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.

Optical matching layer structures in evanescent coupling photodiodes at a wavelength of 1.55 mu m: physics, design and simulation

We have studied the optical matching layers (OMLs) and external quantum efficiency in the evanescent coupling photodiodes (ECPDs) integrating a diluted waveguide as a fibre-to-waveguide coupler, by using the semi-vectorial beam propagation method (BPM). The physical basis of OML has been identified, thereby a general designing rule of OML is developed in such a kind of photodiode. In addition, the external quantum efficiency and the polarization sensitivity versus the absorption and coupling length are analysed. With an optical matching layer, the absorption medium with a length of 30 mu m could absorb 90% of the incident light at 1.55 mu m wavelength, thus the total absorption increases more than 7 times over that of the photodiode without any optical matching layer.

Characterization of entanglement transformation via group representation theory

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group SL(2, C) circle times SL(2, C), composed of local operators acting on the binary composite system, is realized in the four-dimensional complex space in terms of a set of novel bases that are pseudo-orthonormalized. The two-to-one homomorphism is then established for the group SL(2, C) circle times SL(2, C) onto the SO(4, C). It is shown that the resulting representation theory leads to the complete characterization for the entanglement transformation of the binary composite system.

Method for measuring two-qubit entanglement of formation by local operations and classical communication

We present a parametrically efficient method for measuring the entanglement of formation E-f in an arbitrarily given unknown two-qubit state rho(AB) by local operations and classical communication. The two observers, Alice and Bob, first perform some local operations on their composite systems separately, by which the desired global quantum states can be prepared. Then they estimate seven functions via two modified local quantum networks supplemented a classical communication. After obtaining these functions, Alice and Bob can determine the concurrence C and the entanglement of formation E-f.

A criterion for local interconvertibility between all-tripartite Gaussian states

We arrive at a necessary and sufficient criterion that can be readily used for interconvertibility between general, all-tripartite Gaussian states under local quantum operation. The derivation involves a systematic reduction that converts the original complex conditions in high-dimensional, 6n x 6n matrix space eventually into 2 x 2 matrix problems.

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.

Method for detecting concurrence without the structural physical approximation by local operations and classical communication

We present a modified method for detecting the concurrence in an arbitrary two-qubit quantum state rho(AB) with local operations and classical communication. In this method, it is not necessary for the two observers to prepare the quantum state rho(AB) by the structural physical approximation. Their main task is to measure four specific functions via two local quantum networks. With these functions they can determine the concurrence and then the entanglement of formation.

Analog computation using quantum-dot cell network

A novel analog-computation system using a quantum-dot cell network is proposed to solve complex problems. Analog computation is a promising method for solving a mathematical problem by using a physical system analogous to the problem. We designed a novel quantum-dot cell consisting of three-stacked. quantum dots and constructed a cell network utilizing the nearest-neighbor interactions between the cells. We then mapped a graph 3-colorability problem onto the network so that the single-electron configuration of the network in the ground state corresponded to one of the solutions. We calculated the ground state of the cell network and found solutions to the problems. The results demonstrate that analog computation is a promising approach for solving complex problems.