A study of the rate-controlled constrained-equilibrium dimension reduction method and its different implementations

The Rate-Controlled Constrained-Equilibrium (RCCE) method is a thermodynamic based dimension reduction method which enables representation of chemistry involving n _s species in terms of fewer n _r constraints. Here we focus on the application of the RCCE method to Lagrangian particle probability density function based computations. In these computations, at every reaction fractional step, given the initial particle composition (represented using RCCE), we need to compute the reaction mapping, i.e. the particle composition at the end of the time step. In this work we study three different implementations of RCCE for computing this reaction mapping, and compare their relative accuracy and efficiency. These implementations include: (1) RCCE/TIFS (Trajectory In Full Space): this involves solving a system of n _s rate-equations for all the species in the full composition space to obtain the reaction mapping. The other two implementations obtain the reaction mapping by solving a reduced system of n _r rate-equations obtained by projecting the n _s rate-equations for species evaluated in the full space onto the constrained subspace. These implementations include (2) RCCE: this is the classical implementation of RCCE which uses a direct projection of the rate-equations for species onto the constrained subspace; and (3) RCCE/RAMP (Reaction-mixing Attracting Manifold Projector): this is a new implementation introduced here which uses an alternative projector obtained using the RAMP approach. We test these three implementations of RCCE for methane/air premixed combustion in the partially-stirred reactor with chemistry represented using the n _s=31 species GRI-Mech 1.2 mechanism with n _r=13 to 19 constraints. We show that: (a) the classical RCCE implementation involves an inaccurate projector which yields large errors (over 50%) in the reaction mapping; (b) both RCCE/RAMP and RCCE/TIFS approaches yield significantly lower errors (less than 2%); and (c) overall the RCCE/TIFS approach is the most accurate, efficient (by orders of magnitude) and robust implementation.     

A double constrained robust capon beamforming based imaging method for early breast cancer detection

Ultra-wideband （UWB） microwave images are proposed for detecting small malignant breast tumors based on the large contrast of electric parameters between a malignant tumor and normal breast tissue. In this study, an antenna array composed of 9 antennas is applied to the detection. The double constrained robust capon beamforming （DCRCB） algorithm is used for reconstructing the breast image due to its better stability and high signal-to-interference-plus-noise ratio （SINR）. The successful detection of a tumor of 2 mm in diameter shown in the reconstruction demonstrates the robustness of the DCRCB beamforming algorithm. This study verifies the feasibility of detecting small breast tumors by using the DCRCB imaging algorithm.     

A novel linear transformation model for the analysis and optimisation of chemical kinetics

In this study, a novel model for the analysis and optimisation of numerical and experimental chemical kinetics is developed. Concentration–time profiles of non-diffusive chemical kinetic processes and flame speed profiles of fuel–oxidiser mixtures can be described by certain characteristic points, so that relations between the coordinates of these points and the input parameters of chemical kinetic models become almost linear. This linear transformation model simplifies the analysis of chemical kinetic models, hence creating a robust global sensitivity analysis and allowing quick optimisation and reduction of these models. Firstly, in this study the model is extensively validated by the optimisation of a syngas combustion model with a large data set of imitated ignition experiments. The optimisation with the linear transformation model is quick and accurate, revealing the potential for decreasing the numerical costs of the optimisation process by at least one order of magnitude compared to established methods. Additionally, the optimisation on this data set demonstrates the capability of predicting reaction rate coefficients more accurately than by currently known confidence intervals. In a first application, methane combustion models are optimised with a small experimental set consisting of OH(A) and CH(A) concentration profiles from shock tube ignition experiments, species profiles from flow reactor experiments and laminar flame speeds. With the optimised models, especially the predictability for the flame speeds of mixtures of hydrogen, carbon monoxide and methane can be increased compared to established models. With the analysis of the optimised models, new information on the low pressure reaction coefficient of the fall-off reaction H+CH₃(+M)?CH₄(+M) is determined. In addition, the optimised combustion model is quickly and efficiently reduced to validate a new rapid reduction scheme for chemical kinetic models.     

A bound for the pressure integral in a plasma equilibrium

An interpolation inequality for the total variation of the gradient of a composite function is derived by applying the coarea formula. A bound for the pressure integral is studied by establishing ana priori estimate for a solution of the Grad-Shafranov equation of plasma equilibrium. A weak formulation of the Grad-Shafranov equation is given to include singular current profiles.     

A fully automatic three-step liver segmentation method on LDA-based probability maps for multiple contrast MR images

Automatic 3D liver segmentation in magnetic resonance (MR) data sets has proven to be a very challenging task in the domain of medical image analysis. There exist numerous approaches for automatic 3D liver segmentation on computer tomography data sets that have influenced the segmentation of MR images. In contrast to previous approaches to liver segmentation in MR data sets, we use all available MR channel information of different weightings and formulate liver tissue and position probabilities in a probabilistic framework. We apply multiclass linear discriminant analysis as a fast and efficient dimensionality reduction technique and generate probability maps then used for segmentation. We develop a fully automatic three-step 3D segmentation approach based upon a modified region growing approach and a further threshold technique. Finally, we incorporate characteristic prior knowledge to improve the segmentation results. This novel 3D segmentation approach is modularized and can be applied for normal and fat accumulated liver tissue properties.     

һ�ּ򵥵ĻԹ�ŵ����������Ϸ���

以碰撞为能量交换机制,按局部热力学平衡近似处理低气压等离子体,并考虑辉光放电二极之间的电位分布,得到了电子密度与气体压力的关系和电子温度与电场强度的关系。提出了一种利用压强、电压和电流就获得电子温度和密度的诊断方法。用Langmuir探针方法验证了获得的结果。     

一种简单的辉光放电等离子体诊断方法

以碰撞为能量交换机制,按局部热力学平衡近似处理低气压等离子体,并考虑辉光放电二极之间的电位分布,得到了电子密度与气体压力的关系和电子温度与电场强度的关系。提出了一种利用压强、电压和电流就获得电子温度和密度的诊断方法。用Langmuir探针方法验证了获得的结果。     

A new method of asymmetric Abel inversion for magnetic equilibrium configuration state in tokamaks

It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad--Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.     

一种抗噪分形维计算方法及其在声纳图像识别中的应用

用于计算图像分形维的差分盒计数法(DBC)和鲁棒差分盒计数法(RDBC)都对脉冲噪声和斑点噪声较敏感,为此本文提出一种抗噪差分盒计数法(NRDBC),利用剪切局部标准差(TLSD)来计算图像分形维,由于TLSD可有效滤除脉冲噪声和斑点噪声、且对高斯噪声敏感性小,因此NRDBC能对有噪图像进行可靠的分形维估计。利用多分辨率的DBC、RDBC和NRDBC对混有高斯噪声、脉冲噪声和斑点噪声的7种Brodatz纹理以及3种海底的侧扫声纳图像进行了分类实验,结果表明,本文提出的NRDBC可获得更高的识别率和更好的抗噪性。     

A stochastic mixed finite element heterogeneous multiscale method for flow in porous media

A computational methodology is developed to efficiently perform uncertainty quantification for fluid transport in porous media in the presence of both stochastic permeability and multiple scales. In order to capture the small scale heterogeneity, a new mixed multiscale finite element method is developed within the framework of the heterogeneous multiscale method (HMM) in the spatial domain. This new method ensures both local and global mass conservation. Starting from a specified covariance function, the stochastic log-permeability is discretized in the stochastic space using a truncated Karhunen–Loève expansion with several random variables. Due to the small correlation length of the covariance function, this often results in a high stochastic dimensionality. Therefore, a newly developed adaptive high dimensional stochastic model representation technique (HDMR) is used in the stochastic space. This results in a set of low stochastic dimensional subproblems which are efficiently solved using the adaptive sparse grid collocation method (ASGC). Numerical examples are presented for both deterministic and stochastic permeability to show the accuracy and efficiency of the developed stochastic multiscale method.     

A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].