A Note on Global Suprema of Band-Limited Spherical Random Functions

In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell-TIS inequality to establish almost sure upper and lower bounds for their fluctuations. Band limited functions can be viewed as restrictions on the sphere of random polynomials with increasing degrees, and our results show that fluctuations scale as the square root of the logarithm of these degrees

High-frequency asymptotics for Lipschitz-Killing curvatures of excursion sets on the sphere

In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we consider both random spherical harmonics and their smoothed averages, which can be viewed as random wavelet coefficients in the continuous case. For such fields, we consider smoothed polynomial transforms; we focus on the geometry of their excursion sets, and we study their asymptotic behaviour, in the high-frequency sense. We focus on the analysis of Euler-Poincar\'{e} characteristics, which can be exploited to derive extremely accurate estimates for excursion probabilities. The present analysis is motivated by the investigation of asymmetries and anisotropies in cosmological data. The statistics we focus on are also suitable to deal with spherical random fields which can only be partially observed, the canonical example being provided by the masking effect of the Milky Way on Cosmic Microwave Background (CMB) radiation data.Comment: Published at http://dx.doi.org/10.1214/15-AAP1097 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Wall-resolved large eddy simulation over NACA0012 airfoil

The work presented here forms part of a project on Large-Eddy Simulation (LES) of aeroengine aeroacoustic interactions. In this paper we concentrate on LES of near-field flow over an isolated NACA0012 airfoil at zero angle of attack with Rec=2e5. The predicted unsteady pressure/velocity field is used in an analytically-based scheme for far-field trailing edge noise prediction. A wall resolved implicit LES or so-callednumerical Large Eddy Simulation (NLES) approach is employed to resolve streak-like structure in the near-wall flow regions. The mean and RMS velocity and pressure profile on airfoil surface and in wake are validated against experimental data and computational results from other researchers. The results of the wall-resolved NLES method are very encouraging. The effects of grid-refinement and higher-order numerical scheme on the wall-resolved NLES approach are also discussed

Central limit theorem for exponentially quasi-local statistics of spin models on Cayley graphs

Central limit theorems for linear statistics of lattice random fields (including spin models) are usually proven under suitable mixing conditions or quasi-associativity. Many interesting examples of spin models do not satisfy mixing conditions, and on the other hand, it does not seem easy to show central limit theorem for local statistics via quasi-associativity. In this work, we prove general central limit theorems for local statistics and exponentially quasi-local statistics of spin models on discrete Cayley graphs with polynomial growth. Further, we supplement these results by proving similar central limit theorems for random fields on discrete Cayley graphs and taking values in a countable space but under the stronger assumptions of {\alpha}-mixing (for local statistics) and exponential {\alpha}-mixing (for exponentially quasi-local statistics). All our central limit theorems assume a suitable variance lower bound like many others in the literature. We illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology, statistical physics and random networks. Examples of clustering spin models include quasi-associated spin models with fast decaying covariances like the off-critical Ising model, level sets of Gaussian random fields with fast decaying covariances like the massive Gaussian free field and determinantal point processes with fast decaying kernels. Examples of local statistics include intrinsic volumes, face counts, component counts of random cubical complexes while exponentially quasi-local statistics include nearest neighbour distances in spin models and Betti numbers of sub-critical random cubical complexes.Comment: Minor changes incorporated based on suggestions by referee

Field measurement & verification of residential duct leakage methods and CFD analysis of HVAC mixing box

The research work in this thesis is subdivided to providing the initial results of the experimental work followed by simulation work at the end. The experimental work proposes a new measurement technique for measuring total and local leakages in ducts. The experimental work in this research tries to focus effort on finding the approximate locations of leaks in the HVAC residential duct systems to direct better the effort of duct sealing. This technique can provide several advantages over existing techniques. It will eventually have a greater potential to locate leaks so that retrofitting in ducts can be focused on leaky locations. Field studies were performed in 11 houses in Las Vegas. Out of these, 4 houses were selected for fixing the leakages in them and the tests were repeated on these houses to verify the duct leakage reduction and benefits. The proposed method can offer a more cost effective approach when compared to other methods in the future. It reduces the total leakage for different houses by 14.4% to 46.5% of the total initial leakage rate. The second part of this thesis consists of performing a CFD study of HVAC Mixing box. Return air is supplied from the top of the box and outside air supplied from the back of mixing box. The temperature and velocity profiles of air in the HVAC mixing box were analyzed. The effects of carbon dioxide concentration in the mixing box were also analyzed. The current CFD simulation results were compared to previous field measurements of temperature stratification in a mixing box published in the International Journal of Energy Research in 2001. The CFD results showed that within the experimental error given in the previous paper the CFD temperature distribution predictions were reasonably close to the experimental results indicating that a detailed CFD approach can be used for predictive purposes