To study the temperature in a gas subjected to electromagnetic radiations, one may use the Radiative Transfer equations coupled with the Navier-Stokes equations. The problem has 7 dimensions; however ...with minimal simplifications it is equivalent to a small number of integro-differential equations in 3 dimensions. We present the method and a numerical implementation using an H-matrix compression scheme. The result is very fast: 240K physical points, all directions of radiation and 683 frequencies require less than 35 minutes on an Apple M1 Laptop. The method is capable of handling variable absorption and scattering functions of spatial positions and frequencies.
The implementation is done using htool,1 a matrix compression library interfaced with the PDE solver freefem++. Applications to the temperature in the French Chamonix valley are presented at different hours of the day with and without snow or cloud and with a variable absorption coefficient taken from the Gemini measurements. The software is precise enough to assert temperature differences due to increased absorption in the vibrational frequency subrange of greenhouse gases.
This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary ...order and the preconditioner is constructed using additive Schwarz domain decomposition methods. The theory developed here shows that if the absorption is large enough, and if the subdomain and coarse mesh diameters and overlap are chosen appropriately, then the classical two-level overlapping additive Schwarz preconditioner (with PEC boundary conditions on the subdomains) performs optimally--in the sense that GMRES converges in a wavenumber-independent number of iterations--for the problem with absorption. An important feature of the theory is that it allows the coarse space to be built from low-order elements even if the PDE is discretised using high-order elements. It also shows that additive methods with minimal overlap can be robust. Numerical experiments are given that illustrate the theory and its dependence on various parameters. These experiments motivate some extensions of the preconditioners which have better robustness for problems with less absorption, including the propagative case. At the end of the paper we illustrate the performance of these on two substantial applications; the first (a problem with absorption arising from medical imaging) shows the empirical robustness of the preconditioner against heterogeneity, and the second (scattering by a COBRA cavity) shows good scalability of the preconditioner with up to 3,000 processors.
•Feasibility of a microwave tomographic imaging technique for brain strokes.•Scalable domain decomposition solver for Maxwell’s equations on thousands of cores.•Implementation of a nonlinear ...optimization algorithm in a parallel framework.•Synthetic data generated from a very accurate virtual head model.
The motivation of this work is the detection of cerebrovascular accidents by microwave tomographic imaging. This requires the solution of an inverse problem relying on a minimization algorithm (for example, gradient-based), where successive iterations consist in repeated solutions of a direct problem. The reconstruction algorithm is extremely computationally intensive and makes use of efficient parallel algorithms and high-performance computing. The feasibility of this type of imaging is conditioned on one hand by an accurate reconstruction of the material properties of the propagation medium and on the other hand by a considerable reduction in simulation time. Fulfilling these two requirements will enable a very rapid and accurate diagnosis. From the mathematical and numerical point of view, this means solving Maxwell’s equations in time-harmonic regime by appropriate domain decomposition methods, which are naturally adapted to parallel architectures.
Abstract
The paper concerns the numerical resolution of the inverse source problem for electroencephalography. We propose an approach which is able to take into account some heterogeneity properties ...(namely a varying electrical conductivity) of the head tissues, in particular of the skull layer. It combines two consecutive steps: (i) a data completion procedure from the scalp to the cortex using the quasi-reversibility method, (ii) a source estimation method from these cortical transmitted data within the brain (modeled as sphere), developed in the software tool FindSources3D. Numerical simulations in the case of the multi-layered spherical head model illustrate both the promising and limiting features of the approach.
Dynamic hydrogels are viscoelastic materials that can be designed to be self-healing, malleable, and injectable, making them particularly interesting for a variety of biomedical applications. To ...design dynamic hydrogels, dynamic covalent crosslinking reactions are attracting increasing attention. However, dynamic covalent hydrogels tend to swell, and often lack stability. Boronate ester-based hydrogels, which result from the dynamic covalent reaction between a phenylboronic acid (PBA) derivative and a diol, are based on stable precursors, and can therefore address these limitations. Yet, boronate ester formation hardly occurs at physiological pH. To produce dynamic covalent hydrogels at physiological pH, we performed a molecular screening of PBA derivatives in association with a variety of diols, using hyaluronic acid as a polymer of interest. The combination of Wulff-type PBA (wPBA) and glucamine stood out as a unique couple to obtain the desired hydrogels. We showed that optimized wPBA/glucamine hydrogels are minimally- to non-swelling, stable long term (over months), tunable in terms of mechanical properties, and cytocompatible. We further characterized their viscoelastic and self-healing properties, highlighting their potential for biomedical applications.
Testing libraries of phenylboronic acid derivatives and diols revealed a new crosslinking couple for the formation of viscoelastic hydrogels with tunable properties and long-term stability.
► We developed a phenomenological model for nuclear graphite oxidation. ► Model results compare favorably with reported data for IG-110, IG-430 and NBG-25. ► A new Sherwood number correlation ...developed for diffusion velocity in boundary layer. ► Chemical kinetics parameters and gasification rate determined functions of weight loss and experimental conditions.
A phenomenological oxidation kinetics model of graphite is presented and its results are compared with the reported experimental gasification data for nuclear graphite of IG-110, IG-430 and NBG-25. The model uses four elementary chemical kinetics reactions, employs Gaussian-like distributions of the specific activation energies for adsorption of oxygen and desorption of CO gas, and accounts for the changes in the effective surface areas of free active sites and stable oxide complexes with weight loss. The distributions of the specific activation energies for adsorption and desorption, the values of the pre-exponential rate coefficients for the four elementary chemical reactions and the surface area of free active sites are obtained from the reported measurements using a multi-parameter optimization algorithm. At high temperatures, when gasification is diffusion limited, the model calculates the diffusion velocity of oxygen in the boundary layer using a semi-empirical correlation developed for air flows at Reynolds numbers ranging from 0.001 to 100. The model also accounts for the changes in the external surface area, the oxygen pressure in the bulk gas mixture and the effective diffusion coefficient in the boundary layer with weight loss. The model results of the total gasification rate and weight loss with time in the experiments agree well with the reported measurements for the three types of nuclear graphite investigated, at temperatures from 723 to 1226
K and weight loss fractions up to ∼0.86.
A model of the chemical kinetics and primary reactions of graphite oxidation is developed and successfully validated for pyrolytic carbon thin films. The model uses Gaussian distributions of the ...activation energies for adsorption and desorption and the measured active surface area (ASA) as a function of burn-off. The activation energies distributions and the pre-exponential rate coefficients for the four elementary oxidation kinetics reactions in the model are obtained from the reported measurements of the gases yields and adsorbed oxygen using a multi-parameter optimization algorithm. The model calculates the production rates of CO and CO
2 and the gasification rate as functions of temperature and oxygen partial pressure, and its predictions are in excellent agreement with reported experimental measurements. Results for pyrolytic carbon thin films show that when the oxygen pressure is kept constant, the gasification rate depends on both temperature and ASA until a full burn-off is reached. By contrast, in a depleting oxygen environment, only partial burn-off is possible; gasification ceases following the consumption of the free oxygen in the enclosure. This model represents the first phase in an ongoing effort to develop a model for predicting the oxidation kinetics of nuclear graphite following a massive air ingress in high temperature reactors.
A series of gasification experiments, using two right cylinder specimens (∼12.7×25.4mm and 25.4×25.4mm) of PCEA nuclear graphite in ambient airflow, measured the total gasification flux at weight ...losses up to 41.5% and temperatures (893–1015K) characteristics of those for in-pores gasification Mode (a) and in-pores diffusion-limited Mode (b). The chemical kinetics parameters for the gasification of PCEA graphite are determined using a multi-parameters optimization algorithm from the measurements of the total gasification rate and transient weight loss in experiments. These parameters are: (i) the pre-exponential rate coefficients and the Gaussian distributions and values of specific activation energies for adsorption of oxygen and desorption of CO gas; (ii) the specific activation energy and pre-exponential rate coefficient for the breakup of stable un-dissociated C(O2) oxygen radicals to form stable (CO) complexes; (iii) the specific activation energy and pre-exponential coefficient for desorption of CO2 gas and; (iv) the initial surface area of reactive free sites per unit mass. This area is consistently 13.5% higher than that for nuclear graphite grades of NBG-25 and IG-110 and decreases inversely proportional with the square root of the initial mass of the graphite specimens in the experiments. Experimental measurements successfully validate the chemical-reactions kinetics model that calculates continuous Arrhenius curves of the total gasification flux and the production rates of CO and CO2 gases. The model results at different total weight losses agree well with measurements and expand beyond the temperatures in the experiments to the diffusion-limited mode of gasification. Also calculated are the production rates of CO and CO2 gases and their relative contributions to the total gasification rate in the experiments as functions of temperature, for total weight losses of 5% and 10%.
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