Prediction of compliant wall drag reduction, part 1

Computer codes developed to test Bushnell's compliant wall drag reduction model are discussed. One code computes the evolution of mean velocity profiles during the period between bursts as forced by an imposed large-scale pressure pulse due to earlier bursts. Another code computes the local stability characteristics of these computed profiles. The programs use Chebyshev polynomials to resolve the normal boundary layer (y) direction and a staggered grid of mesh points to resolve the x direction. Typically, 257 grid points and 33 Chebyshev polynomials are used in the computations

Prediction of compliant wall drag reduction, part 2

A numerical model of turbulent boundary layer flows over compliant walls was investigated. The model is based on Burton's observation that outer flow structures in turbulent boundary layers produce large scale pressure fluctuations near the wall. The results of calculations indicate that certain small wavelength wall motions can have a significant effect upon the stability of turbulent boundary layers

Stability analysis for laminar flow control, part 2

Topics covered include: (1) optimization of the numerics of the SALLY stability analysis code; (2) relation between temporal and spatial stability theory; (3) compressible flow stability calculations; (4) spectral methods for the boundary layer equations; and (5) numerical study of nonlinear, nonparallel stability of incompressible flows

Current and entanglement in a Bose-Hubbard lattice

We study the generation of entanglement for interacting cold atoms in an optical lattice. The entanglement is generated by managing the interaction between two distinct atomic species. It is found that the current of one of the species can be used as a good indicator of entanglement generation. The thermalization process between the species is also shown to be closely related to the evolution of the current.Comment: 10 pages, 5 figure

Numerical studies of laminar and turbulent drag reduction

Two-dimensional incompressible flow over wavy surfaces is studied numerically by spectral methods. Turbulence effects are modeled. Results for symmetric and asymmetric wave forms are presented. Effect of propagating surface waves on drag reduction is studied. Comparisons between computer simulations and experimental results are made

Drag reduction effects in turbulent boundary layers over wavy walls

Two dimensional incompressible flow over wavy surfaces are analyzed numerically by spectral methods. Algorithms for periodic flows (Fourier modes in the periodic flow direction and Chebycheff modes in the normal direction), and inflow-outflow boundary conditions (Chebycheff modes used in both directions) are described. Results obtained using both codes are reported for laminar flows. Comparisons with known theoretical and experimental results are made

Numerical studies of laminar and turbulent drag reduction, part 2

The flow over wave shaped surfaces is studied using a Navier Stokes solver. Detailed comparisons with theoretical results are presented, including the stability of a laminar flow over wavy surfaces. Drag characteristics of nonplanar surfaces are predicted using the Navier-Stokes solver. The secondary instabilities of wall bounded and free shear flows are also discussed

Stability analysis for laminar flow control, part 1

The basic equations for the stability analysis of flow over three dimensional swept wings are developed and numerical methods for their solution are surveyed. The equations for nonlinear stability analysis of three dimensional disturbances in compressible, three dimensional, nonparallel flows are given. Efficient and accurate numerical methods for the solution of the equations of stability theory were surveyed and analyzed

Relaxation dynamics of an exactly solvable electron-phonon model

We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a stationary density matrix. Two initial nonequilibrium situations are considered. A sudden quench of the electron-phonon coupling, starting from the noninteracting canonical equilibrium at temperature T in the electron as well as in the phonon subsystems, leads to a rather simple dynamics. A richer time evolution emerges if the initial state is taken as the product of the phonon vacuum and the filled Fermi sea supplemented by a highly excited additional electron. Our model has a natural set of constants of motion, with as many elements as degrees of freedom. In accordance with earlier studies of such type of models we find that expectation values which become stationary can be described by the density matrix of a generalized Gibbs ensemble which differs from that of a canonical ensemble. For the model at hand it appears to be evident that the eigenmode occupancy operators should be used in the construction of the stationary density matrix.Comment: 15 pages, 11 figures, published versio

Quantum theory of a two-mode open-cavity laser

We develop the quantum theory of an open-cavity laser assuming that only two modes compete for gain. We show that the modes interact to build up a collective mode that becomes the lasing mode when pumping exceeds a threshold. This collective mode exhibits all the features of a typical laser mode, whereas its precise behavior depends explicitly on the openness of the cavity. We approach the problem by using the density-matrix formalism and derive the master equation for the light field. Our results are of particular interest in the context random laser systems.Comment: 20 pages, 5 figure