Conjugate gradient algorithm for consistent generalized Sylvester-transpose matrix equations

<abstract><p>We develop an effective algorithm to find a well-approximate solution of a generalized Sylvester-transpose matrix equation where all coefficient matrices and an unknown matrix are rectangular. The algorithm aims to construct a finite sequence of approximated solutions from any given initial matrix. It turns out that the associated residual matrices are orthogonal, and thus, the desire solution comes out in the final step with a satisfactory error. We provide numerical experiments to show the capability and performance of the algorithm.</p></abstract>

EVALUATION OF CORRESNDENCE MATRICES TAKING INTO ACCOUNT TRANSPORT FLOW RESTRICTIONS

Travel demand forecasting models are a key analysis tool used in transport network planning and infrastructure development. Relevant research within this topic is aimed at reducing the time and minimizing costs associated with the development of a forecasting model for travel demand, which is used for forecasting and planning. The study evaluates the possibility of recovering an exact correspondence matrix based on an overloaded network, which considers the conditions relative to the base / initial matrix, traffic flow and their impact on the quality of the generated matrix

Development of a Simpler but Accurate Free Gas Deviation Factor for Fractured (Dual-Porosity) Volumetric Gas Reservoir Fluid

Gas compressibility factor, also known as gas deviation factor or Z-factor, is a thermodynamic correction factor which describes the deviation of a real gas from ideal gas behaviour. The, free gas Z-factor in the Material Balance Equation (MBE) of single-porosity gas reservoirs with insignificant rock (matrix) compaction (after pressure depletion) does not reflect cases in low-permeability gas reservoirs having remarkable rock compaction. Through gas MBE modifications, previous researchers developed Z-factors for dual-porosity (fractured) low permeability gas reservoirs by incorporating gas desorption; however, their approaches create complexity for routine calculations. Therefore this study was designed with the purpose of deriving a free gas Z-factor for single-porosity low-permeability gas reservoirs and further modifying it for more simplicity and accuracy in a dual-porosity scenario. The free gas Z-factor derived for single-porosity low-permeability gas reservoirs is expressed as: where , , , , and are single-porosity Z-factor without rock compaction at pressure , water compressibility, initial water saturation, matrix compressibility, initial gas saturation and pressure depletion, respectively. However, the developed dual porosity free gas Z-factor model incorporates ratio of dual porosity to initial matrix porosity, and it is expressed as: where and are initial matrix porosity and fracture porosity, respectively. The Z-factor model was graphically and statistically correlated with an existing free gas Z-factor model for dual porosity reservoirs. For all the hydraulically fractured shale gas formations considered, the correlations yield R2 values of 1.000.

THE METHOD OF FICTITIOUS REACTIONS IN THE MODELING OF THE CONTACT SURFACE ON THE EXAMPLE OF FLANGED CONNECTIONS.

An iterative method for calculating flanged connections in the finite element formulation is proposed. The essence of the proposed method is to separate the contact problem into a separate localized process that depends only on the initial distribution of forces from the main load on the flange connection. In the initial matrix of stiffness of unrelated bodies, a binding matrix of contact with elements of high rigidity is added. The calculation is performed in two phases: the first phase determines the movement of the actual loads on the second, through a vector of dummy reactions, iterative specified voltage at the contact surfaces. The results obtained by the proposed method are compared with the experimental results and with the approximate calculation method.

Convergence properties of the Broyden-like method for mixed linear–nonlinear systems of equations

We consider the Broyden-like method for a nonlinear mapping $F:\mathbb {R}^{n}\rightarrow \mathbb {R}^{n}$ F : ℝ n → ℝ n that has some affine component functions, using an initial matrix B0 that agrees with the Jacobian of F in the rows that correspond to affine components of F. We show that in this setting, the iterates belong to an affine subspace and can be viewed as outcome of the Broyden-like method applied to a lower-dimensional mapping $G:\mathbb {R}^{d}\rightarrow \mathbb {R}^{d}$ G : ℝ d → ℝ d , where d is the dimension of the affine subspace. We use this subspace property to make some small contributions to the decades-old question of whether the Broyden-like matrices converge: First, we observe that the only available result concerning this question cannot be applied if the iterates belong to a subspace because the required uniform linear independence does not hold. By generalizing the notion of uniform linear independence to subspaces, we can extend the available result to this setting. Second, we infer from the extended result that if at most one component of F is nonlinear while the others are affine and the associated n − 1 rows of the Jacobian of F agree with those of B0, then the Broyden-like matrices converge if the iterates converge; this holds whether the Jacobian at the root is invertible or not. In particular, this is the first time that convergence of the Broyden-like matrices is proven for n > 1, albeit for a special case only. Third, under the additional assumption that the Broyden-like method turns into Broyden’s method after a finite number of iterations, we prove that the convergence order of iterates and matrix updates is bounded from below by $\frac {\sqrt {5}+1}{2}$ 5 + 1 2 if the Jacobian at the root is invertible. If the nonlinear component of F is actually affine, we show finite convergence. We provide high-precision numerical experiments to confirm the results.

Crack Deflection Near a Ply Interface in a Composite Laminate

The deflection of a matrix crack near 0°/90° interface in a cross-ply laminate was studied numerically. In the finite element (FE) model, an initial matrix crack was introduced in the 90° layers away from the 0°/90° interface. The initial matrix crack could be initiated either at the middle of 90° layer or at one side of 0°/90° interface. The 0° layers and a part of the initial matrix crack were modeled using homogenized layer properties to simplify the model. The nonuniformly distributed fibers were modeled explicitly close to the 0°/90° interface in order to study the influence of this nonuniformity on the crack deflection process. The Energy Release Rate (ERR) of debond crack tip was calculated using Virtual Crack Closure Technique (VCCT) to study the debond growth. Maximum principal stress was then adopted to access the debond crack kinking qualitatively. It’s found that when a macro-size matrix crack forms and propagate towards ply interface, the subsequent debonding and debond cracking process in nearby intact fiber shows some distinct differences compared to the same processes at single isolated fiber without considering the interaction with nearby debonded fiber and existing matrix crack. Meanwhile, present analysis shows clear influence of microstructures on the crack deflection process by affecting the fiber/matrix debonding and debond kinking processes.

CELLULAR AUTOMATA ALGORITHMS FOR PSEUDORANDOM NUMBERS GENERATION

Work describes four permutation algorithms of square matrices based on cyclic rows and columns shifts. This choice of discrete transformation algorithms is justified by the convenience of the cellular automaton (CA) formulation. Output matrices can be considered as pseudo-random sequences of numbers. As a result of numerical calculation, empirical formulas are obtained for the permutation period and the function of the period of a single CA-cell on the order of the matrix n. As a parameter of CA dynamics, we analyze two "mixing metrics" on permutations of the matrix (compared to the initial matrix).

Gypsum-Cement Composites Based on Volcanic Ash

The studies’ results to determine the gypsum, ash and Portland cement components proportions, which would ensure a decrease in the specific binder consumption, as well as the ash grain composition’s effect on the properties of the gypsum cement pozzolan composite, are presented. It was revealed that the use of volcanic ash together with Portland cement in gypsum concrete composites allows reducing gypsum consumption by up to 50% without a significant decrease in strength characteristics. At the same time, the developed gypsum concrete composites have increased water resistance. The influence of the ash particle size distribution on the strength properties of the composite is ambiguous; in the compositions with a high ash content it is advisable to use larger fractions, and with a content of less than 50% ash in the composite, - the small fractions. To study the parameters’ effect of the dispersed reinforcement with basalt fibers on the properties of a gypsum-cement composite, an experiment with such a second-order composite rotatable plan as regular hexagon was conducted. It was found that the maximum values ​​of optimization parameters are observed in the central area of ​​the plan with and . The compressive strength of a fiber gypsum cement pozzolan composite increases by 1.15-1.18 times, when bending, by 1.56-1.72 times with respect to the strength of the initial matrix.

The interesting spectral interlacing property for a certain tridiagonal matrix

In this paper, a new tridiagonal matrix, whose eigenvalues are the same as the Sylvester-Kac matrix of the same order, is provided. The interest of this matrix relies also in that the spectrum of a principal submatrix is also of a Sylvester-Kac matrix given rise to an interesting spectral interlacing property. It is proved alternatively that the initial matrix is similar to the Sylvester-Kac matrix.

Ten years of ecosystem services matrix: Review of a (r)evolution

With the Ecosystem Service (ES) concept's popularisation, the need for robust and practical methodologies for ES assessments has increased. The ES matrix approach, linking ecosystem types or other geospatial units with ES in easy-to-apply lookup tables, was first developed ten years ago and, since then, has been broadly used. Whereas detailed methodological guidelines can be found in literature, the ES matrix approach seems to be often used in a quick (and maybe even "quick and dirty”) way. Based on a review of scientific publications, in which the ES matrix approach was used, we present the diversity of application contexts, highlight trends of uses and propose future recommendations for improved applications of the ES matrix. A total of 109 studies applying the ES matrix approach and one methodological study without concrete applications were considered for the review. Amongst the main patterns observed, the ES matrix approach allows the assessment of a higher number of ES than other ES assessment methods. ES can be jointly assessed with indicators for ecosystem condition and biodiversity in the ES matrix. Although the ES matrix allows us consider many data sources to achieve the assessment scores for the individual ES, in the reviewed studies, these were mainly used together with expert-based scoring (73%) and/or ES scores that were based on an already-published ES matrix or deduced by information found in related scientific publications (51%). We must acknowledge that 27% of the studies did not clearly explain their methodology. This points out a lack of method elucidation on how the data had been used and where the scores came from. Although some studies addressed the need to consider variabilities and uncertainties in ES assessments, only a minority of studies (15%) did so. Our review shows that, in 29% of the studies, an already-existing matrix was used as an initial matrix for the assessment (mainly the same matrix from one of the Burkhard et al. papers). In 16% of the reviewed studies, no other data were used for the matrix scores or no adaptation of the existing matrix used was made. However, the actual idea of the ES scores, included in the Burkhard et al.'s matrices published 10 years ago, was to provide some examples and give inspiration for one's own studies. Therefore, we recommend to use only scores assessed for a specific study or, if one wishes to use pre-existing scores from another study, to revise them in depth, taking into account the local context of the new assessment. We also recommend to systematically report and consider variabilities and uncertainties in each ES assessment. We emphasise the need for all scientific studies to describe clearly and extensively the whole methodology used to score or evaluate ES in order to be able to rate the quality of the scores obtained. In conclusion, the application of the ES matrix has to become more transparent and integrate more variability analyses. The increasing number of studies that use the ES matrix approach confirms its success, appropriability, flexibility and utility for decision-making, as well as its ability to increase awareness of ES.