“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.

Institutional designs to face the dark side of total allowable catches

Setting total allowable catches (TACs) is an endogenous process in which different agents and institutions, often with conflicting interests and opportunistic behaviour, try to influence policy-makers. Such policy-makers, far from being the benevolent social planners many would wish them to be, may also pursue self-interest when making final decisions. Although restricted knowledge of stock abundance and population dynamics, and weakness in enforcement, have effects, these other factors may explain the reason why TAC management has failed to guarantee sustainable exploitation of fish resources. Rejecting the exogeneity of the TAC and taking advantage of fruitful debate on economic policy (i.e. the rules vs. discretion debate, and that surrounding the independence of central banks), two institutional developments are analysed as potential mechanisms to face up to misconceptions about TACs: long-term harvest control rules, and a central bank of fish.

Survey report of NOAA Ship McArthur II cruises AR-04-04, AR-05-05 and AR-06-03: Habitat classification of side scan sonar imagery in support of deep-sea coral/sponge explorations at the Olympic Coast National Marine Sanctuary

Habitat mapping and characterization has been defined as a high-priority management issue for the Olympic Coast National Marine Sanctuary (OCNMS), especially for poorly known deep-sea habitats that may be sensitive to anthropogenic disturbance. As a result, a team of scientists from OCNMS, National Centers for Coastal Ocean Science (NCCOS), and other partnering institutions initiated a series of surveys to assess the distribution of deep-sea coral/sponge assemblages within the sanctuary and to look for evidence of potential anthropogenic impacts in these critical habitats. Initial results indicated that remotely delineating areas of hard bottom substrate through acoustic sensing could be a useful tool to increase the efficiency and success of subsequent ROV-based surveys of the associated deep-sea fauna. Accordingly, side scan sonar surveys were conducted in May 2004, June 2005, and April 2006 aboard the NOAA Ship McArthur II to: (1) obtain additional imagery of the seafloor for broader habitat-mapping coverage of sanctuary waters, and (2) help delineate suitable deep-sea coral/sponge habitat, in areas of both high and low commercial-fishing activities, to serve as sites for surveying-in more detail using an ROV on subsequent cruises. Several regions of the sea floor throughout the OCNMS were surveyed and mosaicked at 1-meter pixel resolution. Imagery from the side scan sonar mapping efforts was integrated with other complementary data from a towed camera sled, ROVs, sedimentary samples, and bathymetry records to describe geological and biological (where possible) aspects of habitat. Using a hierarchical deep-water marine benthic classification scheme (Greene et al. 1999), we created a preliminary map of various habitat polygon features for use in a geographical information system (GIS). This report provides a description of the mapping and groundtruthing efforts as well as results of the image classification procedure for each of the areas surveyed. (PDF contains 60 pages.)

Olympic Coast National Marine Sanctuary Habitat Mapping: Survey report and classification of side scan sonar data from surveys HMPR-114-2004-02 and HMPR-116-2005-01.

The Olympic Coast National Marine Sanctuary (OCNMS) continues to invest significant resources into seafloor mapping activities along Washington’s outer coast (Intelmann and Cochrane 2006; Intelmann et al. 2006; Intelmann 2006). Results from these annual mapping efforts offer a snapshot of current ground conditions, help to guide research and management activities, and provide a baseline for assessing the impacts of various threats to important habitat. During the months of August 2004 and May and July 2005, we used side scan sonar to image several regions of the sea floor in the northern OCNMS, and the data were mosaicked at 1-meter pixel resolution. Video from a towed camera sled, bathymetry data, sedimentary samples and side scan sonar mapping were integrated to describe geological and biological aspects of habitat. Polygon features were created and attributed with a hierarchical deep-water marine benthic classification scheme (Greene et al. 1999). For three small areas that were mapped with both side scan sonar and multibeam echosounder, we made a comparison of output from the classified images indicating little difference in results between the two methods. With these considerations, backscatter derived from multibeam bathymetry is currently a costefficient and safe method for seabed imaging in the shallow (<30 meters) rocky waters of OCNMS. The image quality is sufficient for classification purposes, the associated depths provide further descriptive value and risks to gear are minimized. In shallow waters (<30 meters) which do not have a high incidence of dangerous rock pinnacles, a towed multi-beam side scan sonar could provide a better option for obtaining seafloor imagery due to the high rate of acquisition speed and high image quality, however the high probability of losing or damaging such a costly system when deployed as a towed configuration in the extremely rugose nearshore zones within OCNMS is a financially risky proposition. The development of newer technologies such as intereferometric multibeam systems and bathymetric side scan systems could also provide great potential for mapping these nearshore rocky areas as they allow for high speed data acquisition, produce precisely geo-referenced side scan imagery to bathymetry, and do not experience the angular depth dependency associated with multibeam echosounders allowing larger range scales to be used in shallower water. As such, further investigation of these systems is needed to assess their efficiency and utility in these environments compared to traditional side scan sonar and multibeam bathymetry. (PDF contains 43 pages.)

Benthic habitat mapping in the Olympic Coast National Marine Sanctuary: Classification of side scan sonar data from survey HMPR-108-2002-01: Version I

In September 2002, side scan sonar was used to image a portion of the sea floor in the northern OCNMS and was mosaiced at 1-meter pixel resolution using 100 kHz data collected at 300-meter range scale. Video from a remotely-operated vehicle (ROV), bathymetry data, sedimentary samples, and sonar mapping have been integrated to describe geological and biological aspects of habitat and polygon features have been created and attributed with a hierarchical deep-water marine benthic classification scheme (Greene et al. 1999). The data can be used with geographic information system (GIS) software for display, query, and analysis. Textural analysis of the sonar images provided a relatively automated method for delineating substrate into three broad classes representing soft, mixed sediment, and hard bottom. Microhabitat and presence of certain biologic attributes were also populated into the polygon features, but strictly limited to areas where video groundtruthing occurred. Further groundtruthing work in specific areas would improve confidence in the classified habitat map. (PDF contains 22 pages.)

Detecting fish aggregations from reef habitats mapped with high resolution side scan sonar imagery

As part of a multibeam and side scan sonar (SSS) benthic survey of the Marine Conservation District (MCD) south of St. Thomas, USVI and the seasonal closed areas in St. Croix—Lang Bank (LB) for red hind (Epinephelus guttatus) and the Mutton Snapper (MS) (Lutjanus analis) area—we extracted signals from water column targets that represent individual and aggregated fish over various benthic habitats encountered in the SSS imagery. The survey covered a total of 18 km2 throughout the federal jurisdiction fishery management areas. The complementary set of 28 habitat classification digital maps covered a total of 5,462.3 ha; MCDW (West) accounted for 45% of that area, and MCDE (East) 26%, LB 17%, and MS the remaining 13%. With the exception of MS, corals and gorgonians on consolidated habitats were significantly more abundant than submerged aquatic vegetation (SAV) on unconsolidated sediments or unconsolidated sediments. Continuous coral habitat was the most abundant consolidated habitat for both MCDW and MCDE (41% and 43% respectively). Consolidated habitats in LB and MS predominantly consisted of gorgonian plain habitat with 95% and 83% respectively. Coral limestone habitat was more abundant than coral patch habitat; it was found near the shelf break in MS, MCDW, and MCDE. Coral limestone and coral patch habitats only covered LB minimally. The high spatial resolution (0.15 m) of the acquired imagery allowed the detection of differing fish aggregation (FA) types. The largest FA densities were located at MCDW and MCDE over coral communities that occupy up to 70% of the bottom cover. Counts of unidentified swimming objects (USOs), likely representing individual fish, were similar among locations and occurred primarily over sand and shelf edge areas. Fish aggregation school sizes were significantly smaller at MS than the other three locations (MCDW, MCDE, and LB). This study shows the advantages of utilizing SSS in determining fish distributions and density.

Pumped double quantum dot with spin-orbit coupling

We study driven by an external electric field quantum orbital and spin dynamics of electron in a one-dimensional double quantum dot with spin-orbit coupling. Two types of external perturbation are considered: a periodic field at the Zeeman frequency and a single half-period pulse. Spin-orbit coupling leads to a nontrivial evolution in the spin and orbital channels and to a strongly spin-dependent probability density distribution. Both the interdot tunneling and the driven motion contribute into the spin evolution. These results can be important for the design of the spin manipulation schemes in semiconductor nanostructures.

A perturbation procedure for nonlinear oscillations (The dynamics of two oscillators with weak nonlinear coupling)

This thesis considers in detail the dynamics of two oscillators with weak nonlinear coupling. There are three classes of such problems: non-resonant, where the Poincaré procedure is valid to the order considered; weakly resonant, where the Poincaré procedure breaks down because small divisors appear (but do not affect the O(1) term) and strongly resonant, where small divisors appear and lead to O(1) corrections. A perturbation method based on Cole's two-timing procedure is introduced. It avoids the small divisor problem in a straightforward manner, gives accurate answers which are valid for long times, and appears capable of handling all three types of problems with no change in the basic approach.

One example of each type is studied with the aid of this procedure: for the nonresonant case the answer is equivalent to the Poincaré result; for the weakly resonant case the analytic form of the answer is found to depend (smoothly) on the difference between the initial energies of the two oscillators; for the strongly resonant case we find that the amplitudes of the two oscillators vary slowly with time as elliptic functions of ϵ t, where ϵ is the (small) coupling parameter.

Our results suggest that, as one might expect, the dynamical behavior of such systems varies smoothly with changes in the ratio of the fundamental frequencies of the two oscillators. Thus the pathological behavior of Whittaker's adelphic integrals as the frequency ratio is varied appears to be due to the fact that Whittaker ignored the small divisor problem. The energy sharing properties of these systems appear to depend strongly on the initial conditions, so that the systems not ergodic.

The perturbation procedure appears to be applicable to a wide variety of other problems in addition to those considered here.

Space-frequency coupling, conical waves, and small-scale filamentation in water

Numerical simulations of fs laser propagation in water have been made to explain the small-scale filaments in water we have observed by a nonlinear fluorescence technique. Some analytical descriptions combined with numerical simulations show that a space-frequency coupling mainly from the interplay among self-phase modulation, dispersion and phase mismatching will reshape the laser beam into a conical wave which plays a major role of energy redistribution and can prevent laser beam from self-guiding over a long distance. An effective group velocity dispersion is introduced to explain the pulse broadening and compression in the filamentation. (c) 2005 American Institute of Physics.

Seismic structure above and below the core-mantle boundary

Seismic structure above and below the core-mantle boundary (CMB) has been studied through use of travel time and waveform analyses of several different seismic wave groups. Anomalous systematic trends in observables document mantle heterogeneity on both large and small scales. Analog and digital data has been utilized, and in many cases the analog data has been optically scanned and digitized prior to analysis.

Differential travel times of S - SKS are shown to be an excellent diagnostic of anomalous lower mantle shear velocity (V s) structure. Wavepath geometries beneath the central Pacific exhibit large S- SKS travel time residuals (up to 10 sec), and are consistent with a large scale 0(1000 km) slower than average V_s region (≥3%). S - SKS times for paths traversing this region exhibit smaller scale patterns and trends 0(100 km) indicating V_s perturbations on many scale lengths. These times are compared to predictions of three tomographically derived aspherical models: MDLSH of Tanimoto [1990], model SH12_WM13 of Suet al. [1992], and model SH.10c.17 of Masters et al. [1992]. Qualitative agreement between the tomographic model predictions and observations is encouraging, varying from fair to good. However, inconsistencies are present and suggest anomalies in the lower mantle of scale length smaller than the present 2000+ km scale resolution of tomographic models. 2-D wave propagation experiments show the importance of inhomogeneous raypaths when considering lateral heterogeneities in the lowermost mantle.

A dataset of waveforms and differential travel times of S, ScS, and the arrival from the D" layer, Scd, provides evidence for a laterally varying V_s velocity discontinuity at the base of the mantle. Two different localized D" regions beneath the central Pacific have been investigated. Predictions from a model having a V_s discontinuity 180 km above the CMB agree well with observations for an eastern mid-Pacific CMB region. This thickness differs from V_s discontinuity thicknesses found in other regions, such as a localized region beneath the western Pacific, which average near 280 km. The "sharpness" of the V_s jump at the top of D", i.e., the depth range over which the V_s increase occurs, is not resolved by our data, and our data can in fact may be modeled equally well by a lower mantle with the increase in V_s at the top of D" occurring over a 100 krn depth range. It is difficult at present to correlate D" thicknesses from this study to overall lower mantle heterogeneity, due to uncertainties in the 3-D models, as well as poor coverage in maps of D" discontinuity thicknesses.

P-wave velocity structure (V_p) at the base of the mantle is explored using the seismic phases SKS and SPdKS. SPdKS is formed when SKS waves at distances around 107° are incident upon the CMB with a slowness that allows for coupling with diffracted P-waves at the base of the mantle. The P-wave diffraction occurs at both the SKS entrance and exit locations of the outer core. SP_dKS arrives slightly later in time than SKS, having a wave path through the mantle and core very close to SKS. The difference time between SKS and SP_dKS strongly depends on V_p at the base of the mantle near SK Score entrance and exit points. Observations from deep focus Fiji-Tonga events recorded by North American stations, and South American events recorded by European and Eurasian stations exhibit anomalously large SP_dKS - SKS difference times. SKS and the later arriving SP_dKS phase are separated by several seconds more than predictions made by 1-D reference models, such as the global average PREM [Dziewonski and Anderson, 1981] model. Models having a pronounced low-velocity zone (5%) in V_p in the bottom 50-100 km of the mantle predict the size of the observed SP_dK S-SKS anomalies. Raypath perturbations from lower mantle V_s structure may also be contributing to the observed anomalies.

Outer core structure is investigated using the family of SmKS (m=2,3,4) seismic waves. SmKS are waves that travel as S-waves in the mantle, P-waves in the core, and reflect (m-1) times on the underside of the CMB, and are well-suited for constraining outermost core V_p structure. This is due to closeness of the mantle paths and also the shallow depth range these waves travel in the outermost core. S3KS - S2KS and S4KS - S3KS differential travel times were measured using the cross-correlation method and compared to those from reflectivity synthetics created from core models of past studies. High quality recordings from a deep focus Java Sea event which sample the outer core beneath the northern Pacific, the Arctic, and northwestern North America (spanning 1/8th of the core's surface area), have SmKS wavepaths that traverse regions where lower mantle heterogeneity is pre- dieted small, and are well-modeled by the PREM core model, with possibly a small V_p decrease (1.5%) in the outermost 50 km of the core. Such a reduction implies chemical stratification in this 50 km zone, though this model feature is not uniquely resolved. Data having wave paths through areas of known D" heterogeneity (±2% and greater), such as the source-side of SmKS lower mantle paths from Fiji-Tonga to Eurasia and Africa, exhibit systematic SmKS differential time anomalies of up to several seconds. 2-D wave propagation experiments demonstrate how large scale lower mantle velocity perturbations can explain long wavelength behavior of such anomalous SmKS times. When improperly accounted for, lower mantle heterogeneity maps directly into core structure. Raypaths departing from homogeneity play an important role in producing SmKS anomalies. The existence of outermost core heterogeneity is difficult to resolve at present due to uncertainties in global lower mantle structure. Resolving a one-dimensional chemically stratified outermost core also remains difficult due to the same uncertainties. Restricting study to higher multiples of SmKS (m=2,3,4) can help reduce the affect of mantle heterogeneity due to the closeness of the mantle legs of the wavepaths. SmKS waves are ideal in providing additional information on the details of lower mantle heterogeneity.