Mathematical Modeling of Near-Wall Flows of Two-Phase Mixture with Evaporating Droplets

In the framework of the two-continuum approach, using the matched asymptotic expansion method, the equations of a laminar boundary layer in mist flows with evaporating droplets were derived and solved. The similarity criteria controlling the mist flows were determined. For the flow along a curvilinear surface, the forms of the boundary layer equations differ from the regimes of presence and absence of the droplet inertia deposition. The numerical results were presented for the vapor-droplet boundary layer in the neighborhood of a stagnation point of a hot blunt body. It is demonstrated that, due to evaporation, a droplet-free region develops near the wall inside the boundary layer. On the upper edge of this region, the droplet radius tends to zero and the droplet number density becomes much higher than that in the free stream. The combined effect of the droplet evaporation and accumulation results in a significant enhancement of the heat transfer on the surface even for small mass concentration of the droplets in the free stream. 在双连续介质理论框架下,采用匹配渐进展开方法导出并求解了具有蒸发液滴的汽雾流中层流边界层方程,给出了控制汽雾流的相似判据。对于沿曲面的流动,边界层方程的形式取决于是否存在液滴的惯性沉积。给出了热钝体验点附近蒸汽。液滴边界层的数值计算结果。它们表明：由于蒸发,在边界层内近壁处形成了一个无液滴区域；在该区上边界处,液滴半径趋于零而液滴数密度急剧增高。液滴蒸发及聚集的联合效应造成了表面热流的显著增加,甚至在自由来流中液滴质量浓度很低时此效应依然存在。

Extremum principle of crystal plasticity

An analytical method for determining slip shear rate under prescribed stress rate or prescribed strain rate has been presented on the basis of the incremental theory of crystal plasticity. The problem has been reduced to a quadric convex programming.In order to analyse the plastic response of crystals subjected to external load, two new extremum principles are proposed. They are equivalent to the boundary-value problem of crystal plasticity. By the new extremum principles, the slip shear rates are independent function which can be obtained from the variational equation.

Optical intrinsically fuzzy mathematical morphology for gray-scale image processing

Intrinsically fuzzy morphological erosion and dilation are extended to a total of eight operations that have been formulated in terms of a single morphological operation--biased dilation. Based on the spatial coding of a fuzzy variable, a bidirectional projection concept is proposed. Thus, fuzzy logic operations, arithmetic operations, gray-scale dilation, and erosion for the extended intrinsically fuzzy morphological operations can be included in a unified algorithm with only biased dilation and fuzzy logic operations. To execute this image algebra approach we present a cellular two-layer processing architecture that consists of a biased dilation processor and a fuzzy logic processor. (C) 1996 Optical Society of America

Logic-operated mathematical morphology and its optical implementation

A more powerful tool for binary image processing, i.e., logic-operated mathematical morphology (LOMM), is proposed. With LOMM the image and the structuring element (SE) are treated as binary logical variables, and the MULTIPLY between the image and the SE in correlation is replaced with 16 logical operations. A total of 12 LOMM operations are obtained. The optical implementation of LOMM is described. The application of LOMM and its experimental results are also presented. (C) 1999 Optical Society of America.

FUZZY SOLID SETS FOR MATHEMATICAL MORPHOLOGY AND OPTICAL IMPLEMENTATION

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated. (C) 1995 Optical Society of America

Fuzzy inferring mathematical morphology and optical implementation

Fuzzification is introduced into gray-scale mathematical morphology by using two-input one-output fuzzy rule-based inference systems. The fuzzy inferring dilation or erosion is defined from the approximate reasoning of the two consequences of a dilation or an erosion and an extended rank-order operation. The fuzzy inference systems with numbers of rules and fuzzy membership functions are further reduced to a simple fuzzy system formulated by only an exponential two-input one-output function. Such a one-function fuzzy inference system is able to approach complex fuzzy inference systems by using two specified parameters within it-a proportion to characterize the fuzzy degree and an exponent to depict the nonlinearity in the inferring. The proposed fuzzy inferring morphological operators tend to keep the object details comparable to the structuring element and to smooth the conventional morphological operations. Based on digital area coding of a gray-scale image, incoherently optical correlation for neighboring connection, and optical thresholding for rank-order operations, a fuzzy inference system can be realized optically in parallel. (C) 1996 Society of Photo-Optical Instrumentation Engineers.

Optoelectronic implementation of mathematical morphology

An optoelectronic implementation based on optical neighborhood operations and electronic nonlinear feedback is proposed to perform morphological image processing such as erosion, dilation, opening, closing and edge detection. Results of a numerical simulation are given and experimentally verified.

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.

Packing LUT clusters with network flow programming

This paper describes a two-step packing algorithm for LUT clusters of which the LUT input multipliers are depopulated. In the first step, a greedy algorithm is used to search for BLE locations and cluster inputs. If the greedy algorithm fails, the second step with network flow programming algorithm is employed. Numerical results illustrate that our two-step packing algorithm obtains better packing density than one-step greedy packing algorithm.

Design and Verification of the Programming Circuit in an Application-Specific FPGA

In this paper we present a methodology and its implementation for the design and verification of programming circuit used in a family of application-specific FPGAs that share a common architecture. Each member of the family is different either in the types of functional blocks contained or in the number of blocks of each type. The parametrized design methodology is presented here to achieve this goal. Even though our focus is on the programming circuitry that provides the interface between the FPGA core circuit and the external programming hardware, the parametrized design method can be generalized to the design of entire chip for all members in the FPGA family. The method presented here covers the generation of the design RTL files and the support files for synthesis, place-and-route layout and simulations. The proposed method is proven to work smoothly within the complete chip design methodology. We will describe the implementation of this method to the design of the programming circuit in details including the design flow from the behavioral-level design to the final layout as well as the verification. Different package options and different programming modes are included in the description of the design. The circuit design implementation is based on SMIC 0.13-micron CMOS technology.