Splitting Method Research Articles

Efficient Heuristic Management of Cloud Data Lakes for Enhanced Big Data Handling in Cloud Computing Environments

Efficient control of cloud data lakes is important for improving big data dealing in cloud computing settings. Cloud data lakes serve as stores for vast amounts of organized, semi-structured, and unstructured data from varied sources, offering scaling and freedom in data storage and processing. However, the sheer amount and range of data offer difficulties in improving storage, access, and analysis processes. This study suggests a heuristic method to handle these issues by improving the order and recovery of data within cloud data lakes. The heuristic method focuses on automatically handling data splitting, storage, and caching strategies based on data access trends and task factors. By leveraging heuristic principles, such as adaptable splitting and predictive caching, the suggested method aims to reduce delay and improve total query speed. Key components of the heuristic management include adaptable splitting methods that actively change data partition sizes based on access frequency and data distribution patterns. This flexible method ensures that frequently accessed data is easily available, while less accessed data is efficiently saved to improve storage usage. Furthermore, predictive storing methods expect future data access patterns using machine learning models or previous data trends. By strategically saving relevant datasets in memory or high-speed storage, the system reduces delay for repeated questions, thereby improving real-time data processing capabilities. The success of the suggested heuristic management method is tested through models and benchmarks using real big data tasks. Comparative research against standard static splitting and caching methods shows significant changes in query response times and resource utilization efficiency.

High-order stability for a stochastic reaction-diffusion equation under random fluctuation on ℝ N

In this article, we systematically study the high-order stability for a stochastic reaction-diffusion equation under random fluctuation. We obtain the convergence of solutions and upper semi-continuity of random attractors for the fluctuation equations in the initial space L 2(ℝ N ), without an additional assumption on the nonlinearity. By means of a splitting method, we technically prove that the L p ∩H 1-difference of solutions is controlled by the L 2-difference of initial values near the initial time, where p , p > 2 , is the dissipation exponent of the nonlinearity. This along with the L 2-stability is sufficient for us to establish the L p ∩H 1-stability of random attractors. By utilizing some iteration arguments, we show that the solution is uniformly bounded on a bounded interval near the initial time in L δ (ℝ N ) for arbitrary δ > p, in which space the convergence of solutions and the upper semi-continuity of random attractors are also established.

RBF–based IMEX finite difference schemes for pricing option under liquidity switching

In this work, we introduce two accurate and efficient finite difference methods based on radial basis functions (RBF–FD) for pricing European and American options under liquidity shocks. The problem is formulated as the semi-linear complementarity and PDE systems for American and European options, respectively. In the context of temporal semi-discretization, we provide two backward difference formulas of order one and two (BDF1 & BDF2). Furthermore, we discuss the stability and convergence properties of the proposed methods. For the American option, to solve the semi-linear system of complementarity problems (LCPs), we combine the RBF-FD approaches with an operator splitting (OS) method. To illustrate the efficiency and accuracy of the suggested methods, we provide numerical examples for both European and American call options and verify them with the existing work in the literature. In numerical discussion, we show the Greeks (Delta & Gamma) plots for the American options.

Research on efficient design method of high torque motor with dual airgap hybrid rotor for aircraft engines

AbstractHigh torque density and high reliability motors have a wide application prospect in aerospace field, so a hybrid rotor and dual stator motor is studied in this paper. Firstly, to address the problem that the difference in power density between the inner and outer unit motor is so large that it is not suitable for electromagnetic design using the power splitting method, a main dimensioning calculation method based on the equal‐power volume transformation is proposed. The influence of thermal load on the output performance of the inner and outer unit motors is taken into account comprehensively. The main dimensioning expressions for such motors are derived. Secondly, the output performance consistency between the inner and outer unit motors is theoretically analysed, and the optimal angle between the d‐axis of the permanent magnet rotor and the d‐axis of the reluctance rotor is obtained when the motor is operated in the maximum torque per ampere control mode. Finally, a prototype with a rated power of 46.7 kW was developed and load experiments were conducted on it, and the experimental results verified the correctness and feasibility of the theoretical analysis method.

Armature Reaction Analysis and Suppression of Voice Coil Actuator Based on an Improved Magnetic Equivalent Circuit Model

The high thrust density voice coil actuator (VCA) is a key component for the deployers to determine the CubeSats' separation velocity in orbit directly. To improve the VCA's thrust density and power consumption, it is essential to analyze the armature reaction under heavy current work conditions. This paper proposes a dynamic splitting method of the magnetic equivalent circuit (MEC) model for analyzing the armature reaction of the VCA. This MEC model can effectively reveal the interaction mechanism between the dynamic winding field and the permanent magnet (PM) field, which provides an approach to readily and quickly analyze the armature reaction. Based on the understanding of the mechanism, we found an effective way to suppress the armature reaction and propose a new VCA with double PM flux circuits. The electromagnetic performances of the new configuration are evaluated by comparing it with the conventional one. Both the theoretical and experimental results show that the new structure achieves lower magnetic saturation, lower armature reaction, and higher thrust density. A research prototype was constructed and experimentally tested to verify the theoretical results of the armature reaction, magnetic field, thrust, separation velocity, and other performances. The new VCA realizes a wide and accurate modulation of separation velocity for the CubeSats.

Fracture of the C15 CaAl2 Laves phase at small length scales

The cubic C15 CaAl2 Laves phase is an important brittle intermetallic precipitate in ternary Mg–Al–Ca structural alloys. Although knowledge of the mechanical properties of the co-existing phases is essential for the design of improved alloys, the fracture toughness of the C15 CaAl2 intermetallic has not yet been studied experimentally due to limitations posed by macroscale testing of defect-free specimens. Here, miniaturised testing techniques like micropillar splitting and microcantilever bending methods are used to experimentally determine the fracture toughness of the CaAl2 Laves phase. It is found that the toughness value of ~ 1 MPa·√m obtained from pillar splitting with a sharp cube corner geometry is largely insensitive to sample heat treatment, the ion beam used during fabrication, micropillar diameter, and surface orientation. From correlative nanoindentation and electron channelling contrast imaging supported by electron backscatter diffraction, fracture is observed to take place mostly on {011} planes. Atomistic fracture simulations on a model C15 NbCr2 Laves phase showed that the preference of {011} cleavage planes over the more energetically favourable {111} planes is due to lattice trapping and kinetics controlling fracture planes in complex crystal structures, which may provide insights into the experimental results for CaAl2. Using rectangular microcantilever bending tests where the notch plane was misoriented to the closest possible {112} cleavage plane by ~ 8° and the closest {001}, {011}, and {111} planes by > 20°, a toughness of ~ 2 MPa·√m was determined along with the electron microscopy observation of significant deviations of the crack path, demonstrating that preferential crystallographic cleavage planes determine the toughness in this material. Further investigation using pentagonal microcantilevers with precise alignment of the notch with the cleavage planes revealed similar fracture toughness values for different low-index planes. The results presented here are the first detailed experimental study of fracture toughness of the C15 CaAl2 Laves phase and can be understood in terms of crack plane and crack front-dependent fracture toughness.Graphical

Quantum information splitting among N-quantum nodes within a quantum network by using Bell states

In quantum information processing, it is essential to ensure the security of quantum information so that it cannot be stolen and interrupted by an eavesdropper. For ensuring the security of information, quantum information splitting (QIS) method is used in which quantum communication is made more secure by splitting the quantum information among the various quantum nodes within a quantum network in such a way that any one node can retrieve the quantum information completely with the collaboration of remaining quantum nodes. In this paper, by using Bell states as the quantum channel we present a simple and precise scheme for quantum information splitting of an arbitrary single-qubit quantum information state among N (N ≥ 2) recipient nodes which are separately entangled with the sender node only and not with one another. We also generalize our scheme to the splitting of multi-qubit quantum information state among the N recipient nodes by using 2-qubit Bell states as the quantum resource. In comparison to the previous existing QIS schemes which require multi-qubit entangled states as the quantum resource, our proposed QIS scheme is very simple and feasible.

The dimension coupling method for 3D transient heat conduction problem with variable coefficients

In this study, a dimension coupling method (DCM) is presented to study the variable coefficients transient heat conduction problems. The dimension splitting method (DSM) is introduced to split the 3D domain into some 2D domains, which are discretized by selecting the improved element-free Galerkin (IEFG) method; thus the corresponding discretized equation in each 2D domain is derived, and the finite element method (FEM) is employed to deal with these discretized equations in a third direction, and the time-dependent term is discretized by selecting the finite difference method (FDM), thus the final solved equation of the transient heat conduction problems is obtained. In the first example, the convergence is proved by increasing the nodes and meshes on the influence of relative errors. Some numerical results illustrate that the proposed method can substantially enhance the computational efficiency of the IEFG method. When an exact solution of the numerical example is a nonlinear function about splitting direction with natural boundary condition is given, the proposed method has shorter computing time than the hybrid element-free Galerkin (HEFG) method when dealing with this situation.

A modification of the forward–backward splitting method for monotone inclusions

A modification of the forward–backward splitting method for monotone inclusions

Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method.

This study aims to investigate how inert gas affects the partial pressure of alveolar and venous blood using a fast and accurate operator splitting method (OSM). Unlike previous complex methods, such as the finite element method (FEM), OSM effectively separates governing equations into smaller sub-problems, facilitating a better understanding of inert gas transport and exchange between blood capillaries and surrounding tissue. The governing equations were discretized with a fully implicit finite difference method (FDM), which enables the use of larger time steps. The model employed partial differential equations, considering convection-diffusion in blood and only diffusion in tissue. The study explores the impact of initial arterial pressure, breathing frequency, blood flow velocity, solubility, and diffusivity on the partial pressure of inert gas in blood and tissue. Additionally, the effects of anesthetic inert gas and oxygen on venous blood partial pressure were analyzed. Simulation results demonstrate that the high solubility and diffusivity of anesthetic inert gas lead to its prolonged presence in blood and tissue, resulting in lower partial pressure in venous blood. These findings enhance our understanding of inert gas interaction with alveolar/venous blood, with potential implications for medical diagnostics and therapies.

Mathematical Modeling of the Process of Acid Rain Formation in Case of Emissions from Thermal Power Plants

Purpose. It is known that acid rain has a negative impact on the environment. The formation of acid precipitation in the atmosphere occurs as a result of the chemical interaction of fuel combustion products and atmospheric humidity. Acid rain leads to crop losses, deterioration of soil fertility, and acidification of water in reservoirs. The development of scientifically based methods for studying the intensity of such acidic pollution of the air and soil surface in regions with significant emissions from thermal power plants remains an urgent problem. To solve this problem, it is important to use mathematical modeling, since it is impossible to determine the impact of emissions from thermal power plants on the formation of acid rain experimentally. Therefore, the main goal of the work is to create a mathematical model for predicting the formation of acid rain in the event of emissions from thermal power plants. Methodology. To predict the process of acid rain formation, a three-dimensional equation of convective diffusion transport of a pollutant is used, which takes into account the wind speed profile, atmospheric stratification, emission intensity of an impurity, and wind direction. This equation is also used to describe the process of water vapor transport in atmospheric air. To describe the process of acid formation in atmospheric air, a stoichiometric relationship is used. The numerical integration of the modeling equation of transfer was carried out using the splitting method. Findings. A multifactorial numerical model was built that allows determining the zones where acid rain is formed. The problem of predicting the formation of acid rain in the case of emissions from thermal power plants on the basis of the constructed numerical model is considered. Originality. A numerical model is proposed to predict the occurrence of acid rain due to emissions from thermal power plants. The model is multifactorial and takes into account convection, atmospheric diffusion, and an uneven wind profile. A computer code has been created that allows for rapid assessment of acid pollution zones. Practical value. The developed computer code for analyzing the zones of acidic pollution of the environment in the case of industrial emissions makes it possible to predict the intensity of such pollution in various meteorological conditions.

A second-order Strang splitting scheme for the generalized Allen–Cahn type phase-field crystal model with FCC ordering structure

In this paper, we consider the generalized Allen–Cahn-type phase-field crystal model with face-centered-cubic ordering structure (PFC-FCC). Due to the combined complexity of the eighth-order spatial derivative and inherent nonlinearity, it poses a significant challenge to design a numerical scheme of high accuracy, stability, and efficiency to solve the PFC-FCC model. Endeavoring towards this objective, we adopt operator splitting method to address the PFC-FCC model. Based on Fourier spectral method for spatial discretization and SSP-RK method for temporal discretization, we propose an effective and easy-to-implement second-order scheme. We are also able to proffer an analytical proof for discrete mass conservation, and engage a discussion on an optimal error estimate for the second-order scheme. In addition, the energy stability of the numerical scheme is derived. Ultimately, a series of numerical experiments specifically designed to substantiate its accuracy, efficiency, and capability for phase transition are performed.

Families of efficient low order processed composition methods

New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or more parts which are explicitly solvable. The new schemes are shown to be more efficient than previous state-of-the-art splitting methods.

Clinical Predictors of Postmortem Amyloid and Nonamyloid Cerebral Small Vessel Disease in Middle-Aged to Older Adults.

Sporadic cerebral small vessel disease (CSVD) is a class of important pathologic processes known to affect the aging brain and to contribute to cognitive impairment. We aimed to identify clinical risk factors associated with postmortem CSVD in middle-aged to older adults. We developed and tested risk models for their predictive accuracy of a pathologic diagnosis of nonamyloid CSVD and cerebral amyloid angiopathy (CAA) in a retrospective sample of 160 autopsied cases from the Edinburgh Brain Bank. Individuals aged 40 years and older covering the spectrum of healthy aging and common forms of dementia (i.e., highly-prevalent etiologies such as Alzheimer disease (AD), vascular cognitive impairment (VCI), and mixed dementia) were included. We performed binomial logistic regression models using sample splitting and cross-validation methods. Demographics, lifestyle habits, traditional vascular risk factors, chronic medical conditions, APOE4, and cognitive status were assessed as potential predictors. Forty percent of our sample had a clinical diagnosis of dementia (AD = 33, VCI = 26 and mixed = 5) while others were cognitively healthy (n = 96). The mean age at death was 73.8 (SD 14.1) years, and 40% were female. The presence of none-to-mild vs moderate-to-severe nonamyloid CSVD was predicted by our model with good accuracy (area under the curve [AUC] = 0.84, sensitivity [SEN] = 72%, specificity [SPE] = 95%), with the most significant clinical predictors being age, history of cerebrovascular events, and cognitive impairment. The presence of CAA pathology was also predicted with high accuracy (AUC = 0.86, SEN = 93%, SPE = 79%). Significant predictors included alcohol intake, history of cerebrovascular events, and cognitive impairment. In a subset of atypical dementias (n = 24), our models provided poor predictive performance for both nonamyloid CSVD (AUC = 0.50) and CAA (AUC = 0.43). CSVD pathology can be predicted with high accuracy based on clinical factors in patients within the spectrum of AD, VCI, and normal aging. Whether this prediction can be enhanced by the addition of fluid and neuroimaging biomarkers warrants additional study. Improving our understanding of clinical determinants of vascular brain health may lead to novel strategies in the prevention and treatment of vascular etiologies contributing to cognitive decline. This study provides Class II evidence that selected clinical factors accurately distinguish between middle-aged to older adults with and without cerebrovascular small vessel disease (amyloid and nonamyloid) pathology.

Reconstruction of Chitosan Network Orders Using the Meniscus Splitting Method for Designing pH-Responsive Materials.

Chitosan is a product of deacetylated chitin and a natural polymer that is attractive as a functional and biocompatible material in the pursuit of alternative materials to synthetic plastics for a sustainable society. Although hierarchical architectures, from precise molecular structures to nanofibers and twisted structures, have been clarified, the expansion of the anisotropic microstructures of chitosan into millimeter-scale materials is in the process of development. In this study, a chitosan network was reconstructed from an aqueous solution by using the meniscus splitting method to form a three-dimensionally ordered microstructure. A chitosan membrane deposited on the millimeter scale formed a useful anisotropically pH-responsive hydrogel. During the evaporation of the aqueous solution from a finite space, chitosan underwent ordered deposition by capillary force to form a membrane with oriented microstructures and microlayers. Unlike the cast films formed between solid-liquid and air-liquid interfaces, this membrane formed between two air-liquid interfaces. As a result, the membranes with ordered microstructures were capable of signifying directional swelling in aqueous environments and reversible/irreversible swelling-deswelling changes by controlling the pH range. We envision that the anisotropic pH response of the chitosan network can be utilized under physiological conditions as a next-generation material.

Hybrid energy storage sizing in energy hubs: A continuous spectrum splitting approach

Renewable powered energy hub is a promising way to realize efficient use of renewable resources through multi-energy integration. To cope with the fluctuation of renewable power at different timescales, long-term and short-term energy storage devices are essential. This paper proposes a frequency-domain approach to determine the appropriate capacities of hydrogen and battery energy storage units in an electricity–hydrogen–heat integrated energy hub. The net demand is mapped to the frequency domain via discrete Fourier transformation (DFT). A continuous spectrum splitting method is developed to allocate the frequency components among generator, hydrogen storage and battery storage. Compared with the time-domain method, it makes better use of the spectral characteristics of the year-round data, leading to robust sizing results without complex modeling of uncertainty. In contrast to the existing cut-off frequency method which assigns high-frequency components to battery storage and low-frequency components to generators according to a cut-off frequency, the proposed framework allows a single spectrum component to be allocated to multiple system devices, which not only makes the optimization model convex but also improves optimality. In addition, the spectrum clustering process further reduces the number of core variables and the computational efficiency is high. The rationality of the sizing results is verified through online operation, where the proposed method achieves an average of 1.93% total load shedding rate compared with 4.42% of the time-domain method, verifying the operation reliability under uncertainty. While fully utilizing the spectrum characteristics, the investment cost is about 22% less than the cut-off frequency result.

Water splitting via electrocatalysis and photocatalysis: Engineering stumbling blocks and advancements

Renewable green hydrogen is produced using solar or wind-powered photocatalysis and electrocatalysis of water. In today's world, more than a third of nations have national plans for widespread green hydrogen generation. A variety of electrocatalytic water splitting methods exist such as alkaline water electrolyzer (AWE), proton exchange membrane (PEM), anion exchange membrane (AEM), solid oxide water electrolyzer (SOWE), and proton conducting ceramic electrolyzer (PCCEL). Nowadays, the high cost of producing hydrogen is a major barrier to the broad adoption of PEC and PEM, even though these processes are more efficient than conventional water-splitting technologies. A variety of carbon dopants, including graphene oxide, graphitic-carbon nitride, nanosheets, nitrogen, and other non-noble metals, are discussed in the present work and their applications in PEC and PEM catalysts. Based on the literature review, it is noticed that the hydrogen's levelized production cost (LCOH) for PEC is 8.43 USD/kg, whereas that for electrochemical water splitting systems is just 6.22 USD/kg. As a result, scientists are still looking for better, cheaper ways to produce green hydrogen. When combined with carbon dopants in catalysts, green hydrogen shows promise way as a sustainable energy source that can help bring the world closer to climate neutrality.

Enhancing Performance of Power Allocation for VLC Networks by Non-Orthogonal Multiple Access-MIMO

Visible light communication, or VLC, networks emerged as a viable option for data access, particularly indoors. Their cost-effectiveness, protection to radio frequency (RF) intrusion, and extraordinarily high data speeds make them a desirable option for the upcoming generation of indoor networking technologies. In this paper, we propose the Exponential Gain Ratio Power Allocation (EGRPA), an effective and low-complex power splitting method, to increase the attainable sum amount in Multiple Input Multiple Output (MIMO) VLC downlink networks. Using numerical simulations, we assess the enactment of an indoor 2x2 MIMO VLC downlink model for several users. We also use Non-Orthogonal Multiple Access (NOMA) for enhancing spectrum efficacy. The usefulness and resilience of the suggested power splitting approach are established by the simulation outcomes, especially in scenarios with a high user count. In particular, the EGRPA power allocation algorithm shows a sum rate enhancement of more than 38.7%, 7.86%, and 7.04% for a system with three users when compared to the GRPA method, Normalized Gain Difference Power Allocation (NGDPA) method, and Logarithmic GRPA (NLGRPA) method, correspondingly.

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO2 sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

Numerical Investigation of Supersonic Flow over a Wedge by Solving 2D Euler Equations Utilizing the Steger–Warming Flux Vector Splitting (FVS) Scheme

Supersonic flow over a half-angle wedge (θ = 15°) with an upstream Mach number of 2.0 was investigated using 2D Euler equations where sea level conditions were considered. The investigation employed the Steger–Warming flux vector splitting (FVS) method executed in MATLAB 9.13.0 (R2022b) software. The study involved a meticulous comparison between theoretical calculations and numerical results. Particularly, the research emphasized the angle of oblique shock and downstream flow properties. A substantial iteration count of 2000 iteratively refined the outcomes, underscoring the role of advanced computational resources. Validation and comparative assessment were conducted to elucidate the superiority of the Steger–Warming flux vector splitting (FVS) scheme over existing methodologies. This research serves as a link between theoretical rigor and practical applications in high-speed aerospace design, enhancing the efficiency of aircraft components.