Rounding Research Articles

THE EVOLUTION OF A CLAY CRUST IN A BOREHOLE

Based on the previously proposed quasi-stationary model of clay crust formation when drilling wells in depth intervals with permeable rocks, software was created and computational experiments were performed, which made it possible to clarify the contribution of various physical parameters to the process of its growth.Based on the analysis of the results of computational experiments, the contribution of the physical parameters of the formation and clay crust to the dependence of its size on time has been clarified. The model assumes that the filtration pressure fields are described by stationary piezo conductivity equations. This made it possible to construct explicit dependences of pressure, thickness of the clay crust, radius of the zone of pressure disturbances in the reservoir during drilling and other parameters on time. Simple approximate formulas have been found for the dependence of the thickness of the clay crust, the filtration rate and the radius of the pressure disturbance zone in the reservoir on time, which describe their evolution with high accuracy.Based on the analysis of the calculation results, it was found that the thickness of the clay crust significantly depends on the permeability of the reservoir and repression, and these parameters determine the process of its formation. The porosity of the collector makes a smaller contribution, and the filtration and capacitance parameters of the clay crust have little effect on its thickness.New possibilities for estimating the physical parameters of reservoirs based on cavernometry have been identified. The solution of this problem is especially important for horizontal wells, in which the clay crust intervals have a significant length, and its formation occurs under conditions of a wide range of reservoir properties of the formation. The considered problem is of practical importance, since the zone of penetration of drilling mud filtrate into the formation has a screening effect on the use of geophysical methods to determine reservoir saturation. The results obtained can be used both to improve the interpretation of geophysical methods and to develop those.When conducting computational experiments using an exact formula, the stochastic behavior of the calculated curves was found. It was found that the noted effect is associated with rounding error, and in this sense is a manifestation of the features of the processor. An approach is proposed to eliminate the detected stochastic errors.

The Performance of Fixed Step Size and Adaptive Step Size Numerical Methods for Solving Deterministic Cell-Growth Models

Deterministic cell-growth models describe the growth of cell populations using fixed mathematical rules, assuming no randomness in the system. These models are often based on differential equations that account for the rates of cell division, death, and other biological processes. The solution to the system is obtained via numerical methods. Most of the developed approaches are based on fixed step sizes. However, fixed step size implementation failed to offer the optimal solutions when dealing with stiff challenges. Fixed step size methods can be unstable for stiff equations, where some components of the solution change much more rapidly than others. The step size, required to maintain stability can become impractically small. Thus, the adaptive step size method is required. Adaptive step size methods adjust the step size dynamically based on the behavior of the solution, aiming to maintain a desired level of accuracy while optimizing computational efficiency. These methods are particularly useful for solving ordinary differential equations (ODEs) where the solution can vary rapidly in some regions and slowly in others. This study is devoted to comparing the implementation of fixed step size and adaptive step size in solving ordinary differential equations (ODEs). The fixed step size and adaptive step size numerical method are solved in this study via the fourth order Runge-Kutta method (RK4) and Runge-Kutta Fehlberg 45 method (RKF45). The performance of both numerical methods used will be analyzed by comparing the numerical results approximated with the actual data. Subsequently, the absolute error, relative error, and rounding-off error will be calculated to compare both approaches. Based on the more precise findings, this work has shown that adaptive step size is predicted to be the optimal representation for solving ODEs. As a result, this may help mathematicians to choose the most effective numerical approach for solving ODEs.

High-precision Roundness Measuring System for Tungsten Ball Tips with the Diameter of Less than 100 µm

Abstract Tungsten balls with a diameter of less 100 μm can function as probe tips for micro-coordinate measuring machines (CMMs) to measure ultraprecise workpieces with complex features. A high-precision measuring system was developed to evaluate the roundness of self-made tungsten ball tips. The system based on two-point method was composed of two oppositely placed interferometers and a turntable. The turntable rotated the tested ball, and the interferometers measured the variation in radius. A new model based on minimum zone method was proposed to evaluate roundness. The fabrication principle of tungsten balls was introduced and the analysis was conducted on the maximum permissible contact force and bending stress of tungsten ball tips. The elastic mechanism was designed based on the analysis. A ruby sphere with a sphericity of 130 nm was measured to verify the system's effectiveness. Repeated experiments were performed for two tungsten ball tips. Results show the roundness error of tungsten ball-A is between 550.9 and 586.2 nm with a standard deviation of 11.0 nm while tungsten ball-B’s roundness error is between 898.5 and 959.9 nm with a standard deviation of 21.7 nm. The uncertainty is calculated as 144.6 nm. The developed system can stably measure the roundness of tungsten ball tips.

Improved Laguerre Spectral Methods with Less Round-off Errors and Better Stability

Improved Laguerre Spectral Methods with Less Round-off Errors and Better Stability

A high-performance ray tracing particle tracking model for the simulation of microplastics in inland and coastal aquatic environments

In this study, we present a high-performance Particle Tracking Model (PTM) designed for simulating any type of particles, with a focus on microplastics. The PTM is efficient compared to existing models, parallelized, and utilizes a ray tracing algorithm incorporating both ray reflection and ray refraction in order to traverse particles as well as find the location of each particle over three-dimensional unstructured grids. Various numerical corrections are implemented in the model to address computational round-off errors and discontinuities in the water surface level of the input hydrodynamic models. To increase the accuracy of the model, partially reflective boundary conditions are imposed as well as the capability to simulate microplastics beaching and washout in very shallow areas or dry computational cells. Several tests are conducted to study the performance, scalability, and accuracy of the model. The proposed model is tested with over 3.88 billion double-precision particles on three-dimensional computational grids with up to approximately one million cells. The tests show that the ray tracing approach is efficient, achieves over 17× faster runtime, and offers greater accuracy compared to using an auxiliary grid for particle location finding. For larger timesteps, the ray tracing PTM with refraction shows improved accuracy compared to the ray tracing PTM without refraction. The model's capabilities are tested in a real-world case study over the Saguenay Fjord, Quebec, Canada. The model is utilized to reproduce the paths of five surface drifters. A second numerical test is conducted in the Fjord and high particle concentration areas are identified.

A hybrid GRA-PCA-TOPSIS Technique Optimization of EDD Process Parameter on Drilling of AL8011/B4C/aloevera composites

A class of cutting-edge materials called hybrid aluminum metal matrix composites has been produced for applications such as the automobile, aerospace, and electronics industry and where weight and strengths are crucial factors. In the present research work, AA8011 composite reinforced with boron carbide particles and green aloevera has been fabricated using an economical stir casting process. In this 1% to 3% of boron carbide and 1% to 2% aloevera were used to fabricate the three different combinations of composites. The electrical discharge drilling process variables such as discharge current, pulse-on time, pulse-off time, and dielectric fluid pressure are investigated using the tubular copper electrode on drilling of hybrid composites. Performance aspects including drilling rate, roundness error, taper angle, and electrode wear rate have been analyzed, and the effect of process variables with the response surface methodology–central composite experimental design. The process parameters during the drilling of composites were optimized using a novel multi-criteria decision-making technique called the hybrid grey relational analysis–pulse component analysis–technique for order of preference by similarity to ideal solution method in order to maximize the drilling rate while concurrently minimizing other aspects. The optimum conditions were reached using the hybrid optimization method and a 1.5 mm tubular copper electrode with an input current of 9 Ampere , pulse on time 25 [Formula: see text]s, pulse off time 12 [Formula: see text]s, and pressure 60 kg/cm2. In comparison to the initial settings, the optimal condition shows a 25% faster drilling rate, with a 23% better roundness value, 14% lesser taper angle, and 7% lesser electrode wear rate.

The influence of parasitic modes on stable lattice Boltzmann schemes and weakly unstable multi-step Finite Difference schemes

Numerical analysis for linear constant-coefficient multi-step Finite Difference schemes is a longstanding topic, developed approximately fifty years ago. It relies on the stability of the scheme, and thus—within the L2 setting—on the absence of multiple roots of the amplification polynomial on the unit circle. This allows for the decoupling, while discussing the convergence of the method, of the study of the consistency of the scheme from the precise knowledge of its parasitic/spurious modes, so that the methods can be essentially studied as if they had only one step. Furthermore, stability alleviates the need to delve into the complexities of floating-point arithmetic on computers, which can be challenging topics to address. In this paper, we demonstrate that in the case of “weakly” unstable Finite Difference schemes with multiple roots on the unit circle, although the schemes may remain stable, considering parasitic modes is essential in studying their consistency and, consequently, their convergence. This research was prompted by unexpected numerical results on stable lattice Boltzmann schemes, which can be rewritten in terms of multi-step Finite Difference schemes. Unlike Finite Difference schemes, rigorous numerical analysis for lattice Boltzmann schemes is a contemporary topic with much left for future discoveries. Initial expectations suggested that third-order initialization schemes would suffice to maintain the accuracy of fourth-order schemes. However, this assumption proved incorrect for weakly unstable Finite Difference schemes and for stable lattice Boltzmann methods. This borderline scenario underscores that particular care must be adopted for lattice Boltzmann schemes, and the significance of genuine stability in facilitating the construction of Lax-Richtmyer-like theorems and in mastering the impact of round-off errors concerning Finite Difference schemes. Despite the simplicity and apparent lack of practical usage of the linear transport equation at constant velocity considered throughout the paper, we demonstrate that high-order lattice Boltzmann schemes for this equation can be used to tackle nonlinear systems of conservation laws relying on a Jin-Xin approximation and high-order splitting formulæ.

An enhanced key expansion module based on 2D hyper chaotic map and Galois field

Key expansion is an essential component in block cryptography, which serves the round function. By analyzing key expansion module of AES, it is found that the round-keys are highly correlated, and current round-key can be derived from its previous or the next round-key. To address these weaknesses, first, a 2D exponential chaotic map (2D-ECM) that exhibits ergodicity and superior randomness was constructed. Then, the Lyapunov exponents (LEs) were calculated based on the singular value decomposition (SVD) method. In addition, TestU01 test results showed that the sequences generated by 2D-ECM have better randomness. Further, an enhanced key expansion module was designed utilizing 2D-ECM and primitive polynomial over GF(2n), which has irreversibility and parallelism, and the round-keys are independent of each other. Simulation results and performance analysis demonstrated the effectiveness of the proposed enhanced key expansion module.

Introducing the symposium: Spinoza on perfectionism and education

This paper introduces the symposium on Spinoza on perfectionism and education. It frames the key issue of Spinoza’s perfectionism in terms of a perennial educational problem and introduces the different contributions to this special issue, where Steven Nadler’s main paper is followed by a series of full paper responses by a group of Spinoza scholars and educational theorists. To round off the special issue, Nadler comments on the responses to his main paper.

Evaluation of rotating components by combining individual classification with adaptive updating searching method in aero engine

Abstract In order to evaluate the roundness error of rotating components in aero engine with increased speed and more accurate estimation, this paper presents an enhanced method that integrates individual classification with adaptive updating searching (ICAUS) strategy. The individual classification method simulates the renewal regulations of various candidate points as iterations increase, subsequently generating new solutions for the next iteration. Additionally, an adaptive updating search zone method that varies in accordance with the increment of iterations is incorporated. These newly generated solutions are distributed within the updated search zone to ensure that the global optimal solution is not overlooked and the search zone is constrained to prevent excessive divergence, thereby enhancing computational efficiency. To validate the efficacy and accuracy of the proposed method, we utilized datasets and conducted comparative experiments using experimental methods previously studied by predecessors. The experimental results and comparisons demonstrate that the proposed ICAUS method exhibits superior convergence characteristics compared to previous studies. Across five distinct datasets, the average computation time satisfying the terminal conditions ranged from 0.0013s to 0.0018s, the standard deviation of the roundness was less than 6.2051×10–9 mm and the optimal solutions were obtained within 10 to 20 iterations, achieving the solution accuracy of ε = 10–8 mm.

Comparative Analysis of Simultaneous Electrochemical and Electrodischarge Machining Process

Abstract Recent advances have established electrochemical discharge machining (ECDM) as an effective alternative to electrical discharge machining (EDM) for producing microholes in conductive materials. However, ECDM leaves nonuniform layers, including recast layers and heat-affected zones, rendering it unsuitable for materials vital to aerospace, defence, and biomedical applications. To address this issue, the present work investigates a novel electrochemical machining (ECM)-based frugal engineering process known as simultaneous electrochemical and electrodischarge machining (SECEDM) for microhole fabrication. To evaluate the process effectiveness, the machining results of the SECEDM process were compared with ECDM, EDM, and ECM. The obtained results present the fundamental distinction between the process mechanism of SECEDM and ECDM. SECEDM has been reported to produce microholes with improved machined surfaces characterized by their freedom from recast layer and ECDM-induced defects. Moreover, SECEDM facilitated meticulously controlled high-speed anodic dissolution of work material, surpassing the material removal rate (MRR) achieved through ultrasonic-assisted ECDM (U-ECDM), ECM, and EDM processes by 2.67, 4.2, and 6.2 times, respectively. Furthermore, the substantial 67.72% and 68.82% reduction in the average machined hole diameter than ECM and U-ECDM, respectively, with a noteworthy 13.69% enhancement in average roundness error achieved while maintaining the repeatability accuracy with an accuracy range within ±0.009 mm through SECEDM process underscore SECEDM's accuracy and repeatability. In addition, lower surface roughness by 31.6% and 68% compared to ECM and EDM, along with reduced carbon and oxygen content as examined through energy dispersive X-ray (EDX) analysis, signifies the SECEDM process efficiency in microfabrication.

Enhancing cathode design by considering complex motion and variations of electric field distribution in counter-rotating electrochemical machining

The counter-rotating electrochemical machining (CRECM) shows unique potential in the machining of thin-walled rotating parts with complex convex structures. CREM realizes the shaping of complex convex structures through the relative rotation of the cathode and anode. The complex motion pattern and electric field distribution make it difficult to apply the existing cathode design methods to CRECM. To solve this problem, the matrix equations of cathode motion based on the kinematics and the electric field simulation model are established. The motion trajectories and edge contours at different angles are analyzed. The rotational overlap theory of motion trajectories under the windows at different angles is proved. Besides, the relationship between electric field distribution and the convex structure forming under different angle windows is studied, and the fundamental reason for deviations occurs when the convex profile is rotated to coincide is revealed. Therefore, a prediction model of the sidewall dissolution is established to correct this deviation, thereby deriving a high-precision design formula for the cathode windows of the high convex structures. By designing a cathode with oval-like windows to curry out CRECM experiments, the array-arranged (30×5) circular high convex structure with a maximum roundness error of 0.065 mm is successfully fabricated.

A novel feedrate scheduling method using modifying S-shaped feedrate profile with a round-off error elimination approach for CNC machining

A novel feedrate scheduling method using modifying S-shaped feedrate profile with a round-off error elimination approach for CNC machining

S-слівна арифметика та високоточні обчислення

The intricacies of using S-word arithmetic, the influence of the value of the parameter S on the estimation of the rounding error are analyzed; what are high-precision calculations and where they are used. The problems of two-key cryptography, computer steganography and the problem of transcomputational complexity are considered as areas of application of S-word arithmetic. For the development of S-word arithmetic algorithms, sequential, parallel, quantum computing models are used, and systems of residual classes are used. The architectural features of the computer system for the implementation of an effective algorithm in various models of calculations are considered. For the parallel computing model, the importance of reducing the connected steps is indicated, which can increase the amount of processed data, but allows to involve a larger number of parallel processors. This approach is in conflict with a method that reduces the amount of processed data, and there is a need to maintain a balance between these two methods in a parallel computing model. For the quantum computing model, the connection of qubits is a key factor in determining the quantum volume. The physical scheme determines which pairs of qubits can be entangled in a quantum computer. Peculiarities of transferring algorithms to another computing model are considered. An analysis of the complexity of implementing S-word arithmetic operations in sequential, parallel, and quantum computing models is carried out. For the parallel computing model, the importance of reducing the connected steps is indicated, which can increase the amount of processed data, but allows to involve a larger number of parallel processors. This approach is in conflict with a method that reduces the amount of processed data, and there is a need to maintain a balance between these two methods in a parallel computing model. For the quantum computing model, the connection of qubits is a key factor in determining the quantum volume. The physical scheme determines which pairs of qubits can be entangled in a quantum computer. Information is provided about the ongoing scientific forum «Calculation optimization issues», the subject of which is closely related to the topic (1969-2023)

Fatigue behavior of multi-row film cooling holes manufactured by lasers with different pulses under complex-temperature fields

This research investigates the fatigue behavior of multi-row film cooling holes produced by lasers with diverse pulse widths amid intricate thermal environments. Through laser drilling experiments, conjugate heat transfer simulations, and crystal plasticity finite element analyses, it explores the interplay of temperature and stress fields among multiple holes in these structures, and factors influencing fatigue damage and its severity. Additionally, it anticipates the fatigue fracture paths of multi-row film cooling hole structures. Findings reveal that while the drilling process and aerodynamic parameters significantly impact cooling effectiveness, their influence on cooling distribution is negligible. Fatigue damage distribution is shaped by structural imperfections from different processes, stress field interference among multiple holes, and material property alterations due to temperature changes. The extent of damage is primarily dictated by roundness errors resulting from the drilling process, with taper playing a minor role. Nonetheless, stress interference among multiple holes notably exacerbates stress concentration at the interference zone, leading to increased damage levels in film cooling holes crafted by picosecond lasers with minimal roundness errors. Moreover, in complex thermal environments, fatigue fracture paths of multi-row film cooling holes migrate and evolve contingent on temperature-induced shifts in material properties.

Combining Precision Boosting with LP Iterative Refinement for Exact Linear Optimization

This article studies a combination of the two state-of-the-art algorithms for the exact solution of linear programs (LPs) over the rational numbers in practice, that is, without any roundoff errors or numerical tolerances. By integrating the method of precision boosting inside an LP iterative refinement loop, the combined algorithm is able to leverage the strengths of both methods: the speed of LP iterative refinement, in particular, in the majority of cases when a double-precision floating-point solver is able to compute approximate solutions with small errors, and the robustness of precision boosting whenever extended levels of precision become necessary. We compare the practical performance of the resulting algorithm with both pure methods on a large set of LPs and mixed-integer programs (MIPs). The results show that the combined algorithm solves more instances than a pure LP iterative refinement approach while being faster than pure precision boosting. When embedded in an exact branch-and-cut framework for MIPs, the combined algorithm is able to reduce the number of failed calls to the exact LP solver to zero while maintaining the speed of the pure LP iterative refinement approach. History: Accepted by Antonio Frangioni, Area Editor for Design and Analysis of Algorithms: Continuous. Funding: The work for this article has been conducted within the Research Campus Modal funded by the German Federal Ministry of Education and Research (BMBF) [Grants 05M14ZAM and 05M20ZBM].

Roundness Errors Prevention of the Machined Surface in WEDM

Roundness Errors Prevention of the Machined Surface in WEDM

Enhanced lightweight encryption algorithm based on chaotic systems

In order to improve security and efficiency, this study presents a novel lightweight encryption technique that makes use of chaotic systems. Our method creatively combines the new chaotic KLEIN_64 algorithm with the Keccak-256 hash function, offering a solid basis for producing initial values essential for causing chaotic maps during the encryption process. After a deep validation with rigorous NIST testing, our chaotic pseudo random generator, LAC, exhibits excellent reliability and cryptographic robustness. Furthermore, the complexity of the cryptographic round function is improved by incorporating a second chaotic pseudo random generator that combines chaotic LFSR and Skew Tent Maps, thereby fortifying security measures.Designed with resource-limited applications in mind, our approach ensures that the cryptosystem remains both lightweight and efficient, meeting the stringent constraints typical of such environments. The practical feasibility and performance of our approach are extensively evaluated through FPGA implementation on the Zybo 7Z010 platform. Our implementation achieves a remarkable throughput of 2.820 Gbps while maintaining optimal resource utilization and efficiency. Extensive experimental results confirm the superior security of our cryptosystem, with correlation tests, entropy measurement, and histogram analysis showcasing robustness against statistical attacks. Moreover, the cryptosystem shows little fluctuation in the Unified Average Changing Intensity (UACI) and Non-Linear Pixel Change Rate (NPCR), confirming its resistance to differential attacks. Overall, our technique advances lightweight cryptography by providing a robust and efficient solution to modern cybersecurity challenges. In particular, our approach is well-suited for applications with limited resources, ensuring that security is maintained without compromising on performance or efficiency, thus fulfilling the needs of modern, constrained environments.

Round-Off Error Suppression by Statistical Averaging

Round-Off Error Suppression by Statistical Averaging

FRAST: TFHE-Friendly Cipher Based on Random S-Boxes

A transciphering framework, also known as hybrid homomorphic encryption, is a practical method of combining a homomorphic encryption (HE) scheme with a symmetric cipher in the client-server model to reduce computational and communication overload on the client side. As a server homomorphically evaluates a symmetric cipher in this framework, new design rationales are required for “HE-friendly” ciphers that take into account the specific properties of the HE schemes. In this paper, we propose a new TFHE-friendly cipher, dubbed FRAST, with a TFHE-friendly round function based on a random S-box to minimize the number of rounds. The round function of FRAST can be efficiently evaluated in TFHE by a new optimization technique, dubbed double blind rotation. Combined with our new WoP-PBS method, the double blind rotation allows computing multiple S-box calls in the round function of FRAST at the cost of a single S-box call. In this way, FRAST enjoys 2.768 (resp. 10.57) times higher throughput compared to Kreyvium (resp. Elisabeth) for TFHE keystream evaluation in the offline phase of the transciphering framework at the cost of slightly larger communication overload.