scholarly journals Formation of Moments Influence Matrix in Frame Based on Graph of its Design Scheme

2021 ◽  
Vol 346 ◽  
pp. 03087
Author(s):  
V.А. Monakhov ◽  
А.I. Shein
Keyword(s):  
Incidence Matrix ◽  
Frame Structure ◽  
Matrix Transformations ◽  
Bending Moments ◽  
Influence Matrix ◽  
Design Scheme ◽  
Displacement Vectors ◽  
The Matrix ◽  
Nodal Displacements ◽  
The Relationship

A procedure is proposed for the automated construction of the bending moments influence matrix in the frame based on the graph of its discrete model. Forming the incidence matrix of the graph characterizing the topological structure of the design scheme of the frame, through matrix transformations of the displacement vectors, at the transition from local coordinate systems to a global system, it is possible to establish the relationship between the nodal displacements and the displacement increments of individual sections in the direction of the axis of the segment and perpendicular to it. The composition of only three initial matrices of the frame structure, the incidence matrix of the graph, the node coordinate matrix and the matrix of the frame model internal rigidity, solves the problem of automatic formation of the bending moments influence matrix with the help of a PC. The procedure proposed for the construction of the influence matrix, makes it possible to find the forces in the frame structure caused by external load, in the matrix form.

scholarly journals Of the matrics of the equilibrium of the rod formation system based on the principle the duality of the problems of structures mechanics

2019 ◽  
Vol 298 ◽  
pp. 00055
Author(s):  
Vladimir Monakhov
Keyword(s):  
Cross Sections ◽  
Incidence Matrix ◽  
Matrix Form ◽  
Duality Principle ◽  
Core System ◽  
The Core ◽  
The Matrix ◽  
Equilibrium Matrix ◽  
Nodal Displacements ◽  
Formation System

The formation of the equilibrium matrix of the core system in the matrix form is based on the use of the mechanical model of the system obtained by its discretization. The topological structure of the model is set using the graph and the accompanying incidence matrix. The matrix transformation of the vector of nodal displacements in combination with the extended incidence matrix allows determining the absolute elongations and distortions of each finite element. The composition of only two matrices (matrix of incidence and lengths of elements) and the skew vector leads to a geometric matrix characterizing the dependence of concentrated bending deformations in the calculated cross sections of the core system from the nodal displacements for a given load. Based on the duality principle, by transposing the geometric matrix, the equilibrium equation of the core system is derived in matrix form.

Determining Diagonal Branches in Mine Ventilation Networks

2014 ◽  
Vol 59 (4) ◽  
pp. 1097-1105 ◽  
Author(s):  
Andrzej Krach
Keyword(s):  
Incidence Matrix ◽  
Mine Ventilation ◽  
Ventilation Network ◽  
The Matrix ◽  
End Node ◽  
The Relationship ◽  
Ventilation Networks ◽  
Graph Nodes

Abstract The present paper discusses determining diagonal branches in a mine ventilation network by means of a method based on the relationship A⊗ PT(k, l) = M, which states that the nodal-branch incidence matrix A, modulo-2 multiplied by the transposed path matrix PT(k, l ) from node no. k to node no. l, yields the matrix M where all the elements in rows k and l - corresponding to the start and the end node - are 1, and where the elements in the remaining rows are 0, exclusively. If a row of the matrix M is to contain only „0” elements, the following condition has to be fulfilled: after multiplying the elements of a row of the matrix A by the elements of a column of the matrix PT(k, l), i.e. by the elements of a proper row of the matrix P(k, l ), the result row must display only „0” elements or an even number of „1” entries, as only such a number of „1” entries yields 0 when modulo-2 added - and since the rows of the matrix A correspond to the graph nodes, and the path nodes level is 2 (apart from the nodes k and l, whose level is 1), then the number of „1” elements in a row has to be 0 or 2. If, in turn, the rows k and l of the matrix M are to contain only „1” elements, the following condition has to be fulfilled: after multiplying the elements of the row k or l of the matrix A by the elements of a column of the matrix PT(k, l), the result row must display an uneven number of „1” entries, as only such a number of „1” entries yields 1 when modulo-2 added - and since the rows of the matrix A correspond to the graph nodes, and the level of the i and j path nodes is 1, then the number of „1” elements in a row has to be 1. The process of determining diagonal branches by means of this method was demonstrated using the example of a simple ventilation network with two upcast shafts and one downcast shaft.

Soil and Stream Water Chemistry During Spring Snowmelt

1992 ◽  
Vol 23 (1) ◽  
pp. 13-26 ◽  
Author(s):  
W. H. Hendershot ◽  
L. Mendes ◽  
H. Lalande ◽  
F. Courchesne ◽  
S. Savoie
Keyword(s):  
Stream Water ◽  
Base Cations ◽  
Stream Chemistry ◽  
Stream Water Chemistry ◽  
The Matrix ◽  
Adsorption Desorption ◽  
The Relationship ◽  
Best Fit ◽  
Spring Snowmelt ◽  
Over Time

In order to determine how water flowpath controls stream chemistry, we studied both soil and stream water during spring snowmelt, 1985. Soil solution concentrations of base cations were relatively constant over time indicating that cation exchange was controlling cation concentrations. Similarly SO4 adsorption-desorption or precipitation-dissolution reactions with the matrix were controlling its concentrations. On the other hand, NO3 appeared to be controlled by uptake by plants or microorganisms or by denitrification since their concentrations in the soil fell abruptly as snowmelt proceeded. Dissolved Al and pH varied vertically in the soil profile and their pattern in the stream indicated clearly the importance of water flowpath on stream chemistry. Although Al increased as pH decreased, the relationship does not appear to be controlled by gibbsite. The best fit of calculated dissolved inorganic Al was obtained using AlOHSO4 with a solubility less than that of pure crystalline jurbanite.

Effect of mechanical restraint on the rate of corrosion in concrete

1998 ◽  
Vol 25 (1) ◽  
pp. 81-86 ◽  
Author(s):  
N Hearn ◽  
J Aiello
Keyword(s):  
Mix Design ◽  
Concrete Repair ◽  
Accelerated Corrosion ◽  
One Dimensional ◽  
Mechanical Restraint ◽  
Corrosion Rates ◽  
Accelerated Corrosion Tests ◽  
The Matrix ◽  
The Relationship

Experimental work on prismatic concrete specimens was conducted to determine the relationship between mechanical restraint and the rate of corrosion. The current together with the changes in strain of the confining frame were monitored during the accelerated corrosion tests. The effect of mix design and cracking on the corrosion rates was also investigated. The results show that one-dimensional mechanical restraint retards the corrosion process, as indicated by the reduction in the steel loss. Improved quality of the matrix, with and without cracking, reduces the rate of steel loss. In the inferior quality concrete, the effect of cracking on the corrosion rate is minimal.Key words: corrosion, concrete, repair.

ExperimentSubset: an R package to manage subsets of Bioconductor Experiment objects

2021 ◽  
Author(s):  
Irzam Sarfraz ◽  
Muhammad Asif ◽  
Joshua D Campbell
Keyword(s):  
Single Cell ◽  
R Package ◽  
Poor Quality ◽  
Data Matrix ◽  
Supplementary Information ◽  
Data Provenance ◽  
Rna Seq ◽  
Efficient Management ◽  
The Matrix ◽  
The Relationship

Abstract Motivation R Experiment objects such as the SummarizedExperiment or SingleCellExperiment are data containers for storing one or more matrix-like assays along with associated row and column data. These objects have been used to facilitate the storage and analysis of high-throughput genomic data generated from technologies such as single-cell RNA sequencing. One common computational task in many genomics analysis workflows is to perform subsetting of the data matrix before applying down-stream analytical methods. For example, one may need to subset the columns of the assay matrix to exclude poor-quality samples or subset the rows of the matrix to select the most variable features. Traditionally, a second object is created that contains the desired subset of assay from the original object. However, this approach is inefficient as it requires the creation of an additional object containing a copy of the original assay and leads to challenges with data provenance. Results To overcome these challenges, we developed an R package called ExperimentSubset, which is a data container that implements classes for efficient storage and streamlined retrieval of assays that have been subsetted by rows and/or columns. These classes are able to inherently provide data provenance by maintaining the relationship between the subsetted and parent assays. We demonstrate the utility of this package on a single-cell RNA-seq dataset by storing and retrieving subsets at different stages of the analysis while maintaining a lower memory footprint. Overall, the ExperimentSubset is a flexible container for the efficient management of subsets. Availability and implementation ExperimentSubset package is available at Bioconductor: https://bioconductor.org/packages/ExperimentSubset/ and Github: https://github.com/campbio/ExperimentSubset. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Characterization of percolation behavior in conductor–dielectric 0-3 composites

2014 ◽  
Vol 04 (04) ◽  
pp. 1450035 ◽  
Author(s):  
Lin Zhang ◽  
Patrick Bass ◽  
Zhi-Min Dang ◽  
Z.-Y. Cheng
Keyword(s):  
Dielectric Constant ◽  
Percolation Threshold ◽  
Frequency Dependence ◽  
Experimental Results ◽  
Effective Dielectric Constant ◽  
Filler Concentration ◽  
Percolation Behavior ◽  
The Matrix ◽  
The Relationship

The equation ε eff ∝ (ϕc - ϕ)-s which shows the relationship between effective dielectric constant (εeff) and the filler concentration (φ), is widely used to determine the percolation behavior and obtain parameters, such as percolation threshold φc and the power constant s in conductor–dielectric composites (CDCs). Six different systems of CDCs were used to check the expression by fitting experimental results. It is found that the equation can fit the experimental results at any frequency. However, it is found that the fitting constants do not reflect the real percolation behavior of the composites. It is found that the dielectric constant is strongly dependent on the frequency, which is mainly due to the fact that the frequency dependence of the dielectric constant for the composites close to φc is almost independent of the matrix.

Metal-Reinforced Ceramic Composites for Turbine Vanes

1972 ◽  
Author(s):  
S. A. Bortz
Keyword(s):  
Ceramic Matrix Composites ◽  
Ceramic Composites ◽  
Matrix Composites ◽  
Fiber Reinforced ◽  
Metal Fiber ◽  
Turbine Engine ◽  
Turbine Vanes ◽  
The Matrix ◽  
The Relationship ◽  
Structural Matrix

Experiments have been performed which indicate the potential of metal-fiber reinforced-ceramic matrix composites for use as a high temperature structural matrix. The results of this work reveal that metal-fiber reinforced ceramics obey compostie theory, and that after cracks occur in the matrix, a pseudo-ductility can be introduced into the composite. This toughness can be predicted from equations of work required to pull the fibers through the matrix. The relationship between strength, toughness, and crack depths, are dependent on the inter-facial bond between the fibers and matrix as well as fiber diameter and length. Based on the results of these experiments, multicomponent materials with superior resistance to failure from oxidation, thermal shock, and high mechanical stresses in air above 2400 F can be postulated. These materials have potential for use as gas turbine engine vanes.

Plasma Spraying of Self-Lubricating Cr2O3-CaF2 Coatings

1997 ◽  
Author(s):  
F. Vos ◽  
L. Delaey ◽  
M. De Bonte ◽  
L. Froyen
Keyword(s):  
Plasma Spraying ◽  
Matrix Material ◽  
Production Method ◽  
Atmospheric Plasma ◽  
Spray Parameters ◽  
The Matrix ◽  
Preparation Step ◽  
Plasma Sprayed ◽  
The Relationship ◽  
Selection Of

Abstract Results are presented of a project analysing the relationship between the production parameters of plasma sprayed self-lubricating Cr2O3-CaF2 coatings and their structural, wear and lubricating properties. The production method consists of a preparation step where a powder blend of the matrix material (Cr203) and solid lubricant (CaF2) is agglomerated, followed by atmospheric plasma spraying (APS) of the agglomerates. Selection of the most appropriate agglomeration and plasma spray parameters as well as the microstructure of the coatings will be discussed.

scholarly journals On Domain of Nörlund Sequences

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 268 ◽  
Author(s):  
Kuddusi Kayaduman ◽  
Fevzi Yaşar
Keyword(s):  
Banach Space ◽  
Bounded Variation ◽  
Sequence Space ◽  
Convergent Series ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Nörlund Matrix ◽  
Inclusion Relations ◽  
The Matrix ◽  
New Space

In 1978, the domain of the Nörlund matrix on the classical sequence spaces lp and l∞ was introduced by Wang, where 1 ≤ p < ∞. Tuğ and Başar studied the matrix domain of Nörlund mean on the sequence spaces f0 and f in 2016. Additionally, Tuğ defined and investigated a new sequence space as the domain of the Nörlund matrix on the space of bounded variation sequences in 2017. In this article, we defined new space and and examined the domain of the Nörlund mean on the bs and cs, which are bounded and convergent series, respectively. We also examined their inclusion relations. We defined the norms over them and investigated whether these new spaces provide conditions of Banach space. Finally, we determined their α­, β­, γ­duals, and characterized their matrix transformations on this space and into this space.

The Relationship Between Magnetism and Microstructure of Ethylene Pyrolysis Furnace Tubes after a Long-term Service

2018 ◽  
Vol 24 (5) ◽  
pp. 478-487 ◽  
Author(s):  
Jingfeng Guo ◽  
Tieshan Cao ◽  
Congqian Cheng ◽  
Xianming Meng ◽  
Jie Zhao
Keyword(s):  
Saturation Magnetization ◽  
Outer Region ◽  
Cr Content ◽  
Pyrolysis Furnace ◽  
The Matrix ◽  
Furnace Tube ◽  
Primary Carbides ◽  
The Relationship ◽  
Very High

AbstractThe magnetism and microstructure of Cr25Ni35Nb and Cr35Ni45Nb alloy tubes after 5 years of service were investigated in this paper. The saturation magnetization of the Cr25Ni35Nb alloy tube in the thickness direction is more than 20 emu/g, and the tube becomes ferromagnetic. The inner and outer walls of Cr35Ni45Nb alloy tubes also become ferromagnetic. But the saturation magnetization of the Cr35Ni45Nb alloy tubes approaches to zero in the center zone. The primary carbides M7C3 and NbC are changed into M23C6 and G phase at the outer region of the furnace tube. However, the M23C6-type carbides were replaced by carbon-rich carbides M7C3 at the carburization zone. Cr-depleted zones are formed at the inner and outer walls of the furnace tubes owing to oxidation. Carburization and oxidation reduce the Cr content of the matrix. Accordingly, the saturation magnetization is very high at the carburization zone and Cr-depleted zone. The magnetism of Cr25Ni35Nb and Cr35Ni45Nb alloy tubes has a high correlation with the Cr content of the matrix. Carburization and oxidation are the main reasons that make the paramagnetic ethylene pyrolysis furnace tube change to ferromagnetic.

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