Dominant Matrix Research Articles

Determination of oxidation rates and volatile oxidation products for HTGR graphite matrix material exposed to steam atmospheres

High-temperature gas-cooled reactors (HTGRs) in operation use tristructural isotropic (TRISO) particles embedded in graphite and carbonized resin matrix to form the fuel element. This graphite matrix material serves as a supportive structural element, heat transfer medium, and neutron moderator. In HTGR designs, fuel compacts are exposed to helium coolant, which facilitates high outlet temperatures (750°C<T<950°C) and subsequently greater thermal efficiency than current commercial power reactors. However, data pertaining to the oxidation resistance of graphite matrix material in HTGR accident or off-normal conditions (<50k kPa pH2O, 800°C<T<1600°C) is limited. In this study, both the oxidation behavior of matrix graphite material and its gas-phase products, including CO, CO2, and H2, are quantified in varied oxidant atmospheres using a coupled thermogravimetric analyzer and mass spectrometer. Oxidation rates reported here for varied steam (H2O [g]) atmospheres are predominantly linear and comparable with literature values in the range of tested temperatures (800–1200°C). Changes in dominant matrix oxidation products from primarily CO to a mixture of CO, CO2, and H2 were observed at higher temperatures (≥1000°C) and steam atmospheres (≥5 kPa pH2O). Kinetic data indicates that there was no shift in oxidation regime with chemical oxidation occurring at all temperatures and H2O (g) atmospheres tested. These data provide insight into the oxidation behavior of graphite matrix material and will inform future testing conditions, notably mixed atmospheric conditions, of HTGR fuel elements.

Fast Power Series Solution of Large 3-D Electrodynamic Integral Equation for PEC Scatterers

This paper presents a new fast power series solution method to solve the Hierarchal Method of Moment (MoM) matrix for a large complex, perfectly electric conducting (PEC) 3D structures. The proposed power series solution converges in just two (2) iterations which is faster than the conventional fast solver–based iterative solution. The method is purely algebraic in nature and, as such applicable to existing conventional methods. The method uses regular fast solver Hierarchal Matrix (H-Matrix) and can also be applied to Multilevel Fast Multipole Method Algorithm (MLFMA). In the proposed method, we use the scaling of the symmetric near-field matrix to develop a diagonally dominant overall matrix to enable a power series solution. Left and right block scaling coefficients are required for scaling near-field blocks to diagonal blocks using Schur’s complement method. However, only the right-hand scaling coefficients are computed for symmetric near-field matrix leading to saving of computation time and memory. Due to symmetric property, the left side-block scaling coefficients are just the transpose of the right-scaling blocks. Next, the near-field blocks are replaced by scaled near-field diagonal blocks. Now the scaled near-field blocks in combination with far-field and scaling coefficients are subjected to power series solution terminating after only two terms. As all the operations are performed on the near-field blocks, the complexity of scaling coefficient computation is retained as O(N)O⁢(N). The power series solution only involves the matrix-vector product of the far-field, scaling coefficients blocks, and inverse of scaled near-field blocks. Hence, the solution cost remains O(NlogN)O⁢(N⁢l⁢o⁢g⁢N). Several numerical results are presented to validate the efficiency and robustness of the proposed numerical method.

Refinement of Multiparameters Overrelaxation (RMPOR) Method

In this paper, we present refinement of multiparameters overrelaxation (RMPOR) method which is used to solve the linear system of equations. We investigate its convergence properties for different matrices such as strictly diagonally dominant matrix, symmetric positive definite matrix, and M-matrix. The proposed method minimizes the number of iterations as compared with the multiparameter overrelaxation method. Its spectral radius is also minimum. To show the efficiency of the proposed method, we prove some theorems and take some numerical examples.

Refinement of Extended Accelerated Over-Relaxation Method for Solution of Linear Systems

Given any linear stationary iterative methods in the form z^(i+1)=Jz^(i)+f, where J is the iteration matrix, a significant improvements of the iteration matrix will decrease the spectral radius and enhances the rate of convergence of the particular method while solving system of linear equations in the form Az=b. This motivates us to refine the Extended Accelerated Over-Relaxation (EAOR) method called Refinement of Extended Accelerated Over-Relaxation (REAOR) so as to accelerate the convergence rate of the method. In this paper, a refinement of Extended Accelerated Over-Relaxation method that would minimize the spectral radius, when compared to EAOR method, is proposed. The method is a 3-parameter generalization of the refinement of Accelerated Over-Relaxation (RAOR) method, refinement of Successive Over-Relaxation (RSOR) method, refinement of Gauss-Seidel (RGS) method and refinement of Jacobi (RJ) method. We investigated the convergence of the method for weak irreducible diagonally dominant matrix, matrix or matrix and presented some numerical examples to check the performance of the method. The results indicate the superiority of the method over some existing methods.

A stable parallel algorithm for block tridiagonal toeplitz–block–toeplitz linear systems

In this paper, we present a direct parallel block WZ algorithm, named DPBWZA, for the solution of block tridiagonal toeplitz–block–toeplitz (TBT) linear system Ax=f. The algorithm is based on the proposed block WZ factorization of the coefficient matrix A. Existence of the block WZ factorization for block tridiagonal TBT block diagonally dominant matrix is proved. Error analysis of the parallel algorithm DPBWZA is presented and numerical stability of the algorithm is established. Numerical experiments are conducted to demonstrate the efficiency, stability and accuracy of the Direct Parallel Block WZ Algorithm on GPU platform. Forward and backward errors are computed and DPBWZA is found to be highly accurate, numerically stable and as efficient as the subroutine csrlsvlu of GPU accelerated cuSolverSP library.

Religiones, teologías y colonialidad: hacia la decolonización de los estudios académicos de las religiones y las teologías

This text analyses the routes to develop decolonial academic studies of religions and theologies. Based on a literature review of the subject, the text discusses the following questions: What does it mean to advance decolonial academic studies of religions and theologies? To what extent is it possible for the academic study of religion and theology to go beyond the dominant colonial matrix of power? What specific challenges are faced by scholars interested in developing decolonial discussions of religions and theologies?

Aluminum Recovery from White Aluminum Dross by a Mechanically Activated Phase Separation and Remelting Process

The aluminum recovery from white aluminum dross by a mechanical treatment and sizing followed by remelting process was investigated. The dross was subjected to a ball mill, and the obtained particles were sized in different ranges. They were studied by advanced materials characterization techniques. It was found that the larger particles contain high metallic portions, and most non-metallic components of the dross are in the fine fraction < 1 mm. The Al-rich particles (> 1 mm) were remelted at 900°C to recover aluminum. It was found that the metal structure after remelting is homogeneous and consisted of a dominant metallic aluminum matrix, containing an average of > 96% Al with around 99% total metallic components. The results show that the applied method is a good economic alternative for the aluminum recovery from white dross, which is important for the valorization/recycling of industrial waste and circular economy.

Multistability of Hopfield neural networks with a designed discontinuous sawtooth-type activation function

In this paper, a class of discontinuous sawtooth-type activation function is designed and the multistability of Hopfield neural networks (HNNs) with such kind of activation function is studied. By virtue of the Brouwer’s fixed point theorem and the property of strictly diagonally dominant matrix (SDDM), some sufficient conditions are presented to ensure that the n-neuron HNN can have at least 7n equilibria, among which 4n equilibria are locally exponentially stable and the remaining 7n-4n equilibria are unstable. Then, the obtained results are extended to a more general case. We continue to increase the number of the peaks of the sawtooth-type activation function and we find that the n-neuron HNN can have (2k+3)n equilibria, (k+2)n of them are locally exponentially stable and the remaining equilibria are unstable. Therein, k denotes the total number of the peaks in the designed activation function. That is to say, there is a quantitative relationship between the number of the peaks and the number of the equilibria. It implies that one can improve the storage capacity of a HNN by increasing the number of the peaks of the activation function in theory and in practice. To some extent, this method is convenient and flexible. Compared with the existing results, HNN with the designed sawtooth-type activation function can have more total equilibria as well as more locally stable equilibria. Finally, two examples are presented to demonstrate the validity of the obtained results.

Adaptive PI Control for Consensus of Multiagent Systems With Relative State Saturation Constraints.

The relative state between neighbors represents the difference of two connected agents' states, and it possesses specific physical meanings in practice. Under this background, the saturation constraints in the relative state inevitably occur. This article studies the consensus problems under the relative state saturation constraints. Novel adaptive proportional-integral (PI) protocols are designed to solve the constrained consensus problem. Specifically, the adaptive coupling weights and the saturation functions are embedded into the proposed protocols, and the former can render the protocols independent of any global topology graph information, while the latter can confine the relative state to stay in its constrained set. Sufficient conditions are identified under which the constrained consensus can be achieved. Considering that the solution matrix is required to be diagonally dominant, an iterative learning-based heuristic algorithm is proposed to seek the diagonally dominant positive-definite solution matrix. For the special case that the input matrix is row full rank, more stringent saturation functions are constructed, and it not only achieves the constrained consensus but also realizes the nonovershoot and shorter settling time associated with edge states. Besides, this result can be applied to preserve connectivity of the communication network. The theoretical analyses are validated by a simulation example.

A computationally efficient symmetric diagonally dominant matrix projection-based Gaussian process approach

Although kernel approximation methods have been widely applied to mitigate the O(n3) cost of the n×n kernel matrix inverse in Gaussian process methods, they still face computational challenges. The ‘residual’ matrix between the covariance matrix and the approximating component is often discarded as it prevents the computational cost reduction. In this paper, we propose a computationally efficient Gaussian process approach that achieves better computational efficiency, O(mn2), compared with standard Gaussian process methods, when using m≪n data. The proposed approach incorporates the ‘residual’ matrix in its symmetric diagonally dominant form which can be further approximated by the Neumann series. We have validated and compared the approach with full Gaussian process approaches and kernel approximation based Gaussian process variants, both on synthetic and real air quality data.

Graph-Based Sparsification and Synthesis of Dense Matrices in the Reduction of RLC Circuits

The integration of more components into modern integrated circuits (ICs) has led to very large RLC parasitic networks consisting of millions of nodes that have to be simulated in many times or frequencies to verify the proper operation of the chip. Model order reduction (MOR) techniques have been employed routinely to substitute the large-scale parasitic model with a model of lower order with a similar response at the input–output ports. However, established MOR techniques generally result in dense system matrices that render their simulation impractical. To this end, in this article, we propose a methodology for the sparsification of the dense circuit matrices resulting from MOR of general RLC circuits, which employs a sequence of algorithms based on the computation of the nearest diagonally dominant matrix and the sparsification of the corresponding graph. In addition, we describe a procedure for synthesizing the sparsified reduced-order model into an RLC circuit with only positive elements. Experimental results indicate that a high sparsity ratio of the reduced system matrices can be achieved with very small loss of accuracy.

Bioleaching of metals from secondary materials using glycolipid biosurfactants

With the global demand for economically important metals increasing, compounded by the depletion of readily accessible ores, secondary resources and low-grade ores are being targeted to meet growing demands. Novel technologies developed within biobased industries, such as microbial biosurfactants, could be implemented to improve the sustainability of traditional hydrometallurgy techniques. This study investigates newly developed microbial biosurfactants (acidic- and bolaform glycolipids) for the leaching of metals (particularly Cu and Zn) from a suite of mine tailings, metallurgical sludges and automotive shredder residues. Generally, acidic sophorolipids were the most performant, and optimal Cu leaching was observed from a fayalite slag (27%) and a copper sulfide mine tailing (53%). Further investigation of the leached fayalite material showed that leaching was occurring from small metallic Cu droplets in this material via a corrosion-based mechanism, and/or from Cu-Pb sulfides, selective against the dominant Fe-silicate matrix. This study highlights that acidic sophorolipid microbial biosurfactants have the potential to leach Cu and Zn from low-grade secondary materials. It also provides important fundamental insights into biosurfactant-metal and mineral interactions that are currently unexplored. Together, the convergence of leaching and mining industries with bio-industries can improve material recovery and will positively impact the bio- and circular economies and the environment.

Petrophysical evaluation of lower Cenomanian Bahariya reservoir, Salam oil field, Shushan basin, north Western Desert, Egypt.

Petrophysical evaluation of the lower Bahariya sediments was performed based on comprehensive interpretation of complete wireline logs suite from two wells in Salam oil field, southwest Shushan basin in the north Western Desert, Egypt. Several petrophysical parameters such as shale volume (VSH), total and effective porosities (PHIT, PHIE), water saturation (SW) and hydrocarbon saturation (SH) were deduced and utilized in the petrophysical subdivision of the lower Bahariya sediments. Neutron versus density, matrix volumetric versus matrix grain density and M-N crossplots revealed that quartzose sandstone is the dominant matrix component within the lower Bahariya sediments. Additionally, the litho-saturation crossplots typified the presence of oil-bearing intervals often associated with the quartzose sandstones with minimal contents of silts and clays. Dispersed and laminated clays are detrimental to the reservoir quality by obstructing the pore spaces and thus reducing the hydrocarbon flow storage and flow capacities. The obtained petrophysical results reveal that the lower Bahariya sediments have a good reservoir quality with high effective porosity values exceeding 18% and low water saturation values ~ 35%. The upper part of the lower Bahariya sediments hosts the most promising reservoir intervals which should be considered during future exploration and development of the oil fields in the study area. Petrophysical evaluation of the lower Bahariya sediments was performed based on comprehensive interpretation of complete wireline logs suite from two wells in Salam oil field, southwest Shushan basin in the north Western Desert, Egypt. Several petrophysical parameters such as shale volume (VSH), total and effective porosities (PHIT, PHIE), water saturation (SW) and hydrocarbon saturation (SH) were deduced and utilized in the petrophysical subdivision of the lower Bahariya sediments. Neutron versus density, matrix volumetric versus matrix grain density and M-N crossplots revealed that quartzose sandstone is the dominant matrix component within the lower Bahariya sediments. Additionally, the litho-saturation crossplots typified the presence of oil-bearing intervals often associated with the quartzose sandstones with minimal contents of silts and clays. Dispersed and laminated clays are detrimental to the reservoir quality by obstructing the pore spaces and thus reducing the hydrocarbon flow storage and flow capacities. The obtained petrophysical results reveal that the lower Bahariya sediments have a good reservoir quality with high effective porosity values exceeding 18% and low water saturation values ~ 35%. The upper part of the lower Bahariya sediments hosts the most promising reservoir intervals which should be considered during future exploration and development of the oil fields in the study area.

A unified linear mixed model for familial relatedness and population structure in genetic association studies.

Familial relatedness (FR) and population structure (PS) are two major sources for genetic correlation. In the human population, both FR and PS can further break down into additive and dominant components to account for potential additive and dominant genetic effects. In this study, besides the classical additive genomic relationship matrix, a dominant genomic relationship matrix is introduced. A link between the additive/dominant genomic relationship matrices and the coancestry (or kinship)/double coancestry coefficients is also established. In addition, a way to separate the FR and PS correlations based on the estimates of coancestry and double coancestry coefficients from the genomic relationship matrices is proposed. A unified linear mixed model is also developed, which can account for both the additive and dominance effects of FR and PS correlations as well as their possible random interactions. Finally, this unified linear mixed model is applied to analyze two study cohorts from UK Biobank.

Application of the parallel diagonal dominant algorithm for the incompressible Navier-Stokes equations

The accuracy and the applicability of the parallel diagonal dominant (PDD) algorithm are explored for highly scalable computation of the incompressible Navier-Stokes equations which are integrated using a fully-implicit fractional-step method in parallel computational environments. The PDD algorithm is known to be applicable only for an evenly diagonal dominant matrix. In the present study, however, it is shown mathematically that the PDD algorithm is utilizable even for non-diagonal dominant matrices derived from discretization of incompressible momentum equations. The order of accuracy and the error characteristics are investigated in detail in terms of the Courant-Friedrichs-Lewy (CFL) number and the grid spacing by conducting simulations of decaying vortices in both two and three dimensions, flow in a lid-driven cavity, and flow over a circular cylinder. In order to reduce communication cost, which is one of bottlenecks in parallel computation, an aggregative data communication method is combined with the PDD algorithm. Parallel performance of the present PDD-based method is investigated by measuring the speedup, efficiency, overhead, and serial fraction.

Output event triggered consensus control of nonlinear multi-agent systems with relative state constraints

The relative state constraints is inevitable in multi-agent systems(MASs) because of limited sensing capabilities of the sensors. In this paper, the consensus problem of nonlinear MASs with relative state constraints is investigated in an edge perspective. First, the consensus problem is proved to be equivalent to a stabilization problem characterized by the edge dynamics. Then the edge system is confined to a hypercube for the satisfaction of relative constraints. Finally, an output event-triggered control protocol that can exponentially stabilize the edge dynamics with constraints is proposed. Sufficient conditions on system stability are provided, the Singular triggering and the Zeno-behaviour are also excluded. A simple learning-based iterative algorithm is proposed to calculate the diagonally dominant matrix, which is crucial to the controller gain design. The effectiveness of the results is illustrated through numerical examples.

Mechanical and microstructural properties of ultra-translucent dental zirconia ceramic stabilized with 5 mol% yttria

Monolithic dental prostheses fabricated from 3 mol.% yttria-stabilized zirconia (3YZ) are becoming increasingly popular. Recently, 5 mol.% yttria-stabilized zirconia (5YZ) which significantly improves the translucency of 3YZ has been prepared. However, its mechanical and microstructural properties, especially those affected by low-temperature degradation (LTD), have not been fully elucidated yet. The objective of the present study was to establish the relationship between the flexural strength of 5YZ with or without autoclave-induced LTD and its microstructural properties. For this purpose, a total of 320 bar-shaped specimens were cut from 5YZ and 3YZ blocks, and half of the specimens in each group were autoclaved at 134 °C for 50 h. Their flexural strengths were determined by conducting three-point bending tests, and the obtained results were analyzed by the Weibull statistical method. Grain sizes and crystalline structures of the specimens were analyzed by scanning electron microscopy (SEM) and X-ray diffraction, respectively. Additionally, the LTD-induced phase transformation was examined by Raman microscopy and cross-sectional surface analysis. The characteristic strengths of 5YZ and 3YZ were approximately 620 and 950 MPa, respectively, and 5YZ was found to be more resistant to LTD in terms of phase transformation than 3YZ. However, a low amount of the monoclinic phase was detected even in 5YZ after 50 h of autoclaving, which significantly decreased its flexural strength and reliability. The results of SEM analysis revealed that 5YZ was composed of two distinct regions: a dominant matrix with large grains (median size: 0.8 μm) and scattered areas with small grains (median size: 0.4 μm). Phase transformation analysis and fractography data indicated that the small-grain region was strongly affected by LTD and likely represented a fracture origin. The described properties should be considered during the clinical application of monolithic 5YZ dental prostheses.

Nekrasov Type Matrices and Upper Bounds for Their Inverses

The paper considers the so-called P-Nekrasov and {P1, P2}-Nekrasov matrices, defined in terms of permutation matrices P, P1, P2, which generalize the well-known notion of Nekrasov matrices. For such matrices A, available upper bounds on ‖A−1‖∞ are recalled, and new upper bounds for the P-Nekrasov and {P1, P2}-Nekrasov matrices are suggested. It is shown that the latter bound generally improves the earlier bounds, as well as the bound for the inverse of a P-Nekrasov matrix and the classical bound for the inverse of a strictly diagonally dominant matrix. Bibliography: 12 titles.

Event-Triggered Fuzzy Control of Repeated Scalar Nonlinear Systems and its Application to Chua’s Circuit System

This paper addresses the problem of event-triggered $\mathcal {H}_{\infty }$ control for continuous Takagi-Sugeno fuzzy systems with repeated scalar nonlinearities. A feasible stability solution is first proposed based on the fuzzy-rule-dependent Lyapunov functional methods and positive definite diagonally dominant matrix techniques, which not only reduces the conservativeness of the resulting closed-loop dynamic system, but also ensures the concerned fuzzy system is asymptotically stable with a specified $\mathcal {H}_{\infty }$ disturbance attenuation performance. Then, sufficient conditions are presented for the existence of admissible state-feedback controller, and the cone complementarity linearization approach is employed to convert the non-convex feasibility problem into a sequential minimization one subject to linear matrix inequalities, which can be validly solved by employing standard numerical software. In the end, a numerical example and a Chua’s chaotic circuit system are provided to show the applicability of the proposed theories.

Second-refinement of Gauss-Seidel iterative method for solving linear system of equations

Although large and sparse linear systems can be solved using iterative methods, its number of iterations is relatively large. In this case, we need to modify the existing methods in order to get approximate solutions in a small number of iterations. In this paper, the modified method called second-refinement of Gauss-Seidel method for solving linear system of equations is proposed. The main aim of this study was to minimize the number of iterations, spectral radius and to increase rate of convergence. The method can also be used to solve differential equations where the problem is transformed to system of linear equations with coefficient matrices that are strictly diagonally dominant matrices, symmetric positive definite matrices or M-matrices by using finite difference method. As we have seen in theorem 1and we assured that, if A is strictly diagonally dominant matrix, then the modified method converges to the exact solution. Similarly, in theorem 2 and 3 we proved that, if the coefficient matrices are symmetric positive definite or M-matrices, then the modified method converges. And moreover in theorem 4 we observed that, the convergence of second-refinement of Gauss-Seidel method is faster than Gauss-Seidel and refinement of Gauss-Seidel methods. As indicated in the examples, we demonstrated the efficiency of second-refinement of Gauss-Seidel method better than Gauss-Seidel and refinement of Gauss-Seidel methods.