Structure simplification of dynamic process models

Lumped process models derived from first engineering principles are usually too detailed for control purposes where only the major dynamic characteristics of the system should be captured. Two common steps of simplifying dynamic process models, the steady-state variable removal and the variable lumping simplification steps are investigated in this paper, in order to show if they preserve the key properties: the structural controllability, observability and stability of the models. In order to enable the formal analysis, these simplification steps are represented as context sensitive graph transformations acting on the structure graphs of the dynamic process models. It is shown that the simplification transformations above preserve the structural controllability and observability of process models. But only the steady-state variable removal transformation has been found not to destroy their structural stability. The variable lumping structure simplification transformation is further specialized to the case of cascade process models. It is shown that the inverse of this transformation does exist in this case, and both transformations preserve structural controllability and observability.     

A computational model of bounded developable surfaces with application to image‐based three‐dimensional reconstruction

Developable surfaces have been extensively studied in computer graphics because they are involved in a large body of applications. This type of surfaces has also been used in computer vision and document processing in the context of three‐dimensional (3D) reconstruction for book digitization and augmented reality. Indeed, the shape of a smoothly deformed piece of paper can be very well modeled by a developable surface. Most of the existing developable surface parameterizations do not handle boundaries or are driven by overly large parameter sets. These two characteristics become issues in the context of developable surface reconstruction from real observations. Our main contribution is a generative model of bounded developable surfaces that solves these two issues. Our model is governed by intuitive parameters whose number depends on the actual deformation and including the “flat shape boundary”. A vast majority of the existing image‐based paper 3D reconstruction methods either require a tightly controlled environment or restricts the set of possible deformations. We propose an algorithm for reconstructing our model's parameters from a general smooth 3D surface interpolating a sparse cloud of 3D points. The latter is assumed to be reconstructed from images of a static piece of paper or any other developable surface. Our 3D reconstruction method is well adapted to the use of keypoint matches over multiple images. In this context, the initial 3D point cloud is reconstructed by structure‐from‐motion for which mature and reliable algorithms now exist and the thin‐plate spline is used as a general smooth surface model. After initialization, our model's parameters are refined with model‐based bundle adjustment. We experimentally validated our model and 3D reconstruction algorithm for shape capture and augmented reality on seven real datasets. The first six datasets consist of multiple images or videos and a sparse set of 3D points obtained by structure‐from‐motion. The last dataset is a dense 3D point cloud acquired by structured light. Our implementation has been made publicly available on the authors' web home pages. Copyright © 2012 John Wiley & Sons, Ltd.     

Carbon‐Nanotube–PDMS Composite Coatings on Optical Fibers for All‐Optical Ultrasound Imaging

Polymer–carbon nanotube composite coatings have properties that are desirable for a wide range of applications. However, fabrication of these coatings onto submillimeter structures with the efficient use of nanotubes has been challenging. Polydimethylsiloxane (PDMS)–carbon nanotube composite coatings are of particular interest for optical ultrasound transmission, which shows promise for biomedical imaging and therapeutic applications. In this study, methods for fabricating composite coatings comprising PDMS and multiwalled carbon nanotubes (MWCNTs) with submicrometer thickness are developed and used to coat the distal ends of optical fibers. These methods include creating a MWCNT organogel using two solvents, dip coating of this organogel, and subsequent overcoating with PDMS. These coated fibers are used as all‐optical ultrasound transmitters that achieve high ultrasound pressures (up to 21.5 MPa peak‐to‐peak) and broad frequency bandwidths (up to 39.8 MHz). Their clinical potential is demonstrated with all‐optical pulse‐echo ultrasound imaging of an aorta. The fabrication methods in this paper allow for the creation of thin, uniform carbon nanotube composites on miniature or temperature‐sensitive surfaces, to enable a wide range of advanced sensing capabilities.     

Long Distance Enhancement of Nonlinear Optical Properties Using Low Concentration of Plasmonic Nanostructures in Dye Doped Monolithic Sol–Gel Materials

Monolithic sol–gel silica composites incorporating platinum‐based chromophores and various types of gold nanoparticles (AuNPs) are prepared and polished to high optical quality. Their photophysical properties are investigated. The glass materials show well‐defined localized surface plasmon resonance (SPR) absorbance from the visible to NIR. No redshifts of the AuNP plasmon absorption peaks due to the increase in nanoparticle doping concentration are observed in the glasses, proving that no or very small SPR coupling effects occur between the AuNPs. At 600 nm excitation, but not at 532 nm, the AuNPs improve the nonlinear absorption performance of glasses codoped with 50 × 10^?3 m of a Pt‐acetylide chromophore. The glasses doped with lower concentrations of AuNPs (2–5 μm average distance) and 50 × 10^?3 m in chromophore, show a marked improvement in nonlinear absorption, with no or only small improvement for the more highly AuNP doped glasses. This study shows the importance of excitation wavelength and nanoparticle concentration for composite systems employing AuNPs to improve two‐photon absorption of chromophores.     

Practical Product Path Guiding Using Linearly Transformed Cosines

Path tracing is now the standard method used to generate realistic imagery in many domains, e.g., film, special effects, architecture etc. Path guiding has recently emerged as a powerful strategy to counter the notoriously long computation times required to render such images. We present a practical path guiding algorithm that performs product sampling, i.e., samples proportional to the product of the bidirectional scattering distribution function (BSDF) and incoming radiance. We use a spatial-directional subdivision to represent incoming radiance, and introduce the use of Linearly Transformed Cosines (LTCs) to represent the BSDF during path guiding, thus enabling efficient product sampling. Despite the computational efficiency of LTCs, several optimizations are needed to make our method cost effective. In particular, we show how we can use vectorization, precomputation, as well as strategies to optimize multiple importance sampling and Russian roulette to improve performance. We evaluate our method on several scenes, demonstrating consistent improvement in efficiency compared to previous work, especially in scenes with significant glossy inter-reflection.     

Can water level stations be used for thermal assessment in aquatic ecosystem?

Many studies focus on stream water temperature (WT) because it is considered a key ecological factor. However, few of them have investigated the use of WT data from water level monitoring networks, which often measure WT as ancillary data. Our study was conducted in southern Belgium at a high temporal resolution with continuous data recorded at intervals of 10 min between 2012 and 2016 and large spatial scale greater than 16,000 km². This study aimed to assess whether a regional water level network (140 stations) is reliable for continuous WT monitoring based on a Bland–Altman analysis with WT collected through a European monitoring network (Water Framework Directive). This study also investigates whether WT data acquired by water level stations can be used to perform both state‐of‐the‐art visualization of thermal regimes and spatio‐temporal queries for specific ecological monitoring. We found that the water level stations were reliable tools in recording continuous WT in the streams of the study area. The temperature difference between the two WT monitoring networks was ?0.57°C on average. Our positive results promote the use of WT from water level stations in order to globally characterize the thermal regime of streams as well as to provide spatial or temporal information on this regime at high frequencies. As an example, our data showed the effectiveness for brown trout (Salmo trutta fario L.) in spatializing thermal risk areas related to the thermal requirement of this fish species; in 2015, 19% of stations located in brown trout fish zone recorded temperatures above 25°C.     

Stability properties of the Discontinuous Galerkin Material Point Method for hyperbolic problems in one and two space dimensions

In this paper, stability conditions are derived for the Discontinuous Galerkin Material Point Method (DGMPM) on the scalar linear advection equation for the sake of simplicity and without loss of generality for linear problems. The discrete systems resulting from the application of the DGMPM discretization in one and two space dimensions are first written. For these problems, a second-order Runge-Kutta and the forward Euler time discretizations are respectively considered. Moreover, the numerical fluxes are computed at cell faces by means of either the Donor-Cell Upwind or the Corner Transport Upwind methods for multidimensional problems. Second, the discrete scheme equations are derived assuming that all cells of a background grid contain at least one particle. Although a Cartesian grid is considered in two space dimensions, the results can be extended to regular grids. The von Neumann linear stability analysis then allows the computation of the critical Courant number for a given space discretization. Although the DGMPM is equivalent to the first-order finite volume method if one particle lies in each element, so that the Courant number can be set to unity, other distributions of particles may restrict the stability region of the scheme. The study of several configurations is then proposed.     

Influence of lignin's pH on polyurethane flexible foam formation and how to control it

Low pH of commercial lignins has a catastrophic impact on the polyurethane foaming reactions. Experiments were performed with 10 wt% of lignin with various pHs in polyols. Virgin lignin (pH 2.5, 35% moisture) has the most negative impact as it reduces the initial foam rising rate by 85% and the foam's final height by 35% as compared to the reference foam, lignin free. Drying of this lignin at 80°C for 12 h can reduce this impact while alkaline treatment to bring the lignin's pH to 6.6 almost cancel it. As revealed by in situ dielectric constant measurements, both reactions, gelling via polymerization and blowing via CO₂ degassing, are impacted. In situ Fourier transform infrared analysis of the foaming process demonstrated that blowing reaction is the most pH sensitive. Two methods to counter the pH influence by pH modification were tested and provide interesting results but also significant drawbacks limiting their applicability.     

Stratified Markov Chain Monte Carlo Light Transport

Markov chain Monte Carlo (MCMC) sampling is a powerful approach to generate samples from an arbitrary distribution. The application to light transport simulation allows us to efficiently handle complex light transport such as highly occluded scenes. Since light transport paths in MCMC methods are sampled according to the path contributions over the sampling domain covering the whole image, bright pixels receive more samples than dark pixels to represent differences in the brightness. This variation in the number of samples per pixel is a fundamental property of MCMC methods. This property often leads to uneven convergence over the image, which is a notorious and fundamental issue of any MCMC method to date. We present a novel stratification method of MCMC light transport methods. Our stratification method, for the first time, breaks the fundamental limitation that the number of samples per pixel is uncontrollable. Our method guarantees that every pixel receives a specified number of samples by running a single Markov chain per pixel. We rely on the fact that different MCMC processes should converge to the same result when the sampling domain and the integrand are the same. We thus subdivide an image into multiple overlapping tiles associated with each pixel, run an independent MCMC process in each of them, and then align all of the tiles such that overlapping regions match. This can be formulated as an optimization problem similar to the reconstruction step for gradient-domain rendering. Further, our method can exploit the coherency of integrands among neighboring pixels via coherent Markov chains and replica exchange. Images rendered with our method exhibit much more predictable convergence compared to existing MCMC methods.