Academic literature on the topic 'Generalized Essential Matrix'

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear impulsive dynamical systems in terms of a hybrid vector dissipation inequality involving a vector hybrid supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The chapter also defines generalized notions of a vector available storage and a vector required supply and shows that they are element-by-element ordered, nonnegative, and finite. Extended Kalman-Yakubovich-Popov conditions, in terms of the local impulsive subsystem dynamics and the interconnection constraints, are developed for characterizing vector dissipativeness via vector storage functions for large-scale impulsive dynamical systems. Finally, using the concepts of vector dissipativity and vector storage functions as candidate vector Lyapunov functions, the chapter presents feedback interconnection stability results of large-scale impulsive nonlinear dynamical systems.

Geological data, notably geochemical data, often take the form of a regionalized composition. The concept of regionalized composition combines the concepts of composition and coregionalization. A composition, also known in the literature as a closed array (Chayes 1962), is a random vector whose components add up to a constant. A coregionalization is a set of two or more regionalized variables defined over the same spatial domain, which is modeled as a realization of a vector random function. Here the term regionalized composition is used both for the vector random function used to model a composition and for the realization that we can observe. A regionalized composition can be, for example, a heavy-mineral suite along a river valley. The minerals are quantitatively determined through frequency counts and represented as percent-proportions of the entire heavy-mineral occurrence. Another example is the set of grades in a lead-copper-zinc deposit. In this instance, all components of each specimen are not quantitatively recorded and the grades are also not expressed as proportions of the whole of the measured components: only a small fraction of the composition in ppm is accounted for in each specimen. The problem with the statistical analysis of compositions has been stated historically in terms of correlations: the covariances are subject to essential nonstochastic controls, i.e., distortions which are due to the constant-sum constraint. These numerically induced covariances and correlations arise also with regionalized compositions and are called spurious spatial correlations. They falsify the picture of the spatial covariance structure and can lead to misinterpretations. This problem arises not only when the whole regionalized composition is analyzed, but also when interest lies only in a subvector. A second problem, singularity of the covariance matrix of a composition, has generally been considered only from a numerical point of view. Singularity is a direct consequence of the constant-sum constraint and, as in other multivariate methods, it rules out the use of estimation techniques such as cokriging of all components. Numerically the problem can be tackled either by taking generalized inverses or, equivalently, leaving one component out to avoid singularity of the matrices of coefficients.

Abstract Patzek et al. (2013, 2014) proposed the generalized physics-based scaling curve method as an alternative approach to the empirical decline curve analysis that predicted shale gas well production. Independently, (Patzek, 2019; Patzek et al., 2019) also introduced the Generalized Extreme Value statistics to evaluate cohorts of shale wells and their survival rates. In this work, we built a conceptual reservoir model of a typical, hydraulically fractured well in the northeast Pennsylvania Marcellus shale using a commercial reservoir simulator (CMG-GEM) to validate the generalized master c

A meshless local Petrov-Galerkin (MLPG) method is proposed to obtain the numerical solution of nonlinear heat transfer problems. The moving least squares scheme is generalized, to construct the field variable and its derivative continuously over the entire domain. The essential boundary conditions are enforced by the direct scheme. The radiation heat transfer coefficient is defined, and the nonlinear boundary value problem is solved as a sequence of linear problems each time updating the radiation heat transfer coefficient. The matrix formulation is used to drive the equations for a 3 dimensio

Abstract In order to extend the operation regime of existing gas turbine combustion systems to lower the minimum loads, the applicability of matrix burners (arrays of jet flames) as an alternative to conventional swirl stabilized burners has been considered. In comparison to well-studied single jet flame systems, the effects of geometry and thermodynamic parameters on characteristics of matrix burner systems have not been studied in detail. Information, which is essential for design processes e.g. scaling of matrix burners, is not yet available in public domain. This work involves a systematic

Design research has generated many computational tools to aid the designer over the years. Most of these tools are focused on either the preliminary steps of customer need gathering or the concluding steps of embodiment or detail design. The conceptual design phase has seen fewer computational tools even though well known methods are available such as brainstorming, intrinsic and extrinsic searches and morphological analysis. In this paper a generalized computational conceptual design tool is presented to aid designers at the conceptual design stage. It relies on storing and reusing existing d

Fifty years ago, the railcar industry relied entirely on classical analysis methods using fundamental solid mechanics theory to establish design and manufacturing protocols. While this method produced working designs, the assumptions required by this type of analysis often led to overdesigned railcars. In the 1950s, the generalized mathematical approach of Finite Element Analysis (FEA) was developed to model the structural behaviors of mechanical systems. FEA involves creating a numerical model by discretizing a continuous system into a finite system of grid divisions. Each grid division, or e

In both simple ferrite-carbide materials, and more complex ferritic steels, cleavage is mediated by the fracture of the particles they contain. If particle cracking is easy, then extension of the resulting particle-sized microcracks into the ferrite matrix, can become the critical step in inducing fracture. Under these circumstances, brittle fracture is essentially stress-controlled, and several models use this as a basis for failure prediction. Fracture toughness data from a series of MnMoNi steels are presented, together with observations of fracture initiation sites, and calculations of the