Maximum principle for a nonlinear size-structured model of fish and fry management

This paper investigates the maximum principle for a nonlinear size-structured model that describes the optimal management of the fish resources taking into account harvesting the fish and putting the fry. We establish the well-posedness of the state system by Banach fixed-point theorem. Necessary conditions for optimality are established via the normal cone technique and adjoint system. The existence of a unique optimal policy is proved via Ekeland's variational principle and fixed-point reasoning. Finally, some examples and numerical results demonstrate the effectiveness of the theoretical results in our paper

Optimal harvesting in a unidirectional consumer–resource mutualisms system with size structure in the consumer

This paper considers the optimal harvesting problem for a size-structured model of unidirectional consumer–resource mutualisms in which the consumer species has both positive and negative effects on the resource species, while the resource has only a positive effect on the consumer. First, we show the existence of a unique nonnegative solution of the system and give the continuous dependence of solutions on the control variable. Next, the adjoint system is derived, which is necessary for optimality and the existence of a unique optimal policy. Then necessary conditions for optimality are established via the normal cone and adjoint system. Moreover, the existence of a unique optimal strategy is proved via Ekeland’s variational principle and fixed-point reasoning in convex analysis. Finally, we use numerical simulations to verify the main results and find other dynamic properties of the system

A Simple But Effective Evolutionary Algorithm for Complicated Optimization Problems

A simple but effective evolutionary algorithm is proposed in this paper for solving complicated optimization problems. The new algorithm presents two hybridization operations incorporated with the conventional genetic algorithm. It takes only 4.1% ~ 4.7% number of function evaluations required by the conventional genetic algorithm to obtain global optima for the benchmark functions tested. Application example is also provided to demonstrate its effectiveness.Singapore-MIT Alliance (SMA

A Meshfree Weak- Strong-form (MWS) method for solid and fluid mechanics

Mesh free methods can be largely categorized into two main categories: mesh free methods based on strong forms (e.g. collocation methods) and mesh free methods based on the weak forms (EFG, MLPG, PIM, etc.; see Mesh Free Methods, by G. R. Liu, CRC Press, 2002). The mesh free collocation method is simple to implement and computationally efficient. However, it is often found unstable and less accurate, especially for problems governed by partial differential equations with Neumann (derivative) boundary conditions, such as solid mechanics problems with stress (natural) boundary conditions. On the other hand, the mesh free methods based on the weak form exhibits very good stability and excellent accuracy. However, the numerical integration makes them computational expensive, and the background mesh (global or local) for integration is responsible for not being “truly” mesh free. In this paper, a new idea of combination of both the strong form and the local weak form is proposed to develop truly meshless method for 2-D elasto-statics. A novel truly meshfree method, the meshfree weak-strong (MWS) form method, is originated by Liu et al. (2002) based on a combined formulation of both the strong and local weak forms. As shown in Figure 1, the problem domain and boundaries are represented by properly scattered nodes. The key idea of the MWS method is that in establishing the discrete system equations, both the strong-form and the local Petrov-Galerkin weak-form are used for the same problem, but for different nodes. This paper details the MWS method for solid and fluid mechanics problems. In the MWS method, the problem domain and its boundary is represented by a set of points or nodes. The strong form or collocation method is used for all the internal nodes and the nodes on the essential (Dirichlet) boundaries. The local weak form (Petrov-Galerkin weak form) is used for nodes on the natural (Neumann) boundaries. There is no need for numerical integrations for all the internal nodes and the nodes on the essential boundaries. The local numerical integration is performed only for the nodes on the natural/Neumann boundaries. The natural/Neumann boundary conditions can then be easily imposed to produce stable and accurate solutions. The locally supported radial point interpolation method (RPIM) and moving least squares (MLS) approximation are used to construct the shape functions. The final system matrix will be sparse and banded for computational efficiency. Numerical examples of solids and fluids are presented to demonstrate the efficiency, stability and accuracy of the proposed meshfree method.Singapore-MIT Alliance (SMA

Smoothed Finite Element Method

In this paper, the smoothed finite element method (SFEM) is proposed for 2D elastic problems by incorporation of the cell-wise strain smoothing operation into the conventional finite elements. When a constant smoothing function is chosen, area integration becomes line integration along cell boundaries and no derivative of shape functions is needed in computing the field gradients. Both static and dynamic numerical examples are analyzed in the paper. Compared with the conventional FEM, the SFEM achieves more accurate results and generally higher convergence rate in energy without increasing computational cost. In addition, as no mapping or coordinate transformation is performed in the SFEM, the element is allowed to be of arbitrary shape. Hence the well-known issue of the shape distortion of isoparametric elements can be resolved.Singapore-MIT Alliance (SMA

Optimization of Passive Constrained Layer Damping Treatments for Vibration Control of Cylindrical Shells

This paper presents the layout optimization of passive constrained layer damping (PCLD) treatment for vibration control of cylindrical shells under a broadband force excitation. The equations governing the vibration responses are derived using the energy approach and assumed-mode method. These equations provided relationship between the integrated displacement response over the whole structural volume, i.e. the structural volume displacement (SVD), of a cylindrical shell to structural parameters of base structure and multiple PCLD patches, Genetic algorithms (GAs) based penalty function method is employed to find the optimal layout of rectangular PCLD patches with minimize the maximum displacement response of PCLD-treated cylindrical shells. Optimization solutions of PCLD patches’ locations and shape are obtained under the constraint of total amount of PCLD in terms of percentage added weight to the base structure. Examination of the optimal layouts reveals that the patches tend to increase their coverage in the axial direction and distribute over the whole surface of the cylindrical shell for optimal control of the structural volume displacement.Singapore-MIT Alliance (SMA

A comparative study of intercultural sensitivity among postgraduates majoring in International Chinese Education in China context

Based on a survey sample of 435 China postgraduates majoring in International Chinese Education with different undergraduate English learning experience, the research attempted to find out how five elements proposed by Chen & Starosta (2000), interacted or influenced with each other. Those five elements incorporated in Intercultural Communication Competence Scale (ICCS), developed by Chen & Starosta (2000), are interaction engagement, respect for cultural differences, interaction confidence, interaction enjoyment and interaction attentiveness. The survey results from the multiple regression charts demonstrated that the elements composed of intercultural sensitivity actually interacted or influenced interactants’ actual intercultural communication process

Hopf bifurcation in a reaction-diffusive-advection two-species competition model with one delay

In this paper, we investigate a reaction-diffusive-advection two-species competition model with one delay and Dirichlet boundary conditions. The existence and multiplicity of spatially non-homogeneous steady-state solutions are obtained. The stability of spatially nonhomogeneous steady-state solutions and the existence of Hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system. By the normal form theory and the center manifold reduction, the stability and bifurcation direction of Hopf bifurcating periodic orbits are derived. Finally, numerical simulations are given to illustrate the theoretical results

Existence of Multiple Positive Periodic Solutions of Delayed Predator-Prey Models with Functional Responses

AbstractIn this paper, by applying the continuation theorem of coincidence degree theory, we establish some new criteria for the existence of multiple positive periodic solutions for the delayed predator-prey model.x′(t)=x(t)(r(t)−a(t)x(t))−b(t)f(x(t))y(t),y′(t)=y(t)(c(t)f(x(t−τ))−d(t)),when functional response function f is monotonic or nonmonotonic