A mathematical model of external electrostatic field of a special collector for electrospinning of nanofibers

This article focuses on the analysis of electrostatic field generated by a special collector consisting of two parallel cylindrical conductors used for electrospinning. Computed values of critical electrical potential obtained by an analytical model are compared with measurements. Here we show that the gap distance between the special collector and a spinning electrode, i.e., a syringe needle, has not substantial effect on the critical potential if the special collector distance from the syringe needle is higher than the gap distance between cylindrical conductors. The presented model is a good analytical approximation of electric field created by the used special collector.     

Quantization of soluble classical constrained systems

The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the determination of the classical brackets which does neither require Dirac’s formalism nor the symplectic method of Faddeev and Jackiw. This approach is based on the computation of the brackets between the constants of integration of the exact solutions of the equations of motion. From them all brackets of the dynamical variables of the system can be deduced in a straightforward way.     

Morphological center operator for enhancing small target obtained by infrared imaging sensor

Infrared small target in image obtained by infrared imaging sensor is usually different from the surrounding regions, which is the important region in infrared image for different applications. However, the infrared small target is dim and embedded in clutter background, which makes the small target difficult to be detected or recognized. So, it is important to enhance infrared small target. Morphological center operator could smooth important image features, which may be well used for infrared small target enhancement. To well enhance infrared small target, a morphological center operator based method is proposed. The morphological center operator is specified to suppress most of the background of the infrared image through the strategy of feature extraction. Then, the infrared small target is well enhanced. Experimental results show that, the proposed method performs well for enhancing infrared small target and the performance is better than some other methods. So, the proposed method could further improve the performance of infrared imaging sensor.     

Development of an improved dosemeter for assessments of risk to the eye

To develop an improved dosemeter to assess photon and beta exposures of the eye lens, and in response to issues surrounding the preferred values of H_lens to be used for guiding operational radiation protection, a programme of re-optimization of the current PHE thermoluminescence dosemeter has been performed. In particular, refinements of the filter located in front of the sensitive ⁷LiF:Mg,Cu,P element have been considered, so that the dose response characteristics of the device provide a better and more conservative estimate of risk. The investigation was performed using the Monte Carlo modelling software MCNP5, to produce a final design that featured a filter containing a 9.5 mm diameter polypropylene hemisphere truncated to a maximum thickness of 3.0 mm. The responses of this design in photon and electron fields are presented here, contrasted against those of the existing PHE eye dosemeter, with respect to the operational quantity H_p(3,E,θ) and both current and suggested values for the absorbed dose per fluence risk profile for the lens of the eye.     

Modelling the impact of dam failure scenarios on flood inundation using SPH

Flooding resulting from collapse of a dam is a highly destructive event. It is important to accurately predict the flow behaviour so that potential mitigation strategies can be investigated for disaster management planning. The meshless SPH method has previously been able to model this class of extreme flow events. In this paper, we extend the method to include modelling of dam wall fragments. Collisions between dam wall fragments, between fragments and terrain and full two-way coupling between fragments and the free surface water flow is included. This gives a method that can specifically investigate the impact of the dam wall failure scenario on the subsequent inundation. The historical St. Francis dam failure is used to demonstrate the impact of including the dam fragments. It also provides a means of quantitatively investigating their effect in terms of arrival time and water height at a downstream power station. The scenario with multiple independently timed failures of different parts of the wall (which closely matches the historical failure) gives excellent agreement with the observed data and gives the best match of all failure scenarios. Traditionally such modelling is performed by solving the two dimensional shallow water equations which is not able to capture the three dimensional nature of the flow in earlier stages of dam flooding. We specifically investigate the three dimensional nature of flow structures and formation of multiple downstream hydraulic jumps. These strongly influence water height and therefore control the extent of flooding of tributary valleys.     

The comparison of different mathematical methods to determine the BOD parameters,a new developed method and impacts of these parameters variations on the design of WWTPs

One of the most common tests for the determination of strength and organic content of wastewater is the biochemical oxygen demand (BOD). This test is widely applied to define organic water pollution and to control the performance of wastewater treatment plants. Generally, BOD is standardized by the measurement of oxygen consumption in 5 days (BOD₅). But, determination of the ultimate biochemical oxygen demand (BOD_u), which is taken 28 days and the reaction rate constant (k) are necessary to understand the organic strength of the wastewater. In this study, the different mathematical methods in order to determine the BOD parameters (BOD_u, k) and two different BOD test method (respirometer and dilution method) are investigated comparatively. Also, a new method based on cubic spline method to estimate ultimate BOD values is developed. Moreover, the impacts of BOD parameters on the design of an activated sludge and aerated lagoon systems are analyzed by using a written user-friend program, which is developed for designing WWTPs by the mean of C++ programming language.     

A new mixed integer linear programming model for the multi level uncapacitated facility location problem

This paper considers the multi level uncapacitated facility location problem (MLUFLP). A new mixed integer linear programming (MILP) formulation is presented and validity of this formulation is given. Experimental results are performed on instances known from literature. The results achieved by CPLEX and Gurobi solvers, based on the proposed MILP formulation, are compared to the results obtained by the same solvers on the already known formulations. The results show that CPLEX and Gurobi can optimally solve all small and medium sized instances and even some large-scale instances using the new formulation.     

An MPEC formulation and its cutting constraint algorithm for continuous network design problem with multi-user classes

Continuous network design problem (CNDP) is to determine the set of link capacity expansions and the corresponding equilibrium flows for which the measures of performance index for the network is optimal. Conventionally, CNDP assumed users to be homogeneous, that is, all travelers on the same link of the network are identical insofar as congestion effect and they have the same value of time (VOT). In fact, it does not accord with the real situation that all have the same VOT. So, multiple user classes with different VOT should be considered. This paper examines the CNDP with different VOT for multiple user classes, which is generally expressed as a mathematical programming with equilibrium constraint (MPEC). Then, the cut constraint algorithm (CCA) is presented to solve the problem. The numerical experiments on the examples from the literature are illustrated to demonstrate that our model and algorithm are feasible.     

Optimisation of integrated reverse logistics networks with different product recovery routes

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward production route, two alternative recovery routes, including repair and remanufacturing and a disposal route. It is assumed that demand and return quantities are uncertain. A quality level is assigned to each of the returned products. Due to uncertainty in the return quantity, quantity of returned products of a certain quality level is uncertain too. The uncertainties are modelled using fuzzy trapezoidal numbers. Quality thresholds are used to segregate the returned products into repair, remanufacturing or disposal routes. A two phase fuzzy mixed integer optimisation algorithm is developed to provide a solution to the inventory control and production planning problem. In Phase 1, uncertainties in quantity of product returns and quality of returns are considered to calculate the quantities to be sent to different recovery routes. These outputs are inputs into Phase 2 which generates decisions on component procurement, production, repair and disassembly. Finally, numerical experiments and sensitivity analysis are carried out to better understand the effects of quality of returns and RL network parameters on the network performance. These parameters include quantity of returned products, unit repair costs, unit production cost, setup costs and unit disposal cost.     

Locally logical mathematics: An emerging teacher honoring both students and mathematics

This case study explores the mathematics engagement and teaching practice of a beginning secondary school teacher. The focus is on the mathematical opportunities available to her students (the classroom mathematics) and how they relate to the teacher's personal capacity and tendencies for mathematical engagement (her personal mathematics). We use a mathematical process-and-action approach to analyze mathematical engagement and then employ the teaching triad—mathematical challenge, sensitivity to students, and management of learning—to situate mathematical engagement within the larger context of teaching practice. The article develops the construct of locally logical mathematics to underscore the cogency of mathematical engagement in the classroom as part of a coherent mathematical system that is embedded within a teaching practice. Contributions of the study include the process-and-action approach, especially in tandem with the teaching triad, as a tool to understand nuances of mathematical engagement and differences in demand between written and implemented tasks.