Integrated component scheduling models for chip shooter machines

This paper focuses on minimizing printed circuit board (PCB) assembly time for a chipshootermachine, which has a movable feeder carrier holding components, a movable X–Y table carrying a PCB, and a rotary turret with multiple assembly heads. The assembly time of the machine depends on two inter-related optimization problems: the component sequencing problem and the feeder arrangement problem. Nevertheless, they were often regarded as two individual problems and solved separately. This paper proposes two complete mathematical models for the integrated problem of the machine. The models are verified by two commercial packages. Finally, a hybrid genetic algorithm previously developed by the authors is presented to solve the model. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total assembly time.

Mechanisms of convective drying in thick beds of solids

The literature on heat and mass transfer mechanisms in the convective drying of thick beds of solids has been critically reviewed. Related mathematical models of heat transfer are also considered. Experimental and theoretical studies were made of the temperature distribution within beds, and of drying rates, with various materials undergoing convective drying. The experimental work covered thick beds of hygroscopic and non-hygroscopic materials (glass beads of different diameters, polystyrene pellets, activated alumina and wood powder) at air temperatures of 54°C to 84°C. Tests were carried out in a laboratory drying apparatus comprising a wind tunnel through which the air, of controlled temperature and humidity, was passed over a sample suspended from a balance. Thermocouples were inserted at different depths within the sample bed. The temperature distribution profiles for both hygroscopic and non-hygroscopic beds exhibited a clear difference between the temperatures at the surface and bottom during the constant rate period. An effective method was introduced for predicting the critical moisture content. During the falling rate the profiles showed the existence of a receding evaporation plane; this divided the system into a hotter dry zone in the upper section and a wet zone near the bottom. A graphical procedure was established to predict accurately the position of the receding evaporation front at any time. A new mathematical model, based on the receding evaporation front phenomenon, was proposed to predict temperature distributions throughout a bed during drying. Good agreement was obtained when the model was validated by comparing its predictions with experimental data. The model was also able to predict the duration of each drying stage. In experiments using sample trays of different diameters, the drying rate was found to increase with a decrease in the effective length of the bed surface. During the constant rate period with trays of a small effective length, i.e. less than 0.08 m, an 'inversion' in temperature distribution occurred in the bed; the bottom temperature increased and became greater than that of the surface. Experimental measurements were verified in several ways to ensure this phenomenon was real. Theoretical explanations are given for both the effective length and temperature inversion phenomena.

Concepts and methods of quantitative assessment of risk to groundwater resources

This work presents a two-dimensional approach of risk assessment method based on the quantification of the probability of the occurrence of contaminant source terms, as well as the assessment of the resultant impacts. The risk is calculated using Monte Carlo simulation methods whereby synthetic contaminant source terms were generated to the same distribution as historically occurring pollution events or a priori potential probability distribution. The spatial and temporal distributions of the generated contaminant concentrations at pre-defined monitoring points within the aquifer were then simulated from repeated realisations using integrated mathematical models. The number of times when user defined ranges of concentration magnitudes were exceeded is quantified as risk. The utilities of the method were demonstrated using hypothetical scenarios, and the risk of pollution from a number of sources all occurring by chance together was evaluated. The results are presented in the form of charts and spatial maps. The generated risk maps show the risk of pollution at each observation borehole, as well as the trends within the study area. This capability to generate synthetic pollution events from numerous potential sources of pollution based on historical frequency of their occurrence proved to be a great asset to the method, and a large benefit over the contemporary methods.

A Mathematical Apparatus for Domain Ontology Simulation. Logical Relationship Systems

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers

For metal and metal halide vapor lasers excited by high frequency pulsed discharge, the thermal effect mainly caused by the radial temperature distribution is of considerable importance for stable laser operation and improvement of laser output characteristics. A short survey of the obtained analytical and numerical-analytical mathematical models of the temperature profile in a high-powered He-SrBr2 laser is presented. The models are described by the steady-state heat conduction equation with mixed type nonlinear boundary conditions for the arbitrary form of the volume power density. A complete model of radial heat flow between the two tubes is established for precise calculating the inner wall temperature. The models are applied for simulating temperature profiles for newly designed laser. The author’s software prototype LasSim is used for carrying out the mathematical models and simulations.