This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result analytic expressions of some integrals involved in the expansion terms are derived.

We discuss two ways of measuring angular diameter distances in the Universe: (i) Baryon Acoustic Oscillation (BAO) , and (ii) strong gravitational lensing. For (i), we study the effects of survey geometry and selection functions on the 2-point correlation function of Lyman- alpha emitters in 1.9 < z < 3.5 for Hobby-Eberly Telescope Dark Energy Experiment (HETDEX). We develop a method to extract the BAO scale (hence a volume-averaged angular diameter distance D_V, which is a combination of the angular diameter distance and the Hubble expansion rate, i.e., [cz〖(1+z)〗^2 〖D_A〗^2 H^(-1) ]^(1/3)) from a spherically averaged 1-d correlation function. We quantify the statistical errors on such measurements. By using log-normal realizations of the HETDEX dataset, we show that we can determine DV from HETDEX at 2% accuracy using the 2-point correlation function. This study is complementary to the on-going effort to characterize the power spectrum using HETDEX. For (ii), a previous study (Para ficz and Hjorth 2009) looked at the case of a spherical lens following a singular isothermal distribution of matter and an isotropic velocity distribution, and found that combining measurements of the Einstein ring radius with the time delay of a strong lens system directly leads to a measurement of the angular diameter distance, D_A. Since this is a very new method, it requires more careful investigations of various real-world eff ects such as a realistic matter density pro file, an anisotropic velocity distribution, and external convergence. In more realistic lens confi gurations we find that the velocity dispersion is the dominant source of the uncertainty ; in order for this method to achieve competitive precision on measurements of DA, we need to constrain the velocity dispersion, down to the percent level. On the other hand, external convergence and velocity dispersion anisotropy have negligible e ect on our result. However, we also claim that the dominant source of the uncertainty depends largely on the image con figuration of the system, which leads us to the conclusion that studying the angular dependence of the lens mass distribution is a necessary component. / text

This thesis reports on a comprehensive experimental study of the collective dynamics of colloidal hard sphere suspensions. The main quantity measured is the coherent Intermediate Scattering Function (ISF) using a range of techniques based on Dynamic Light Scattering (DLS). The collective dynamics are measured as a function of scattering vector for volume fractions spanning from dilute samples, through the fluid phase and the metastable region, up until deep in the glass region. This work describes two major explorations: (i) the effect of volume of fraction on the q-dependency of the collective dynamics; and (ii) a study of the ageing processes in colloidal glasses. The present work is unique in the application of several advanced experimental techniques, and in the level of averaging that has been carried out, enabling a more sophisticated analysis than has previously been possible. This includes the characterization of non-Fickian processes and the determinatio n of the current-current correlation function (CCCF) in the metastable fluid, and the quantitative characterization of the ageing process in the hard sphere glass. In addition, by combining aspects of the coherent and incoherent ISFs, this work also allows the expression of the collective dynamics in terms of the single particle displacement. The results show a dynamical change at the freezing point (f), which exposes the incapacity of the system to dissipate thermal energy via diffusing momentum currents, i.e. viscous flow. The structural impediments responsible for this, associated with dynamical heterogeneities, begin at the structure factor peak, and spread to other spatial modes as the volume fraction increases. Above the glass transition (g), structural relaxation becomes arrested at all spatial modes probed, i.e. flow is arrested. It is found that, following the quench, samples above the glass volume fraction approach some final

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Yes / Metamodelling or surrogate modelling techniques are frequently used across the engineering disciplines in conjunction with expensive simulation models or physical experiments. With the proliferation of metamodeling techniques developed to provide enhanced performance for specific problems, and the wide availability of a diverse choice of tools in engineering software packages, the engineering task of selecting a robust metamodeling technique for practical problems is still a challenge. This research introduces a framework for describing the typology of engineering problems, in terms of dimensionality and complexity, and the modelling conditions, reflecting the noisiness of the signals and the affordability of sample sizes, and on this basis presents a systematic evaluation of the performance of frequently used metamodeling techniques. A set of metamodeling techniques, selected based on their reported use for engineering problems (i.e. Polynomial, Radial Basis Function, and Kriging), were systematically evaluated in terms of accuracy and robustness against a carefully assembled set of 18 test functions covering different types of problems, sampling conditions and noise conditions. A set of four real-world engineering case studies covering both computer simulation and physical experiments were also analysed as validation tests for the proposed guidelines. The main conclusions drawn from the study are that Kriging model with Matérn 5/2 correlation function performs consistently well across different problem types with smooth (i.e. not noisy) data, while Kriging model with Matérn 3/2 correlation function provides robust performance under noisy conditions, except for the very high noise conditions, where the Kriging model with nugget appears to provide better models. These results provide engineering practitioners with a guide for the choice of a metamodeling technique for problem types and modelling conditions represented in the study, whereas the evaluation framework and benchmarking problems set will be useful for researchers conducting similar studies.

The surface width, a global quantity that depends on time, is used to characterize the temporal evolution of growing surfaces. One of the most successful concepts for describing the property of the surface width is the famous Family-Vicsek scaling relation. We discuss an extended scaling relation that yields a complete description for various growth models. For two linear Langevin equations, namely the Edwards-Wilkinson equation and the Mullins-Herring equation, we furthermore study analytically the behavior of global quantities related to the surface width or to a quantity which is conjugated to the diffusion constant. The global quantities depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response functions. For global functions related to the surface width, we show that the scaling behavior of the response can depend on how the system is perturbed. Different dynamic regimes, characterized by a power-law or by an exponential relaxation, are identified, and a dynamic phase diagram is constructed. We discuss global fluctuation-dissipation ratios and how to use them for the characterization of non-equilibrium growth processes. We also numerically study the same two-time quantities for the non-linear Kardar-Parisi-Zhang equation. For global functions related to the quantity which is conjugated to the diffusion constant of the linear Langevin equations, we show that the integrated response is proportional to the correlation in the linear response regime. In the aging regime, the autocorrelation and autoresponse exponents are identical and the aging exponent for the response is equal to the aging exponent for the correlation. We investigate the non-equilibrium fluctuation-dissipation theorem for non-equilibrium states based on this quantity. In the non-linear response regime a certain dissipation-fluctuation ratio approximates unity for small waiting times but approaches the ratio of perturbed and unperturbed diffusion constants for larger waiting times. / Ph. D.

This thesis presents the implementation and validation of a new methodology developed by Glegg et al. (2004) for solving the trailing edge noise problem. This method is based on the premises that the noise produced by a surface can be computed by the integral of the cross product between the velocity and vorticity fields, of the boundary layer and shed vorticity (Howe (1978)). To extract the source terms, proper orthogonal decomposition is applied to the velocity cross spectrum to extract modes of the unsteady velocity and vorticity. The new formulation of the trailing edge noise problem by Glegg et al. (2004) is attractive because it applies to the high frequencies of interest but does not require an excessive computational effort. Also, the nature of the formulation permits the identification of the modes producing the noise and their associated velocity fluctuations as well as the regions of the boundary layer responsible for the noise production. The source terms were obtained using the direct numerical simulation of a turbulent channel flow by Moser et al. (1998). Two-point velocity and vorticity statistics of this data set were obtained by averaging 41 instantaneous fields. For comparisons purposes, experimental boundary layer data by Adrian et al. (2000) was chosen. Statistical reduction of 50 velocity fields obtained by particle image velocimetry was performed and analysis of the two-point correlation function showed features similar to the DNS data case. Also, proper orthogonal decomposition revealed identical dominant modes and eddy structures in the flow, therefore justifying considering the channel flow as an external boundary layer for noise calculations. Comparison of noise predictions with experimental data from Brooks et al. (1989) showed realistic results with the largest discrepancies, on the order of 5 dB, occurring at the lowest frequencies. The DNS results are least applicable at these frequencies, since these correspond to the longest streamwise lengthscales, which are the most affected by the periodicity conditions used in the DNS and also are the least representative of the turbulence in an external boundary layer flow. Most of the noise was shown to be produced by low-frequency streamwise velocity modes in the bottom 10% of the boundary layer and locations closest to the wall. Only 6 modes were required to obtain noise levels within 1 dB of the total noise. Finally, the method for predicting spatial velocity correlation from Reynolds stress data in wake flows, originally developed by Devenport et al. (1999, 2001) and Devenport and Glegg (2001), was adapted to boundary-layer type flows. This method, using Reynolds stresses and the prescription of a lengthscale to extrapolate the full two-point correlation, was shown to produce best results for a lengthscale prescribed as proportional to the turbulent macroscale. Noise predictions using modeled two-point statistics showed good agreement with the DNS inferred data in all but frequency magnitude, a probable consequence of the modeling of the correlation function in the streamwise direction. Other quantities associated to noise were seen to be similar to the ones obtained using the DNS. / Master of Science

The scope of this thesis is in the time-dependent formulation of the two dimensional model of resonant electron-diatomic molecule collisions in the range of low energies. In its time independent form the model was previously numerically solved without the Born-Oppenheimer approximation with use of modern tools such as the finite element method with discrete variable representation (FEM-DVR) or exterior complex scaling (ECS). Within the scope of this model we numerically solve the evolution problem, with use of the Crank-Nicolson method and the Padé approximation. Later we evaluate the cross section of the elastic and some inelastic processes with the correlation function approach. At last we make a comparison of the evolution and the cross sections to time dependent formulation of the local complex potential approximation of the electron-molecule collisions.

<p>We investigate the clustering of HI-selected galaxies in the ALFALFA survey and compare results with those obtained for HIPASS. Measurements of the angular correlation function and the inferred 3D-clustering are compared with results from direct spatial-correlation measurements. We are able to measure clustering on smaller angular scales and for galaxies with lower HI masses than was previously possible. We calculate the expected clustering of dark matter using the redshift distributions of HIPASS and ALFALFA and show that the ALFALFA sample is somewhat more anti-biased with respect to dark matter than the HIPASS sample. We are able to conform the validity of the dark matter correlation predictions by performing simulations of the non-linear structure formation. Further we examine how the bias evolves with redshift for radio galaxies detected in the the first survey.</p>