous fluid layers, it has been customary to adopt the hydrostatic assumption for the pressure field in each layer which, in turn, leads to a depth‐independent horizontal velocity field in each of these layers and significant simplifications to the governing equations. Under this hydrostatic paradigm, each layer will then have its motion governed by the well‐known reduced dimension shallow‐water equations. For the so‐called ‐layer or reduced gravity shallow‐water equations, similarity solutions for fixed volume gravity currents released in rectangular geometry have been found. Very few attempts have been made to evaluate contributions arising from the possible loss of hydrostatic balance in the context of the problems treated using the classic shallow‐water approach. Where such attempts have been pursued, they have usually been carried out in a time‐independent context or using layer‐averaged equations and very small amplitude disturbances. The vast majority of these studies into nonhydrostatic effects do not include any relevant numerical work to assess these effects. In this paper, we develop an approach for evaluating nonhydrostatic contributions to the flow field for bottom gravity currents in deep surroundings and rectangular geometry. Our approach makes no assumptions on the amplitudes of the disturbances and does not depend on layer‐averaging in the governing equations. We seek asymptotic expansions of the solutions to the Euler equations for a shallow fluid by using the small parameter δ², where δ is the aspect ratio of the flow regime. At leading order the equations enforce hydrostatic balance while those obtained at first order retain certain nonhydrostatic effects which we evaluate. Our method for evaluation of these first‐order contributions employs the self‐similar nature of the solution to the leading‐order equations in the new first‐order equations without any vertical averaging procedures being employed.     

On the flow around Glauert-Goldschmied body in the narrow channel and separation control strategy

Previously, there was tested a wire dielectric barrier discharge (DBD) plasma actuator to generate sufficiently strong ionic wind to affect freely developed boundary layer in the narrow channel. This paper will report about next step – to installation of actuator inside a streamlined body. The experiment will take place inside perspex rectangular (250 × 100 mm) channel and main task is to find the appropriate place for actuator fitting for three different flow regimes. Hence, the separation point and recirculation area will be investigated via PIV anemometry for base case and for active flow control methods (e.g. plasma actuator) as well as frequency spectrum of the flow will be evaluated to describe the nature of the flow. The measurement plane will be perpendicular to the bottom of the channel and in longitudinal level. These essential information will be used for actuator design, actuator embedding and to tune actuator frequency in order to suppress the recirculation area as much as possible. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Behavioral optimal insurance

The present work studies the optimal insurance policy offered by an insurer adopting a proportional premium principle to an insured whose decision-making behavior is modeled by Kahneman and Tversky’s Cumulative Prospect Theory with convex probability distortions. We show that, under a fixed premium rate, the optimal insurance policy is a generalized insurance layer (that is, either an insurance layer or a stop–loss insurance). This optimal insurance decision problem is resolved by first converting it into three different sub-problems similar to those in Jin and Zhou (2008); however, as we now demand a more regular optimal solution, a completely different approach has been developed to tackle them. When the premium is regarded as a decision variable and there is no risk loading, the optimal indemnity schedule in this form has no deductibles but a cap; further results also suggests that the deductible amount will be reduced if the risk loading is decreased. As a whole, our paper provides a theoretical explanation for the popularity of limited coverage insurance policies in the market as observed by many socio-economists, which serves as a mathematical bridge between behavioral finance and actuarial science.     

Interfacial long traveling waves in a two‐layer fluid with variable depth

Long wave propagation in a two‐layer fluid with variable depth is studied for specific bottom configurations, which allow waves to propagate over large distances. Such configurations are found within the linear shallow‐water theory and determined by a family of solutions of the second‐order ordinary differential equation (ODE) with three arbitrary constants. These solutions can be used to approximate the true bottom bathymetry. All such solutions represent smooth bottom profiles between two different singular points. The first singular point corresponds to the point where the two‐layer flow transforms into a uniform one. In the vicinity of this point nonlinear shallow‐water theory is used and the wave breaking criterion, which corresponds to the gradient catastrophe is found. The second bifurcation point corresponds to an infinite increase in water depth, which contradicts the shallow‐water assumption. This point is eliminated by matching the “nonreflecting” bottom profile with a flat bottom. The wave transformation at the matching point is described by the second‐order Fredholm equation and its approximated solution is then obtained. The results extend the theory of internal waves in inhomogeneous stratified fluids actively developed by Prof. Roger Grimshaw, to the new solutions types.     

On iterative optimization ol structured Markov decision processes with discounted rewards

The paper gives a survey on solution techniques for Markov decision processes with respect to the total reward criterion. We will discuss briefly a number of problem structures which guarantee that the optimal policy possesses a specific structure which can be exploited in numerical solution procedures. However, the main emphasis is on iterative methods. It is shown by examples that the effect of a number of modifications of the standard iterative method, which are advocated in the literature, is limited in some realistic situations. Numerical evidence is provided to show that exploiting the structure of a problem under consideration of ten yields a more substantial reduction of the required computational effort than some of the existing acceleration procedures.

We advocate that this structure should be analyzed and used in choosing the appropriate solution procedure. The appropriate procedure might be composed on one hand by blending several of the acceleration concepts that are described in literature. On the other hand it should exploit the structure of optimal policies. This latter can often be done by using monotonicity properties of the computed value vector or policy. To illustrate the influence of the structure of a problem and if available, the structure of optimal policies, we sketch and solve four test problems with several successive approximation methods. In the final part of the paper, the required computational efforts are compared.     

Multiobjective PDE-constrained optimization using the reduced-basis method

In this paper the reduced basis (RB) method is applied to solve quadratic multiobjective optimal control problems governed by linear parametrized variational equations. These problems often arise in applications, where the quality of the system behavior has to be measured by more than one criterium. The weighted sum method is exploited for defining scalar-valued linear-quadratic optimal control problems built by introducing additional optimization parameters. The optimal controls corresponding to specific choices of the optimization parameters are efficiently computed by the RB method. The accuracy is guaranteed by an a-posteriori error estimate. An effective sensitivity analysis allows to further reduce the computational times for identifying a suitable and representative set of optimal controls.     

Deterministic optimal maneuver strategy for multi-target missions

This paper presents an optimal strategy for making impulsive correction to a multi-target trajectory by a single maneuver. The concept of an optimal maneuver time is introduced. The choice of suitable weighting functions is explored to enable one to properly translate the subjective desire of mission success into an objective cost function whose minimization yields the optimal strategy. It is shown that a number of strategies previously formulated are derivable from one general expression. A number of other interesting properties of the optimal strategy are described. Numerical results are presented for a typical two-target mission. It is shown that the strategy formulated is optimal. For some perturbations, there exists an optimal maneuver time different from the time of initiation of the perturbation. That is, the physical properties of the trajectory can be exploited to select the optimal time of making a corrective maneuver.