The motion and the core structure of a geostrophic vortex - one-time scale inner solution and the motion of the vortex

By means of the matched asymptotic expansion method with one-time scale analysis we have shown that the inviscid geostrophic vortex solution represents our leading solution away from the vortex. Near the vortex there is a viscous core structure, with the length scale O(a). In the core the viscous stresses (or turbulent stresses) are important, the variations of the velocity and the equivalent height are finite and dependent of time. It also has been shown that the leading inner solutions of the core structure are the same for two different time scales of S/(ghoo)1/2 and S/a (ghoo)1/2. Within the accuracy of O(a) the velocity of a geostrophic vortex center is equal to the velocity of the local background flow, where the vortex is located, in the absence of the vortex. Some numerical examples demonstrate the contributions of these results.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

Solar UV radiation drives CO2 fixation in marine phytoplankton: A double-edged sword

Photosynthesis by phytoplankton cells in aquatic environments contributes to more than 40% of the global primary production (Behrenfeld et al., 2006). Within the euphotic zone (down to 1% of surface photosynthetically active radiation [PAR]), cells are exposed not only to PAR (400-700 nm) but also to UV radiation (UVR; 280-400 nm) that can penetrate to considerable depths (Hargreaves, 2003). In contrast to PAR, which is energizing to photosynthesis, UVR is usually regarded as a stressor (Hader, 2003) and suggested to affect CO2-concentrating mechanisms in phytoplankton (Beardall et al., 2002). Solar UVR is known to reduce photosynthetic rates (Steemann Nielsen, 1964; Helbling et al., 2003), and damage cellular components such as D1 proteins (Sass et al., 1997) and DNA molecules (Buma et al., 2003). It can also decrease the growth (Villafane et al., 2003) and alter the rate of nutrient uptake (Fauchot et al., 2000) and the fatty acid composition (Goes et al., 1994) of phytoplankton. Recently, it has been found that natural levels of UVR can alter the morphology of the cyanobacterium Arthrospira (Spirulina) platensis (Wu et al., 2005b). On the other hand, positive effects of UVR, especially of UV- A (315-400 nm), have also been reported. UV- A enhances carbon fixation of phytoplankton under reduced (Nilawati et al., 1997; Barbieri et al., 2002) or fast-fluctuating (Helbling et al., 2003) solar irradiance and allows photorepair of UV- B-induced DNA damage (Buma et al., 2003). Furthermore, the presence of UV-A resulted in higher biomass production of A. platensis as compared to that under PAR alone (Wu et al., 2005a). Energy of UVR absorbed by the diatom Pseudo-nitzschia multiseries was found to cause fluorescence (Orellana et al., 2004). In addition, fluorescent pigments in corals and their algal symbiont are known to absorb UVR and play positive roles for the symbiotic photosynthesis and photoprotection (Schlichter et al., 1986; Salih et al., 2000). However, despite the positive effects that solar UVR may have on aquatic photosynthetic organisms, there is no direct evidence to what extent and howUVR per se is utilized by phytoplankton. In addition, estimations of aquatic biological production have been carried out in incubations considering only PAR (i. e. using UV-opaque vials made of glass or polycarbonate; Donk et al., 2001) without UVR being considered (Hein and Sand-Jensen, 1997; Schippers and Lurling, 2004). Here, we have found that UVR can act as an additional source of energy for photosynthesis in tropical marine phytoplankton, though it occasionally causes photoinhibition at high PAR levels. While UVR is usually thought of as damaging, our results indicate that UVR can enhance primary production of phytoplankton. Therefore, oceanic carbon fixation estimates may be underestimated by a large percentage if UVR is not taken into account.

Preparation of a carbon supported Pt catalyst using an improved organic sol method and its electrocatalytic activity for methanol oxidation

The organic sol method for preparing ultrafine transition metal colloid particles reported for the first time by Bonnemann et al. [H. Bonnemann, W Brijoux, R. Brinkmann, E. Dinjus, T. Jou beta en, B. Korall, Angew. Chem. Int. Ed. Engl., 30 (1991) 1312] has been improved in this paper. The improved organic sol method uses SnCl2 as the reductant and methanol as the organic solvent. Thus, this method is very simple and inexpensive. It was found that the average size of the Pt particles in the Pt/C catalysts can be controlled by adjusting the evaporating temperature of the solvent. Therefore, the Pt/C catalysts prepared by the same method are suitable for evaluating the size effect of the Pt particles on electrocatalytic performance for methanol oxidation. The results of the X-ray diffraction (XRD) and transmission electron microscopy (TEM) showed that when the evaporating temperatures of the solvent are 65, 60, 50, 40, and 30 degrees C, the average sizes of the Pt particles in the Pt/C catalysts prepared are: 2.2, 3.2, 3.8, 4.3, and 4.8 nm, respectively. The X-ray photoelectron spectroscopic (XPS) results demonstrated that the small Pt particles are easily oxidized and the decomposition/adsorption of methanol cannot proceed on the surfaces of Pt oxides.

地幔柱与岩浆成矿-峨嵋山大火成岩省地震波速层物相解释及典型PGE矿床成岩成矿机制研究

地幔柱概念在19世纪60至70年代就被提出，但是由于板块构造理论在解释地球上岩浆活动的分布规律时取得了空前的成功，在当时这一理论是被排斥的。板块边界概念可以解释地球上绝大部分的岩浆产出，但在解释板内岩浆的成因时往往显得力不从心，尽管这些岩浆的体积只占地球岩浆总量的2％。地幔柱理论模型发展到现在得到不同学科的支持。地质学、地球化学、地球物理学、古生物学、比较行星学、实验岩石学等等都提供了直接或间接的证据，证明地幔柱几乎存在整个地：质历史时期。当前地幔柱理论中在地球化学领域有两大研究热点：高钦低钦玄武岩的起源以及地幔柱中是否存在循环俯冲洋壳物质。完全解决这些问题才可能深入系统地建立地慢柱成矿作用模型。现在已经建立了一些矿床类型与地慢柱作用的联系：如现在认为赋存在金伯利岩中的金刚石矿床的形成与地慢柱作用密不可分，一些岩浆硫化物矿床和岩浆氧化物矿床很显然是地慢柱岩浆作用形成的，如西伯利亚火成岩省的Noril'sk-Talnakh铜镍铂族元素矿床以及KeweenawaJI大陆裂谷体系的Dultlth杂岩体的Cu-Ni矿床。另外还有赋存在大型基性一超基性层状岩体中的PGE、Ni和cu矿床，如Great Dyke和布什维尔德杂岩体。一些超大型热液矿床也与地慢柱有可能的联系（Pirajno，2000）：如270oMa形成的超大型Kidd Creek火山成因块状硫化物矿床（Bleeker et al.，1 999；Wynan et al.，1999）和南澳大利亚1600Ma形成的超大型olymPicD翻矿床。本文的研究工作包含两方面内容：通过热力学计算峨眉山玄武岩在深部的结晶分异，对峨眉山大火成岩省的岩浆量分布和岩浆氧化物矿床（华Ti磁铁矿矿床）的分布以及下地壳高波速层的物相进行理论解释；对峨眉山大火成岩省金宝山PGE典型矿床进行成岩成矿的地球化学研究，预测整个大火成岩省的岩浆硫化物矿床产出位置。大多数峨眉山玄武岩的 MgO＜7％，Ni为4-232ppm，它们是原始岩浆结晶分异后的产物。峨眉山玄武岩省下地壳和上地幔之间存在厚度为：8-25km1，P彼速为7.1-7.8km／s的附加层（高地震波速层）。滇西地区出露的洲套第三纪富碱斑岩，地球化学和同位素研究表明斑岩的岩浆源是来自“壳一慢混合层”，源区的形成时代为220-25Ma，与峨眉山玄武岩的形成时代一致。所以有理由认为该附加层是由峨眉山玄武岩在此结晶分异形成的。与地慢柱有关的洋岛Hawaii、Marquesas Islands；海底高原Oniong Java、大陆火山岩省ColumbiaRiver Plateaus地震彼研究都表明在上地慢顶部有一高速附加层，Farnetani etal.（1996）的研歼表明高速附加层是由来自地幔柱的岩浆在此结晶分异形成的。玄武岩是一种混合的部分熔融产物，是不同成分的地幔橄榄岩在不同的压力下熔出的。这种降压熔融高温高压实验是做不到的。熔出的熔体成分是温度、压力及橄榄岩成分（源区）的函数，形成的岩浆是一个多压熔融的集合体。热力学计算能够较为精确地计算出生成的岩浆成分和约束岩浆产生的过程。岩浆的结晶分异也是同样的情形，尤其是分离结晶过程，实验岩石学是很精确难模拟其过程的。热力学计算使用的MELTS程序，MELTS适用范围很广，适用于模拟岩石熔融生成岩浆和岩浆的冷却结晶。现今峨眉山大火成岩省的地壳厚度为40恤，这被认为是后期褶皱加厚的缘故。根据峨眉山玄武岩中辉石斑晶成分和玄武岩本身成分计算出分异结晶的压力为6kb，那么当时的地壳厚度约为20km：选择氧逸度为QFM，这一氧逸度范围认为是大多数大陆溢流玄武岩结晶分异时的氧化还原环境。热力学计算结果通过峨眉山玄武岩成分进行约束和验证。Al2O3、NaZO＋K 20、CaO与MgO计算的演化趋势线与实际观察的演化符合较好，橄榄石和斜方辉石的结晶使得CaO随着MgO的降低而增高；当单斜辉石成为液相线矿物时，cao也随着Mgo的降低而降低了。单斜辉石在岩浆演化到MgO＝10．3％时成为液相线矿物。整个计算过程中斜长石未成为液相线矿物，这与大多数玄武岩不具有Eu异常是一致的，并月＿Al2O3随着MgO的减小单调增加也说明了这点。不过大多数峨眉山玄武岩常含有斜长石斑晶，这是低压下结晶分异的结果。由于斜长石密度小，所有很难与高铁玄武岩分离。整个计算的难点也是创新点是波速计算。通过分离的堆晶矿物组合中各种矿物的成分和质量分数计算的附加层波速比观察值高，不过堆积岩体常常会有残留岩浆存在矿物晶粒间，这样会降低岩石的压缩波速。大型基性一超基性岩体常常会残留有或者捕获5-30％的岩浆。假定两个高波速附加层分别捕获7叭，和巧％的残留岩浆，计算的结果就大体等于观察值。热力学和质量平衡计算研究表明：高地震波速层为橄榄辉石岩一辉石岩的巨型侵入岩体；峨眉山中岩区的岩浆量最大也符合含V-Ti磁铁矿矿床只产在中岩区，如太和、白马、攀枝花、红格等岩体；西岩区的岩浆量最小表明几乎没有可能在西岩区形成有规模的V-Ti磁铁矿矿床，实际观察仅仅只见到数量少而小的岩体；东岩区下地壳厚达20灿1的高波速层暗示东岩区上地壳的侵入岩体积也应该具有相当规模，应该是V－Ti磁铁矿矿床成矿区。目前在东岩区很少发现与峨眉山玄武岩有关的岩浆矿床的主要原因是：东岩区的剥蚀深度不够，没有可观的侵入岩体出露，而中岩区侵入岩都侵入在元古代地层中。按照质量平衡的计算方法，最保守的估算整个峨眉地慢柱岩浆事件产生的岩浆量为8.9*106km3，上地壳峨眉山玄武岩和侵入岩体积为3.9*106km3。如果按照初始覆盖面积5x106km2计算（与西伯利亚暗色岩初始覆盖面积相当），喷发高峰期为2Ma，计算的喷发速率为3.9km3／year。这并不亚于西伯利亚暗色岩的喷发速率4km3／year。这对于研究峨眉山大火成岩浆事件与二叠·三叠交界或end-QuadaluPian生物灭绝之间的可能联系具有重要意义。本文另一方面的研究工作是：首先系统地介绍了岩浆硫化物矿床的基本原理，然后通过金宝山PGE矿床实例研究，提出金宝山岩体成岩模式，并且对整个峨眉山大火成岩省的岩浆硫化物矿床产出位置进行理论预测。详细地球化学研究表明金宝山镁铁一超镁铁岩是峨眉山大火成岩省古老火山岩浆房的残留物。岩体主要由底部超镁铁岩和上部镁铁岩组成，两种岩石的质量大致相同。根据超镁铁岩的矿物组合计算的成岩时的氧逸度较高，热力学方法计算的成岩压力为2kb左右。超镁铁岩的包嵌结构和铁铁岩的微晶一细晶结构说明超镁铁岩为镁铁岩结晶的矿物堆积形成的。镁铁一超镁铁岩的蚀变程度不同以及Sc、Sr、Eu等元素在两类岩石中的不同特征指示了整个成岩过程。金宝山岩体的原始岩浆 MgO=8％说明高镁玄武岩并不是形成PGE矿床的必要条件。金宝山的成岩模式是：在火山喷发前，岩浆侵位时橄榄石和少量铬尖晶石先结晶，沉淀在岩浆房底部；随后结晶的是斜方辉石和斜长石，斜方辉石也沉淀在岩浆房底部，斜长石由于密度较小集中中岩浆房上部，岩浆房的中部是：少量的斜长石小斑晶。由于斜方辉石和斜长石的结晶，这样岩浆中的Sc、Sr和Eu就会亏损，也是岩浆房底部堆积岩的原始捕获岩浆。火山喷发后，由于压力的突然降低，岩浆房底部的堆晶会发生再熔融，几乎消耗掉所有的斜方辉石，橄榄石也呈熔蚀状浑圆形态，重新熔融的斜方辉石导致超镁铁岩中残留岩浆比原始捕获岩浆更加富Sc，这种岩浆由于富MgO和在快速冷却的环境下同时结晶，最终形成光性方位一致的单刹辉石。喷发后岩浆房空间的剩余导致围岩-灰岩进入，造成岩浆房中剩余岩浆强烈的碳酸盐化。峨眉山玄武岩Cr-Mg#的相关关系定义一条正常玄武岩演化线。大多数这些玄武岩的Ni也保持了这种演化关系，其中低钦玄武岩和过渡型高钦玄武岩Ni-Mg＃相关关系远离了正常演化线，这些玄武岩的Cu-Mg#相关关系也有类似的情形。峨眉山低钦和过渡类型高钦玄武岩Ni和 Cu的非正常亏损，表明它们在地表下经历了硫饱和事件。金宝山岩浆硫化物矿床成岩模型的建立，为在整个大火成岩省寻找岩浆硫化物矿床提供了一种新认识。低钦和过渡型高钦玄武岩的古老火山口下部是岩浆硫化物矿床的所在地。

Organic carbon source and burial during the past one hundred years in Jiaozhou Bay, North China

Organic carbon (OC), total nitrogen (TN), and Pb-210 in core sediment were measured to quantify the burial of organic carbon and the relative importance of allochthonous and autochthonous contributions during the past one hundred years in Jiaozhou Bay, North China. The core sediment was dated using Pb-210 chronology, which is the most promising method for estimation of sedimentation rate on a time scale of 100-150 years. The variation of the burial flux of organic carbon in the past one hundred years can be divided into the following three stages: (1) relatively steady before 1980s; (2) increasing rapidly from the 1980s to a peak in the 1990s, and (3) decreasing from the 1990s to the present. The change is consistent with the amount of solid waste and sewage emptied into the bay. The OC:TN ratio was used to evaluate the source of organic carbon in the Jiaozhou Bay sediment. In the inner bay and bay mouth, the organic carbon was the main contributor from terrestrial sources, whereas only about half of organic carbon was contributed from terrestrial source in the outer bay. In the inner bay, the terrestrial source of organic carbon showed a steady change with an increase in the range of 69%-77% before 1990 to 93% in 2000, and then decreased from 2000 because of the decrease in the terrestrial input. In the bay mouth, the percentage of organic carbon from land reached the highest value with 94% in 1994. In the outer bay, the sediment source maintained steady for the past one hundred years.

Burst event detection in wall turbulence by WVITA method

Wavelet Variable Interval Time Average (WVITA) is introduced as a method incorporating burst event detection in wall turbulence. Wavelet transform is performed to unfold the longitudinal fluctuating velocity time series measured in the near wall region of a turbulent boundary layer using hot-film anemometer. This unfolding is both in time and in space simultaneously. The splitted kinetic of the longitudinal fluctuating velocity time series among different scales is obtained by integrating the square of wavelet coefficient modulus over temporal space. The time scale that related to burst events in wall turbulence passing through the fixed probe is ascertained by maximum criterion of the kinetic energy evolution across scales. Wavelet transformed localized variance of the fluctuating velocity time series at the maximum kinetic scale is put forward instead of localized short time average variance in Variable Interval Time Average (VITA) scheme. The burst event detection result shows that WVITA scheme can avoid erroneous judgement and solve the grouping problem more effectively which is caused by VITA scheme itself and can not be avoided by adjusting the threshold level or changing the short time average interval.

Molecular Dynamics Simulation of Barnacle Cement

Barnacle cement is an underwater adhesive that is used for permanent settlement. Its main components are insoluble protein complexes that have not been fully studied. In present article, we chose two proteins of barnacle cement for study, 36-KD protein and Mrcp-100K protein. In order to investigate the characteristic of above two proteins, we introduced the method of molecular modeling. And the simulation package GROMACS was used to simulate the behavior of these proteins. In this article, before the simulations, we introduce some theories to predict the time scale for polymer relaxation. During the simulation, we mainly focus on two properties of these two proteins: structural stability and adhesive force to substrate. First, we simulate the structural stability of two proteins in water, and then the stability of 36-KD protein in seawater environment is investigated.We find that the stability varies in the different environments. Next, to study adhesive ability of two proteins, we simulate the process of peeling the two proteins from the substrate (graphite). Then, we analyze the main reasons of these results. We find that hydrogen bonds in proteins play an important role in the protein stability. In the process of the peeling, we use Lennard–Jones 12-6 potential to calculate the van der Waals interactions between proteins and substrate.

Effects Of Subgrid-Scale Modeling On Lagrangian Statistics In Large-Eddy Simulation

The application of large-eddy simulation (LES) to turbulent transport processes requires accurate prediction of the Lagrangian statistics of flow fields. However, in most existing SGS models, no explicit consideration is given to Lagrangian statistics. In this paper, we focus on the effects of SGS modeling on Lagrangian statistics in LES ranging from statistics determining single-particle dispersion to those of pair dispersion and multiparticle dispersion. Lagrangian statistics in homogeneous isotropic turbulence are extracted from direct numerical simulation (DNS) and the LES with a spectral eddy-viscosity model. For the case of longtime single-particle dispersion, it is shown that, compared to DNS, LES overpredicts the time scale of the Lagrangian velocity correlation but underpredicts the Lagrangian velocity fluctuation. These two effects tend to cancel one another leading to an accurate prediction of the longtime turbulent dispersion coefficient. Unlike the single-particle dispersion, LES tends to underestimate significantly the rate of relative dispersion of particle pairs and multiple-particles, when initial separation distances are less than the minimum resolved scale due to the lack of subgrid fluctuations. The overprediction of LES on the time scale of the Lagrangian velocity correlation is further confirmed by a theoretical analysis using a turbulence closure theory.

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

Molecular Dynamics Simulation of Barnacle Cement

Barnacle cement is an underwater adhesive that is used for permanent settlement. Its main components are insoluble protein complexes that have not been fully studied. In present article, we chose two proteins of barnacle cement for study, 36-KD protein and Mrcp-100K protein. In order to investigate the characteristic of above two proteins, we introduced the method of molecular modeling. And the simulation package GROMACS was used to simulate the behavior of these proteins. In this article, before the simulations, we introduce some theories to predict the time scale for polymer relaxation. During the simulation, we mainly focus on two properties of these two proteins: structural stability and adhesive force to substrate. First, we simulate the structural stability of two proteins in water, and then the stability of 36-KD protein in seawater environment is investigated. We find that the stability varies in the different environments. Next, to study adhesive ability of two proteins, we simulate the process of peeling the two proteins from the substrate (graphite). Then, we analyze the main reasons of these results. We find that hydrogen bonds in proteins play an important role in the protein stability. In the process of the peeling, we use Lennard-Jones 12-6 potential to calculate the van der Waals interactions between proteins and substrate.

“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure

Two different spatial levels are involved concerning damage accumulation to eventual failure. nucleation and growth rates of microdamage nN* and V*. It is found that the trans-scale length ratio c*/L does not directly affect the process. Instead, two independent dimensionless numbers: the trans-scale one * * ( V*)including the * **5 * N c V including mesoscopic parameters only, play the key role in the process of damage accumulation to failure. The above implies that there are three time scales involved in the process: the macroscopic imposed time scale tim = /a and two meso-scopic time scales, nucleation and growth of damage, (* *4) N N t =1 n c and tV=c*/V*. Clearly, the dimensionless number De*=tV/tim refers to the ratio of microdamage growth time scale over the macroscopically imposed time scale. So, analogous to the definition of Deborah number as the ratio of relaxation time over external one in rheology. Let De be the imposed Deborah number while De represents the competition and coupling between the microdamage growth and the macroscopically imposed wave loading. In stress-wave induced tensile failure (spallation) De* < 1, this means that microdamage has enough time to grow during the macroscopic wave loading. Thus, the microdamage growth appears to be the predominate mechanism governing the failure. Moreover, the dimensionless number D* = tV/tN characterizes the ratio of two intrinsic mesoscopic time scales: growth over nucleation. Similarly let D be the “intrinsic Deborah number”. Both time scales are relevant to intrinsic relaxation rather than imposed one. Furthermore, the intrinsic Deborah number D* implies a certain characteristic damage. In particular, it is derived that D* is a proper indicator of macroscopic critical damage to damage localization, like D* ∼ (10–3~10–2) in spallation. More importantly, we found that this small intrinsic Deborah number D* indicates the energy partition of microdamage dissipation over bulk plastic work. This explains why spallation can not be formulated by macroscopic energy criterion and must be treated by multi-scale analysis.