Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1994. / Vita. Abstract. Includes bibliographical references (leaves 105-107). Also available via the Internet.

Measurements of the turbulent flow field through a highly staggered cascade propulsor configuration in the Virginia Tech cascade wind tunnel have been taken. Predictions of the same flow using Rapid Distortion Theory (RDT) were performed. Measurements and predictions were compared. The comparison was oriented to check the aptness of RDT in describing this kind of flow. Since this study represents the initial steps of a major project, the RDT model was kept simple. The non-penetration condition (blade blocking effect) was not modeled and the viscous effects were roughly accounted for. This work reveals the capabilities of RDT in predicting the development of turbulence convected through a highly staggered cascade propulsor configuration formed by non-symmetrical airfoils. This present study was possible thank to the support from the Office of Naval Research, in particular Candace Wark and Pat Purtell, under grant number NAG 00014-99-1-0230. / Master of Science

Thesis (M.Sc.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2008/05/29). Includes bibliographical references.

Rapid distortion theory (RDT) is applied to compressible ideal-gas turbulence subjected to homogeneous shear flow. The study examines the linear or rapid processes present in turbulence evolution. Specific areas of investigation include:(i) characterization of the multi-stage flow behavior,(ii) changing role of pressure in the three-regime evolution and (iii) influence of thermodynamic fluctuations on the different regimes. Preliminary investigations utilizing the more accurate Favre-averaged RDT approach show promise however, this approach requires careful validation and testing. In this study the Favre-averaged RDT approach is validated against Direct Numerical Simulation (DNS) and Reynolds-averaged RDT results. The three-stage growth of the flow field statistics is first confirmed. The three regime evolution of turbulence is then examined in three different timescales and the physics associated with each regime is discussed in depth. The changing role of pressure in compressible turbulence evolution shows three distinct stages. The physics of each stage is clearly explained. Next, the influence of initial velocity and thermodynamic fluctuations on the flow field are investigated. The evolution of turbulence is shown to be strongly dependent on the initial gradient Mach number and initial temperature fluctuations which tend to delay the onset of the second regime of evolution. The initial turbulent Mach number, which quantifies velocity fluctuations in the flow, influences turbulence evolution only weakly. Comparison of Reynolds-averaged RDT against Favre-averaged RDT for simulations of nonzero initial flow field fluctuations shows the higher fidelity of the latter approach.

The objective of the thesis is to characterize the linear and nonlinear aspects of inertial and pressure effects in turbulent flows. In the first part of the study, computations of Navier-Stokes and 3D Burgers equations are performed in the rapid distortion (RD) limit to analyze the inviscid linear processes in homogeneous turbulence. By contrasting the results of Navier- Stokes RD equations and Burgers RD equations, the effect of pressure can be isolated. The evolution of turbulent kinetic energy and anisotropy components and invariants are examined. In the second part of the thesis, the velocity gradient dynamics in turbulent flows are studied with the help of inviscid 3D Burgers equations and restricted Euler equations. The analytical asymptotic solutions of velocity gradient tensor are obtained for both Burgers and restricted Euler equations. Numerical computations are also performed to identify the stable solutions. The results are compared and contrasted to identify the effect of pressure on nonlinear velocity gradient dynamics. Of particular interest are the sign of the intermediate principle strain-rate and tendency of vorticity to align with the intermediate principle strain-rate. These aspects of velocity gradients provide valuable insight into the role of pressure in the energy cascade process.

Compressible ideal-gas turbulence subjected to homogeneous shear is investigated at the rapid distortion limit. Specific issues addressed are (i) the interaction between kinetic and internal energies and role of pressure-dilatation; (ii) the modifications to pressure-strain correlation and Reynolds stress anisotropy and (iii) the effect of the composition of velocity fluctuations (solenoidal vs. dilatational). Turbulence evolution is found to be strongly influenced by gradient Mach number, the initial solenoidal-to-dilatational ratio of the velocity field and the initial intensity of the thermodynamic fluctuations. The balance between the initial fluctuations in velocity and thermodynamic variables is also found to be very important. Any imbalance in the two fluctuating fields leads to high levels of pressure-dilatation and intense exchange. For a given initial condition, it is found that the interaction via the pressuredilatation term between the momentum and energy equations reaches a peak at an intermediate gradient Mach number. The energy exchange between internal and kinetic modes is negligible at very high or very low Mach number values due to lack of pressure dilatation. When present, the exchange exhibits oscillations even as the sum of the two energies evolves smoothly. The interaction between shear and solenoidal initial velocity field generates dilatational fluctuations; for some intermediate levels of shear Mach number dilatational fluctuations account for 20% of the total fluctuations. Similarly, the interaction between shear and initial dilatation produces solenoidal oscillations. Somewhat surprisingly, the generation of solenoidal fluctuations increases with gradient Mach number. Larger levels of pressure-strain correlation are seen with dilatational rather than solenoidal initial conditions. Anisotropies of solenoidal and dilatational components are investigated individually. The most interesting observation is that solenoidal and dilatational turbulence tend toward a one componential state but the energetic component is different in each case. As in incompressible shear flows, with solenoidal fluctuations, the streamwise (1,1) component of Reynolds stress is dominant. With dilatational fluctuations, the stream-normal (2,2) component is the strongest. Overall, the study yields valuable insight into the linear processes in high Mach number shear flows and identifies important closure modeling issues.

M. Tech. Electrical Engineering. / This study proposes a distributive joint power and rate adaptation algorithm (JRPA) in ad hoc networks based on coupled interference minimisation. In the proposed method, the influence of coupled interference was controlled by dynamically adjusting network users' transmit power choices. The users are therefore aware of the current link status while determining their data rates. In addition, every maximize utility of other users as it maximizes its utility due to the inevitable cooperation, hence, improving a collective network performance. Solving this network utility maximization problem results in a supermodular game equivalence where users cooperate to maximise both local and global utility, hence the supermodular game theory concept was used to analyse the optimality and convergence of the proposed solution.

We consider the asymptotic minimum rate under the logarithmic loss distortion constraint. More specifically, we find the asymptotic minimum rate expression when given distortions get close to 0. The problem under consideration is separate encoding and joint decoding of correlated two information sources, subject to a logarithmic loss distortion constraint. We introduce a test channel, whose transition probability (conditional probability mass function) captures the encoding and decoding process. Firstly, we find the expression for the special case of doubly symmetric binary sources with binary-output test channels. Then the result is extended to the case where the test channels are arbitrary. When given distortions get close to 0, the asymptotic rate coincides with that for the aforementioned special case. Finally, we consider the general case and show that the key findings for the special case continue to hold. / Thesis / Master of Applied Science (MASc)

It is known that transform techniques do not represent an optimal way in which to code a signal in terms of theoretical rate distortion bounds. A signal may be coded more efficiently if side information is included with the signal during transmission. This side information can then be used to reconstruct the image at some later time. In this thesis, the type of transform coding used is Multiple Bases Representation (MBR). This coding scheme is known to perform better than transform coding that uses a single basis. The method of Projection Onto Convex Sets (POCS) is used to reconstruct an approximation to the MBR signal using the side information. Thus, any number of constraints may be used as long as they form closed and convex sets and the side information is a priori knowledge required to implement projections onto the defined closed and convex sets. Several closed and convex sets are examined including the MBR, positivity, sign, zero crossing, minimum increase, and minimum decrease constraints. Constraints that tend to limit energy are not as effective as constraints that introduce energy into the signal especially when the observed image is used as the initialization vector. When a different initialization vector is used, the POCS reconstruction performs considerably better. Two initialization vectors are proposed; the observed signal plus white noise and the observed signal plus a constant. The performance of POCS with initialization by the observed signal plus a constant is superior to that when using the observed signal only. One nonconvex constraint is considered. The Laplacian histogram constraint requires other convex constraints to help ensure convergence of the reconstruction algorithm, but produces good quality images. / Master of Science

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1980. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by Demosthenis Teneketzis. / Ph.D.