“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.

Dynamic optical coupled system employing even-numbered Dammann gratings

Dammann gratings are well known for their ability to generate arrays of Lmiform-intensity beams from an incoming monochromatic beam. We apply the even-numbered Dammann grating to achieve dynamic optical coupled technology. A 1 x N dynamic optical coupled system is developed by employing two complementary even-numbered Dammann gratings. With this system we can achieve a beam splitter and combiner as a switch between them according to the relative shift between the gratings. Also, this system is a preferable approach in integral packaging. More importantly, this device has the potential to be applied to the splitting of a large array, e.g., 8 x 16 array and 64 x 64 array, which is difficult to be realized with conventional splitting methods. We experimentally demonstrated a 1 x 8 coupler at the wavelength of 1550 nm. Furthermore we analyze the effects of the alignment errors between gratings and the wavelength-dependent error on efficiency and uniformity. The experimental results and the influence of alignment error and wavelength-dependent error are analyzed in detail. (c) 2006 Optical Society of America.

Even aberration measurement of lithographic projection system based on optimized phase-shifting marks

In the present paper, we propose a novel method for measuring the even aberrations of lithographic projection optics by use of optimized phase-shifting marks on the test mask. The line/space ratio of the phase-shifting marks is optimized to obtain the maximum sensitivities of Zernike coefficients corresponding to even aberrations. Spherical aberration and astigmatism can be calculated from the focus shifts of phase-shifting gratings oriented at 0 degrees, 45 degrees, 90 degrees and 135 degrees at multiple illumination settings. The PROLITH simulation results show that, the measurement accuracy of spherical aberration and astigmatism obviously increase, after the optimization of the measurement mark. (C) 2008 Elsevier B.V. All rights reserved.

Numbers of migratory waterbirds at Lake Lashihai, China

Between October 1999 and April 2000, WC surveyed the waterbirds at Lake Lashihai, China. A total of 52 species were recorded, of which one species was a resident, 34 were winter visitors, and 17 were passage migrants. Species richness was highest in November. Passage migrants mainly occurred in October, November, and April, and they stayed longer at the lake during their autumn migration than during the spring migration. The seasonal distribution pattern of total numbers of all waterbirds was bimodal. One peak occurred between late December and early January, and the other in middle March. The seasonal distribution patterns of 15 common species have been classified a. bimodal, unimodal, or irregular. The numbers of five common species were variable in middle winter, and their numerical Change in contiguous weeks were more than 30%, suggesting that local movements might be frequent.

Seasonal Variations in Chlorophyll a Concentrations in Relation to Potentials of Sediment Phosphate Release by Different Mechanisms in a Large Chinese Shallow Eutrophic Lake (Lake Taihu)

The relationship between chlorophyll a and fractionation of sediment phosphorus, inorganic phosphate-solubilizing bacteria (IPB), and organic phosphate-mineralizing bacteria (OPB) was evaluated in a large Chinese shallow eutrophic lake (Lake Taihu) and its embayment (Wuli Bay). At the three study sites, the increase of chlorophyll a concentrations in April paralleled those of the iron bound phosphate accounting for major portion of sediment inorganic phosphate, and in June significantly higher OPB and IPB numbers (especially OPB) in sediment were main contributors to the peaks of chlorophyll a concentration. Even though IPB peaked from February to June, it should serve as an unimportant P source due to the irrelevancy with chlorophyll a and soluble reactive phosphorus (SRP). By contrast, at the other site in the embayment, the calcium-bound phosphate was predominant and solid, which was difficult to be released, and neither IPB nor OPB were detectable in the sediment, indicating weak potential for phosphorus release from the sediment, which was reflected in the small seasonal variation in SRP concentration in water column. Hence, the extents to which the three general mechanisms behind phosphate release from sediment (desorption of iron bound phosphate, solubilization by IPB and enzymatic hydrolysis by OPB) operated were different depending on seasons and sites in Lake Taihu, they may jointly drive phosphate release and accelerate the eutrophication processes.

Bioinformatic identification of genes encoding C1q-domain-containing proteins in zebrafish

C1q is the first subcomponent of classical pathway in the complement system and a major link between innate and acquired immunities. The globular (gC1q) domain similar with C1q was also found in many non-complement C1q-domain-containing (C1qDC) proteins which have similar crystal structure to that of the multifunctional tumor necrosis factor (TNF) ligand family, and also have diverse functions. In this study, we identified a total of 52 independent gene sequences encoding C1q-domain-containing proteins through comprehensive searches of zebrafish genome, cDNA and EST databases. In comparison to 31 orthologous genes in human and different numbers in other species, a significant selective pressure was suggested during vertebrate evolution. Domain organization of C1q-domain-containing (C1qDC) proteins mainly includes a leading signal peptide, a collagen-like region of variable length, and a C-terminal C1q domain. There are 11 highly conserved residues within the C1q domain, among which 2 are invariant within the zebrafish gene set. A more extensive database searches also revealed homologous C1qDC proteins in other vertebrates, invertebrates and even bacterium, but no homologous sequences for encoding C1qDC proteins were found in many species that have a more recent evolutionary history with zebrafish. Therefore, further studies on C1q-domain-containing genes among different species will help us understand evolutionary mechanism of innate and acquired immunities.

Range-wide Yangtze freshwater dolphin expedition: The last chance to see Baiji?

Background, Aim and Scope. There are two species of fresh water cetaceans surviving in the Yangtze River system in China: Baiji (Lipotes vexillifer) and Yangtze finless porpoise (Neophocaena phocaenoides asiaeorientalis). As a result of the expansion of human activities on the river, their distribution ranges appear to be decreasing and in the case of the Baiji, are even being restricted to several sections. The Baiji is the world's most critically endangered cetacean species with a population estimated at only a few tens of individuals. The Yangtze finless porpoise is the world's only freshwater-adapted population of the species, and it has been estimated that only around 1,000 individuals remain in the river system. In order to prevent the extinction of Baiji and a sharp decline in the abundance of the porpoise, in situ conservation (i.e. in the river) and two ex situ conservation (i.e. in semi-natural reserves and in captivity) strategies were proposed and have been implemented since the early 1990s. In view of both the severely endangered status of the animals and the severely degraded conditions of their habitats, the feasibility and actual status of these two strategies are raised for discussion. Main Features. The threats faced by the cetaceans are mainly from the unfettered exploitation of the river's resources. In the past 20 years, five nature reserves have been established along the river. Imposing maximum prohibition of harmful and illegal fishing methods in the reserves might prolong the process of extinction of these cetaceans in the wild, but so far, the administrative measures taken in the reserves have not yet kept the abundance from sharply declining. As human use of the river and its resources is expected to intensify for many decades into the future, the ability of the river to continue to support these species is certainly undecided. Therefore, rescuing animals from the river and establishing viable breeding populations in semi-natural reserves, in which the environment is similar to the main stream of the river, and in captivity, has to be considered urgently as the short-term goal of ex situ strategies. Since the abundance of porpoises is higher than that of the Baiji, we have first established breeding populations of them in the semi-natural reserves and in captivity. But, considering the extremely low density of Baiji in the river, an immediate range-wide Yangtze Baiji survey is an urgent need for locating and capturing sufficient Baiji for successfully establishing a breeding population of them in semi-natural reserves. Results. Two semi-natural reserves (in Shishou, Hubei Province, and Tongling, Anhui Province) have been set up along the river in order to establish breeding populations of the Baiji and the porpoises. So far, several small groups of porpoises that were caught in the main stream of the river have successively been introduced into the semi-natural reserves. Under careful management, these animals in both of the semi-natural reserves not only survive, but can also reproduce naturally and successfully. At least one or three calves were born in each reserve each year. Additionally, a breeding group of porpoises is being established at the Baiji Dolphinarium at the Institute of Hydrobiology, Chinese Academy of Sciences, Wuhan. There are presently four adults and one calf living in the Dolphinarium. The calf, born in July, 2005, is the first captive bred Yangtze Finless Porpoise in the world. In preparation for the range-wide Yangtze cetacean survey, a 9-day pilot expedition on the river near Wuhan was conducted in March, 2006, in order to develop methods for locating the Baiji. No Baiji were expected to be seen in such a short period but about 40 porpoise sightings were observed. Results of the pilot survey indicated that traditional visual and acoustical survey methods for cetaceans should be adapted to find the elusive Baiji in the river. Currently, the range-wide Yangtze cetacean survey is in preparation. The survey will cover over 1,700 km of the Yangtze River from Yichang to Shanghai, and is expected to provide detailed information on Baiji and porpoise numbers and distribution patterns in the river. Discussion. Although the short-term goal of ex situ conservation is to rescue cetaceans from the river and to establish viable breeding populations in semi-natural reserves and in captivity, the long-term goal of releasing the animals back into the river when the threats have decreased and the natural environment has been improved, should not be neglected. Moreover, the in situ conservation efforts in the natural reserves, and even in the entire Yangtze River system, including the lakes, should not be ignored or abandoned at any time. The activities contributing to the conservation of the Baiji and the porpoise in the wild have the incidental effect of benefiting the entire Yangtze ecosystem and other rare threatened species. The dynamics of the groups of porpoises in semi-natural reserves should be monitored continually, in order to guide the establishment of breeding groups of Baiji in these semi-natural reserves in the near future. Conclusions. Under the existing severely degraded conditions of the Yangtze system, the sharply fall populations of Baiji and porpoises will not be suspended in the foreseeable future. Therefore, ex situ conservation should be emphasized, and the severely threatened Baiji in the river should be removed and translocated to semi-natural reserves for establishing viable breeding populations. The successful program of capturing, translocating and maintaining finless porpoises in the Shishou semi-natural reserve has demonstrated its adequacy as an ex situ environment for cetaceans. Following the successful pilot survey in the river, the immediate range-wide Yangtze cetacean survey is proposed and is in preparation. The range-wide survey is expected to ensure that any remaining Baiji can be found reliably and captured successfully after the survey. Recommendations and Perspectives. During the range-wide survey, not only the Baiji but also the porpoise as well as their habitats should be investigated based on visual and acoustical methods that adapted to the river and the animals. Meanwhile, the current risk levels to the Baiji and porpoises should be evaluated at each area where Baiji or porpoises can be reliably sighted. Any capture efforts should be targeted on the most threatened areas, or where there is maximum risk of injury or death. The immediate track of the Baiji should be carried out once a Baiji is sighted during the range-wide survey in order to obtain the movement route of the animals, which is crucial information for the successful capture operation. Additionally, the need to establish new semi-natural reserves for the porpoises should be placed on the agenda of local and central governments in the near future.

Culture of the terrestrial cyanobacterium, Nostoc flagelliforme (Cyanophyceae), under aquatic conditions

Both colonies and free-living cells of the terrestrial cyanobacterium, Nostoc flagelliforme (Berk. & Curtis) Bornet & Flahault, were cultured under aquatic conditions to develop the techniques for the cultivation and restoration of this endangered resource. The colonial filaments disintegrated with their sheaths ruptured in about 2 days without any desiccating treatments. Periodic desiccation played an important role in preventing the alga from decomposing, with greater delays to sheath rupture with a higher frequency of exposure to air. The bacterial numbers in the culture treated with seven periods of desiccation per day were about 50% less compared with the cultures without the desiccation treatment. When bacteria in the culture were controlled, the colonial filaments did not disintegrate and maintained the integrity of their sheath for about 20 days even without the desiccation treatments, indicating the importance of desiccation for N. flagelliforme to prevent them from being disintegrated by bacteria. On the other hand, when free-living cells obtained from crushed colonial filaments were cultured in liquid medium, they developed into single filaments with sheaths, within which multiple filaments were formed later on as a colony. Such colonial filaments were developed at 15, 25, and 30degreesC at either 20 or 60 mumol photons.m(-2).s(-1); colonies did not develop at 180 mumol photons.m(-2).s(-1), though this light level resulted in the most rapid growth of the cells. Conditions of 60 mumol photons.m(-2).s(-1) and 25degrees C appeared to result in the best colonial development and faster growth of the sheath-held colonies of N. flagelliforme when cultured indoor under aquatic conditions.

Modes in square resonators

Modes in square resonators are analyzed and classified according to the irreducible representations of the point group C-4v. If the mode numbers p and q that denote the number of wave nodes in the directions of two orthogonal square sides are unequal and have the same even-odd characteristics, the corresponding double modes are accidentally degenerate and can be combined into two new distributions with definite parities relative to the square diagonal mirror planes. The distributions with odd parities belong to the whispering-gallery-like modes in square resonators. The mode frequencies and quality factors are also calculated by the finite-difference time-domain technique and Pade approximation method. The numerically calculated mode frequencies agree with the theoretical ones very well and the whispering-gallery-like modes have quality factors much higher than other modes, including their accidentally degenerate counterparts in square resonators.

Mode analysis and Q-factor enhancement due to mode coupling in rectangular resonators

Modes in rectangular resonators are analyzed and classified according to symmetry properties, and quality factor (Q-factor) enhancement due to mode coupling is observed. In the analysis, mode numbers p and q are used to denote the number of wave nodes in the direction of two orthogonal sides. The even and odd mode numbers correspond to symmetric and antisymmetric field distribution relative to the midlines of sides, respectively. Thus, the modes in a rectangle resonator can be divided into four classes according to the parity of p and q. Mode coupling between modes of different classes is forbidden; however, anti-crossing mode coupling between the modes in the same class exists and results in new modes due to the combination of the coupled modes. One of the combined modes has very low power loss and high Q-factor based on far-field emission of the analytical field distribution, which agrees well with the numerical results of the finite-difference time-domain (FDTD) simulation. Both the analytical and FDTD results show that the Q-factors of the high Q-factor combined modes are over one order larger than those of the original modes. Furthermore, the general condition required to achieve high-Q modes in the rectangular resonator is given based on the analytical solution.

WG-like modes selectivity in a square cavity with posts

We investigate the characteristics of Whispering-Gallery(WG)-like modes in a square cavity with posts by employing the two-dimentional (2D) finite-difference time-domain (FDTD) technique combined with the effective index method. The results indicate that the posts can result in mode selection in the WG-like modes. The WG-like modes with odd mode numbers are not much sensitive to the sizes of the posts. However, the quality factor (i.e. Q-factor) of the WG-like modes with even mode numbers decreases sharply with the increasing size of the posts. The decreasing Q-factor is attributed to mode leakage and scattering loss due to the presence of the post. The mode selection increases with the mode spacing of square cavity twice in an optimized strucure.

Complex networks constructed from irrational number sequences

In this paper, we construct (d, r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r = 0,1,...,d-1), and the undirected edges indicate the adjacency between two consecutive groups. (3, r) and (4, r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.