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Search Results: 1 - 10 of 8360 matches for " Minglei Kang "
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Blow-Up Criteria for Three-Dimensional Boussinesq Equations in Triebel-Lizorkin Spaces
Minglei Zang
Discrete Dynamics in Nature and Society , 2012, DOI: 10.1155/2012/539278
Abstract: We establish a new blow-up criteria for solution of the three-dimensional Boussinesq equations in Triebel-Lizorkin spaces by using Littlewood-Paley decomposition. 1. Introduction and Main Results In this paper, we consider the regularity of the following three-dimensional incompressible Boussinesq equations: where denotes the fluid velocity vector field, is the scalar pressure, is the scalar temperature, is the constant kinematic viscosity, is the thermal diffusivity, and , while and are the given initial velocity and initial temperature, respectively, with . Boussinesq systems are widely used to model the dynamics of the ocean or the atmosphere. They arise from the density-dependent fluid equations by using the so-called Boussinesq approximation which consists in neglecting the density dependence in all the terms but the one involving the gravity. This approximation can be justified from compressible fluid equations by a simultaneous low Mach number/Froude number limit; we refer to [1] for a rigorous justification. It is well known that the question of global existence or finite-time blow-up of smooth solutions for the 3D incompressible Boussinesq equations. This challenging problem has attracted significant attention. Therefore, it is interesting to study the blow-up criterion of the solutions for system (1.1). Recently, Fan and Zhou [2] and Ishimura and Morimoto [3] proved the following blow-up criterion, respectively: Subsequently, Qiu et al. [4] obtained Serrin-type regularity condition for the three-dimensional Boussinesq equations under the incompressibility condition. Furthermore, Xu et al. [5] obtained the similar regularity criteria of smooth solution for the 3D Boussinesq equations in the Morrey-Campanato space. Our purpose in this paper is to establish a blow-up criteria of smooth solution for the three-dimensional Boussinesq equations under the incompressibility condition in Triebel-Lizorkin spaces. Now we state our main results as follows. Theorem 1.1. Let , be the smooth solution to the problem (1.1) with the initial data for . If the solution satisfies the following condition then the solution can be extended smoothly beyond . Corollary 1.2. Let , be the smooth solution to the problem (1.1) with the initial data for . If the solution satisfies the following condition then the solution can be extended smoothly beyond . Remark 1.3. By Corollary 1.2, we can see that our main result is an improvement of (1.2). 2. Preliminaries and Lemmas The proof of the results presented in this paper is based on a dyadic partition of unity in Fourier
Beam optimization of RFQ and SFRFQ combined accelerator at Peking University
Minglei Kang,Yuanrong Lu,Zhi Wang,Kun Zhu,Xueqing Yan,Shuli Gao,Shixiang Peng,Zhiyu Guo,Jiaxun Fang,Jiaer Chen
Physics , 2010,
Abstract: The Peking University Integral Split Ring Radio Frequency Quadrupole(ISR RFQ) accelerator was constructed in 1999 with a high duty factor 16.7% and repetition frequency 166Hz, and it was able to accelerate N+, O+,O-, C+ and He+ from 1.6kev/u to 65keV/u. It was later upgraded as an injector of the Separated Function RFQ (SFRFQ). The experiments indicated that the maximum accelerated O+ beam current could exceed 3.2mA with energy 1.03MeV and an energy spread (FWHM) 3.1%. Then the beam transports through a 1m-long magnetic triplet to the entrance of SFRFQ and is finally accelerated to 1.64MeV. The beam conditioning of RFQ were carefully optimized to satisfy the requirements of the SFRFQ. The combined accelerator eventually can deliver 0.53mA O+ beam with energy 1.65MeV, which has sufficiently demonstrated the feasibility of the SFRFQ structure.
Beam specific planning target volumes incorporating 4DCT for pencil beam scanning proton therapy of thoracic tumors
Liyong Lin,MingLei Kang,Sheng Huang,Rulon Mayer,Andrew Thomas,Timothy D. Solberg,James E. McDonough,Charles B. Simone II
Physics , 2015,
Abstract: The purpose of this study is to determine whether organ sparing and target coverage can be simultaneously maintained for pencil beam scanning (PBS) proton therapy treatment of thoracic tumors in the presence of motion, stopping power uncertainties and patient setup variations. Ten consecutive patients that were previously treated with proton therapy to 66.6/1.8 Gy (RBE) using double scattering (DS) were replanned with PBS. Minimum and maximum intensity images from 4DCT were used to introduce flexible smearing in the determination of the beam specific PTV (BSPTV). Datasets from eight 4DCT phases, using +-3% uncertainty in stopping power, and +-3 mm uncertainty in patient setup in each direction were used to create 8X12X10=960 PBS plans for the evaluation of ten patients. Plans were normalized to provide identical coverage between DS and PBS. The average lung V20, V5, and mean doses were reduced from 29.0%, 35.0%, and 16.4 Gy with DS to 24.6%, 30.6%, and 14.1 Gy with PBS, respectively. The average heart V30 and V45 were reduced from 10.4% and 7.5% in DS to 8.1% and 5.4% for PBS, respectively. Furthermore, the maximum spinal cord, esophagus and heart dose were decreased from 37.1 Gy, 71.7 Gy and 69.2 Gy with DS to 31.3 Gy, 67.9 Gy and 64.6 Gy with PBS. The conformity index (CI), homogeneity index (HI), and global maximal dose were improved from 3.2, 0.08, 77.4 Gy with DS to 2.8, 0.04 and 72.1 Gy with PBS. All differences are statistically significant, with p values <0.05, with the exception of the heart V45 (p= 0.146). PBS with BSPTV achieves better organ sparing and improves target coverage using a repainting method for the treatment of thoracic tumors. Incorporating motion-related uncertainties is essential in maintaining marginal coverage and homogenous dose of treatment targets.
Logarithmically Improved Regularity Criteria for a Fluid System with the Linear Soret Effect
Minglei Zang,Xiaoyan Guan
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/420721
Abstract: We consider the 3D fluid system with the linear Soret effect. We obtain a logarithmically improved regularity criterion in the BMO space.
Levenberg-Marquardt Method for Mathematical Programs with Linearly Complementarity Constraints  [PDF]
Cong Zhang, Limin Sun, Zhibin Zhu, Minglei Fang
American Journal of Computational Mathematics (AJCM) , 2015, DOI: 10.4236/ajcm.2015.53020
Abstract: In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC.
An Implicit Smooth Conjugate Projection Gradient Algorithm for Optimization with Nonlinear Complementarity Constraints  [PDF]
Cong Zhang, Limin Sun, Zhibin Zhu, Minglei Fang
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.610152
Abstract: This paper discusses a special class of mathematical programs with equilibrium constraints. At first, by using a generalized complementarity function, the discussed problem is transformed into a family of general nonlinear optimization problems containing additional variable μ. Furthermore, combining the idea of penalty function, an auxiliary problem with inequality constraints is presented. And then, by providing explicit searching direction, we establish a new conjugate projection gradient method for optimization with nonlinear complementarity constraints. Under some suitable conditions, the proposed method is proved to possess global and superlinear convergence rate.
Modeling for Collapsing Cavitation Bubble near Rough Solid Wall by Mulit-Relaxation-Time Pseudopotential Lattice Boltzmann Model  [PDF]
Minglei Shan, Yipeng Zhu, Cheng Yao, Qingbang Han, Changping Zhu
Journal of Applied Mathematics and Physics (JAMP) , 2017, DOI: 10.4236/jamp.2017.56106
Abstract: Cavitation bubble collapse near rough solid wall is modeled by the multi-relaxation-time (MRT) pseudopotential lattice Boltzmann (LB) model. The modified forcing scheme, which can achieve LB model’s thermodynamic consistency by tuning a parameter related with the particle interaction range, is adopted to achieve desired stability and density ratio. The bubble collapse near rough solid wall was simulated by the improved MRT pseudopotential LB model. The mechanism of bubble collapse is studied by investigating the bubble profiles, pressure field and velocity field evolution. The eroding effects of collapsing bubble are analyzed in details. It is found that the process and the effect of the interaction between bubble collapse and rough solid wall are affected seriously by the geometry of solid boundary. At the same time, it demonstrates that the MRT pseudopotential LB model is a potential tool for the investigation of the interaction mechanism between the collapsing bubble and complex geometry boundary.
Extraction of Glycyrrhizic Acid and Glabridin from Licorice
Minglei Tian,Hongyuan Yan,Kyung Ho Row
International Journal of Molecular Sciences , 2008, DOI: 10.3390/ijms9040571
Abstract: The extraction and separation conditions of glycyrrhizic acid and glabridin from licorice were investigated. By changing the different extraction solvents, procedures, times and temperature, the optimum extraction condition was established: the used of ethanol/water (30:70, v/v) as an extraction solvent, and 60 min dipping time under 50°C. The extracts of licorice were separated and determined by reversed-phase high performance liquid chromatography with a methanol/water (70:30, v/v, containing 1% acetic acid) as the mobile phase. Under the optimum extraction condition, 2.39 mg/g of glycyrrhizic acid and 0.92 mg/g of glabridin were extracted from Chinese licorice and the recoveries were 89.7% and 72.5% respectively.
Effect of Mobile Phase Additives on the Resolution of Four Bioactive Compounds by RP-HPLC
Shengnan Li,Minglei Tian,Kyung Ho Row
International Journal of Molecular Sciences , 2010, DOI: 10.3390/ijms11052229
Abstract: The use of mobile phase additives enhances the separation and resolution of the bioactive compounds on the C 18 column. Chlorogenic acid, caffeic acid, rutin, and scoparone from Herba Artemisiae Scopariae were investigated as the target compounds. Acetic acid, triethylamine, inorganic salts, and several ionic liquids were added as mobile phase additives into methanol/water (40:60, v/v). The result revealed that a mobile phase with 0.01 mol/L of ionic liquid [BMIM][BF 4] enabled the optimum separation of the four target compounds.
Effect of Ionic Liquids as the Mobile Phase Additives on the HPLC Resolution of Four Active Compounds from Sophora flavescens Ait
Minglei Tian,Junyu Liu,Kyung Ho Row
Molecules , 2009, DOI: 10.3390/molecules14062127
Abstract: The retention behaviour of four active compounds from Sophora Flavescens Ait using three ionic liquids as mobile phase modifiers was examined. The effect of the pH and the amount of ionic liquid modifier on the retention of these compounds was determined in methanol/water (v/v) as the mobile phase containing different ionic liquids ranging in concentration from 0.1 mmol/L to 3.0 mmol/L. The ionic liquids showed promise as additives in high-performance liquid chromatography.
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