A self-closed system of equations of damage evolution

This paper introduces a statistical mesomechanical approach to the evolution of damage. A self-closed formulation of the damage evolution is derived.

Tidal oscillations at the head of Monterey Submarine Canyon and their relation to oceanographic sampling and the circulation of water in Monterey Bay. Annual report, Part 6, September 1972

During a 25-hour hydrographic times series at two stations near the head of Monterey Submarine Canyon, an internal tide was observed with an amplitude of 80 to 115 m in water depths of 120 and 220 m respectively. These large oscillations produced daily variations in hydrographic and chemical parameters that were of the same magnitude as seasonal variations in Monterey Bay. Computed velocities associated with the internal tide were on the order of 10 em/sec, and this tidally induced circulation may have a significant role in the exchange of deep water between Monterey Submarine Canyon and the open ocean. (PDF contains 49 pages)

Mass Energy and Flow in closed ecosystems

The general equations of biomass and energy transfer for an n-species, closed ecosystem are written. It is demonstrated how in "ecological time" the parameters describing the dynamics of biomass transfer are related to the parameters of energy transfer, such as respiration, fixation, and energy content. This relationship is determinate for the straight-chain ecosystem, and a simple example is worked out. The results show how the density dependent terms in population dynamics arise naturally, and how the stable system exhibits a hierarchy in energy per unit biomass. A procedure is proposed for extending the theory to include webbed systems, and the particular difficulties involved in the extension are brought before the scientific community for discussion.

IP Simulation of Micro Gas Flows under 3-D Head Sliders

Gas film lubrication of a three-dimensional flat read-write head slider is calculated using the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method, respectively. The pressure distributions on the head slider surface at different velocities and flying heights obtained by the two methods are in excellent agreement. IP method is also employed to deal with head slider with three-dimensional complex configuration. The pressure distribution on the head slider surface and the net lifting force obtained by the IP method also agree well with those of DSMC method. Much less (of the order about 10(2) less) computational time (the sum of the time used to reach a steady stage and the time used in sampling process) is needed by the IP method than the DSMC method and such an advantage is more remarkable as the gas velocity decreases.

EXPERIMENTAL AND THEORETICAL STUDY OF BINARY DROPLET HEAD-ON COLLISIONS IN MEMS

The experimental and theoretical investigations into the head-on collision between a landing droplet with another one resting on the PDMS substrate were addressed in this talk. The colliding process of the two droplets was recorded with highspeed camera. Four different responses after collision were observed in our experiments: complete rebound, coalescence, partial rebound with conglutination, and coalescence accompanied by conglutination. The contact time between the two colliding droplets was found to be in the range of 10-20 milliseconds. For the complete bouncing case, Hertz contact model was applied to estimate the contact time of the binary head-on colliding droplets with both the droplets considered as elastic bodies. The estimated contact time was in good agreement with the experimental result.

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

A comparison of seafloor habitats and associated benthic fauna in areas open and closed to bottom trawling along the central California Continental Shelf

Executive Summary: A number of studies have shown that mobile, bottom-contact fishing gear (such as otter trawls) can alter seafloor habitats and associated biota. Considerably less is known about the recovery of these resources following such disturbances, though this information is critical for successful management. In part, this paucity of information can be attributed to the lack of access to adequate control sites – areas of the seafloor that are closed to fishing activity. Recent closures along the coast of central California provide an excellent opportunity to track the recovery of historically trawled areas and to compare recovery rates to adjacent areas that continue to be trawled. In June 2006 we initiated a multi-year study of the recovery of seafloor microhabitats and associated benthic fauna inside and outside two new Essential Fish Habitat (EFH) closures within the Cordell Bank and Gulf of the Farallones National Marine Sanctuaries. Study sites inside the EFH closure at Cordell Bank were located in historically active areas of fishing effort, which had not been trawled since 2003. Sites outside the EFH closure in the Gulf of Farallones were located in an area that continues to be actively trawled. All sites were located in unconsolidated sands at equivalent water depths. Video and still photographic data collected via a remotely operated vehicle (ROV) were used to quantify the abundance, richness, and diversity of microhabitats and epifaunal macro-invertebrates at recovering and actively trawled sites, while bottom grabs and conductivity/temperature/depth (CTD) casts were used to quantify infaunal diversity and to characterize local environmental conditions. Analysis of still photos found differences in common seafloor microhabitats between the recovering and actively trawled areas, while analysis of videographic data indicated that biogenic mound and biogenic depression microhabitats were significantly less abundant at trawled sites. Each of these features provides structure with which demersal fishes, across a wide range of size classes, have been observed to associate. Epifaunal macro-invertebrates were sparsely distributed and occurred in low numbers in both treatments. However, their total abundance was significantly different between treatments, which was attributable to lower densities at trawled sites. In addition, the dominant taxa were different between the two sites. Patchily-distributed buried brittle stars dominated the recovering site, and sea whips (Halipteris cf. willemoesi) were most numerous at the trawled site though they occurred in only five of ten transects. Numerical classification (cluster analysis) of the infaunal samples also revealed a clear difference between benthic assemblages in the recovering vs. trawled areas due to differences in the relative abundances of component species. There were no major differences in infaunal species richness, H′ diversity, or J′ evenness between recovering vs. trawled site groups. However, total infaunal abundance showed a significant difference attributable to much lower densities at trawled sites. This pattern was driven largely by the small oweniid polychaete Myriochele gracilis, which was the most abundant species in the overall study region though significantly less abundant at trawled sites. Other taxa that were significantly less abundant at trawled sites included the polychaete M. olgae and the polychaete family Terebellidae. In contrast, the thyasirid bivalve Axinopsida serricata and the polychaetes Spiophanes spp. (mostly S. duplex), Prionospio spp., and Scoloplos armiger all had significantly to near significantly higher abundances at trawled sites. As a result of such contrasting species patterns, there also was a significant difference in the overall dominance structure of infaunal assemblages between the two treatments. It is suggested that the observed biological patterns were the result of trawling impacts and varying levels of recovery due to the difference in trawling status between the two areas. The EFH closure was established in June 2006, within a month of when sampling was conducted for the present study, however, the stations within this closure area are at sites that actually have experienced little trawling since 2003, based on National Marine Fishery Service trawl records. Thus, the three-year period would be sufficient time for some post-trawling changes to have occurred. Other results from this study (e.g., similarly moderate numbers of infaunal species in both areas that are lower than values recorded elsewhere in comparable habitats along the California continental shelf) also indicate that recovery within the closure area is not yet complete. Additional sampling is needed to evaluate subsequent recovery trends and persistence of effects. Furthermore, to date, the study has been limited to unconsolidated substrates. Ultimately, the goal of this project is to characterize the recovery trajectories of a wide spectrum of seafloor habitats and communities and to link that recovery to the dynamics of exploited marine fishes. (PDF has 48 pages.)

On Bounded Strictly Positive Operators of Closed Range and Some Applications to Asymptotic Hyperstability of Dynamic Systems

The problem discussed is the stability of two input-output feedforward and feedback relations, under an integral-type constraint defining an admissible class of feedback controllers. Sufficiency-type conditions are given for the positive, bounded and of closed range feed-forward operator to be strictly positive and then boundedly invertible, with its existing inverse being also a strictly positive operator. The general formalism is first established and the linked to properties of some typical contractive and pseudocontractive mappings while some real-world applications and links of the above formalism to asymptotic hyperstability of dynamic systems are discussed later on.