The Experts below are selected from a list of 321 Experts worldwide ranked by ideXlab platform

Dieter Lilge - One of the best experts on this subject based on the ideXlab platform.

Randolf D Kohn - One of the best experts on this subject based on the ideXlab platform.

Andrei A. Kulikovsky - One of the best experts on this subject based on the ideXlab platform.

  • How important is oxygen transport in agglomerates in a PEM fuel cell catalyst layer?
    Electrochimica Acta, 2014
    Co-Authors: Andrei A. Kulikovsky
    Abstract:

    We derive analytical solution for the polarization curve of the cathode catalyst layer (CCL), taking into account oxygen transport in agglomerates of carbon particles. The solution shows that in modern catalyst layers with agglomerates of the radius 100 nm, the oxygen transport in agglomerates manifests itself at cell potentials below 100 mV only. Thus, the account of this transport in CCL Modeling is redundant, i.e., the standard macro-Homogeneous Model is adequate for CCL performance simulations. © 2014 Elsevier Ltd.

Stephen Mann - One of the best experts on this subject based on the ideXlab platform.

  • Applications of the Homogeneous Model
    Geometric Algebra for Computer Science, 2020
    Co-Authors: Leo Dorst, Daniel Fontijne, Stephen Mann
    Abstract:

    The Homogeneous Model is well-suited to applications in which incidences of offset flat subspaces are central, but less so when metric properties are also important. In this, it plays a role similar to Grassmann-Cayley algebra. This chapter gives details on its direct use in applications. In the first part, it discusses the coordinate representations of the Homogeneous elements. This naturally embeds the powerful Plucker coordinates for line computations, which are seen to be are a natural extension of Homogeneous point coordinates (using the outer product). This chapter shows how to master them and derive new application formulas simply. Those coordinates for lines, as well as points and planes, permit compact formulation of the affine transformations as matrices. In the second part, it gives an advanced application of the Homogeneous Model. It is well-suited to encode the projective geometry involved in the imaging of the world by one or more pinhole cameras. The Homogeneous Model permits easy specification of how observations in the various cameras are connected, which permits using observations by one camera to guide the search for corresponding features in another camera. This chapter treats the fairly advanced subjects of stereo-vision based on point and line matches in 2 or 3 cameras. Both subjects of this chapter are incidental to the main flow of the book, though the section on Plucker coordinates prepares for the implementation of geometric algebra in Part III.

  • The Homogeneous Model
    Geometric Algebra for Computer Science (Revised Edition), 2020
    Co-Authors: Leo Dorst, Daniel Fontijne, Stephen Mann
    Abstract:

    While the 3-D vector space Model can nicely Model directions, it is usually considered to be inadequate for use in 3-D computer graphics, primarily because of a desire to treat points and vectors as different elements that are transformed differently by translations. Instead, people commonly use an extension of linear algebra known as Homogeneous coordinates. This is often described as augmenting a 3-D vector v with coordinates (v1,v2,v3) T to a 4-vector (v1,v2,v3,1) T . This extension makes nonlinear operations such as translations implementable as linear mappings. For the Homogeneous Model in geometric algebra, the Modeling principle is the same: it embeds the n-dimensional base space R n in an (n +1)-dimensional representational vector space R n+1 , of which it then uses the inherent algebra. That produces a complete algebraic framework, which is well suited to compute with oriented flats, subspaces offset from the origin in R n represented as blades in R n+1 . The algebra of R n+1 provides generally applicable formulas for translation, rotation, and even affine and projective transformations in the base space R n . The operations of meet and join always return sensible results for incidences of flats. Some of the incidence constructions are cross ratios and can be interpreted as defining motion-invariant measures. Then motions and transformations are studied and show that all direct flats are moved by the same linear transformation and all dual flats by another. This simplifies the code even more.

  • Chapter 12 – Applications of the Homogeneous Model
    Geometric Algebra for Computer Science (Revised Edition), 2020
    Co-Authors: Leo Dorst, Daniel Fontijne, Stephen Mann
    Abstract:

    Publisher Summary The Homogeneous Model is well suited to applications in which incidences of offset flat subspaces are central, but less so when metric properties are also important. It plays a role similar to Grassmann–Cayley algebra. They require 6-D vectors and corresponding matrices, which appear extraneous to the usual 4-D data structures in Homogeneous coordinate software. The Plucker coordinate representation and its associated matrices show how an implementation of geometric algebra can make use of the sparseness of the geometrically significant structures. In principle, the Clifford algebra of the 4-D representation space has 24 = 16 dimensions, and arbitrary linear transformations on this algebra would therefore require 16 × 16 matrices, to be applied to a 16 × 1 vector, for some 2 × 162 = 512 operations per transformation.

  • 11 – The Homogeneous Model
    Geometric Algebra for Computer Science, 2020
    Co-Authors: Leo Dorst, Daniel Fontijne, Stephen Mann
    Abstract:

    Publisher Summary While the 3-D vector space Model can nicely Model directions, it is usually considered to be inadequate for use in 3-D computer graphics, primarily because of a desire to treat points and vectors as different elements that are transformed differently by translations. Instead, people commonly use an extension of linear algebra known as Homogeneous coordinates. This is often described as augmenting a 3-D vector v with coordinates (v1,v2,v3)T to a 4-vector (v1,v2,v3,1)T. This extension makes nonlinear operations such as translations implementable as linear mappings. For the Homogeneous Model in geometric algebra, the Modeling principle is the same: it embeds the n-dimensional base space Rn in an (n +1)-dimensional representational vector space Rn+1, of which it then uses the inherent algebra. That produces a complete algebraic framework, which is well suited to compute with oriented flats, subspaces offset from the origin in Rn represented as blades in Rn+1. The algebra of Rn+1 provides generally applicable formulas for translation, rotation, and even affine and projective transformations in the base space Rn. The operations of meet and join always return sensible results for incidences of flats. Some of the incidence constructions are cross ratios and can be interpreted as defining motion-invariant measures. Then motions and transformations are studied and show that all direct flats are moved by the same linear transformation and all dual flats by another. This simplifies the code even more.

S Srinivasan - One of the best experts on this subject based on the ideXlab platform.

  • an evaluation of the macro Homogeneous and agglomerate Model for oxygen reduction in pemfcs
    Electrochimica Acta, 1998
    Co-Authors: Frederic Gloaguen, P Convert, S Gamburzev, O Velev, S Srinivasan
    Abstract:

    The kinetics of oxygen reduction reaction on platinum/carbon powders in a Nafion film were evaluated with rotating disk electrode and gas diffusion electrode. The effects of the activation, mass transport and ohmic overpotentials were simulated via an “effectiveness factor” approach. The macro-Homogeneous Model was suitable to simulate the ORR kinetics at the RDE. On the other hand, it was found that the macro-Homogeneous Model does not simulate the operation of a porous gas diffusion cathode in PEMFC. With this Model, the diffusion overpotential in the cathode is considerably overestimated. Conversely, the good agreement between calculated and experimental Tafel plots demonstrates the validity of the agglomerate Model, even though the active layers of the PEMFC electrodes were thin and contained no PTFE. These results provided evidence for a two step transport process in the active layer of PEMFC electrodes.