A Study On Vortex Knots

In this thesis an attempt is made to study vortex knots based on the work of Keener . It is seen that certain mistakes have been crept in to the details of this paper. We have chosen this study for an investigation as it is the first attempt to study vortex knots. Other works had given attention to this. In chapter 2 we have considered these corrections in detail. In chapter 3 we have tried a simple extension by introducing vorticity in the evolution of vortex knots. In chapter 4 we have introduced a stress tensor related to vorticity. Chapter 5 is the general conclusion.Knot theory is a branch of topology and has been developed as an independent branch of study. It has wide applications and vortex knot is one of them. As pointed out earlier, most of the studies in fluid dynamics exploits the analogy between vorticity and magnetic induction in the case of MHD. But vorticity is more general than magnetic induction and so it is essential to discuss the special properties of vortex knots, independent of MHD flows. This is what is being done in this thesis.

Characteristics of ABL during active and weak phases of monsoon

Understanding of the Atmospheric Boundary Layer (ABL) is imperative in the arena of the monsoon field. Here, the features of the ABL are studied employing Conserved Variable Analysis (CVA) using equivalent potential temperature and humidity. In addition, virtual potential temperature and wind are used during active and weak phases of monsoon. The analysis is carried out utilising the radiosonde observations during the monsoon months for two stations situated in the west coast of India. All these parameters show considerable variations during active and weak monsoon phases in both the stations. The core speed and core height vary with these epochs. The core speed is found to be more than 38 knots in the active monsoon phase around 1.2 km over Trivandrum and around 2 km over Mangalore. But during weak monsoon phase the core wind speed is decreased and core height is elevated over both stations. The wind direction shows an additional along shore component during weak monsoon period. The Convective Boundary Layer (CBL) height shows increase during weak monsoon phase over both stations due to less cloudiness and subsequent insolation. The CBL height during the southwest monsoon is more over Mangalore and is attributed by the orographic lifting in the windward side of the Western Ghats while the influence of the Ghats is less over Trivandrum.

Modelling the warm H(2) infrared emission of the Helix nebula cometary knots

Molecular hydrogen emission is commonly observed in planetary nebulae. Images taken in infrared H(2) emission lines show that at least part of the molecular emission is produced inside the ionized region. In the best studied case, the Helix nebula, the H(2) emission is produced inside cometary knots (CKs), comet-shaped structures believed to be clumps of dense neutral gas embedded within the ionized gas. Most of the H(2) emission of the CKs seems to be produced in a thin layer between the ionized diffuse gas and the neutral material of the knot, in a mini-photodissociation region (mini-PDR). However, PDR models published so far cannot fully explain all the characteristics of the H(2) emission of the CKs. In this work, we use the photoionization code AANGABA to study the H(2) emission of the CKs, particularly that produced in the interface H(+)/H(0) of the knot, where a significant fraction of the H(2) 1-0 S(1) emission seems to be produced. Our results show that the production of molecular hydrogen in such a region may explain several characteristics of the observed emission, particularly the high excitation temperature of the H(2) infrared lines. We find that the temperature derived from H(2) observations, even of a single knot, will depend very strongly on the observed transitions, with much higher temperatures derived from excited levels. We also proposed that the separation between the H alpha and [N II] peak emission observed in the images of CKs may be an effect of the distance of the knot from the star, since for knots farther from the central star the [N II] line is produced closer to the border of the CK than H alpha.

Least squares splines with free knots: global optimization approach

Splines with free knots have been extensively studied in regard to calculating the optimal knot positions. The dependence of the accuracy of approximation on the knot distribution is highly nonlinear, and optimisation techniques face a difficult problem of multiple local minima. The domain of the problem is a simplex, which adds to the complexity. We have applied a recently developed cutting angle method of deterministic global optimisation, which allows one to solve a wide class of optimisation problems on a simplex. The results of the cutting angle method are subsequently improved by local discrete gradient method. The resulting algorithm is sufficiently fast and guarantees that the global minimum has been reached. The results of numerical experiments are presented.

Many routes lead to Rome : potential causes for the multi-route migration system of Red Knots, Calidris canutus islandica

Migrants, such as birds or representatives of other taxa, usually make use of several stopover sites to cover the distance between their site of origin and destination. Potentially, multiple routes exist, but often little is known about the causes and consequences of alternative migration routes. Apart from their geographical distribution, the suitability of potential sites might play an important role in the animals’ decisions for a particular itinerary. We used an optimal-migration model to test three nonmutually exclusive hypotheses leading to variations in the spring migration routes of a subspecies of Red Knot, Calidris canutus islandica, which migrates from wintering grounds in Western Europe to breeding grounds in Greenland and the Canadian Arctic: the breeding location hypothesis, the energy budget hypothesis, and the predation risk hypothesis. Varying only breeding location, the model predicted that birds breeding in the Canadian Arctic and on West Greenland stop over on Iceland, whereas birds breeding in East and Northeast Greenland migrate via northern Norway, a prediction that is supported by empirical findings. Energy budgets on stopover sites had a strong influence on the choice of route and staging times. Varying foraging-intensity and mass-dependent predation risk prompted the birds to use less risky sites, if possible. The effect of simultaneous changes in the energy budget and predation risk strongly depended on the site where these occurred. Our findings provide potential explanations for the observations that C. canutus islandica uses a diverse array of migration routes. Scrutinizing the three alternative driving forces for the choice of migratory routes awaits further, specific data collection in rapidly developing fields of research (e.g., predation risk assessment, GPS tracking). Generally, the type of modeling presented here may not only highlight alternative explanations, but also direct follow-up empirical research.

Do Red Knots (Calidris Canutus Islandica) routinely skip Iceland during southward migration?

Subspecies Calidris canutus islandica of the Red Knot breeds on the arctic tundra of northeastern Canada and northern Greenland and winters along the coasts of northwestern Europe. During northward migration, it stops over in either Iceland or northern Norway. It has been assumed that it does the same during southward migration. Using ratios of stable carbon isotopes (δ ¹³ C) in whole blood, blood cells, and plasma, we investigated evidence for a stopover in Iceland en route from the breeding grounds to the Dutch Wadden Sea. With the expected diet (shellfish) and stopover duration at Iceland (12-15 days, maximum 17 days) and the turnover rates of blood cells (15.1 days) and plasma (6.0 days), Red Knots that stopped in Iceland should arrive with a blood (cell) δ ¹³ C midway between a tundra (-24.7[per thousand]) and a marine value (-14.0[per thousand]) and a plasma δ¹³ C approaching the marine value (-15.3[per thousand]). However, many adults arriving at the Wadden Sea had δ¹³ C ratios in blood (cells) and plasma below these levels, and some arrived with clear tundra signals in blood cells, suggesting that they skipped Iceland during southward migration. Surprisingly, available data suggest this also to be true for juveniles during their first southward migration. The δ ¹³ C signature of second-year birds confirmed that they oversummered in the Wadden Sea. Our findings contradict the largely untested idea that juvenile shorebirds make more stopovers than adults as well as the idea that the migration between the Nearctic and Europe is necessarily a two-leg process.

Northward migration of Afro-Siberian Knots Calidris canutus canutus : high variability in Red Knot numbers visiting staging sites on the French Atlantic coast, 1979–2009

The Afro–Siberian Red Knot subspecies, Calidris canutus canutus, winters mainly on Banc d’Arguin, Mauritania, West Africa. An International Wader Study Group project carried out in 1979 suggested that during northward migration Red Knots cover their migration between the wintering grounds and the Siberian breeding grounds in two long-distance non-stop flights, stopping only in the Wadden Sea in Schleswig-Holstein, Germany. Each year Red Knots also visit staging sites along the French Atlantic coast in addition to the German Wadden Sea. Ever since 1979, the French staging sites have been counted on a regular basis and here we present the count data from these 30 years. In some years more than 20% of the population used the French Atlantic coast as a staging site, but numbers are highly variable from one year to the next. We suggest that high numbers in France might occur when birds have to stop short of the Wadden Sea because of head-winds and/or a lack of tail-winds en route from West Africa.

On 4 June 2008 Siberian Red Knots at Elbe Mouth kissed the canonical evening migration departure rule goodbye

Observations of departing Siberian-breeding Red Knots Calidris canutus canutus from their central staging site during northward migration, the Schleswig-Holstein Wadden Sea, Germany, in early June 2008, challenge the established notion that departing long-distance migrating waders only leave around sunset. During four days we scanned several thousand Red Knots for colour-ringed individuals and found a total of 20 different individuals that were previously ringed at either their main wintering site, the Banc d'Arguin in Mauritania, or at stopover sites on the Atlantic coast of France. Body masses of captured Red Knots in Schleswig-Holstein were higher than 200 g and hematocrite values showed an average of 58%, clearly indicating that they were ready for take-off. On all except one evening, we noted impressive departure movements during the incoming tide. On that exceptional evening a cold front thunderstorm passed over the area. Late the next morning, thousands of Red Knots departed during the incoming tide. We assume that the birds avoided taking off in adverse weather conditions and elaborate why Red Knots presumably traded off advantages from departing during twilight. We suggest that during spring migration, schedules are so tight that further delays decrease fitness, either because it would cause another full day of exposure to high predation risk by falcons, or because of conditions upon arrival on the tundra.

Stochastic atmospheric assistance and the use of emergency staging sites by migrants

Numerous animals move vast distances through media with stochastic dynamic properties. Avian migrants must cope with variable wind speeds and directions en route, which potentially jeopardize fine-tuned migration routes and itineraries. We show how unpredictable winds affect flight times and the use of an intermediate staging site by red knots (Calidris canutus canutus) migrating from west Africa to the central north Siberian breeding areas via the German Wadden Sea. A dynamic migration model incorporating wind conditions during flight shows that flight durations between Mauritania and the Wadden Sea vary between 2 and 8 days. The number of birds counted at the only known intermediate staging site on the French Atlantic coast was strongly positively correlated with simulated flight times. In addition, particularly light-weight birds occurred at this location. These independent results support the idea that stochastic wind conditions are the main driver of the use of this intermediate stopover site as an emergency staging area. Because of the ubiquity of stochastically varying media, we expect such emergency habitats to exist in many other migratory systems, both airborne and oceanic. Our model provides a tool to quantify the effect of winds and currents en route.

Exemplification and deconstructive writing: dancing with Massumi, Derrida, and others

I am experimenting with ‘exemplification’ (Massumi, 2002) and ‘deconstrucitve writing’ (Maclure, 2010) by applying them to selected data from research for my doctoral thesis. Central to both is the power of examples to expose detail and divergence that lead to new and different possibilities and connections. I have been inspired by Derrida’s (Maclure, 2003; Spitzer, 2011) notion of the fabric of a text with ‘tears’, ‘cuts’, ‘knots or aporias’. Therefore, I have created a fabric of text with tears and aporias: one that encourages readers to think and read doubly (Derrida, cited in Spitzer, 2011). I write in an ‘inattentive’ way (Massumi, 2002): juxtaposing examples (narratives) with the identities of the narrators, my responses to their narratives, and theoretical and other musings to play with the ambiguity of reality and identity. The interplay of inattention, exemplification, and deconstructive writing allows for interpretation, reinterpretation, affective responses, and new and different impressions and possibilities. My aim in writing this paper is threefold: (1) to explore the application of a Derridean perspective to some of my research, (2) to practise exemplification and deconstructive writing, and (3) to write in an inattentive and creative way.

Knots of relation

Array

Bending stiffness evaluation of Teca and Guajara lumber through tests of transverse and longitudinal vibration

The grading of structural lumber besides contributing for increasing the structure's safety, due to the reduction of the material variability, also allows its rational use. Due to the good correlation between strength and bending stiffness, the latter has been used in estimating the mechanical strength of lumber pieces since the 60's. For industrial application, there are equipment and techniques to evaluate the bending stiffness of lumber, through dynamic tests such as the longitudinal vibration technique, also known as stress wave, and the transverse vibration technique. This study investigated the application of these two techniques in the assessment of the modulus of elasticity in bending of Teca beams (Tectona grandis), from reforestation, and of the tropical species Guajara (Micropholis venulosa). The modulus of elasticity estimated by dynamic tests showed good correlation with the modulus measured in the static bending test. Meantime, we observed that the accuracy of the longitudinal vibration technique was significantly reduced in the evaluation of the bending stiffness of Teca pieces due to the knots existing in this species.

Magnetic susceptibility and electric conductivity of marine surficial sediments by benthic electromagnetic profiling

Distribution, accumulation and diagenesis of surficial sediments in coastal and continental shelf systems follow complex chains of localized processes and form deposits of great spatial variability. Given the environmental and economic relevance of ocean margins, there is growing need for innovative geophysical exploration methods to characterize seafloor sediments by more than acoustic properties. A newly conceptualized benthic profiling and data processing approach based on controlled source electromagnetic (CSEM) imaging permits to coevally quantify the magnetic susceptibility and the electric conductivity of shallow marine deposits. The two physical properties differ fundamentally insofar as magnetic susceptibility mostly assesses solid particle characteristics such as terrigenous or iron mineral content, redox state and contamination level, while electric conductivity primarily relates to the fluid-filled pore space and detects salinity, porosity and grain-size variations. We develop and validate a layered half-space inversion algorithm for submarine multifrequency CSEM with concentric sensor configuration. Guided by results of modeling, we modified a commercial land CSEM sensor for submarine application, which was mounted into a nonconductive and nonmagnetic bottom-towed sled. This benthic EM profiler Neridis II achieves 25 soundings/second at 3-4 knots over continuous profiles of up to hundred kilometers. Magnetic susceptibility is determined from the 75 Hz in-phase response (90% signal originates from the top 50 cm), while electric conductivity is derived from the 5 kHz out-of-phase (quadrature) component (90% signal from the top 92 cm). Exemplary survey data from the north-west Iberian margin underline the excellent sensitivity, functionality and robustness of the system in littoral (~0-50 m) and neritic (~50-300 m) environments. Susceptibility vs. porosity cross-plots successfully identify known lithofacies units and their transitions. All presently available data indicate an eminent potential of CSEM profiling for assessing the complex distribution of shallow marine surficial sediments and for revealing climatic, hydrodynamic, diagenetic and anthropogenic factors governing their formation.

Ichthyoplankton density and zooplankton biomass in the Benguela upwelling system during MSM17/3 in January and February 2011

Ichthyoplankton density (fish eggs and larvae) and bulk zooplankton biomass in January/February 2011 were determined for 38 stations in the northern Benguela upwelling system, based on oblique Multinet hauls during the FS Maria S. Merian MSM17/3 cruise. A HYDROBIOS Multinet, type Midi (0.25 m**2 mouth area) was equipped with five nets of 500 µm-mesh size, temperature and oxygen probes, and an inner and outer flow meter to monitor the net's trajectory (for volume filtered calculations) as well as net clogging. The Multinet was handled over the side, towed horizontally at 2 knots. Winch speed when fearing was 0.5 or 0.3 m/s, heaving velocity 0.2 - 0.3 m/s. The Multinet was towed obliquely at 38 stations sampling the upper 200 m of the water column, which were divided into five different depth strata after inspection of temperature and oxygen concentration depth profiles. Ichthyoplankton densities and zooplankton biomass were calculated for each depth stratum (=single net) from total abundance and the volume of water filtered [individuals per m**3 and g wet weight per m**3, respectively]. In addition, densities and biomass were integrated over the area for each station [individuals per m**2], as sum of calculations for each net: Sum ([individuals per m**3]*Delta (depth bot[m]-depth top [m]).