Diagonal Systems Research Articles

საქართველოს რელიეფის მორფოსტრუქტურული ანალიზი

As a result of the morphostructural analysis of the relief of Georgia, a scheme of tectonic faults has been compiled, the validity of which has been reinforced by the study of space materials. The faults represent straight-line structures and create an orthogonal diagonal system grid. The scheme explains the morphology of many geological structures and geological outcrops, as well as the peculiarities of the location of mineral deposits.

Parallel cyclic reduction of padded bordered almost block diagonal matrices

The solution of linear systems is a crucial and indispensable technique in the field of numerical analysis. Among linear system solvers, the cyclic reduction algorithm stands out for its natural inclination to parallelization. So far, the cyclic reduction has been applied primarily to linear systems with almost block diagonal matrices. Some of its variants widen the usage to almost block diagonal matrices with a last block of rows introducing a set of non-zero elements in the first group of columns. In this work, we extend cyclic reduction to matrices with additional non-zero elements below and to the right without any limitations. These matrices, called padded bordered almost block diagonal, arise from the discretization of optimal control problems featuring arbitrary boundary conditions and free parameters. Nonetheless, they also appear in two-point boundary value problems with free parameters. The proposed algorithm is based on the LU factorizations, and it is designed to be executed in parallel on multi-thread architectures. The algorithm performance is assessed through numerical experiments with different matrix sizes and threads. The computation times and speedups obtained with the parallel implementation indicate that the suggested algorithm is a robust solution for solving padded bordered almost block diagonal linear systems. Furthermore, its structure makes it suitable for the use of different matrix factorization techniques, such as QR or SVD. This flexibility enables tailored customization of the algorithm on the basis of the specific application requirements.

Homotopy Perturbation Method for Semi-Bounded Solution of the System of Cauchy-Type Singular Integral Equations of the First Kind

In this paper, we introduce the standard Homotopy Perturbation Method (HPM) for obtaining semi-bounded solutions of the first kind of system of Cauchy-type singular integral equations (CSIEs) with constant coefficients. We use the Gauss elimination technique to reduce the system of CSIEs to a diagonal triangle system of algebraic equations. We then apply the HPM to solve the resulting equations. By applying the theory of semi-bounded solutions of CSIEs, we can determine the inverse operators for the first kind of CSIEs. We demonstrate that the proposed method is exact for the system of characteristic SIEs, regardless of the choice of initial guesses (in the Holder class of functions). To illustrate the validity and accuracy of our proposed method, we supply and analyse three examples. We compare the results obtained using our method with those obtained using the Chebyshev collocation and Galerkin methods. Our method includes the ability to solve the complex-valued system of CSIEs. Based on the numerical results, we conclude that the HPM is more dominant than the other methods.

Study on geothermal energy self-recycling extraction and ScCO2 storage in the horizontal well annuli with fracture network system

With the extensive exploitation of fossil fuels, a substantial number of production and injection wells have been or are on the verge of being abandoned. However, many of these wells present viable opportunities for geothermal energy extraction, as they are situated in geothermal reservoirs with favourable temperatures. In alignment with carbon neutrality policies, supercritical CO2 (ScCO2) has emerged as the preferred working fluid for geothermal extraction, facilitating subsequent storage. This study has developed three transient models to characterize the heat and mass transfer processes of ScCO2 circulating within a horizontal wellbore and the reservoir's fracture network. Finite element method and Comsol Multiphysics 6.1 software are employed to solve these models. Results show that ScCO2 efficiently flows from the annuli into the hydraulic fracture network and then circulates back through the annuli completing a self-recycling heat extraction process. The findings reveal several key insights: (a) Lower injection mass flow rates and flow rates lead to more efficient extraction of thermal energy within horizontal wellbores. (b) Low-temperature ScCO2 enhance thermal energy recovery. (c) The larger the coverage area of the fracture network, the more effective the heat extraction. (d) The efficiency of heat extraction and ScCO2 storage in the horizontal well-fracture network self-circulation system is 3 to 5 times and 6 to 7 times higher than that of the horizontal well self-recycling and injection-production systems. (e) Periodic thermal extraction proves to be more efficient than continuous methods. (f) The cumulative heat production of the vertical dual well injection-production system is the highest, reaching 2.45 × 1011 kJ. But it's still lower than the self-circulating system. The heat extraction effect of the diagonal dual well injection-production system is the lowest, which is 1.83 × 1011 kJ. (g) Three developed transient models facilitate efficient heat extraction and ScCO2 storage reservoir screening and evaluation. In conclusion, the self-recycling system has achieved efficient heat extraction and carbon dioxide storage, providing a theoretical basis for future energy conversion and management.

Determining the directions of dangerous ecogeochemical impact of surface reservoirs of highly mineralized mine and open pit waters using a complex of geological and geophysical data

The issues of effective use of geological and geophysical methods for spatial assessment of dangerous ecogeochemical impact of storage ponds of highly mineralized mine and open pit waters are considered. An example of such an object is the Svystunovo gully (volume – 12 million m3), into which water is pumped out from all working open pits and mines of Southern and partially Central Kryvbas. To solve ecogeochemical problems associated with dangerous influence of such storage ponds, a well-known method for restoring Precambrian fault systems using a complex of geological, geophysical and geomorphological data was taken. At all research scales, based on the results of calculations of the significance of “weights” of fault signs, a clear trend was revealed for predominance of diagonal fault systems with strike azimuths: 35° - 305° and 45° - 315°. The spatial combination of tectonic information with results of detailed electrical exploration work made it possible to identify local directions of propagation of dangerous ecogeochemical influence of the studied storage pond of highly mineralized waters by anomalies of decrease / increase in geoelectric resistance in the emerging geochemical block of local system of integrated environmental monitoring of Southern Kryvbas.

Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-Assisted URLLC Systems

Optimization of Rate-Splitting Multiple Access in Beyond Diagonal RIS-Assisted URLLC Systems

Analysis of Braking Performance of Distributed Drive Vehicle Under Two-Wheel Hub Motor Failure

For distributed hub-driven vehicles, under braking conditions, when the hub motor fails, it will seriously threaten the safety of the vehicle, and there will be dangerous conditions such as braking distance increase and braking deviation, while the failure of the two-wheel hub motor has a more complex impact on the braking performance of the vehicle. Based on this, this paper selected a distributed hub motor drive vehicle as the research object and simulated the braking performance of the vehicle under the failure of the ipsilateral-side two-wheel hub motor system, coaxial two-wheel hub motor system, and diagonal two-wheel hub motor system. Combined with the vehicle’s driving track, yaw speed, and centroid side deflection Angle, the influence degree of the vehicle’s braking and stability was analyzed. The results show that the failure of the outer two-wheel hub motor has the greatest effect on vehicle braking stability than that of the diagonal wheel failure and the coaxial wheel failure. The effect of two-wheel hub motor failure on vehicle braking is greater than that of diagonal wheel failure and ipsilateral-side wheel failure. With the increase in vehicle braking speed and the decrease in road adhesion coefficient, vehicle instability, and braking performance become worse and worse.

D-Observability for a Coupled System of Wave Equations on Right Angle Triangles

Based on the tiled method, we establish the equivalence between the D-observability for diagonalizable systems on the rectangular domain and the right angle triangle domain, and then get the sufficiency of Kalman’s rank condition to the D-observability for diagonalizable systems on some right angle triangles.

Packaging process optimization for multihead weighing machines with vertical and diagonal double-layered systems: A bi-level approach

Bi-level programming offers a modeling approach for solving problems that involve two decision makers, each with their own objective. This research addresses a bi-level programming application to multihead, vertical, and diagonal double-layered machines. In these machines, hoppers are distributed across two levels: the upper level consists of weighing hoppers that weigh the product coming from the feeding hoppers. The weighed product is then deposited into the hoppers on the lower level, known as booster hoppers, located beneath them in a vertical or diagonal position, depending on the machine type. Simultaneously, they receive a new product to weigh. In the proposed model, weighing hoppers are associated with the leader’s decision variables and optimize the target weight, ensuring it is as close as possible to the weight stated on the label, while also being higher. Meanwhile, booster hoppers are assigned to the follower’s decision variables, optimizing hopper priority. Hopper priority is measured by the time elapsed from the moment the product arrives at the weighing hoppers until it is loaded onto a pack (measured in the number of processed packs). This model has been tested with different filling and combination strategies, considering factors such as the number of heads in the machine, product type (fusilli and ravioli), among others. The results demonstrate that the model successfully reduces the standard deviation of the produced packages for specific combinations of factors. Furthermore, it was observed that response times on each machine increase as the number of heads or the number of hoppers to be combined grows. This is a result of the increased number of combinations required to find the optimal solution. However, this heightened complexity leads to greater effectiveness and more accurate results in terms of the precision of the content delivered to the customer. The proposed solution methodology identifies the optimal machine configuration for minimizing weight deviation in each package. Additionally, it prioritizes the utilization of machines in the lower level of decisions. Consequently, we achieve optimal operating conditions that minimize package overweight, material overcost, and appropriately select the weighing machines. Managerial insights are provided to underscore that customer satisfaction and improved business performance are outcomes of this study.

Diagonalized Legendre spectral method for second-order eigenvalue problems

Diagonalized Legendre spectral methods for solving second-order eigenvalue problems are proposed. A new class of basis functions are constructed by using the matrix decomposition technique, which are simultaneously orthogonal in both L2- and H1-inner products, and lead to diagonal systems for second-order eigenvalue problems with constant coefficients. Numerical experiments show that the suggested approaches possess high-order accuracy and greatly improve the efficiency. Compared with the classical methods, the new methods simplify the calculation process, reduce the amount of calculation, and can effectively avoid the curse of dimensionality of high-dimensional eigenvalue problems.

Darboux integrability for diagonal systems of hydrodynamic type

We prove that (1) diagonal systems of hydrodynamic type are Darboux integrable if and only if the corresponding systems for commuting flows are Darboux integrable, (2) systems for commuting flows are Darboux integrable if and only if the Laplace transformation sequences terminate, (3) Darboux integrable systems are necessarily semihamiltonian. We give geometric interpretation for Darboux integrability of such systems in terms of congruences of lines and in terms of solution orbits with respect to symmetry subalgebras, discuss known and new examples.

Risk-based seismic design of diagonal self-centering shape-memory alloy wire-based bracing system in multi-column bent bridges

In this paper, a risk-based seismic design method for diagonal self-centering braces (SCB) with shape memory alloy (SMA) wires implemented in multi-column bents is proposed to enhance the performance of older concrete bridge classes. An existing SMA-SCB system that improves the performance of older reinforced concrete building frames was adopted to numerically examine further applications to nonductile bridges. To this end, risk-based seismic design of the SMA-SCB to minimize the probability of collapse and demolition of bridge classes was developed by adopting a sophisticated finite element model that reflects the recentering behavior of an actual SMA-SCB; probabilistic bridge models considering uncertainties associated with the material and geometrical properties of bridges; refined failure condition; and the total probability theorem. A comparison of the results of the traditional seismic fragility-based and proposed designs indicated that the amount of SMA-SCB required by the former is nearly half of that required by the proposed approach because the traditional approach overemphasizes the demand at larger ground motion intensities.

Entropy solutions to a non-conservative and non-strictly hyperbolic diagonal system inspired by dislocation dynamics

Entropy solutions to a non-conservative and non-strictly hyperbolic diagonal system inspired by dislocation dynamics

Performance Portable Batched Sparse Linear Solvers

Solving large number of small linear systems is increasingly becoming a bottleneck in computational science applications. While dense linear solvers for such systems have been studied before, batched sparse linear solvers are just starting to emerge. In this paper, we discuss algorithms for solving batched sparse linear systems and their implementation in the Kokkos Kernels library. The new algorithms are performance portable and map well to the hierarchical parallelism available in modern accelerator architectures. The sparse matrix vector product (SPMV) kernel is the main performance bottleneck of the Krylov solvers we implement in this work. The implementation of the batched SPMV and its performance are therefore discussed thoroughly in this paper. The implemented kernels are tested on different Central Processing Unit (CPU) and Graphic Processing Unit (GPU) architectures. We also develop batched Conjugate Gradient (CG) and batched Generalized Minimum Residual (GMRES) solvers using the batched SPMV. Our proposed solver was able to solve 20,000 sparse linear systems on V100 GPUs with a mean speedup of 76x and 924x compared to using a parallel sparse solver with a block diagonal system with all the small linear systems, and compared to solving the small systems one at a time, respectively. We see mean speedup of 0.51 compared to dense batched solver of cuSOLVER on V100, while using lot less memory. Thorough performance evaluation on three different architectures and analysis of the performance are presented.

Admissibility of retarded diagonal systems with one-dimensional input space

Admissibility of retarded diagonal systems with one-dimensional input space

Seismic design and performance analysis of bridge bents retrofitted with multistage buckling-restrained braces

Buckling-restrained braces (BRBs) are often used to retrofit RC bridge bents to increase their strength and stiffness, and dissipate the seismic energy through hysteretic behavior. However, the post-yielding stiffness of BRBs is very low, and the total stiffness of the retrofitted bent drops sharply when the brace yields, which can lead to more serious damage to the primary structure contrary to the design purpose. Accordingly, multistage buckling-restrained braces (MSBRBs), consisting of steel cores with different yield strains, were used for the seismic retrofitting of bridge bents in this study. By controlling the low yield point (LYP) core yield before the bridge bents and high yield point (HYP) core yield after the bents, the expressions for the steel core length related to the geometric parameters of the bridge bents were derived. Furthermore, a preliminary seismic design method based on the structural fuse concept was proposed, which realized that the MSBRB dissipates energy while providing stable stiffness to improve the safety of the entire system. The advantages of the MSBRB in controlling the peak and residual displacement of the RC bent were proved via nonlinear time history analyses. Finally, the effects of the stiffness ratios, yield displacement ratios, and different configurations on the seismic performance of retrofitting bridge bents with MSBRBs were examined. The results showed that seismic performance of reinforced bents can be improved by increasing the stiffness ratio appropriately. The LYP core is primarily related to the energy dissipation capacity of the MSBRBs, and the value of βL should be less than 0.5. The HYP core is largely responsible for controlling the deformation of bridge bent, and βH must be greater than 1.0. Compared to other configurations, the diagonal MSBRB system has a greater energy dissipation capacity and higher seismic reduction rate.

Algebraic-geometry approach to construction of semi-Hamiltonian systems of hydrodynamic type

In this paper, a class of semi-Hamiltonian diagonal systems of hydrodynamic type is constructed using algebraic-geometric methods. For such systems, hydrodynamic integrals and hydrodynamic symmetries are constructed from algebraic-geometric data. Besides, it is described what algebraic-geometric data distinguish in this class Hamiltonian diagonal systems with Hamiltonian structures defined by flat metrics (local Dubrovin-Novikov brackets) and metrics of constant curvature (nonlocal Mokhov-Ferapontov brackets).

A Posteriori Error Estimate of Weak Galerkin FEM for Stokes Problem Using Auxiliary Subspace Techniques

Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems corresponding to the degree of freedom of velocity and pressure respectively, which reduces the computational cost sharply. The upper and lower bounds up to an oscillation term of the error estimator are also shown to address the reliability of the adaptive method without saturation assumption. Numerical simulations are performed to demonstrate the effectiveness and robustness of our algorithm.

ANALISIS SIFAT FISIK TANAH PADA BEBERAPA PENGGUNAAN LAHAN DI DESA MUNERANA KECAMATAN HEWOKLOANG KABUPATEN SIKKA

Soil's physical properties greatly affect the development and absorption of plant nutrients. This study aims to determine the physical properties of the soil on several land uses and slopes using the blepeng method. Soil collection was carried out from corn, nutmeg, cloves, and rainfed rice fields on two slope classes, namely 8-15% and 15-30%. Soil sampling used a diagonal system, where 9 sample points were taken from each location. The variables observed were bulk density, porosity, soil water content, soil texture and soil color. The results of the research show that the soil in Munerana Village, Hewokloang District, Sikka Regency is included in the texture of sandy loam soil, the low water content in the soil ranges from 14.87% to 25.50%, soil porosity is 25.66% to 29.12%, soil fill density is 1.17 me/100 g to 1.97 me/100 g and the soil color is dark reddish gray.

Performance-based seismic design of laterally braced steel frames

Improving the performance of structural frames is one of the most important focuses of today's researchers. The total base shear capacity of the structural frames will increase by reaching the maximum number of plastic hinges. In this work, the effects of bracing system type on different heights of steel frames were investigated. Static pushover analysis was used to evaluate the performance of 4, 8, and 12-story steel frames with seven structural configuration systems. The results showed that the performance of braced frames increased significantly in terms of number of plastic hinges, total base shear and performance point compared to unbraced frames. The capacity curves were maximum in the one-story X-bracing, multi-story X-bracing, and single diagonal bracing systems.