Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

The current distribution of signal and native crayfish in the Broadmead Brook, Wiltshire

Signal crayfish (Pacifastacus leniusculus) have existed in the upper reaches of Broadmead Brook in Wiltshire since 200 individuals were introduced at West Kington in 1981. The population has expanded upstream and downstream since this introduction, however, giving rise to concerns that it may potentially threaten the native crayfish population further downstream. Signal crayfish can act as a vector of crayfish plague - a disease caused by the fungus Aphanomyces astaci Schikora which results in almost complete mortality to the native, white-clawed crayfish Austropotamobius pallipes. The native crayfish in Broadmead Brook have not yet succumbed to crayfish plague and are currently free of the disease. However, as signal crayfish appear to out-compete the native species, the native population could still be under threat. In this article, we highlight the findings of previous crayfish surveys on Broadmead Brook and describe work undertaken in summer 2001 to map the current distribution of native and signal crayfish. Finally, options for controlling the spread of signal crayfish are discussed.

Storm track response to perturbations in climate

This thesis advances our understanding of midlatitude storm tracks and how they respond to perturbations in the climate system. The midlatitude storm tracks are regions of maximal turbulent kinetic energy in the atmosphere. Through them, the bulk of the atmospheric transport of energy, water vapor, and angular momentum occurs in midlatitudes. Therefore, they are important regulators of climate, controlling basic features such as the distribution of surface temperatures, precipitation, and winds in midlatitudes. Storm tracks are robustly projected to shift poleward in global-warming simulations with current climate models. Yet the reasons for this shift have remained unclear. Here we show that this shift occurs even in extremely idealized (but still three-dimensional) simulations of dry atmospheres. We use these simulations to develop an understanding of the processes responsible for the shift and develop a conceptual model that accounts for it.

We demonstrate that changes in the convective static stability in the deep tropics alone can drive remote shifts in the midlatitude storm tracks. Through simulations with a dry idealized general circulation model (GCM), midlatitude storm tracks are shown to be located where the mean available potential energy (MAPE, a measure of the potential energy available to be converted into kinetic energy) is maximal. As the climate varies, even if only driven by tropical static stability changes, the MAPE maximum shifts primarily because of shifts of the maximum of near-surface meridional temperature gradients. The temperature gradients shift in response to changes in the width of the tropical Hadley circulation, whose width is affected by the tropical static stability. Storm tracks generally shift in tandem with shifts of the subtropical terminus of the Hadley circulation.

We develop a one-dimensional diffusive energy-balance model that links changes in the Hadley circulation to midlatitude temperature gradients and so to the storm tracks. It is the first conceptual model to incorporate a dynamical coupling between the tropical Hadley circulation and midlatitude turbulent energy transport. Numerical and analytical solutions of the model elucidate the circumstances of when and how the storm tracks shift in tandem with the terminus of the Hadley circulation. They illustrate how an increase of only the convective static stability in the deep tropics can lead to an expansion of the Hadley circulation and a poleward shift of storm tracks.

The simulations with the idealized GCM and the conceptual energy-balance model demonstrate a clear link between Hadley circulation dynamics and midlatitude storm track position. With the help of the hierarchy of models presented in this thesis, we obtain a closed theory of storm track shifts in dry climates. The relevance of this theory for more realistic moist climates is discussed.

Contribution to the biology and geographical distribution of Aegagropila sauteri (Nees) Kutz. [Translation of: Gidrobiologicheskie Zhurnal, Kiev 4(3), 68-69, 1967]

Aegagropila sauteri is a peculiar green algae, the branched thalli of which, according to the amount of growth, forms velvety spheres of a diameter of 3-4, sometimes to 5-6 cm. and bigger. Investigators attribute it to a special genus of green algae. The authors examine Aegagropila sauteri in Lake Markakol (Kazakhstan).

On distribution of pollen in lakes. [Translation from: Palynology in geological research in the Baltic Soviet Republics p113-119. Vilnius, 1973.]

Systematic investigations of the distribution of pollen in stationary water bodies until now have hardly been conducted. For clarification of the problem of how the pollen of different plants which falls into a lake is deposited in relation to its physical properties, the character of the lake, wind currents and other factors, pollen analyses were carried out of surface samples of the bottom sediments of 13 Lithuanian lakes. Lakes were selected of different sizes (areas from 2333 ha. to 8 ha.) and different depths, not uniformly overgrown, situated in different physico-geographic regions of Lithuania. As a result of the investigation, it was established that in the surface layer of the sediments of the lakes of Lithuania pollen of woody species predominates.

On the problem of the distribution of Acanthocyclops viridis Jurine in the Rybinsk reservoir. [Translation from: Byulleten' Institute Biologii Vodokhranilishch 1958(1), 36-39, 1958. ]

Observations of individual weight, duration of development and production of different stages of Tropodiaptomus incognitus are presented. The study is based on data gathered from Lake Chad in 1968.

The vertical distribution of zooplankton in the Goggausee (the influence of algae and Chaoborus flavicans) [Translation from: Carinthia II 166/186 373-385, 1976]

The Goggausee, a small, shallow, meromictic lake(700m long, 150m wide, max. depth=12m, mean depth=6m), was the site of a week long study (19-26 May 1974) of the limnology department of the University of Vienna. The study comprised pollen analysis and palaeolimnological studies on the one hand, as well as a stock- taking of physiochemical factors, primary production, bacteria, zooplankton, zoo benthos and fish on the other. This paper studies the zooplankton of the lake. The Goggausee is a meromictic lake, with its anoxic deep water, that restricts the vertical distribution of most zooplankton. The aim of the study was to pursue the vertical distribution of the rotifers and Crustacea. Density of individuals, biomass, percentages of zooplankton together and crustaceans and rotifers as groups. Special consideration is given to the the Dipteran Chaoborus flavicans.

Observations on the distribution, daytime migrations and daily food intake rates of Chaoborus flavicans (Meigen) in the Goggausee [Translation from: Carinthia II 165(85), 184-190, 1975]

The Goggausee, in spite of its modest depth (Zmax = 12 metres), shows meromictic properties: autumn and spring circulation extend only to a depth of 8 metres. The water layers below about 10 metres are constantly oxygen-free, the critical zone with at least intermittent oxygen loss lies at a depth of between 6 and 10 metres. A limnological excursion in May 1974 offered an opportunity to investigate the daily vertical migration of the species Chaoborus flavicans with reference to its food supply of zooplankton as well as the chance to carry out some preliminary experiments on its rate of food intake. Among the studied features were the planktonic depth distribution of Chaoborus flavicans and the food intake of Chaoborus larvae under experimental conditions.

Distribution and abundance of fish stocks in Lake Victoria, Tanzania

Trawl surveys to assess the stocks of Lake Victoria for estimates of biomass and yield, together with the establishment of exploitation patterns, are being undertaken under the Lake victoria Fisheries Research Project. Preliminary surveys to establish the sampling stations and strategy were carried out between October 1997 and February 1998. Three cruises to cover the whole of the Tanzanian waters were undertaken with a total of 133 sampling stations. Data on catch rates, species composition and distribution were collected.

Relative abundance and distribution of fish in Kenyan waters of Lake Victoria

Bottom trawl surveys were conducted in Kenyan waters of Lake Victoria during the period September 1997 and March 1999. The means of fish biomass for the two most important species: Lates niloticus (L.) and Oreochromis niloticus (L.) were estimated at 61.5 kg ha and 4.5 kg ha respectively. There were few L. niloticus greater than 80 cm TL and O. niloticus greater than 50 cm TL, though these species attain maximum sizes of 205 cm and 65 cm respectively. Oreochromis niloticus was mostly found shallower than 5 m though some specimens were encountered deeper than 10 m, suggesting that the species has extended its ecological range. Very low catches were obtained from areas under water hyacinth cover. Water in such areas was turbid with oxygen levels below the critical 3.0 mg L.

The complex angular momentum theory of the production of three particles in collisions of two strongly interacting particles at high energy

The problem of the continuation to complex values of the angular momentum of the partial wave amplitude is examined for the simplest production process, that of two particles → three particles. The presence of so-called "anomalous singularities" complicates the procedure followed relative to that used for quasi two-body scattering amplitudes. The anomalous singularities are shown to lead to exchange degenerate amplitudes with possible poles in much the same way as "normal" singularities lead to the usual signatured amplitudes. The resulting exchange-degenerate trajectories would also be expected to occur in two-body amplitudes.

The representation of the production amplitude in terms of the singularities of the partial wave amplitude is then developed and applied to the high energy region, with attention being paid to the emergence of "double Regge" terms. Certain new results are obtained for the behavior of the amplitude at zero momentum transfer, and some predictions of polarization and minima in momentum transfer distributions are made. A calculation of the polarization of the ρ^o meson in the reaction π ^- p → π ^- ρ^op at high energy with small momentum transfer to the proton is compared with data taken at 25 Gev by W. D. Walker and collaborators. The result is favorable, although limited by the statistics of the available data.

Studies on the submerged plant community in Lake Biwa. I. Distribution and productivity of Egeria densa. A submerged plant invader in the south basin [Translation from: Physiol.Ecol.Japan 17, 283-290, 1976]

Egeria densa (PLANCH.) ST. JOHN, a submerged plant invader, forms a wide submerged plant zone, particularly along the west coast of the south basin, Lake Biwa. The macrophyte occupies over 82% of the plant zone in the basin and its biomass reaches 93% of the total. The estimated annual net production was approximately 1 kg dry wt./m2 in a dense area, which is about 4.5 times as much as the net production by phytoplankton in an offshore area of the basin. Although the area covered by the macrophyte is only 5.8% of the total of the basin, it produced about one-tenth of the total annual primary production. In the most productive season Egeria produced 46% of the total primary productivity. Thus, the macrophyte never be neglected when one considers the energy flow or material circulation in the basin. This study was initiated in order to clarify the role of submerged macrophytes, particularly E. densa, in Lake Biwa. The following points are reported in this paper: the distribution of macrophytes in the south basin; seasonal change in standing crop of E. densa; seasonal change in values related to production, utilizing a model proposed by Ikushima with its parameters experimentally determined.