Variational Solutions for Externally Induced Sloshing in Horizontal-Cylindrical and Spherical Vessels

A mathematical model is developed for calculating linear sloshing effects in the dynamic response of horizontal-cylindrical and spherical liquid containers under external excitation, with emphasis on earthquake excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the configuration of the containers, the associated spatial functions are nonorthogonal and the problem is not separable, resulting in a system of coupled nonhomogeneous ordinary linear differential equations of motion. The solution can be obtained through either direct integration or modal analysis. Particular emphasis is given on the rate of convergence of the solution. The cases of half-full cylinders and spheres are examined in detail, where explicit expressions for the coefficients of the governing equations are derived. Using the proposed methodology, sloshing frequencies and masses are calculated rigorously for arbitrary liquid height of horizontal-cylindrical or spherical containers, and the response under two characteristic seismic events is obtained. The results describe the linear dynamic response of such containers and can be used for an efficient seismic analysis and design of industrial pressure vessels.     

Refined Solutions of Externally Induced Sloshing in Half-Full Spherical Containers

A mathematical model is developed for calculating liquid sloshing effects such as hydrodynamic pressures and forces in half-full spherical containers under arbitrary external excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the spherical configuration, the problem is not separable and the associated spatial functions are nonorthogonal. Application of the boundary conditions results in a system of coupled nonhomogeneous ordinary linear differential equations. The system is solved numerically, implementing a typical fourth-order Runge-Kutta integration scheme. The proposed simple methodology is capable of predicting sloshing effects in half-full spherical containers under arbitrary external excitation in an accurate manner. Hydrodynamic pressures and horizontal forces on the wall of a spherical container are calculated for real earthquake ground motion data. Dissipation effects are included in the present formulation, and their influence on the response is examined. Finally, it is shown that for the particular case of harmonic excitation, the system of ordinary differential equations results in a system of linear algebraic equations, which yields an elegant semianalytical solution.     

Theoretical and Numerical Study of Growth in Multi-Component Alloys

In multi-component systems, during diffusion-controlled growth of a precipitate from a supersaturated matrix, differential diffusivities lead to a selection of tie-line compositions different from the thermodynamic tie-line containing the alloy composition. In this paper, we address the multi-component version of the growth problem by extending Zener’s theory, and derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar, cylindrical, and spherical precipitates for independent as well as coupled diffusion of solutes in the scaling regime. We confirm our calculations by sharp interface and phase-field simulations in a ternary setting, in which we also extend the tie-line and growth constant predictions for two well-known limiting cases, namely partition and negligible partition under local equilibrium (PLE and NPLE).     

Modeling matrix grain growth in the presence of growing second phase particles in two phase alloys

In a number of two phase systems such as in α-β titanium alloys, second phase particles as well as the matrix grains grow simultaneously. A systematic study has been undertaken to understand matrix grain growth behavior of such materials in the presence of growing second-phase particles. Using the classical expressions of the driving force for grain growth and a modified form of the Zener retardation to account for preferential location of particles at triple junctions, grain growth of α and β matrices in the presence of growing second phase particles have been modeled by first order nonlinear differential equations. The contributions of grain boundary curvature, nonspherical nature of particles and nonorthogonal nature of particle grain boundary contact angles have also been incorporated into these models. Matrix grain sizes predicted by these methods were found to correlate well with the experimental results.     

考虑空间位形力作用的微米软颗粒溶液微圆管流动规律

针对微米级软颗粒溶液在微小孔道流动不符合泊肃叶流动规律问题，考虑受固体管壁影响软颗粒形变产生的空间位形力作用，基于Navier-Stokes理论，推导软颗粒溶液在圆管中的流速分布及流量表达式，引入颗粒形变因子以表征空间位形力作用的影响；建立考虑空间位形力作用的圆管流动数学模型.由微尺度流动特征实验，得到软颗粒溶液微圆管流动规律，与泊肃叶流动对比，结果显示当管径小于颗粒直径时，相同压力梯度下考虑空间位形力作用的流速比泊肃叶流动拟合结果更接近于实验数据.通过数值计算分析发现，与泊肃叶流动下的速度分布和平均流量相比，当微圆管尺寸减小时，空间位形力作用随之增大，其更大程度上影响流体在微圆管内的流动规律；当颗粒呈非球形且最小投影面积相同时，偏离球形颗粒程度越大，空间位形力作用越大，因此空间位形力作用在微小孔道流动中不可忽略.      

Diffusion in an ensemble of intersecting grain boundaries forming a triple junction

Grain boundary diffusion in an ensemble of three intersecting grain boundaries forming a triple junction is described in the framework of quasi-steady Fisher’s model. Two configurations, which differ in the number of grain boundaries adjacent to the surface with a diffusant source and in the tilt angle to the surface, are considered. Analytical expressions for the diffusant concentration distribution along each grain boundary that constitutes the triple junction and for the point of the triple junction are derived with the proviso of equal diffusion fluxes at the triple point. The expressions for the diffusant concentration distribution along the grain boundaries include not only diffusion constants (grain-boundary and bulk diffusion coefficients) but also structural characteristics of the ensemble of grain boundaries (the depth of the triple junction point and the angle between the grains forming the triple junction). It is shown that, if the coefficients of grain boundary diffusion are equal for all boundaries making the ensemble and for an equilibrium angle of 120° in a polycrystal, the diffusive mass transport rate in the triple junction zone is lower than that in a single grain boundary irrespective of the configuration of grain boundaries.     

Kinetics of neck growth during loose stack sintering

The kinetics of loose stack sintering of spherical iron powder were monitored by measuring some global microstructural attributes associated with the interparticle contact necks. The neck size and the number of interparticle contacts per unit volume were calculated from these data. A direct comparison of the experimental and theoretically predicted neck sizes has been carried out. The neck sizes predicted by the model for surface diffusion controlled sintering are muchhigher than the corre-sponding experimental values. The number of interparticle contacts per particle does not change with isothermal sintering time or temperature, and it is predominantly determined by the initial stacking of particles in the powder mass. The change of atmosphere from dry hydrogen to argon does not affect the neck growth kinetics significantly.     

Cell shape and chromosome partition in prokaryotes or, why E. coli is rod-shaped and haploid

In the rod-shaped cells of E. coli, chromosome segregation takes place immediately after replication has been completed. A septum then forms between the two sister chromosomes. In the absence of certain membrane proteins, cells grow instead as large, multichromosomal spheres that divide successively in planes that are at right angles to one another. Although multichromosomal, the spherical cells cannot be maintained as heterozygotes. These observations imply that, in these mutants, each individual chromosome gives rise to a separate clone of descendant cells. This suggests a model in which sites for cell division form between pairs of sister chromosomes at the time of segregation, but are not used in spherical cells until further rounds of replication have taken place, thus ensuring clonal ('hierarchical') segregation of chromosomes into progeny cells. The role of the morphogenetic membrane proteins is to convert the basically spherical cell into a cylinder that is able to divide as soon as replication and segregation have been completed, and thus to maximise the number of viable cells per genome.     

Erythroclastic bone marrow clusters and prognostication of the character of the course of acute lymphoblastic leukemia

A new variety of bone marrow clusters was revealed, that is formed of mature red cells by bone-marrow macrophages and other myelokaryocytes containing hydrolytic enzymes. Exocytotic lysis of the red cells, contained in these clusters, by cluster-forming cells is frequently observed. This fact permitted calling this variety 'erythroclastic clusters'. The number of clusters, in which exocytotic red cell lysis occurs, was found to grow fourfold in the active phase of acute lymphoblastic leukemia; this fact may be used for the early diagnosis of the disease or for prediction of its recurrence.     

A simple network model simulates hippocampal place fields: Parametric analyses and physiological predictions.

Hippocampal place cells may be the computational units of a neuronal cognitive mapping system. A network model trained to compute locations from distal cues simulated the defining properties of hippocampal place cells (i.e., place-specific activation). The model produced units with detailed properties of place cells, including multiple subfields, "silent" and "noisy" cells, fields that persisted after cue removal, and groups of simulated field that overlapped in multiple clusters. Quantitative variants of the model showed that different properties of the fields were influenced by the complexity of the visual input (the number of spatial cues), the available computational resources (the number of hidden units), and the output encoding used to represent location. The simulations provide a framework for testing relationships between place field properties, variations in spatial environments, and the integrity of the hippocampal system. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Analysis of Local Conditions on Graphite Growth and Shape During Solidification of Ductile Cast Iron

3D X-ray tomography recordings have been used to study graphite growth during solidification of ductile cast iron. Using data from such recordings, it is shown how local growth conditions influence growth rate and morphology of nodules during solidification. Experiments show that it is common for nodules to gradually change shape during solidification so that sphericity decreases. It is also found that different shaped nodules can evolve in direct contact with liquid iron and also after they are encapsulated in austenite. It is observed that a significant proportion of originally complete spherical nodules become less spherical via formation of protrusions on the surface; these new surfaces are observed to grow relatively faster. It is shown that encapsulation of the graphite nodule by austenite may be incomplete and that at the end of solidification, partial encapsulation and the effect of the number of nearest graphite nodules play a crucial role in determining the final graphite morphology.     

Stochastic model of metastases formation

A mathematical model is developed to describe the dynamics of the hematogenous metastatic process to the lung from a solid tumor growing in a peripheral body site. The accumulation of tumor cell clumps of various sizes in the pulmonary circulation and the formation of metastatic foci are described by a non-homogeneous, two-dimensional Markov process. An analytical solution is found for the special case of metastases produced by the intravenous injection of tumor cell clumps. The system is decoupled experimentally to determine the time-varying entrance rate of tumor cell clumps into the circulation from a growing fibrosarcoma and the number of metastatic foci produced by the intravenous injection of tumor clumps. Model validation is based on comparisons of model simulations with data for the development of metastatic foci and the probability of cure following tumor excision. The model is used to simulate hypothetical therapy to prevent tumor metastases.     

A Criterion for ductile fracture in sheets under biaxial loading

A criterion for ductile fracture is developed based on the statistical process of shear joining of voids and on the assumption that the voids responsible for fracture have experienced considerable growth prior to this stage of shearing. From the knowledge of uniaxial flow properties and fracture strain measurement, this model is capable of predicting the strain at fracture for other strain states. The predicted data are in good agreement with experiments. Although this model assumes spherical inclusions, some quantitative estimates for elongated inclusions can also be made.     

A Criterion for ductile fracture in sheets under biaxial loading

A criterion for ductile fracture is developed based on the statistical process of shear joining of voids and on the assumption that the voids responsible for fracture have experienced considerable growth prior to this stage of shearing. From the knowledge of uniaxial flow properties and fracture strain measurement, this model is capable of predicting the strain at fracture for other strain states. The predicted data are in good agreement with experiments. Although this model assumes spherical inclusions, some quantitative estimates for elongated inclusions can also be made.     

An examination of the interparticle contact area during sintering of W-0.3 Wt Pct Co

As a powder compact sinters, its microstructure evolves. One way to quantify the scale of the microstructure is to consider the interparticle contact area. This study examines two known models for calculating the interparticle contact area: the classic two-sphere model and the Voronoi cell model. Both models have particular assumptions about the microstructure that make them not applicable for treating densification to near full density with concurrent grain growth. The classic two-sphere model assumes a regular packing of particles and a perfectly spherical particle geometry and neglects an increasing particle coordination number with sintering. The Voronoi cell model assumes that the scale of the microstructure remains constant; i.e., as long as the compact is densifying, grain growth does not occur. We propose a modified Voronoi cell that accounts for an increasing grain size, making it applicable to a general case where grain growth occurs during sintering. The three models are compared to the interparticle contact area data, obtained by stereology techniques, for W-0.3 wt pct Co sintered from green state to near full density. The original Voronoi cell model fits the data only at low temperatures, before the onset of grain growth. Below approximately 90 pct relative density, the two-sphere model with an assumed coordination number of six (coordination number in a green compact) and the modified Voronoi cell model provide a good fit to the data. At higher densities, both models overestimate the interparticle contact area.     

Clustering estimates of effect magnitude from independent studies.

One method of combining results of a series of studies is to calculate the average of the estimates of effect magnitude obtained from each study. The average estimate of effect magnitude may be misleading, however, when all studies do not share a common effect-magnitude parameter. When the effect-magnitude parameters (correlation coefficients or standardized mean differences) are heterogeneous across studies, it is often desirable to cluster studies into groups that are homogeneous with respect to the effect-size parameter. The present paper presents 2 procedures for clustering correlation coefficients and standardized mean differences when each estimator is based on the same number of observations. One procedure yields disjoint clusters and the other yields possibly overlapping clusters. In each case a method for determining the statistical significance level of the clusterings is given. Preliminary tests of homogeneity of a set of correlations or standardized mean differences are also given. The accuracy of the significance levels when estimators are based on different sample sizes is also studied. (21 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Investigating Damage Evolution at the Nanoscale: Molecular Dynamics Simulations of Nanovoid Growth in Single-Crystal Aluminum

Nanovoid growth was investigated using molecular dynamics to reveal its dependence on void size, strain rate, crystallographic loading orientation, initial nanovoid volume fraction, and simulation cell size. A spherical nanovoid was embedded into a periodic face-centered cubic (fcc) Al lattice, and a remote uniaxial load was applied to elucidate dislocation nucleation and shear loop formation from the void surface as well as the subsequent void growth mechanisms. The nucleation stresses and void growth mechanisms were compared for four different strain rates (10⁷ to 10¹⁰ seconds^?1), five different simulation cell sizes (4-nm to 28-nm lengths), four different initial nanovoid volume fractions, and seven different tensile loading orientations representative of the variability within the stereographic triangle. The simulation results show an effect of the size scale, crystallographic loading orientation, initial void volume fraction, and strain rate on the incipient yield stress for simulations without a void (single-crystal bulk material). For instance, the crystallographic orientation dependence on yield stress was less pronounced for simulations containing a void. As expected, dislocations and shear loops nucleated on various slip systems for the different loading orientations, which included orientations favored for both single slip and multiple slip. The evolution of the nanovoid volume fraction with increasing strain is relatively insensitive to loading orientations, which suggests that the nanoscale plastic anisotropy caused by the initial lattice orientation has only a minor role in influencing the nanovoid growth rate. In contrast, a significant influence of the initial nanovoid volume fractions was observed on the yield stress, i.e., a ~35 pct decrease in yield stress was caused by introducing a 0.4 pct nanovoid volume fraction. Furthermore, a continuum-scale bridging parameter m—which is a material rate sensitivity parameter in continuum damage mechanics—was calculated and found to be close to 1. Consequently, atomistic simulations of this type can indeed inform continuum void growth models for application in multiscale models.     

A simulation study comparing tests for the equality of coefficients of variation

The coefficient of variation is commonly used in medical and biological sciences. In this paper, several parametric and non-parametric tests for the equality of coefficients of variation in kappa populations are reviewed. Simulation studies are conducted to compare the sizes and power of these tests. It is found that the parametric tests perform well if the data are normally distributed, but perform poorly if otherwise. The non-parametric test, however, is rather robust against the underlying distribution. An example using data of the Quality Assurance Program from the Hong Kong Medical Technology Association in Haematology and Serology is provided. The insensitivity of the non-parametric test to outliers is demonstrated.     

Electron microscopic study of cell surface rings during cell division and morphogenesis of Arthrobacter crystallopoietes

The whole cell ultrastructure during cell division and morphogenesis of Arthrobacter crystallopoietes was monitored using electron microscopic techniques. Glucose-grown spherical cells were inoculated into succinate-based medium. In this medium, the organism undergoes a morphogenetic cycle consisting of elongation of spheres to rods, exponential growth as rods, and fragmentation of rods to spherical cells. Raised bands or rings that encircled the cells were evident on the cell surface of both sphere- and rod-shaped cells. Many rod-shaped cells possessed two or more rings arranged adjacent to each other in a parallel orientation. At each cell division a new ring was formed on both siblings. However, as predicted by the proposed model of unidirectional cell growth and by maintaining a ring from the previous generation, unequal numbers of rings were observed on sibling cells. Only one ring was visible on most of the spherical inoculum cells, but in some cases a second ring perpendicular to the other ring was observed. Parallel rings were found on spherical cells resulting from fragmentation or reductive cell division of rods during the stationary growth phase. Thus, these spheres could be distinguished from inoculum spheres containing a single ring or perpendicular orientation of rings. The number of rings per cell and arrangement of rings on the cell surface of sibling cells after cell division, but before cell separation, are discussed with respect to cell age, cell division, and sphere-rod-sphere morphogenesis of A. crystallopoietes.     

Morphology and Growth Kinetics of Straight and Kinked Tin Whiskers

Time-lapse SEM studies of Sn whiskers were conducted to estimate growth kinetics and document whisker morphologies. For straight whiskers, growth rates of 3 to 4 microns per day were measured at room temperature. Two types of kinked whiskers were observed. For Type A kinks, the original growth segment spatial orientation remains unchanged, there are no other changes in morphology or diameter, and growth continues. For Type B kinks, the spatial orientation of the original segment changes and it appears that the whisker bends over. Whiskers with Type B kinks show changes in morphology and diameter at the base, indicating grain boundary motion in the film, which eliminates the conditions suitable for long-term whisker growth. To estimate the errors in the whisker growth measurements, a technique is presented to correct for SEM projection effects. With this technique, the actual growth angles and lengths of a large number of whiskers were collected. It was found that most whiskers grow at moderate or shallow angles with respect to the surface; few straight whiskers grow nearly normal to the surface. In addition, there is no simple correlation between growth angles and lengths for whiskers observed over an approximate 2-year period.