65 research outputs found
Efficient Approximate Scaling of Spherical Functions in the Fourier Domain With Generalization to Hyperspheres
We propose a simple model for approximate scaling of spherical functions in the Fourier domain. The proposed scaling model is analogous to the scaling property of the classical Euclidean Fourier transform. Spherical scaling is used for example in spherical wavelet transform and filter banks or illumination in computer graphics. Since the function that requires scaling is often represented in the Fourier domain, our method is of significant interest. Furthermore, we extend the result to higher-dimensional spheres. We show how this model follows naturally from consideration of a hypothetical continuous spectrum. Experiments confirm the applicability of the proposed method for several signal classes. The proposed algorithm is compared to an existing linear operator formulation
New Developments in Covariance Modeling and Coregionalization for the Study and Simulation of Natural Phenomena
RĂSUMĂ La gĂ©ostatistique sâintĂ©resse Ă la modĂ©lisation des phĂ©nomĂšnes naturels par des champs alĂ©atoires
univariables ou multivariables. La plupart des applications utilisent un modĂšle stationnaire pour reprĂ©senter le phĂ©nomĂšne Ă©tudiĂ©. Il est maintenant reconnu que ce modĂšle nâest pas assez flexible pour reprĂ©senter adĂ©quatement un phĂ©nomĂšne naturel montrant des comportements qui varient considĂ©rablement dans lâespace (un exemple simple de cette hĂ©tĂ©rogĂ©nĂ©itĂ© est le problĂšme de lâestimation de lâĂ©paisseur du mort-terrain en prĂ©sence dâaffleurements).
Pour le cas univariable, quelques modĂšles non-stationnaires ont Ă©tĂ© dĂ©veloppĂ©s rĂ©cemment. Toutefois, ces modĂšles nâont pas un support compact, ce qui limite leur domaine dâapplication. Il y a un rĂ©el besoin dâenrichir la classe des modĂšles non-stationnaires univariable, le premier objectif poursuivi par cette thĂšse.----------ABSTRACT
Geostatistics focus on modeling natural phenomena by univariate or multivariate spatial random fields. Most applications rely on the choice of a stationary model to represent the studied phenomenon. It is now acknowledged that this model is not flexible enough to adequately represent a natural phenomenon showing behaviors that vary substantially in space (a simple example of such heterogeneity is the problem of estimating overburden
thickness in the presence of outcrops). For the univariate case, a few non-stationary models were developed recently. However, these models do not have compact support, which limits in practice their range of application. There is a definite need to enlarge the class of univariate
non-stationary models, a first goal pursued by this thesis
Statistical Mechanics and Thermodynamics of Liquids and Crystals
This book is a printed edition of the Special Issue âStatistical Mechanics and Thermodynamics of Liquids and Crystalsâ that was published in Entropy (MDPI). The articles collected in the book deal with some topical trends in the statistical physics of condensed-matter systems. Such contributions provide an indication of the variety of problems that can arise in the study of strongly correlated particles, giving at the same time a representative account of the methods employed in this widespread field of research
Mathematical Methods in Quantum Chemistry
The field of quantum chemistry is concerned with the analysis and simulation of chemical phenomena on the basis of the fundamental equations of quantum mechanics. Since the âexactâ electronic Schrödinger equation for a molecule with electrons is a partial differential equation in 3 dimension, direct discretization of each coordinate direction into gridpoints yields gridpoints. Thus a single Carbon atom () on a coarse ten point grid in each direction () already has a prohibitive degrees of freedom. Hence quantum chemical simulations require highly sophisticated
model-reduction, approximation, and simulation techniques.
The workshop brought together quantum chemists and the emerging and fast growing community of mathematicians working in the area, to assess recent advances and discuss long term prospects regarding the overarching challenges of
(1) developing accurate reduced models at moderate computational cost,
(2) developing more systematic ways to understand and exploit the multiscale nature of quantum chemistry problems.
Topics of the workshop included:
âą wave function based electronic structure methods,
âą density functional theory, and
âą quantum molecular dynamics.
Within these central and well established areas of quantum chemistry, the workshop focused on recent conceptual ideas and (where available) emerging mathematical results
Computational Studies on the Effective Properties of Two-Phase Heterogeneous Media
The effective elastic modulus and conductivity of a two phase material system are investigated computationally using a Monte Carlo scheme. The continuum contains circular, spherical or ellipsoidal inclusions that are either uniformly or randomly embedded in the matrix. The computed results are compared to the applicable effective medium theories. It is found that the random distribution, permeability and particle aspect ratio have non-negligible effects on the effective material properties. For spherical inclusions, the effective medium approximations agree well with the simulation results in general, but the analytical predictions on void or non-spherical inclusions are much less reliable. It is found that the results for overlapping and nonoverlapping inclusions do not differ very much at the same volume fraction. The effect of the particle morphology is also investigated in the context of prolate and oblate ellipsoidal particles.
The geometric percolation thresholds for circular, elliptical, square and triangular disks in the three-dimensional space are determined precisely by Monte Carlo simulations. These geometries represent oblate particles in the limit of zero thickness. The normalized percolation points, which are estimated by extrapolating the data to zero radius, are &eta c=0.9614 ± 0.0005, 0.8647 ± 0.0006 and 0.7295 ± 0.0006 for circles, squares and equilateral triangles, respectively. These results show that the noncircular shapes and corner angles in the disk geometry tend to increase the interparticle connectivity and therefore reduce the percolation point. For elliptical plate, the percolation threshold is found to decrease moderately when the aspect ratio &epsilon is between 1 and 1.5 but decrease rapidly for &epsilon greater than 1.5. For the binary dispersion of circular disks with two different radii, &eta c is consistently larger than that of equisized plates, with the maximum value located at around r_1/r_2 =0.5
Multitarget Tracking Using Orientation Estimation for Optical Belt Sorting
In optical belt sorting, accurate predictions of the bulk material particlesâ motions are required for high-quality results. By implementing a multitarget tracker tailored to the scenario and deriving novel motion models, the predictions are greatly enhanced. The trackerâs reliability is improved by also considering the particlesâ orientations. To this end, new estimators for directional quantities based on orthogonal basis functions are presented and shown to outperform the state of the art
Directional Estimation for Robotic Beating Heart Surgery
In robotic beating heart surgery, a remote-controlled robot can be used to carry out the operation while automatically canceling out the heart motion. The surgeon controlling the robot is shown a stabilized view of the heart. First, we consider the use of directional statistics for estimation of the phase of the heartbeat. Second, we deal with reconstruction of a moving and deformable surface. Third, we address the question of obtaining a stabilized image of the heart
- âŠ