A simplified mathematical approach for modelling stack ventilation in multi-compartment buildings

A simple mathematical model of stack ventilation flows in multi-compartment buildings is developed with a view to providing an intuitive understanding of the physical processes governing the movement of air and heat through naturally ventilated buildings. Rules of thumb for preliminary design can be ascertained from a qualitative examination of the governing equations of flow, which elucidate the relationships between 'core' variables - flow rates, air temperatures, heat inputs and building geometry. The model is applied to an example three-storey office building with an inlet plenum and atrium. An examination of the governing equations of flow is used to predict the behaviour of steady flows and to provide a number of preliminary design suggestions. It is shown that control of ventilation flows must be shared between all ventilation openings within the building in order to minimise the disparity in flow rates between storeys, and ensure adequate fresh air supply rates for all occupants. © 2013 Elsevier Ltd.

Mathematical model for solids transport power in a decanter centrifuge

A mathematical model of the transport of sedimented solids within a decanter centrifuge has been developed. The primary purpose of the model is to calculate the power, torque and axial force required for the scroll to transport the solids along the bowl. The model is presented in a non-dimensional form and the procedure for implementing the model is included. The model is compared to test data from an existing publication; there was good agreement between the model and data. Example results are presented in the form of graphs to illustrate the influence of key parameters. © 2013 Elsevier Ltd.

Mathematical symbols and computing methods in high dimensional biomimetic informatics and their applications

High dimensional biomimetic informatics (HDBI) is a novel theory of informatics developed in recent years. Its primary object of research is points in high dimensional Euclidean space, and its exploratory and resolving procedures are based on simple geometric computations. However, the mathematical descriptions and computing of geometric objects are inconvenient because of the characters of geometry. With the increase of the dimension and the multiformity of geometric objects, these descriptions are more complicated and prolix especially in high dimensional space. In this paper, we give some definitions and mathematical symbols, and discuss some symbolic computing methods in high dimensional space systematically from the viewpoint of HDBI. With these methods, some multi-variables problems in high dimensional space can be solved easily. Three detailed algorithms are presented as examples to show the efficiency of our symbolic computing methods: the algorithm for judging the center of a circle given three points on this circle, the algorithm for judging whether two points are on the same side of a hyperplane, and the algorithm for judging whether a point is in a simplex constructed by points in high dimensional space. Two experiments in blurred image restoration and uneven lighting image correction are presented for all these algorithms to show their good behaviors.

Discussion on the basic mathematical models of neurons - Double synaptic weight neuron in general-purpose neurocomputer, theory and application

Based on the introduction of the traditional mathematical models of neurons in general-purpose neurocomputer, a novel all-purpose mathematical model-Double synaptic weight neuron (DSWN) is presented, which can simulate all kinds of neuron architectures, including Radial-Basis-Function (RBF) and Back-propagation (BP) models, etc. At the same time, this new model is realized using hardware and implemented in the new CASSANN-II neurocomputer that can be used to form various types of neural networks with multiple mathematical models of neurons. In this paper, the flexibility of the new model has also been described in constructing neural networks and based on the theory of Biomimetic pattern recognition (BPR) and high-dimensional space covering, a recognition system of omni directionally oriented rigid objects on the horizontal surface and a face recognition system had been implemented on CASSANN-H neurocomputer. The result showed DSWN neural network has great potential in pattern recognition.

A mathematical model of crevice and pitting corrosion—I. The physical model

A predictive and self-consistent mathematical model incorporating the electrochemical, chemical and ionic migration processes characterizing the propagation stage of crevice and pitting corrosion in metals is described. The model predicts the steady-state solution chemistry and electrode kinetics (and hence metal penetration rates) within an active corrosion cavity as a function of the many parameters on which these depend, such as external electrode potential and crevice dimensions. The crevice is modelled as a parallel-sided slot filled with a dilute sodium chloride solution. The cavity propagation rates are found to be faster in the case of a crevice with passive walls than one with active walls. The distribution of current over the internal surface of a crevice with corroding walls can be assessed using this model, giving an indication of the future shape of the cavity. The model is extended to include a solid hydroxide precipitation reaction and considers the effect of consequent changes in the chemical and physical environment within the crevice on the predicted corrosion rates. In this paper, the model is applied to crevice and pitting corrosion in carbon steel.