一类神经传导方程的变网格有限元方法及数值分析

研究在神经传播过程中的一类非线性拟双曲方程的初边值问题,对二维情形应用常规变换,提出了两种变网格有限元格式,最后通过细致的分析和估计得到了最佳阶的H1和L2 模误差估计结果,并且第二种格式使时间精度提高一阶,最后对第一种格式作了数值实验,指明方法是高效可行的．     

树干径流模型

以红松代表针叶树,栎树代表阔叶树,通过模拟实验研究树干径流过程,根据实验结果从机理上构造了模型。树干径流模型为一个方程组用“辗转迭代法”求出了数值解。该方程组基本上揭示了树干径流的规律,从实验与模拟结果对比分析中得到了佐证。     

一类神经传播方程的特征差分方法与分析

首先对给定的方程进行恒等变换,再把MMOCAA差分方法与UNO插值相结合,提出了方程的MMOCAA-UNO差分方法,避免了基于k次Lagrange插值的MMOCAA差分方法在方程的解的陡峭前沿附近产生振荡．通过引入插值算子等方法给出了格式的误差估计．数值实验说明理论分析的正确性和格式的有效性．     

非线性拟双曲方程的交替方向变网格有限元方法

研究在神经传播过程中的一类非线性拟双曲方程的初边值问题,提出了一种三维交替方向变网格有限元格式,应用微分方程先验估计的理论和技巧,得到了最佳阶的L^2模误差估计结果。并作了数值实验。指明方法是高效可行的．     

在有限资源条件下的肺结核模型研究

讨论了有限资源下的肺结核模型,得到了基本再生数,考虑了模型的双稳定性,用第二加型复合矩阵研究了模型平衡点的全局渐近稳定性．最后数值模拟验证理论结果．     

一类神经传播方程的特征差分方法和最佳阶l^2误差估计

给出矩形域上一类神经传播方程的特征差分,利用沿特征线方向构造差分逼近格式的方法和技巧．对给定的模型进行离散数值逼近和数值分析．特别是在沿特征线方向构造离散差分格式的过程中,可能会出现离散点在定义域之外的问题．本文提供了一个新的有效的差分逼近的处理方法,得到了该方法的三。一模误差估计．     

固定周期脉冲微分方程到状态依赖脉冲的转化及应用

本文研究了一类二维状态依赖脉冲微分方程的阶1周期解存在性和轨道稳定性条件．然后,将一维固定周期脉冲的微分方程转化为二维状态依赖脉冲微分方程,研究其阶一周期解的存在性和稳定性．作为应用,我们研究了固定周期常数收获的Logistic方程的动力学性质,以及两个固定周期注射药物单室扩散模型的动力学性质．     

核素迁移的二维非平衡吸附数值模式研究

为了进一步研究核素在孔隙介质中的迁移规律,本文将水动力弥散方程与核素在孔隙介质中非平衡吸附关系式相耦合,建立了非平衡吸附数值模式,并给出了非平衡吸附数值模式中吸附解吸速率参数的获取方法．为了检验所建模式与编制的程序的正确性,利用试验场（８５）Ｓｒ迁移的野外试验资料进行了计算,并与核素迁移平衡吸附数值模式的计算结果进行了对比．结果表明,二维非平衡吸附核素迁移数值模式能够更好地描述核素迁移实际．     

果蝇复眼形成过程中的靶波

本文用数值方法,求出了果蝇复眼形成过程的靶波解并对解的稳定性和临界点的分叉问题进行了分析．     

甘油生物歧化非线性动力系统的平衡点及其稳定性分析

针对甘油生物歧化为1,3-丙二醇过程的酶催化动力系统,利用符号化实根隔离法求解系统的平衡点,验证了系统的多稳态现象,利用微分方程稳定性理论,分析了平衡点的稳定性,并结合数值结果讨论了系统的多态现象．本文的结果可为微生物发酵甘油生产1,3-丙二醇的实验优化参数设计提供参考．     

Kinetics of biodegradation of 2,4-dichlorophenoxyacetate in the presence of glucose

Biodegradation of 2,4-dichlorophenoxyacetate (2,4-D) and glucose were studied using a 2,4-D acclimated culture. Biodegradation of glucose by the 2,4-D preacclimated culture follows the typical Monod kinetics after a 20-h lag period in the presence or absence of 2,4-D. Biodegradation of 2,4-D by the same culture follows Andrew's "substrate inhibition" model. When both glucose and 2,4-D are available, mutual inhibition is observed. However, the effect on 2,4-D is masked by the fact that larger concentrations of active biomass are produced when glucose is available. This kind of concurrent utilization and interaction results in a substantial reduction of the mean cell residence time in a continuous flow system. It also extends the area of stability of the process into higher dilution rates as well as into higher influent concentrations.     

Characterization of 3-D collagen hydrogels for functional cell-based biosensing

To address the growing demand for functional cell-based assay technologies with accelerated drug discovery applications, we have proposed the use of human neuroblastoma cells (IMR-32) immobilized in three-dimensional (3-D) collagen hydrogel matrices. The gel protects weakly adherent cells from fluid mechanical forces while providing a more physiologically relevant 3-D environment. Hydrogels made up of collagen, between 0.5 and 1.0mg/ml, exhibited mechanical stability adequate to withstand fluid mechanical forces (<0.11 mN) typical of automated commercial fluid transfer equipment. Collagen-entrapped cells visualized with the aid of confocal microscopy and a potentiometric-sensitive dye, TMRM, exhibited round morphology in comparison to flat morphology typical of cells in two-dimensional (2-D) monolayer cultures. Morphological differentiation characterized by neurite extension and cell aggregation was observed for both 2-D and 3-D cultures. Differentiated IMR-32 cells failed to develop a resting membrane potential typical of excitable cells. Free intracellular calcium was monitored with Calcium Green-1. Depolarization-induced Ca 2+influx was only observed with differentiated 3-D cells unlike 2-D cells, where calcium flux was observed in both differentiated and undifferentiated cells. Taken together, the results revealed that collagen hydrogels (0.5 mg/ml collagen) were suitable structural supports for weakly adherent cells. However, for voltage-dependent calcium channel function applications, further investigations are needed to explain the difference between 2-D monolayer and 3-D collagen-entrapped cells.     

Enzyme integrated silicate-Pt nanoparticle architecture: a versatile biosensing platform

A novel 3-D nanoarchitectured platform based on Pt nanoparticles (nPts) is developed for the sensing of sub-nanomolar levels of hydrogen peroxide and for the fabrication of amperometric biosensor for uric acid, cholesterol and glucose. The nPts have been immobilized on the thiol functional group containing sol-gel silicate 3-D network derived from 3-mercaptopropyltrimethoxysilane (MPTS). The nanoparticles on the 3-D architecture have size distribution between 7 and 10nm. The nPts on the platform efficiently catalyze the oxidation of H(2)O(2) at the potential of +0.45 V in the absence of enzymes and redox mediators. This nanoarchitectured platform is highly sensitive and can detect H(2)O(2) at sub-nanomolar levels (0.1 nM) in neutral solution. The nanoarchitectured platform does not suffer from interference due to other common easily oxidizable interfering agents. Excellent reproducibility, long-term storage and operational stability are observed. This platform is used to determine H(2)O(2) concentration in rainwater and for the fabrication of biosensors. Amperometric oxidase-based biosensing platforms are developed by integrating the enzymes and nPts with the silicate network for the sensing of uric acid cholesterol and glucose. The enzyme encapsulated 3-D architecture retains the enzymatic activity and efficiently detects enzymatically generated H(2)O(2) without any interference. These biosensors are stable and show excellent sensitivity and fast response time. A linear response was obtained for a wide concentration range of all analytes. The practical utilization of the biosensor for the measurement of uric acid, cholesterol and glucose in serum sample is demonstrated. The biological sample analysis was validated with clinical laboratory measurements.     

Comparative behavior of Pd and Ag deposition phenomenon on clean α-Al2O3 (001) surface—A first principle study

The nature of bonding at the interface between deposited silver/palladium and clean Al-terminated (001) surface of α-Al₂O₃ has been investigated using a periodic ab initio method. Substantial inter-planar relaxations within the alumina were found at both the interfaces and the bulk. The periodic calculation with both Ag and Pd deposition shows that 10% of loading on alumina results maximum stability. Surface energy and work function calculations were performed to propose the stability for the metals on the studied surfaces. The deposited Ag forms a three-dimensional (3-D) cluster on top of the alumina surface. The Pd cluster formed on the alumina surface is two-dimensional (2-D) and is distorted to accommodate the Ag cluster in its domain. A further low index calculation can explain the reason for a higher stability of the membrane generated over alumina support with silver and palladium. The results are discussed in view of the existing experimental data and models of metal-oxide interface and a reason for the difference of activity of the metal interaction with alumina surface is postulated.     

Porous coordination polymer of copper(II) assembled from mixed organic ligands pyridine-2,4-dicarboxylic acid and trans-1,2-bis(4-pyridyl)ethylene: Synthesis, crystal structure and magnetic study

A 3-D porous coordination polymer of Cu(II) has been synthesized using two different organic bridging ligands, pyridine-2,4-dicarboxylate (pydc) and trans-1,2-bis(4-pyridyl)ethylene (bpe). Here, pydc and bpe connect two adjacent Cu(II) centers, resulting in a rectangular grid-like 2-D sheet with grid dimensions 10.058 × 15.258 Å. The channels are formed when 2-D networks running along the b-axis which are filled by solvent water molecules. The stability of porous networks, after removal of guest water molecules is confirmed by thermogravimetric analysis and X-ray powder diffraction technique. The low temperature magnetic study has been carried out, which indicates the presence of weak antiferromagnetic coupling with J = −0.59 cm⁻¹.     

Effect of the N-terminus on heme cavity structure, ligand equilibrium, rate constants, and reduction potentials of nitrophorin 2 from Rhodnius prolixus

The D1A mutant of recombinant NP2 has been prepared and shown to have the expression-initiation methionine-0 cleaved during expression in E. coli, as is the case for recombinant NP4, where Ala is the first amino acid for the recombinant protein as well as for the mature native protein. The heme substituent 1H NMR chemical shifts of NP2-D1A and those of its imidazole, N-methylimidazole, and cyanide complexes are rather different from those of NP2-M0D1. This difference is likely due to the much smaller size of the N-terminal amino acid (A) of NP2-D1A, which allows the formation of the closed loop form of this protein, as it does for NP4 (Weichsel, A., Andersen, J. F., Roberts, S. A., and Montfort, W. R. (2000) Nature Struct. Biol. 7, 551-554). The ratio of the two hemin rotational isomers A and B is different for the two proteins, and the rate at which the A:B ratio reaches equilibrium is strikingly different (NP2-M0D1 t1/2 for heme rotation approximately 2 h, NP2-D1A t1/2 approximately 43 h). This difference is consistent with the high stability of the closed loop form of the NP2-D1A protein and infrequent opening of the loops that could allow heme to at least partially exit the binding pocket in order to rotate about its alpha,gamma-meso axis. Consistent with this, the rates of histamine binding and release to/from NP2-D1A are significantly slower than those for NP2-M0D1 at pH 7.5. This work suggests that care must be taken in interpreting data obtained from proteins that carry the expression-initiation M0.     

The optical flow of planar surfaces

The human visual system can recover the 3-D shape of moving objects on the basis of motion information alone. Computational studies of this capacity have considered primarily non-planar rigid objects. With respect to moving planar surfaces, previous studies have shown that the planar velocity field has in general a two-fold ambiguity: there are two different planes engaged in different motions that can induce the same velocity field. The current analysis extends the analysis of the planar velocity field in four directions: (1) the use of flow parameters of the type suggested by Koenderink and van Doorn (Optica Acta, 1975, 22, 773-791), (2) the exclusion of confusable non-planar solutions, (3) a new proof and a new method for computing the 3-D motion and surface orientation (4) a comparison with the information available in orthographic velocity fields, which is important for determining the stability of the 3-D recovery process.     

Regulation and recycling of myosin V

Recently there has been considerable progress in our understanding of regulation for unconventional myosin-V through elucidation of the structure of its inactive conformation and the factors that affect stability of this conformation. The inactive conformation is a folded compact structure characterized by interactions between the myosin head and the C-terminal cargo binding domain. Concentrations of Ca2+ greater than 10 microM disrupt folding. The 3-D structure determined by cryoelectron tomography of 2-D arrays in one study and electron micrographs of isolated molecules reported in another reveal similar features, but suggest different F-actin affinities for the inactive conformation. This has raised the question of how inactive myosin-V is recycled to other sites for additional rounds of cargo transport.     

Particle-Based Multidimensional Multispecies Biofilm Model

In this paper we describe a spatially multidimensional (two-dimensional [2-D] and three-dimensional [3-D]) particle-based approach for modeling the dynamics of multispecies biofilms growing on multiple substrates. The model is based on diffusion-reaction mass balances for chemical species coupled with microbial growth and spreading of biomass represented by hard spherical particles. Effectively, this is a scaled-up version of a previously proposed individual-based biofilm model. Predictions of this new particle-based model were quantitatively compared with those obtained with an established one-dimensional (1-D) multispecies model for equivalent problems. A nitrifying biofilm containing aerobic ammonium and nitrite oxidizers, anaerobic ammonium oxidizers, and inert biomass was chosen as an example. The 2-D and 3-D models generally gave the same results. If only the average flux of nutrients needs to be known, 2-D and 1-D models are very similar. However, the behavior of intermediates, which are produced and consumed in different locations within the biofilm, is better described in 2-D and 3-D models because of the multidirectional concentration gradients. The predictions of 2-D or 3-D models are also different from those of 1-D models for slowly growing or minority species in the biofilm. This aspect is related to the mechanism of biomass spreading or advection implemented in the models and should receive more attention in future experimental studies.     

Particle-based multidimensional multispecies biofilm model

In this paper we describe a spatially multidimensional (two-dimensional [2-D] and three-dimensional [3-D]) particle-based approach for modeling the dynamics of multispecies biofilms growing on multiple substrates. The model is based on diffusion-reaction mass balances for chemical species coupled with microbial growth and spreading of biomass represented by hard spherical particles. Effectively, this is a scaled-up version of a previously proposed individual-based biofilm model. Predictions of this new particle-based model were quantitatively compared with those obtained with an established one-dimensional (1-D) multispecies model for equivalent problems. A nitrifying biofilm containing aerobic ammonium and nitrite oxidizers, anaerobic ammonium oxidizers, and inert biomass was chosen as an example. The 2-D and 3-D models generally gave the same results. If only the average flux of nutrients needs to be known, 2-D and 1-D models are very similar. However, the behavior of intermediates, which are produced and consumed in different locations within the biofilm, is better described in 2-D and 3-D models because of the multidirectional concentration gradients. The predictions of 2-D or 3-D models are also different from those of 1-D models for slowly growing or minority species in the biofilm. This aspect is related to the mechanism of biomass spreading or advection implemented in the models and should receive more attention in future experimental studies.