No description available.

No description available.

In this work, the lattice Boltzmann method (LBM) was validated for direct numerical simulation (DNS) of wall-bounded turbulent flows. The LBM is a discrete-particle-based method that numerically solves the Boltzmann equation as opposed to conventional DNS methods that are based on the Navier-Stokes (NS) equations. The advantages of the LBM are its simple implementation, its ability to handle complex geometries, and its scalability on modern high-performance computers. An LBM code was developed and used to simulate fully-developed turbulent channel flow. In order to validate the results, the turbulence statistics were compared to those calculated from a conventional NS-based finite difference (FD) simulation. In the present study, special care was taken to make sure the computational domains for LBM and FD simulations were the same. Similar validation studies in the literature have used LBM simulations with smaller computational domains in order to reduce the computational cost. However, reducing the size of the computational domain affects the turbulence statistics and confounds the results of the validation. The turbulence statistics calculated from the LBM and FD simulations were found to agree qualitatively; however, there were several significant deviations, particularly in the variance profiles. The largest discrepancy was in the variance of the pressure fluctuations, which differed by approximately 7%. Given that both the LBM and FD simulations resolved the full range of turbulent scales and no models were used, this error was deemed to be significant. The cause of the discrepancy in the pressure variance was found to be the compressibility of the LBM. The LBM allows the density to vary, while the FD method does not since it solves the incompressible form of the NS equations. The effect of the compressibility could be reduced by lowering the Mach number, but this would come at the cost of significantly increasing the computational cost. Therefore, the conclusion of this work is that, while the LBM is capable of producing accurate solutions for incompressible turbulent flows, it is significantly more expensive than conventional methods for simple wall-bounded turbulent flows. / Thesis (Ph.D, Mechanical and Materials Engineering) -- Queen's University, 2011-09-15 23:24:09.968

No abstract available. / Thesis (M.Sc.)-University of Natal, Westville, 1995

No description available.

This thesis presents an improved method to calculate renormalization constants in a regularization invariant momentum scheme using twisted boundary conditions. This enables us to simulate with momenta of arbitrary magnitude and a fixed direction. With this new technique, together with non-exceptional kinematics and volume sources, we are able to take a statistically and theoretically precise continuum limit. Thereafter, all the running of the operators with momentum scale is due to their anomalous dimension. We use this to develop a practical scheme for step scaling with off shell vertex functions. We develop the method on 16³ × 32 lattices to show the practicality of using small volume simulations to step scale to high momenta. We also use larger 24³×64 and 32³×64 lattices to compute renormalization constants very accurately. Combining these with previous analyses we are able to extract a precise value for the light and strange quark masses and the neutral kaon mixing parameter BK. We also analyse eigenvectors of the domain wall Dirac matrix. We develop a practical and cost effective way to compute eigenvectors using the implicitly restarted Lanczos method with Chebyshev acceleration. We show that calculating eigenvectors to accelerate propagator inversions is cost effective when as few as one or two propagators are required. We investigate the technique of low mode averaging (LMA) with eigenvectors of the domain wall matrix for the first time. We find that for low energy correlators, pions for example, LMA is very effective at reducing the statistical noise. We also calculated the η and η′ meson masses, which required evaluating disconnected correlation functions and combining stochastic sources with LMA.

The advances in additive manufacturing removed most of the limitations that were once stopping designers when it comes to the manufacturability of the design. It allowed designers to produce parts with high geometric complexity such as cellular structures. These structures are known for their high strength relative to their low mass, good energy absorption, and high thermal and acoustic insulation compared to their relative solid counter-parts. Lattice structures, a type of cellular structures, have received considerable attention due to their properties when producing light-weight with high strength parts. The design of these structures can pose a challenge to designers due to the sheer number of variables that are present. Traditional optimization approaches become an infeasible approach for designing them, which motivated researchers to search for other alternative approaches. In this research, a new method is proposed by utilizing the material density information obtained from the topology optimization of continuum structures. The efficacy of the developed method will be compared to existing methods, such as the Size Matching and Scaling (SMS) method that combines solid-body analysis and a predefined unit-cell library. The proposed method shows good potential in structures that are subjected to multiple loading conditions compared to SMS, which would be advantageous in creating reliable structures. In order to demonstrate the applicability of the proposed method to practical engineering applications, the design problem of a commercial elevator sling will be considered.

The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most widely known and widely used public-key cryptosystem in the world today. Compared to other public-key cryptosystems, such as elliptic curve cryptography, RSA requires longer keylengths and is computationally more expensive. In order to address these shortcomings, many variants of RSA have been proposed over the years. While the security of RSA has been well studied since it was proposed in 1977, many of these variants have not. In this thesis, we investigate the security of five of these variants of RSA. In particular, we provide detailed analyses of the best known algebraic attacks (including some new attacks) on instances of RSA with certain special private exponents, multiple instances of RSA sharing a common small private exponent, Multi-prime RSA, Common Prime RSA and Dual RSA.

Lemieux recently proposed a new approach that studies randomized quasi-Monte Carlothrough dependency concepts. By analyzing the dependency structure of a rank-1 lattice,Lemieux proposed a copula-based criterion with which we can find a ???good generator??? for the lattice. One drawback of the criterion is that it assumes that a given function can be well approximated by a bilinear function. It is not clear if this assumption holds in general. In this thesis, we assess the validity and robustness of the copula-based criterion. We dothis by working with bilinear functions, some practical problems such as Asian option pricing, and perfectly non-bilinear functions. We use the quasi-regression technique to study how bilinear a given function is. Beside assessing the validity of the bilinear assumption, we proposed the bilinear regression based criterion which combines the quasi-regression and the copula-based criterion. We extensively test the two criteria by comparing them to other well known criteria, such as the spectral test through numerical experiments. We find that the copula criterion can reduce the error size by a factor of 2 when the functionis bilinear. We also find that the copula-based criterion shows competitive results evenwhen a given function does not satisfy the bilinear assumption. We also see that our newly introduced BR criterion is competitive compared to well-known criteria.

Spiral waves occur in several natural phenomena, including reaction fronts in two-dimension excitable media. In this thesis we attempt to characterize the motion of the spiral tip of a rigidly rotating wave and a linearly travelling wave in the context of a lattice perturbation. This system can be reduced to its center manifold, which allows us to describe the system as ordinary differential equations. This in turn means dynamical systems methods are appropriate to describe the motion of the tip. It is in such a context that we work on spiral waves. We study perturbed rotating waves and travelling waves using standard techniques from dynamical systems theory.