Reducing spatial data using an optimized regressive discrete Fourier series

With the development of optical measurement techniques it is possible to obtain vast amounts of data. In vibrometry applications in particular operational deflection shapes are often obtained with very high spatial resolution. Fortunately, many techniques exist to reduce (approximate) the measurement data. One of the most common techniques for evaluating optical measurement data is by means of a Fourier analysis. However, this technique suffers from what is known as leakage when a non-integer number of periods is considered. This gives rise to non-negligible errors, which will obviously hamper the accuracy of the synthesized shape. Another technique such as a discrete cosine transform, used in the widely spread -jpeg standard does not suffer these anomalies but can still prove erroneous at times. One of the more recent approaches is via a so-called regressive discrete Fourier series (introduced by Arruda) which suffers one disadvantage. The problem statement is nonlinear in the parameters and needs a priori information about the deflection shape. This can be resolved by using the optimized regressive discrete fourier series (ORDFS), introduced in this article, which uses a nonlinear least squares approach. In this article the method will be applied in particular to the reduction of data for laser vibrometer measurements performed on an inorganic phosphate cement (IPC) beam (1D), as well as on a car door (2D). The proposed technique will also be validated on simulations to illustrate the properties concerning compression ratio and synthesized mode shape error. The introduced method will be bench marked for compression ratio and synthesized deflection shape error with all prior mentioned techniques.     

Existence and analytical predictions of periodic motions in a periodically forced,nonlinear friction oscillator

The grazing bifurcation, stick phenomena and periodic motions in a periodically forced, nonlinear friction oscillator are investigated. The nonlinear friction force is approximated by a piecewise linear, kinetic friction model with the static force. The total forces for the input and output flows to the separation boundary are introduced, and the force criteria for the onset and vanishing of stick motions are developed through such input and output flow forces. The periodic motions of such an oscillator are predicted analytically through the corresponding mapping structure. Illustrations of the periodic motions in such a piecewise friction model are given for a better understanding of the stick motion with the static friction. The force responses are presented, which agreed very well with the force criteria. If the fully nonlinear friction force is modeled by several portions of piecewise linear functions, the periodically forced, nonlinear friction oscillator can be predicted more accurately. However, for the fully nonlinear friction force model, only the numerical investigation can be carried out.     

A study of radiative properties of fractal soot aggregates using the superposition T-matrix method

We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D_f, is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N_S, and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D_f<2 but increases rapidly when D_f>2. However, a systematic reduction in light absorption with D_f is observed for clusters with sufficiently large N_S, m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed.     

Inertial clustering of particles in high-Reynolds-number turbulence

We report experimental evidence of spatial clustering of dense particles in homogenous, isotropic turbulence at high Reynolds numbers. The dissipation-scale clustering becomes stronger as the Stokes number increases and is found to exhibit similarity with respect to the droplet Stokes number over a range of experimental conditions (particle diameter and turbulent energy dissipation rate). These findings are in qualitative agreement with recent theoretical and computational studies of inertial particle clustering in turbulence. Because of the large Reynolds numbers a broad scaling range of particle clustering due to turbulent mixing is present, and the inertial clustering can clearly be distinguished from that due to mixing of fluid particles.     

Subdiffraction resolution in total internal reflection fluorescence microscopy with a grating substrate

We propose a fluorescence surface imaging system that presents a power of resolution beyond that of the diffraction limit without resorting to saturation effects or probe scanning. This is achieved by depositing the sample on an optimized periodically nanostructured substrate in a standard total internal reflection fluorescence microscope. The grating generates a high-spatial-frequency light grid that can be moved throughout the sample by changing the incident angle. An appropriate reconstruction procedure permits one to recover the fluorescence amplitude from the images obtained for various incidences. Simulations of this imaging system show that the resolution is not limited by diffraction but by the period of the grating.     

Melting and freezing of argon in a granular packing of linear mesopore arrays

Freezing and melting of Ar condensed in a granular packing of template-grown arrays of linear mesopores (SBA-15, mean pore diameter 8 nm) has been studied by specific heat measurements C as a function of fractional filling of the pores. While interfacial melting leads to a single melting peak in C, homogeneous and heterogeneous freezing along with a delayering transition for partial fillings of the pores result in a complex freezing mechanism explainable only by a consideration of regular adsorption sites (in the cylindrical mesopores) and irregular adsorption sites (in niches of the rough external surfaces of the grains and at points of mutual contact of the powder grains). The tensile pressure release upon reaching bulk-liquid-vapor coexistence quantitatively accounts for an upward shift of the melting and freezing temperature observed while overfilling the mesopores.     

Wall shear rate distribution for flow in random sphere packings

The wall shear rate distribution P(gamma) is investigated for pressure-driven Stokes flow through random arrangements of spheres at packing fractions 0.1< or =varphi< or =0.64. For dense packings, P(gamma) is monotonic and approximately exponential. As varphi-->0.1, P(gamma) picks up additional structure which corresponds to the flow around isolated spheres, for which an exact result can be obtained. A simple expression for the mean wall shear rate is presented, based on a force-balance argument.     

Nonaffine deformation of inherent structure as a static signature of cooperativity in supercooled liquids

We unveil the existence of nonaffinely rearranging regions in the inherent structures (IS) of supercooled liquids by numerical simulations of model glass formers subject to static shear deformations combined with local energy minimizations. In the liquid state IS, we find a broad distribution of large rearrangements which are correlated only over small distances. At low temperatures, the onset of the cooperative dynamics corresponds to much smaller displacements correlated over larger distances. This finding indicates the presence of nonaffinely rearranging domains of relevant size in the IS deformation, which can be seen as the static counterpart of the cooperatively rearranging regions in the dynamics. This idea provides new insight into possible structural signatures of slow cooperative dynamics of supercooled liquids and supports the connections with elastic heterogeneities found in amorphous solids.     

Crystallization of dense binary hard-sphere mixtures with marginal size ratio

Molecular dynamics simulations are performed for binary hard-sphere mixtures with a size ratio of gamma =0.9 and a volume fraction of phi=0.58 over a range of compositions. We show how, at this high volume fraction, crystallization depends sensitively on the composition. Evidence is presented that crystallization in these mixtures does not proceed by the standard nucleation and growth paradigm. Rather, some crystallite forms almost immediately and then an interplay between compositional fluctuations and crystal growth is able to dramatically extend the time scale on which further crystallization occurs. This can be seen as a form of geometric frustration.     

Cosmology with weak lensing surveys

Weak gravitational lensing is responsible for the shearing and magnification of the images of high-redshift sources due to the presence of intervening matter. The distortions are due to fluctuations in the gravitational potential, and are directly related to the distribution of matter and to the geometry and dynamics of the Universe. As a consequence, weak gravitational lensing offers unique possibilities for probing the Dark Matter and Dark Energy in the Universe. In this review, we summarise the theoretical and observational state of the subject, focussing on the statistical aspects of weak lensing, and consider the prospects for weak lensing surveys in the future.