Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Characterization of geothermal reservoirs’ parameters by inverse problem resolution and geostatistical simulations

BTES (borehole thermal energy storage)systems exchange thermal energy by conduction with the surrounding ground through borehole materials. The spatial variability of the geological properties and the space-time variability of hydrogeological conditions affect the real power rate of heat exchangers and, consequently, the amount of energy extracted from / injected into the ground. For this reason, it is not an easy task to identify the underground thermal properties to use when designing. At the current state of technology, Thermal Response Test (TRT) is the in situ test for the characterization of ground thermal properties with the higher degree of accuracy, but it doesn’t fully solve the problem of characterizing the thermal properties of a shallow geothermal reservoir, simply because it characterizes only the neighborhood of the heat exchanger at hand and only for the test duration. Different analytical and numerical models exist for the characterization of shallow geothermal reservoir, but they are still inadequate and not exhaustive: more sophisticated models must be taken into account and a geostatistical approach is needed to tackle natural variability and estimates uncertainty. The approach adopted for reservoir characterization is the “inverse problem”, typical of oil&gas field analysis. Similarly, we create different realizations of thermal properties by direct sequential simulation and we find the best one fitting real production data (fluid temperature along time). The software used to develop heat production simulation is FEFLOW 5.4 (Finite Element subsurface FLOW system). A geostatistical reservoir model has been set up based on literature thermal properties data and spatial variability hypotheses, and a real TRT has been tested. Then we analyzed and used as well two other codes (SA-Geotherm and FV-Geotherm) which are two implementation of the same numerical model of FEFLOW (Al-Khoury model).

Bowel function remains subjectively unchanged after ileal resection for construction of continent ileal reservoirs

Construction of a continent catheterizable urinary reservoir or an orthotopic bladder substitute requires substantial bowel resection, which can cause changes in bowel transit time. The reported incidence of chronic diarrhea after ileocecal resection is about 20%. Studies assessing bowel function after resection of 55-60 cm of ileum without compromising the ileocecal valve are scarce, and long-term results have not been reported.

A STUDY OF ILLNESS AND RESERVOIRS ASSOCIATED WITH GIARDIA LAMBLIA IN RURAL EGYPT

A longitudinal investigation of the health effects and reservoirs of Giardia lamblia was undertaken in forty households located in a rural Nile Delta region of Egypt. Stool specimens obtained once weekly for six months from two to four year old children were cyst or trophozoite-positive in 42 percent of the 724 examined. The mean duration of excretion in all but one Giardia-negative child was seven and one-half weeks with a range of one to 17 weeks. Clinical symptoms of illness were frequently observed within a month before or after Giardia excretion in stool of children, but a statistical inference of association was not demonstrated.^ Seventeen percent of 697 specimens obtained from their mothers was Giardia-positive for a mean duration of four weeks and a range of one to 18 weeks. Mothers were observed to excrete Giardia in stool less frequently during pregnancy than during lactation.^ Nine hundred sixty-two specimens were collected from 13 species of household livestock. Giardia was detected in a total of 22 specimens from cows, goats, sheep and one duck. Giardia cysts were detected in three of 899 samples of household drinking water.^ An ELISA technique of Giardia detection in human and animal stool was field tested under variable environmental conditions. The overall sensitivity of the assay of human specimens was 74 percent and specificity was 97 percent. These values for assay of animal specimens were 82 percent and 98 percent, respectively.^ Surface antigen studies reported from the NIH Laboratory of Parasitic Diseases show that antigens of three Egyptian human isolates are different from each other and from most other isolates against which they were tested.^ The ubiquity of human and animal fecal contamination combined with estimates of ill days per child per year in this setting are substantial arguments for the introduction of a suggested mass parasite control program to intervene in the cyclical transmission of agents of enteric disease. ^

Long-term environmental time series of continuously collected data in hydroelectric reservoirs in Brazil

Long-term environmental time series of continuously collected data are fundamental to identify and classify pulses and determine their role in aquatic systems. This paper presents a web based archive for limnological and meteorological data collected by integrated system for environmental monitoring (SIMA). The environmental parameters that are measured by SIMA are: chlorophyll-a (µg/L), water surface temperature (ºC), water column temperature by a thermistor string (ºC), turbidity (NTU), pH, dissolved oxygen concentration (mg/L), electric conductivity (µS/cm), wind speed (m/s) and direction (º), relative humidity (%), short wave radiation (W/m**2), barometric pressure (hPa). The data are collected in preprogrammed time interval (1 hour) and are transmitted by satellite in quasi-real time for any user in a range of 2500 km from the acquisition point. So far 11 hydroelectric reservoirs being monitored using the SIMA buoy. A basic statistics (mean and standard deviation) for some parameters and an example of time series were displayed. The main observed problem are divided into sensors and satellite. The sensors problems is due to the environmental characteristics of each water body. In acid waters the sensors of water quality rapidly degrade, and the collected data are invalid. Another problem is the infestation of periphyton in the sensor. SIMA buoy makes the parameters readings every hour, or 24 readings per day. However, not always received all readings because the system requires satellites passing over the buoy antenna to complete the transfer and due to the satellite constellation position, some locations inland are not met as often as necessary to complete all transmissions. This is the more often causes for lack in the time series.

Contribution of re-regulation reservoirs considering pumping capability to environmentally friendly hydropower operation

Environmental constraints imposed on hydropoweroperation are usually given in the form of minimum environmental flows and maximum and minimum rates of change of flows, or ramp rates. One solution proposed to mitigate the environmental impact caused by the flows discharged by a hydropower plant while reducing the economic impact of the above-mentioned constraints consists in building a re-regulationreservoir, or afterbay, downstream of the power plant. Adding pumpingcapability between the re-regulationreservoir and the main one could contribute both to reducing the size of the re-regulationreservoir, with the consequent environmental improvement, and to improving the economic feasibility of the project, always fulfilling the environmental constraints imposed to hydropoweroperation. The objective of this paper is studying the contribution of a re-regulationreservoir to fulfilling the environmental constraints while reducing the economic impact of said constraints. For that purpose, a revenue-driven optimization model based on mixed integer linear programming is used. Additionally, the advantages of adding pumpingcapability are analysed. In order to illustrate the applicability of the methodology, a case study based on a real hydropower plant is presented

Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs

We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (mesoreservoir). The mesoreservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. As an example, we study transport in monoatomic and diatomic chains of noninteracting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.

Current in coherent quantum systems connected to mesoscopic Fermi reservoirs

We study particle current in a recently proposed model for coherent quantum transport. In this model, a system connected to mesoscopic Fermi reservoirs (meso-reservoir) is driven out of equilibrium by the action of super-reservoirs thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation. We compare exact (numerical) results with theoretical expectations based on the Landauer formula.

Particle and energy transport in quantum disordered and quasi-periodic chains connected to mesoscopic Fermi reservoirs

We study a model of nonequilibrium quantum transport of particles and energy in a many-body system connected to mesoscopic Fermi reservoirs (the so-called meso-reservoirs). We discuss the conservation laws of particles and energy within our setup as well as the transport properties of quasi-periodic and disordered chains.