System Dynamics Modeling for Sustainable Water Management of a Coastal Area in Shandong Province, China

Water is one of the basic materials in human existence and the development of society and economy. Its sustainable management has always been an eternal subject for the management of human society and also a complex systemic problem. How to take advantages of water has been a big event in such an agricultural country like China. As economically developed areas, coastal areas are facing water shortage problems due to the rapid economic and social development and inappropriate and unsustainable water management measures. To fully understand and study such problems faced by the coastal areas needs a systematic and integrated framework to consider the various social-economic, natural and engineering factors that affect the sustainable development of water in those areas. The SD （system dynamics） methodology, which is an approach that has been successfully used in solving complex systematic problems in general, and in solving water management problems in particular for more than 50 years, was applied to a typical coastal area, Longkou City in Shandong Province of China, to study and analyze the future sustainable water management of this city. Then the quantitative modeling and analysis of the water development were carried out through scenario analysis. Four different scenarios （business as usual, economic development, water resources protection, and comprehensive） were designed by changing the values of decision-making variables. The total water demand in 2030 of these four scenarios are 0.455 billion m3, 0.793 billion m3, 0.412 billion m3 and 0.487 billion m3, respectively; the corresponding water deficit of these scenarios are 0.292 billion m3, 0.634 billion m3, 0.254 billion m3 and 0.329 billion m3, respectively. The comparison results indicated that the comprehensive scenario is the optimal one among these designed scenarios. To totally solve the water shortage problem with the economy developed in Longkou City needs to take more effective measures to reduce water consumption and improve water conservation technologies.

Stability analysis of a hybrid flexible-rigid pipe conveying fluid

The stability and dynamical behavior of flexible and articulated rigid pipes conveying fluid have attracted the attention of many researchers in the field of fluid-structure interactions.The system of an articulated pipe composed of a flexible pipe and a rigid pipe is a class of hybrid flexible-rigid dynamical problems involving flow-induced vibrations.This paper establishes the governing equations of motion of a hybrid flexible-rigid pipe system based on Hamilton's principle,with the rigid pipe being hinged to the lower end of a flexible cantilevered pipe via a rotational spring.The coupling equations of motion are discretized via a Galerkin's approach.The mathematical model is validated by comparing the eigenvalue branches of a degenerated system by choosing extreme values of the parameters of the hybrid pipe with previous results.In the theoretical analysis,the critical flow velocities are calculated as a function of the stiffness of the rotational spring,mass ratio and length ratio of the rigid and flexible pipes.The unstable modes are detected from the eigenvalue branches and compared with those of a flexible cantilevered pipe.Numerical results show that the critical flow velocity is greatly influenced by several structural parameters.It is found that a small stiffness of the rotational spring tends to predict higher-mode instability,whereas a large rotational spring stiffness would generate a second-mode instability in most cases.In several system parameter spaces,the hybrid pipe may experience a transference of unstable modes with the increase of flow velocity.It is also shown that the hybrid pipe system may lose stability first in the fourth mode in some cases.Some of the fresh results obtained for the hybrid pipe system are expected to be helpful in understanding and controlling the dynamical responses of hybrid flexible-rigid fluid-conveying pipes.

Multi-recurrence and van der Waerden systems

We explore recurrence properties arising from dynamical approach to the van der Waerden theorem and similar combinatorial problems. We describe relations between these properties and study their consequences for dynamics. In particular, we present a measure-theoretical analog of a result of Glasner on multi-transitivity of topologically weakly mixing minimal maps. We also obtain a dynamical proof of the existence of a C-set with zero Banach density.

ALMOST GLOBAL EXISTENCE OF DIRICHLETINITIAL-BOUNDARY VALUE PROBLEM FORNONLINEAR ELASTODYNAMIC SYSTEMOUTSIDE A STAR-SHAPED DOMAIN

This paper deals with the mixed initial-boundary value problem of Dirichlet type for the nonlinear elastodynamic system outside a star-shaped domain. The almost global existence of solution with small initial data to this problem is proved and a lower bound for the lifespan of solutions is given.