Statistical Fluid Mechanics: Dynamics Equations and Linear Response Theory

The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many macroscopically infinitely small (but microscopically large enough) mass elements with their motion only characterized by center-of-mass velocity. Here we provide a Statistical Mechanical approach to address fluid dynamics by considering statistical velocity distribution of discrete molecules within macroscopically infinitely small volume elements as well as their center-of-mass velocity. Dynamics equations governing the evolution of physical variables have been proposed, Green's functions have been obtained and linear response theory has been applied to study physical situations with external heat perturbation. It is found that the propagation of heat, center-of-mass motion and sound are intrinsically integrated in Statistical fluid dynamics. This work lays down the foundation for applications of Statistical fluid mechanics.Comment: Physics of Fluids, published. Dynamics equation in the diffusive regime is explained additionally from a microscopic picture of scatterin

IST Austria Thesis

The hippocampus is a key brain region for memory and notably for spatial memory, and is needed for both spatial working and reference memories. Hippocampal place cells selectively discharge in specific locations of the environment to form mnemonic represen tations of space. Several behavioral protocols have been designed to test spatial memory which requires the experimental subject to utilize working memory and reference memory. However, less is known about how these memory traces are presented in the hippo campus, especially considering tasks that require both spatial working and long -term reference memory demand. The aim of my thesis was to elucidate how spatial working memory, reference memory, and the combination of both are represented in the hippocampus. In this thesis, using a radial eight -arm maze, I examined how the combined demand on these memories influenced place cell assemblies while reference memories were partially updated by changing some of the reward- arms. This was contrasted with task varian ts requiring working or reference memories only. Reference memory update led to gradual place field shifts towards the rewards on the switched arms. Cells developed enhanced firing in passes between newly -rewarded arms as compared to those containing an unchanged reward. The working memory task did not show such gradual changes. Place assemblies on occasions replayed trajectories of the maze; at decision points the next arm choice was preferentially replayed in tasks needing reference memory while in the pure working memory task the previously visited arm was replayed. Hence trajectory replay only reflected the decision of the animal in tasks needing reference memory update. At the reward locations, in all three tasks outbound trajectories of the current arm were preferentially replayed, showing the animals’ next path to the center. At reward locations trajectories were replayed preferentially in reverse temporal order. Moreover, in the center reverse replay was seen in the working memory task but in the other tasks forward replay was seen. Hence, the direction of reactivation was determined by the goal locations so that part of the trajectory which was closer to the goal was reactivated later in an HSE while places further away from the goal were reactivated earlier. Altogether my work demonstrated that reference memory update triggers several levels of reorganization of the hippocampal cognitive map which are not seen in simpler working memory demand s. Moreover, hippocampus is likely to be involved in spatial decisions through reactivating planned trajectories when reference memory recall is required for such a decision

Modelling reactive transport processes in porous media

Reactive transport modelling has wide applications in geosciences. In the field of hydrogeology, it has been utilised to simulate the biogeochemical processes that disperse and degrade contaminants in the aquifer. For geotechnical applications, such as geological CO2 sequestration, the reaction of CO2 with the ambient saline aquifer determines the final success of storage. In a radioactive waste repository, scientists rely on reactive transport models to predict the mobilisation of hazardous radionuclides within space and time. In this work, the multi-component mass transport code OpenGeoSys, was coupled with two geochemical solvers, the Gibbs Energy Minimization Selektor (GEM) and the Biogeochemical Reaction Network Simulator (BRNS). Both coupled codes were verified against analytical solutions and simulation results from other numerical models. Moreover, the coupling interface was developed for parallel simulation. Test runs showed that the speed-up of reaction part had a very good linearity with number of nodes in the mesh. However, for three dimensional problems with complex geochemical reactions, the model performance was dominated by solving transport equations of mobile chemical components. OpenGeoSys-BRNS was applied to a two dimensional groundwater remediation problem. Its calculated concentration profiles fitted very well with analytical solutions and numerical results from TBC. The model revealed that natural attenuation of groundwater contaminants is mainly controlled by the mixing of carbon source and electron donor. OpenGeoSys-GEM was employed to investigate the retardation mechanism of radionuclides in the near field of a nuclear waste repository. Radium profiles in an idealised bentonite column was modelled with varying clay/water ratios. When clay content is limited, Ba-Sr-Ra sulfate solid solutions have a very strong retardation effect on the aqueous radium. Nevertheless, when clay mineral is abundant, cation exchange sites also attract Sr and Ba, thus dominates the transport of Ra

Towards low-cost gigabit wireless systems at 60 GHz

The world-wide availability of the huge amount of license-free spectral space in the 60 GHz band provides wide room for gigabit-per-second (Gb/s) wireless applications. A commercial (read: low-cost) 60-GHz transceiver will, however, provide limited system performance due to the stringent link budget and the substantial RF imperfections. The work presented in this thesis is intended to support the design of low-cost 60-GHz transceivers for Gb/s transmission over short distances (a few meters). Typical applications are the transfer of high-definition streaming video and high-speed download. The presented work comprises research into the characteristics of typical 60-GHz channels, the evaluation of the transmission quality as well as the development of suitable baseband algorithms. This can be summarized as follows. In the first part, the characteristics of the wave propagation at 60 GHz are charted out by means of channel measurements and ray-tracing simulations for both narrow-beam and omni-directional configurations. Both line-of-sight (LOS) and non-line-of-sight (NLOS) are considered. This study reveals that antennas that produce a narrow beam can be used to boost the received power by tens of dBs when compared with omnidirectional configurations. Meanwhile, the time-domain dispersion of the channel is reduced to the order of nanoseconds, which facilitates Gb/s data transmission over 60-GHz channels considerably. Besides the execution of measurements and simulations, the influence of antenna radiation patterns is analyzed theoretically. It is indicated to what extent the signal-to-noise ratio, Rician-K factor and channel dispersion are improved by application of narrow-beam antennas and to what extent these parameters will be influenced by beam pointing errors. From both experimental and analytical work it can be concluded that the problem of the stringent link-budget can be solved effectively by application of beam-steering techniques. The second part treats wideband transmission methods and relevant baseband algorithms. The considered schemes include orthogonal frequency division multiplexing (OFDM), multi-carrier code division multiple access (MC-CDMA) and single carrier with frequency-domain equalization (SC-FDE), which are promising candidates for Gb/s wireless transmission. In particular, the optimal linear equalization in the frei quency domain and associated implementation issues such as synchronization and channel estimation are examined. Bit error rate (BER) expressions are derived to evaluate the transmission performance. Besides the linear equalization techniques, a low-complexity inter-symbol interference cancellation technique is proposed to achieve much better performance of code-spreading systems such as MC-CDMA and SC-FDE. Both theoretical analysis and simulations demonstrate that the proposed scheme offers great advantages as regards both complexity and performance. This makes it particularly suitable for 60-GHz applications in multipath environments. The third part treats the influence of quantization and RF imperfections on the considered transmission methods in the context of 60-GHz radios. First, expressions for the BER are derived and the influence of nonlinear distortions caused by the digital-to-analog converters, analog-to-digital converters and power amplifiers on the BER performance is examined. Next, the BER performance under the influence of phase noise and IQ imbalance is evaluated for the case that digital compensation techniques are applied in the receiver as well as for the case that such techniques are not applied. Finally, a baseline design of a low-cost Gb/s 60-GHz transceiver is presented. It is shown that, by application of beam-steering in combination with SC-FDE without advanced channel coding, a data rate in the order of 2 Gb/s can be achieved over a distance of 10 meters in a typical NLOS indoor scenario