Добірка наукової літератури з теми "Laplacien et projection"

Polymer electrolyte fuel cells (PEFC) are considered to make a significant contribution to the transition towards carbon free energy conversion, as they produce electric power from hydrogen and oxygen with water as the only by-product [1]. On its way to widespread commercialization, in particular the water management in PEFC is challenging. On one hand, the electrolyte membrane needs to be humidified to be highly conductive for the hydrogen protons. On the other hand, accumulation of the product water in the gas diffusion layer (GDL) on the cathode side mitigates the oxygen transport towards the catalytic surface, which leads to severe performance limitations [2-3]. Previous work has shown that structured GDLs can enhance PEFC performance [5] and additive manufacturing (AM) has been identified as a viable method to fabricate just such [4,6]. Currently available AM technologies are struggling to fulfill the needs in terms of minimal feature size (~8 um fiber diameter) and sample size (at least some cm2). Initial AM prepared GDLs were coarse with finest structures of about 120 um [6] which is in the range of typical GDL thickness. Here, we present AM prepared GDL like structures with 20 um printed features that can reach sizes of some tens of mm2. The 3D printed structures are designed to guide the product water through the GDL by adjusting the throat size [7] and therefore the capillary pressure, which is required in the water phase to percolate through the throats to the neighboring pore as described by Young-Laplace law. Figure 1 shows tomographic data of a test lattice structure manufactured by high-resolution projection micro stereolithography (PµSL). The concept is validated by measuring the pressure in the water phase as a function of the throat size under ex-situ conditions. The desired percolation path of the water is monitored by 2D as well as 3D image data acquired by X-ray radiography and X-ray tomographic microscopy (XTM), respectively. Figure caption: XTM scan of a lattice structure manufactured by P µ SL: a) 3D rendering, b) x-z-plane cross section, c) x-y-plane cross section. Slight deformation in the base layers of the lattice structure is observed. References [1] O. Z. Sharaf et. al., Renewable and Sustainable Energy Reviews, 2014, 32, pp. 810-853 [2] M. F. Mathias et. al., Handbook of Fuel Cells, 2010 [3] J. Ihonen et. al., Journal of the Electrochemical Society, 2004, 151, pp. A1152-A1161 [4] D. Niblett et. al., Journal of the Electrochemical Society, 2020, 167, 013520 [5] C. Csoklich et. al., Energy & Environmental Science, 2022, 15, 1293-1306 [6] D. Niblett et. al., International Journal of Hydrogen Energy, 2022, 47, pp. 23393-23410 [7] D. Niblett et. al., Journal of Power Sources, 2020, 471, 228427 Figure 1

Abstract. Lateral transfer of carbon (C) from terrestrial ecosystems into the inland water network is an important component of the global C cycle, which sustains a large aquatic CO2 evasion flux fuelled by the decomposition of allochthonous C inputs. Globally, estimates of the total C exports through the terrestrial–aquatic interface range from 1.5 to 2.7 Pg C yr−1 (Cole et al., 2007; Battin et al., 2009; Tranvik et al., 2009), i.e. of the order of 2–5 % of the terrestrial NPP. Earth system models (ESMs) of the climate system ignore these lateral transfers of C, and thus likely overestimate the terrestrial C sink. In this study, we present the implementation of fluvial transport of dissolved organic carbon (DOC) and CO2 into ORCHIDEE (Organising Carbon and Hydrology in Dynamic Ecosystems), the land surface scheme of the Institut Pierre-Simon Laplace ESM. This new model branch, called ORCHILEAK, represents DOC production from canopy and soils, DOC and CO2 leaching from soils to streams, DOC decomposition, and CO2 evasion to the atmosphere during its lateral transport in rivers, as well as exchange with the soil carbon and litter stocks on floodplains and in swamps. We parameterized and validated ORCHILEAK for the Amazon basin, the world's largest river system with regard to discharge and one of the most productive ecosystems in the world. With ORCHILEAK, we are able to reproduce observed terrestrial and aquatic fluxes of DOC and CO2 in the Amazon basin, both in terms of mean values and seasonality. In addition, we are able to resolve the spatio-temporal variability in C fluxes along the canopy–soil–water continuum at high resolution (1°, daily) and to quantify the different terrestrial contributions to the aquatic C fluxes. We simulate that more than two-thirds of the Amazon's fluvial DOC export are contributed by the decomposition of submerged litter. Throughfall DOC fluxes from canopy to ground are about as high as the total DOC inputs to inland waters. The latter, however, are mainly sustained by litter decomposition. Decomposition of DOC and submerged plant litter contributes slightly more than half of the CO2 evasion from the water surface, while the remainder is contributed by soil respiration. Total CO2 evasion from the water surface equals about 5 % of the terrestrial NPP. Our results highlight that ORCHILEAK is well suited to simulate carbon transfers along the terrestrial–aquatic continuum of tropical forests. It also opens the perspective that provided parameterization, calibration and validation is performed for other biomes, the new model branch could improve the quantification of the global terrestrial C sink and help better constrain carbon cycle–climate feedbacks in future projections.

Summary Analytical methods are presented to determine pressure-transient and productivity data for deviated wells in layered reservoirs. The computational methods, which are based on Laplace transforms, can be used to generate types curves for use in direct analyses of pressure-transient data and to determine the effective skin of such wells for use in productivity computations. Introduction Deviated wells with full or limited flow entry are very common, especially in offshore developments. The pressure-transient behavior of fully penetrating deviated wells were investigated by Cinco et al.1 for homogeneous reservoirs. Reference 1 also contains a correlation for the pseudoradial skin factor for wells with deviation up to 75°, with modification indicated for anisotropic reservoirs. To investigate the behavior of deviated wells in layered reservoirs, the model from Ref. 1 can be used as a first approximation, modified to limited flow entry if necessary, but it has been difficult to use more exact models. It is possible, though, to generalize the methods used by Larsen2,3 for vertical wells to also cover deviated wells in layered reservoirs with and without crossflow. For reservoirs without crossflow away from the wellbore, i.e., commingled reservoirs, it is well known how Laplace transforms can be used to handle any model with known solution for individual layers. Deviated wells fall into this category. It is therefore enough to consider systems with crossflow. By including deviated wells with limited flow entry, horizontal wells will also be covered as a special subcategory. Analytical models of this type for horizontal wells have been considered by several authors, e.g., by Suzuki and Nanba4 and by Kuchuk and Habashy.5 Reference 4 is based on both numerical methods and analytical methods based on double transforms (Fourier and Laplace). Reference 5 is based on Green's function techniques. Mathematical Approach To accurately describe flow near deviated wells, and also to capture crossflow in layered reservoirs, three-dimensional flow equations are needed within each layer. If the horizontal permeability is independent of direction within each layer, flow within layer j can be described by the equation k j ( ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 ) p j + k j ′ ∂ 2 p j ∂ z 2 = μ ϕ j c t j ∂ p j ∂ t ( 1 ) under normal assumptions, where kj and kj′ denote horizontal and vertical permeability, and the other indexed variables have the standard meaning for each layer. Since an approach similar to that used in Refs. 2 and 3 will be followed, the vertical variation of pressure within each layer must be removed, at least temporarily. One way to accomplish this is to introduce the vertical average P j ( x , y , t ) = 1 h j ∫ z j − 1 z j p j ( x , y , z , t ) d z ( 2 ) of the pressure within layer j, where zj−1 and zj=zj−1+hj are the z coordinates of the lower and upper layer boundaries. There is one apparent problem with the approach above, it cannot handle the boundary condition at the wellbore directly. For each perforated layer, the well segment will therefore be replaced by a uniform flux fracture in the primary solution scheme, as illustrated in Fig. 1 for a fully perforated deviated well and in Fig. 2 for a partially perforated well with variable angle, with a transient skin effect used to correct from a fractured well solution to a deviated well solution. With well angle θj (as deviation from the vertical) and completed well length Lwj in layer j, the associated fracture half-length will be given by the identity x f j = 1 2 L w j s i n θ j ( 3 ) for each j. The completed well length Lwj is assumed to be a single fully perforated interval. The fracture half-length in layers with vertical well segments will be set equal to the wellbore radius rw. To capture deviated wells with more than one interval within a layer, the model can be subdivided by introducing additional layers. Although the well deviation is allowed to vary through the reservoir, the well azimuth will be assumed constant. The projection of the well in the horizontal plane can therefore be assumed to follow the x axis, and hence assume that y=0 along the well. Keeping the well path in a single plane is actually not necessary, but it simplifies the mathematical development and the computational complexity. If Eq. (1) is integrated from zj−1 to as shown in Eq. (2), then the flow equation k j h j ( ∂ 2 ∂ x 2 + ∂ 2 ∂ y 2 ) P j + k j ′ ∂ p j ∂ z | z j − k j ′ ∂ p j ∂ z | z j − 1 = μ ϕ j c t j h j ∂ P j ∂ t ( 4 ) is obtained, with the gradient terms representing flux through the upper and lower boundaries of layer j. In the standard multiple-permeability modeling of layered reservoirs, the gradient terms are replaced by difference terms in the form k j ′ ∂ p j ∂ z | z j = k j + 1 ′ ∂ p j + 1 ∂ z | z j = λ j ′ ( P j + 1 − P j ) ( 5 ) for each j, where λj′ is a constant determined from reservoir parameters or adjusted to fit the well response. For details on how to choose crossflow parameters, see Refs. 2 and 3 and additional references cited in those papers. Additional fracture to well drawdown is assumed not to affect this approach.

La théorie de la contrôlabilité et du contrôle optimal sont des branches des mathématiques qui ont été développées durant la révolution industrielle pour commander des systèmes d'ingénierie. De nos jours, beaucoup de systèmes sont interconnectés tel qu'Internet, les réseaux de transport ou bien les réseaux électriques. Le monde biologique regorge aussi de réseaux : réseaux vasculaires, réseaux d'interaction de gènes ou même les réseaux de connectivité cérébrale. Contrôler ces systèmes complexes interconnectés est un challenge actuel. La dernière décennie a vu une explosion des études qui appliquent la théorie du contrôle à des réseaux. Des avancées importantes ont permis de comprendre comment sélectionner les nœuds qui peuvent en théorie piloter les réseaux entiers. Par contre, en pratique il est difficile de contrôler le réseau lorsque le nombre de nœuds pilotes est réduit. Cette contrainte est malheureusement commune notamment pour le contrôle des réseaux biologiques. Ce manuscrit explore la limite du contrôle par un seul nœud pilote car c'est la situation la plus vraisemblable dans la perspective de la stimulation cérébrale. Nous avons d'abord observé qu'en pratique un seul nœud pouvait contrôler précisément seulement 5 nœuds. Cette limite avait déjà été observée et nous avons voulu la dépasser. Nous avons alors décidé d'agréger les états des nœuds du réseau en quelques composantes qui seraient représentatives. Nous avons utilisé pour cela la méthode de projection sur les vecteurs propres du Laplacien du réseau. Cette méthode est incontournable dans le domaine de la réduction des réseaux et est aussi utilisée en réduction de dimensionnalité. En ne contrôlant que quelques composantes nous réduisons ainsi drastiquement le nombre de contraintes finales et le problème a un meilleur conditionnement. Nous avons appelé notre méthode : le contrôle en basse dimension des réseaux complexes. Nous avons testé et validé notre approche sur des réseaux simulés. Puis nous l'utilisons pour construire une métrique de contrôlabilité qui n'est pas impactée par les problèmes numériques qui surviennent en haute dimension. Nous avons appliqué la métrique à une grande collection de réseau structurel de cerveaux de plus de 6000 sujets sains. Ceci nous a permis de cartographier la contrôlabilité des 9 réseaux majeurs qui sous-tendent la cognition humaine
Controllability and optimal control are specific fields of mathematics that have been developed since the industrial revolution in order to command engineered systems. Nowadays, many systems are interconnected and form networks like the world wide web, transportation networks, or power grids. The biological world is also full of networks: vascular networks, gene regulation, and brain connectivity networks. Gaining control over these large and complex interconnected systems is challenging. During the last decade, there has been an explosion of studies applying controllability theory to networks. Some breakthroughs were made in characterizing the minimum number of controlled nodes and their placement. However, practically controlling networks and steering them toward specific configurations remains challenging mainly when a small fraction of nodes are controlled which is a common constraint, especially for biological networks. This dissertation aims to explore the limit where only one single driver is allowed as it would certainly be the case for brain stimulation perspectives. We observed in practice that one driver node can only control five target nodes. This practical limit was previously observed and documented so we developed a way to aggregate the states of large networks onto a few representative components. For that, we decided to take advantage of the Laplacian eigenmaps method that was already successfully applied in graph embedding and dimensionality reduction techniques. By controlling a few output components, we drastically reduce the number of terminal constraints and ensure that the problem is well-conditioned. We called our method low-dimensional network control. We tested and validated it with synthetic networks. We found that it can be adapted to build a controllability metric that is well-scaled and which does not suffer from numerical issues that arise in high dimension. We applied our method to a large cohort (N > 6k) of healthy participants deriving a detailed map of single-driver controllability for 9 large-scale networks that support human cognition

In the present paper, we discuss a numerical method based on the level set algorithm to simulate two-phase fluid flow systems. Surface tension force at the fluid interface is implemented through the CSF model of Brackbill et al. [1]. The incompressible Navier-Stokes equations were solved on a staggered grid using an explicit projection method. A fifth-order WENO [2] scheme was used for advancing the level set function. We improved the implementation of WENO scheme by staggering the level set function. The Navier-Stokes part of the code was validated by computing the standard lid-driven cavity flow and the free surface part of the code was validated by advecting the interface in a prescribed velocity field. The Young-Laplace law for a static drop has been verified to validate the implementation of surface tension force. We simulated the coalescence of two drops under zero-gravity condition and evaluated the mass conservation property of the level set method.