Two-Point Closure Strategy in the Mapping Closure Approximation Approach

A two-point closure strategy in mapping closure approximation (MCA) approach is developed for the evolution of the probability density function (PDF) of a scalar advected by stochastic velocity fields. The MCA approach is based on multipoint statistics. We formulate a MCA modeled system using the one-point PDFs and two-point correlations. The MCA models can describe both the evolution of the PDF shape and the rate at which the PDF evolves.

Mapping Closure Approximation for Reactive Scalars in Random Flows

The Mapping Closure Approximation (MCA) approach is developed to describe the statistics of both conserved and reactive scalars in random flows. The statistics include Probability Density Function (PDF), Conditional Dissipation Rate (CDR) and Conditional Laplacian (CL). The statistical quantities are calculated using the MCA and compared with the results of the Direct Numerical Simulation (DNS). The results obtained from the MCA are in agreement with those from the DNS. It is shown that the MCA approach can predict the statistics of reactive scalars in random flows.

Fatigue-crack closure measurements on 2024-t3 sheet specimens

A computer-controlled procedure has been developed for automatic measurement of the crack opening stress S-op during fatigue tests. A crack opening displacement gauge (GOD meter) is used to obtain digital data on the load versus COD curves. Three methods for deriving S-op from the data sets are compared: (1) a slope method, (2) a tangent lines intersecting method, and (3) a tangent point method. The effect of the position of the COD meter with respect to the crack tip on S-op is studied in tests of 2024-T3 specimens. Results of crack growth and S-op are presented for CA loading with an overload, and with an overload followed by an underload.

A closure theory of intermittency of turbulence

The variational approach to the closure problem of turbulence theory, proposed in an earlier article [Phys. Fluids 26, 2098 (1983); 27, 2229 (1984)], is extended to evaluate the flatness factor, which indicates the degree of intermittency of turbulence. Since the flatness factor is related to the fourth moment of a turbulent velocity field, the corresponding higher-order terms in the perturbation solution of the Liouville equation have to be considered. Most closure methods discard these higher-order terms and fail to explain the intermittency phenomenon. The computed flatness factor of the idealized model of infinite isotropic turbulence ranges from 9 to 15 and has the same order of magnitude as the experimental data of real turbulent flows. The intermittency phenomenon does not necessarily negate the Kolmogorov k−5/3 inertial range spectrum. The Kolmogorov k−5/3 law and the high degree of intermittency can coexist as two consistent consequences of the closure theory of turbulence. The Kolmogorov 1941 theory [J. Fluid Mech. 62, 305 (1974)] cannot be disqualified merely because the energy dissipation rate fluctuates.

Variational approach to the closure problem of turbulence theory

A new method is proposed to solve the closure problem of turbulence theory and to drive the Kolmogorov law in an Eulerian framework. Instead of using complex Fourier components of velocity field as modal parameters, a complete set of independent real parameters and dynamic equations are worked out to describe the dynamic states of a turbulence. Classical statistical mechanics is used to study the statistical behavior of the turbulence. An approximate stationary solution of the Liouville equation is obtained by a perturbation method based on a Langevin-Fokker-Planck (LFP) model. The dynamic damping coefficient eta of the LFP model is treated as an optimum control parameter to minimize the error of the perturbation solution; this leads to a convergent integral equation for eta to replace the divergent response equation of Kraichnan's direct-interaction (DI) approximation, thereby solving the closure problem without appealing to a Lagrangian formulation. The Kolmogorov constant Ko is evaluated numerically, obtaining Ko = 1.2, which is compatible with the experimental data given by Gibson and Schwartz, (1963).

Physical Blocking Neural Tube Closure Affects Radial Intercalation and Neural Crest Midline-directed Migration in Xenopus Dorsal Explants

神经管闭合缺陷(NTDs)是一种严重的先天畸形疾病,在新生儿中有千分之一的发病率.神经管融合前后,多种组织参与形态发生运动.神经管一经融合,神经嵴细胞就会向背侧中线方向产生单极突出并向此方向迁移形成神经管的顶部.与此同时,神经管从腹侧开始发生辐射状切入以实现单层化.在此,我们在非洲爪蟾的移植体中机械阻断神经管的闭合以检测其细胞运动及随后的图式形成.结果显示神经管闭合缺陷的移植体不能形成单层化的神经管,并且神经嵴细胞滞留在侧面区域不能向背侧中线迁移,而对神经前体标记基因的检测显示神经管的背腹图式形成并未受到影响.以上结果表明神经管的融合对于辐射状切入和神经嵴细胞向背侧中线方向的迁移过程是必需的,而对于神经管的沿背腹轴方向的图式形成是非必需的.

Changes in the benthic macroinvertebrates in Xiangxi Bay following dam closure to form the Three Gorges Reservoir

Benthic macroinvertebrates were assessed monthly in Xiangxi Bay of the Three Gorges Reservoir for two years after the initial closure of the dam. Mean total density of macroinvertebrates varied from 275 ind./m(2) during the first year to 5,094 ind./m(2) during the second year, and the community of 50 taxa was overwhelmingly dominated by oligochaetes and chironomids (44 and 48% of the total taxa, respectively). As sediment accumulated in the substrate of the bay, the species composition changed dramatically, with oligochaetes comprising 91.3-99.3% of the total abundance during the second year. The dominant oligochaetes were Limnodrilus hoffmeisteri and Nais inflata. The chironomids Procladius sp., and Polypedilum scalaenum group sp. were similarly abundant in both years.

Floral closure in response to temperature and pollination in Gentiana straminea Maxim. (Gentianaceae), an alpine perennial in the Qinghai-Tibetan Plateau

Floral closure may be induced by pollination and various other factors, but is rarely studied comprehensively. Different kinds of floral closure should have various effects on reproductive fitness of plants. Two contrasting types of floral closure were observed in the flowers of Gentiana straminea Maxim. in the eastern Qinghai-Tibetan Plateau. The first type occurred prior to pollination during both gender phases, in response mainly to decreasing air temperatures. Flowers closed when decreasing temperatures approached 20 degrees C and subsequently began to reopen the following day during mid-morning when air temperatures warmed to approximately 13-15 degrees C. This kind of floral closure can protect pollen grains on either stamens or stigmas, increasing fitness of both male and female. Following pollination, permanent floral closure occurred, although there was a delay between the dates of pollination and permanent closure, during which flowers continued to show temporary closure in response to low temperature episodes. The time required for permanent, pollination-induced closure varied according to the age of the gender phase, including a prolonged time before closure if pollination occurred early in the female phase. The retaining of permanent closed flowers increased both approaching (to inflorescences) and visiting (to unpollinated flowers) frequencies of individual plants when with fewer open flowers and the persisting corolla is further beneficial for seed sets of these pollinated flowers. Thus, two separate types of floral closure, one in response to environmental cues and the other in response to the age of each gender stage, appeared to have a strong influence on reproductive fitness in this species. These results revealed a different adaptive strategy of alpine plants in the sexual reproduction assurance in addition to the well-known elevated floral longevity, dominant role of more effective pollinators and increased reproduction allocation in the arid habitats.

Multiscale Coupling in Complex Mechanical Systems

Multiscale coupling attracts broad interests from mechanics, physics and chemistry to biology. The diversity and coupling of physics at different scales are two essential features of multiscale problems in far-from-equilibrium systems. The two features present fundamental difficulties and are great challenges to multiscale modeling and simulation. The theory of dynamical system and statistical mechanics provide fundamental tools for the multiscale coupling problems. The paper presents some closed multiscale formulations, e.g., the mapping closure approximation, multiscale large-eddy simulation and statistical mesoscopic damage mechanics, for two typical multiscale coupling problems in mechanics, that is, turbulence in fluids and failure in solids. It is pointed that developing a tractable, closed nonequilibrium statistical theory may be an effective approach to deal with the multiscale coupling problems. Some common characteristics of the statistical theory are discussed.

Thermal fracture characteristics induced by laser beam

The damage mechanism of a cracked material due to laser beam thermal shock is an important problem when the interactions of high power laser beam with materials are studied. The transient thermal stress intensity factors (TSIFs) for a center crack in an infinite plate subjected to laser beam thermal shock are investigated. When the crack is in the heat affected zone, the compressive thermal stress causes the crack surface to come into contact with each other over a certain contact length, but the high tensile stresses around the crack tip tend to open the crack. In this case, the problem may be treated as a pair of embedded cracks problem with a smooth closure condition of the center crack. The TSIFs and the crack contact lengths are calculated with different laser beam spatial shapes. The TSIFs induced by thermal shock are in marked different from those induced by general mechanical loading.