Papers by Antoine Saucier
Applied Surface Science, Mar 1, 2003
A simple analytical approach, based on an energy balance equation, is introduced to describe the ... more A simple analytical approach, based on an energy balance equation, is introduced to describe the melt region of a semiconductor under a focused pulsed laser irradiation. In this model, an approximate analytical solution of the time-dependent hemispherical melt radius is calculated, and satisfactorily compared with experiments on silicon irradiated with a focused, 1 ms beam diameter, visible laser of a few watts with pulse widths of 0.03±10 ms.
Ground Water, Feb 26, 2013
Closed-form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as t... more Closed-form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint-Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed-form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values.
International Journal for Numerical and Analytical Methods in Geomechanics, Feb 18, 2010
The diffusion equation governs thermal conduction and groundwater flow phenomena. In this paper, ... more The diffusion equation governs thermal conduction and groundwater flow phenomena. In this paper, we study the two-dimensional radial propagation of a sinusoidal perturbation radiating from a cylindrical source within an infinite slab of homogeneous material. The solution of this problem has several applications. For instance, it can be used to determine the hydraulic diffusivity of the subsurface based on measurements of the hydraulic head around a vertical well during its development. For thermal problems, it can be used to determine the thermal diffusivity based on measurements of the temperature distribution around a cylindrical heat source generating a sinusoidal power per unit length. In this paper, we present a comprehensive analytical solution of this problem and we compare these solutions with numerical solutions. Two approximate analytical solutions, which can be relevant in practice, are also presented. Finally, we give an upper bound for the survival time of the transient part of the solution and we provide an estimate of the radius of influence of the sinusoidal solicitation.
Aerospace Science and Technology, Aug 1, 2017
The aircraft trajectory optimization problem can be approached by first considering a large set o... more The aircraft trajectory optimization problem can be approached by first considering a large set of possible spatial aircraft trajectories that connect a departure point and an arrival point. For each spatial trajectory in this set, the minimization of the total flight cost leads unavoidably to the problem of selecting a minimal-cost speed-profile, also called optimal speed-profile (OSP). Once the OSP is known for each spatial trajectory, the optimal trajectory is simply the lowest-cost trajectory in the trajectory set, assuming that each trajectory is covered with the OSP. The determination of the OSP for a given spatial trajectory is a fundamental problem that must be resolved to find the optimal trajectory. In this paper, we define the speed-profile optimization problem. If the fuel consumption function is smooth and strictly convex, then we show that using a costindex to account for the cost of time is equivalent to fixing the total travel-time in the optimization problem. We derive the optimality conditions of the OSP for constant altitude trajectories, both for the continuous problem and for a discretized version of the same problem. The analysis of these conditions reveals the relationship between the OSP and the locally-optimal speed-profile (LOSP), which is the speed profile that maximizes the specific range locally: for zero cost-index, the OSP and the LOSP are identical; for positive cost-index, speeds are higher on the OSP than on the LOSP. To compare quantitatively the OSP with the LOSP, we propose a first method to compute the OSP for constant altitude trajectories. The resulting numerical experiments reveal that the OSP uses more fuel but reaches destination sooner, which results in a small reduction of the direct operating cost. The magnitude of the cost savings associated with the OSP appears to be negligible in practice. We conclude that the LOSP is a good approximation of the OSP for constant altitude trajectories.
Stochastic Environmental Research and Risk Assessment, Oct 8, 2014
Multiple-point geostatistics has opened a new field of methodologies by which complex geological ... more Multiple-point geostatistics has opened a new field of methodologies by which complex geological phenomena have been modeled efficiently. In this study, a modified form of direct sampling (DS) method is introduced which not only keeps the strength of DS simulation technique but also speeds it up by one or two orders of magnitude. While previous methods are based on pasting only one point at a time, here the simulation is done by pasting a bunch of nodes at a time, effectively combining the flexibility of DS with the computational advantages of patch-based methods. This bears the potential of significantly speeding up the DS method. The proposed simulation method can be used with unilateral or random simulation paths. No overlap occurs in the simulation procedure because the bunch takes the shape of the empty space around the simulated nodes. Systematic tests are carried on different training images including both categorical and continuous variables, showing that the realizations preserve the patterns existent in the training image. To illustrate the method, a Matlab implementation of the method is attached to the paper.
Physica D: Nonlinear Phenomena, May 1, 1992
We show how the real space renormalization group method can be used to calculate analytically the... more We show how the real space renormalization group method can be used to calculate analytically the scaling exponents of the effective absolute permeability in multifractal porous media. The permeability fields considered are deterministic and random multifractals constructed with multiplicative processes. We discuss the implications of the results on the understanding of fluid ftow in oil reservoirs.
Multiscale Principal Components
Acta Geotechnica, Jul 30, 2019
The modal decomposition method (MDM) is used to analyse the grain size distribution curve (GSDC) ... more The modal decomposition method (MDM) is used to analyse the grain size distribution curve (GSDC) of a soil that was likely to produce internal erosion according to old criteria, and produced internal erosion in laboratory tests. Many previous studies have assumed that such a soil contains a coarse fraction and a fine fraction, the latter being able to migrate within the pores of the coarse fraction. It is shown here that the tested soil had not two fractions, but three grain size modes according to the MDM. The soil was tested in a rigid-wall permeameter under downward seepage. After the experiment, the specimen was divided into four parts, using the lateral piezometers positions to define the parts. The same three grain size modes (same means and variances) were found in the GSDCs of the four parts. In addition, the MDM could quantify internal erosion. The upper part of the specimen had lost the fine mode and had the highest proportion of coarse mode, whereas the medium-mode percentage had little variation with depth. This example explains how the modal decomposition method may help to quantify internal erosion.
Fractal methods and the problem of estimating scaling exponents: A new approach based on upper and lower linear bounds
Chaos Solitons & Fractals, Jun 1, 2006
ABSTRACT
Applied and Computational Harmonic Analysis, May 1, 2005
We show that orthonormal bases of functions with multiscale compact supports can be obtained from... more We show that orthonormal bases of functions with multiscale compact supports can be obtained from a generalization of principal component analysis. These functions, called multiscale principal components (MPCs), are eigenvectors of the correlation operator expressed in different vector subspaces. MPCs are data-adaptive functions that minimize their correlation with the reference signal. Using MPCs, we construct orthogonal bases which are similar to dyadic wavelet bases. We observe that MPCs are natural wavelets, i.e. their average is zero or nearly zero if the signal has a dominantly low-pass spectrum. We show that MPCs perform well in simple data compression experiments, in the presence or absence of singularities. We also introduce concentric MPCs, which are orthogonal basis functions having multiscale concentric supports. Use as kernels in convolution products with a signal, these functions allow to define a wavelet transform that has a striking capacity to emphasize atypical patterns.
A patchwork approach to stochastic simulation: A route towards the analysis of morphology in multiphase systems
Chaos Solitons & Fractals, Apr 1, 2008
We propose a new sequential stochastic simulation approach for black and white images in which we... more We propose a new sequential stochastic simulation approach for black and white images in which we focus on the accurate reproduction of the small scale geometry. Our approach aims at reproducing correctly the connectivity properties and the geometry of clusters which are small with ...
Signal Processing, Jun 1, 2010
We consider the estimation of frequency for a sinusoidal signal contaminated by an additive polyn... more We consider the estimation of frequency for a sinusoidal signal contaminated by an additive polynomial background signal and additive white Gaussian noise. We introduce new periodograms P M ðf Þ that are designed to be insensitive to the presence of any polynomial background signal of degree less than or equal to M. The periodograms P M allow frequency to be estimated efficiently and accurately. The frequency estimatef is given byf ¼ argmax 0 o f o 1 2 P M ðf Þ. The periodograms P M are obtained via least squares estimation. We show that if the signal model is written in a suitable way, then the matrix of the normal equation of the least squares problem can be diagonalized, which reduces significantly the computational burden and leads to simple analytical expressions for the periodogram. P M can be computed efficiently at the Fourier frequencies with the fast Fourier transform, just like the classical periodogram or Lomb's periodogram. If the background signal is not polynomial but is smooth and varies slowly enough for a given window size, then we show that P 3 can be used in sliding window processing for frequency tracking.
Corrective pattern-matching simulation with controlled local-mean histogram
Stochastic Environmental Research and Risk Assessment, Mar 23, 2014
ABSTRACT This paper presents a new stochastic simulation method that improves on our unilateral p... more ABSTRACT This paper presents a new stochastic simulation method that improves on our unilateral patchwork simulation method (Faucher et al., Stoch Environ Res Risk Assess, 27:253–273, 2012) by eliminating anisotropy biases. As in our unilateral method, images are built by assembling patterns together while controlling the local-mean histogram. The patterns, which are square image-pieces, are picked in a reference image. The reference image is used as a data bank holding the statistical informations about the random field to simulate. In contrast with the unilateral method, the path followed by our new simulation is random and guided by local errors. The new method, called corrective pattern-matching simulation, proceeds iteratively by making local corrections to the simulated image. For several types of images, it is shown that our simulations respect conditioning data and reproduce faithfully the reference image visual appearance. It is shown that the control of the local-mean histogram allows to control one-point statistics and multi-point statistics.
Physica D: Nonlinear Phenomena, Dec 1, 1992
The real space renormalization group method is used to calculate analytically the scaling exponen... more The real space renormalization group method is used to calculate analytically the scaling exponents of the effective absolute permeability in multifractal porous media.
Physica D: Nonlinear Phenomena, Apr 1, 1996
In turbulence, the simplest phenomenological models of the energy cascade are multiplicative proc... more In turbulence, the simplest phenomenological models of the energy cascade are multiplicative processes constructed on a regular grid (in short, M.P.G). They have been used mostly for their simplicity, allowing many of their properties to be derived analytically, and their capacity to reproduce the scale invariance properties of various geophysical fields. However, these M.P.G.'s suffer from the drawback of lacking translation invariance in their spatial statistics (spatial homogeneity), and therefore they cannot be fully satisfactory models for geophysical fields. In this paper, we are interested in finding new construction methods for spatially homogeneous random multifractals. We investigate the scaling properties of a new family of gridless models of multifractals.
A new patchwork simulation method with control of the local-mean histogram
Stochastic Environmental Research and Risk Assessment, Jun 9, 2012
ABSTRACT
Multifractal Analysis of Dipmeter Well Logs for Description of Geological Lithofacies
Fractals in Engineering, 1997
We use multifractal analysis as a geostatistical tool for characterization of microresistivity si... more We use multifractal analysis as a geostatistical tool for characterization of microresistivity signals produced by dipmeter well-logging tools. The signal is divided into windows of fixed length. For each window, several texture indices characterizing the irregularity of the microresistivity signal are calculated. Plotted as a function of depths, these texture indices form what we call texture logs. We show that these texture logs can be used to distinguish geological lithofacies differing in their degree of heterogeneity.
Thermal Analysis of Early Neolithic Pottery From Tepe Ganj Dareh, Iran
MRS Proceedings, 1992
ABSTRACTA series of pottery fragments from an early Neolithic site in Iran is analyzed to determi... more ABSTRACTA series of pottery fragments from an early Neolithic site in Iran is analyzed to determire the original baking temperatures. Two magnetic techniques are used: remanent magnetization decay, and hysteresis loop analysis. The results are complementary, although some are, at first sight, contradictory. The causes of these apparent contradictions are explained. The analyses confirm that the pottery was baked under highly variable conditions, probably over open fires. Control of baking was poor, and there was considerable variability not only from one vessel to another but even from one zone to another on the same vessel. Our results suggest the need for caution in interpreting often ambiguous findings in this field of ancient technology.
Scaling of the Effective Permeability in Multifractal Reservoirs
North Sea Oil and Gas Reservoirs — III, 1994
Data-Adaptive Orthogonal Wavelet Abases Obtained Via Principal Component Analysis
International Conference on Imaging Science, Systems and Technology, 2003
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Papers by Antoine Saucier