The mechanical properties of individual WS(2) nanotubes were investigated and directly related to their atomic structure details by in situ transmission electron microscope measurements. A brittle mode deformation was observed in bending tests of short (ca. 1 mu m in length) multilayer nanotubes. This mode can be related to the atomic structure of their shells. In addition, longer nanotubes (6-7 mu m in length) were deformed in situ scanning electron microscope, but no plastic deformation was detected. A "sword-in-sheath" fracture mechanism was revealed in tensile loading of a nanotube, and the sliding of inner shells inside the outermost shell was imaged "on-line". Furthermore, bending modulus of 217 GPa was obtained from measurements of the electric-field-induced resonance of these nanotubes.
An inexact chance-constrained linear programming (ICCLP) model for optimal water pollution management at the watershed scale was developed. We selected the net expenditures of the alternative strategies, including initial capital investment and operating costs, as the objectives of water pollution management. The total environmental capacity of the water bodies at different probability levels (q(i)) was considered a key constraint; other constraints included in the model were government minimum requirements on farmland area, land cover, treatment rate of domestic wastewater and rural wastes, and certain technical constraints. The ICCLP model was applied to Lake Qionghai watershed in China for water quality improvement with the goal of achieving a minimum total cost. Alternative strategies were incorporated following discussions with shareholders and experts. A three-period optimization was conducted based on the alternative strategies; the model parameters were based on field investigations. Five probability levels were considered in the model: q(i)=0.01, 0.25, 0.50. 0.90, and 0.99. The model results showed that the total optimized costs were between US\$[55,710.86,80,691.81] x 10(4) and US\$[72,151.39,101,338.6] x 10(4) under different probability levels. The model results indicate that soil erosion treatment, nonpoint source control measures, and rural waste treatment have much higher costs than other strategies, and our findings indicate that the ICCLP model can effectively deal with optimal water pollution management under uncertainty at the watershed scale.
An inexact chance-constrained linear programming (ICCLP) model for optimal water pollution management at the watershed scale was developed. We selected the net expenditures of the alternative strategies, including initial capital investment and operating costs, as the objectives of water pollution management. The total environmental capacity of the water bodies at different probability levels (q(i)) was considered a key constraint; other constraints included in the model were government minimum requirements on farmland area, land cover, treatment rate of domestic wastewater and rural wastes, and certain technical constraints. The ICCLP model was applied to Lake Qionghai watershed in China for water quality improvement with the goal of achieving a minimum total cost. Alternative strategies were incorporated following discussions with shareholders and experts. A three-period optimization was conducted based on the alternative strategies; the model parameters were based on field investigations. Five probability levels were considered in the model: q(i)=0.01, 0.25, 0.50. 0.90, and 0.99. The model results showed that the total optimized costs were between US$[55,710.86,80,691.81] x 10(4) and US$[72,151.39,101,338.6] x 10(4) under different probability levels. The model results indicate that soil erosion treatment, nonpoint source control measures, and rural waste treatment have much higher costs than other strategies, and our findings indicate that the ICCLP model can effectively deal with optimal water pollution management under uncertainty at the watershed scale.
This paper presents a further numerical study of the interaction dynamics for solitary waves in a nonlinear Dirac model with scalar self-interaction, the Soler model, by using a fourth order accurate Runge-Kutta discontinuous Galerkin method. The phase plane method is employed for the first time to analyze the interaction of Dirac solitary waves and reveals that the relative phase of those waves may vary with the interaction. In general, the interaction of Dirac solitary waves depends on the initial phase shift. If two equal solitary waves are in-phase or out-of-phase initially, so are they during the interaction; if the initial phase shift is far away from 0 and π, the relative phase begins to periodically evolve after a finite time. In the interaction of out-of-phase Dirac solitary waves, we can observe: (a) full repulsion in binary and ternary collisions, depending on the distance between initial waves; (b) repulsing first, attracting afterwards, and then collapse in binary and ternary collisions of initially resting two-humped waves; (c) one-overlap interaction and two-overlap interaction in ternary collisions of initially resting waves.
Interval linear programming (ILP) was developed by Huang and Moore (1993) and was widely applied in environmental and resources management. However, the feasibility of optimal solutions for affect directly in generating several decision alternatives, thus a modified interval linear programming (MILP) model is developed to assure its solution space could be absolutely feasible, and its solution algorithm is proposed to incorporates the associated extra constraints into the upper- and lower- bounds submodels. Moreover, the proofs for determining A and B in corresponding constraints are refined in this study. The results of numeric example and its application in water-quality management of Lake Qionghai Basin (China) further indicated the feasibility and effectiveness of the developed MILP model.