Numerical Formula Research Articles

Numerical simulations of breaking wave propagation through the vegetation on a slope based on a drag coefficient prediction model

Coastal vegetation plays a key role in wave attenuation on sloping beaches. However, accurately predicting the vegetation-related drag coefficient (CD) under breaking waves on slopes remains a challenge. In this study, the Reynolds-averaged Navier–Stokes equations were modified by incorporating a vegetation resistance term to consider the vegetation-induced momentum loss. The stabilized k-ω shear stress transport turbulence model was improved by introducing the vegetation-induced turbulence generation and dissipation terms. The numerical model was validated by two laboratory experiments. Based on experimental wave height data, the CD was determined via a calibration method. The numerical results were found to be highly sensitive to the CD. The calibrated CD achieved excellent agreement with experimental data (RMSE < 0.2). In addition, the calibrated CD showed a high correlation (R2 = 0.85) with the Iribarren number ξ. Finally, a CD prediction formula expressed by the combination of Reynolds number and ξ was proposed via regression analysis, and its performance was evaluated by two additional cases. The limitations and applicability of the CD prediction formula were also discussed. The proposed numerical model and CD prediction formula have the potential to be useful for the numerical simulation of wave interactions with vegetation on slopes.

A Uniformly Convergent Numerical Method for Singularly Perturbed Semilinear Integro-Differential Equations with Two Integral Boundary Conditions

This paper purposes to present a new discrete scheme for the singularly perturbed semilinear Volterra–Fredholm integro-differential equation including two integral boundary conditions. Initially, some analytical properties of the solution are given. Then, using the composite numerical integration formulas and implicit difference rules, the finite difference scheme is established on a uniform mesh. Error approximations for the approximate solution and stability bounds are investigated in the discrete maximum norm. Finally, a numerical example is solved to show -uniform convergence of the suggested difference scheme.

Certain results concerning (p, q)-parameterized beta logarithmic function and their properties

The primary object of this article is to introduce (p, q)-beta logarithmic function with extended beta function by using the logarithmic mean. We evaluate different properties and representations of beta logarithmic function. Further, it is evaluated logarithmic distribution, hypergeometric and confluent hypergeometric functions via logarithmic mean are evaluated and their essential properties are studied. Numerous formulas of (p, q)-beta logarithmic functions such as integral formula, derivative formula, transformation formula and generating function are analyzed.

Comparison of Distance Measurements Based on k-Numbers and Its Influence to Clustering

Heuristic data requires appropriate clustering methods to avoid casting doubt on the information generated by the grouping process. Determining an optimal cluster choice from the results of grouping is still challenging. This study aimed to analyze the four numerical measurement formulas in light of the data patterns from categorical that are now accessible to give users of heuristic data recommendations for how to derive knowledge or information from the best clusters. The method used was clustering with four measurements: Euclidean, Canberra, Manhattan, and Dynamic Time Warping and Elbow approach for optimizing. The Elbow with Sum Square Error (SSE) is employed to calculate the optimal cluster. The number of test clusters ranges from k = 2 to k = 10. Student data from social media was used in testing to help students achieve higher GPAs. 300 completed questionnaires that were circulated and used to collect the data. The result of this study showed that the Manhattan Distance is the best numerical measurement with the largest SSE of 45.359 and optimal clustering at k = 5. The optimal cluster Manhattan generated was made up of students with GPAs above 3.00 and websites/ vlogs used as learning tools by the mathematics and computer department. Each cluster’s ability to create information can be impacted by the proximity of qualities caused by variations in the number of clusters.

Data-driven prediction of the equivalent sand-grain roughness

Surface roughness affects the near-wall fluid velocity profile and surface drag, and is commonly quantified by the equivalent sand-grain roughness {k}_{s}. It is essential to estimate {k}_{s} for accurate fluid dynamic problem modeling. While numerous roughness correlation formulas have been proposed to predict {k}_{s} in the fully rough regime, most of them are restricted to certain roughness types, with various geometric parameters considered in each case, leading to ongoing disagreements regarding its parameterization and lack of universality. In this study, a Particle Swarm Optimized Backpropagation (PSO-BP) method is proposed to predict {k}_{s} based on the selected surface parameters from previous DNS, LES, and experimental results for flow behavior over various surface roughness. The PSO-BP model’s ability to predict {k}_{s} in the fully rough region is evaluated and compared with both the existing roughness correction formulas as well as the traditional BP model. An optimized polynomial function is also proposed to serve as a ‘white box’ for predicting {k}_{s}. It turns out that the PSO-BP method has better performance in the evaluation metrics compared to other methods, yielding a Mean Absolute Error (MAE) of 0.0390, a Mean Squared Error (MSE) of 0.0026 and a Mean Absolute Percentage Error (MAPE) of 28.12%. This novel approach for estimating {k}_{s} has practical applicability and holds promise for improving the precision and efficiency of calculations related to equivalent sand-grain roughness, and thus provides more accurate and effective solutions for CFD and other engineering applications.

Enhancement of graphene absorption: a numerical formula to design a suitable Fabry-Perot cavity in a terahertz spectral window

In this article, we investigate the absorption characteristics of a graphene-embedded FP cavity in a terahertz spectral window. The optical attributes were determined by a 4 × 4 transfer matrix procedure. The findings demonstrate that perfect absorption is completely reliant on the structural characteristics of the FP cavity throughout a broad range of terahertz frequencies. From the obtained dataset, numerical formulae are generated for structural parameters (N FD , N BD ) using a linear regression machine learning algorithm to achieve higher than 90% absorption. The artificial neural network trained using our dataset provided a coefficient of determination (R2)=1, opening up new pathways to design perfect terahertz absorbers. Furthermore, we explored the influence of magnetic biasing on absorption traits, and our findings show that fine absorption improvement is conceivable. The formulated numerical relations have greater importance in the design of perfect terahertz absorbers.

Design and Optimization of Complex High-Frequency Electromagnetic Treatment Cavity

High-frequency electromagnetic water treatment devices play a crucial role in the scale inhibition and fouling control process of industrial water treatment. They are widely used in various factories and can be classified into coaxial treatment cavities and coil-wound treatment cavities. To address the issues of low energy distribution at the edge of the coaxial treatment cavity and weak peak energy in the coil-wound treatment cavity, which result in unstable scale inhibition and fouling control effectiveness, this study derives a numerical calculation formula for electromagnetic energy in a complex treatment cavity based on the theories of active polarization and quasi-static field. A complex high-frequency electromagnetic water treatment device is designed using this formula, and the internal structure of the treatment cavity is visually analyzed using simulation software. Through the optimization of the complex treatment cavity’s structure, the optimal range of the anode-cathode radius ratio is determined. The research results show that the energy distribution in the complex treatment cavity is significantly higher than that in the coaxial and coil-wound cavities. This study provides theoretical and practical guidelines for the design of high-frequency electromagnetic water treatment device cavities.

The Effect of Combination of Calcium Supplement and Physical Exercise on Increasing Muscle Strength in Chronic Ischemic Stroke

Background: Stroke causes muscle weakness which results in limitations in daily activities such as self-care, eating, walking, etc. Objective: This study aims to evaluate the effect of calcium supplement and physical exercise on increasing muscle strength in chronic ischemic stroke patients. Method: This research used a quasi-experimental pretest-posttest with control group design. This research was conducted at Dadi Makassar Hospital and Haji Hospital from March to May 2023. The sample obtained was 37 subjects based purposive sampling with an unpaired numerical comparative formula for two sample groups. Consisting of 18 people in the treatment group who were given calcium supplements at a dose of 500 mg per day and physical exercise (Both training, Proprioceptive Neuromuscular Facilitation (PNF) and strengthening) and 19 people in the control group who were only given physical exercise. The research was carried out for 6 weeks using a Manual Muscle Testing (MMT) measuring instrument for muscle strength. This research used the Wilcoxon and Mann Whitney test. (α&lt;0.05) Results: There is a significant of increasing lower extremity muscle strength between pretest and posttest in treatment group and control group (p=0.001; p=0.014, p&lt;0.05), There is an increasing of the upper extremity muscle strength between pretest and posttest in treatment group and control group (p=0.001; p=0.025). There is no significant difference of increasing muscle strength in the upper and lower limb between two groups (p=0.051). Conclusion: Calcium supplements and physical exercise were no more significant in increasing muscle strength than physical exercise only in chronic ischemic stroke patients.

Protection of schisantherin A against dictamnine-induced hepatotoxicity: Pharmacokinetic insights.

Dictamnine (DIC), as the most abundant furoquinoline alkaloid ingredient of the herbal medicine Cortex Dictamni (CD), can induce severe liver injury. A previous study found that DIC-induced liver injury was initiated by cytochrome P4503A (CYP3A)-mediated metabolic activation and subsequent formation of adducts with cellular proteins. Schisantherin A (SchA) is the major lignan component of the herbal medicine Schisandra chinensis (SC). SC is frequently combined with CD used in numerous Chinese medicinal formulas for the treatment of eczema and urticaria. Furthermore, SC could protect against CD-induced hepatotoxicity. The objective of the study was to investigate the protective effect of SchA on DIC-induced hepatotoxicity based on pharmacokinetic interactions. The studies found that SchA exerted a protective effect on DIC-induced hepatotoxicity in a dose-dependent manner. Pharmacokinetic studies showed that pretreatment with SchA enhanced the area under concentration-time curve(AUC) and maximal concentration (Cmax ) values of DIC in the serum and liver tissue of mice, indicating that SchA could augment the accumulation of DIC in the circulation. In vitro metabolism assays with mouse liver microsomes (MLMs) showed that SchA reduced the production of DIC-glutathione (GSH) conjugate. In addition, SchA significantly reduced the excretion of DIC-GSH conjugate in the urine of mice and relieved hepatic GSH depletion induced by DIC. These results suggested that SchA could inhibit the metabolic activation of DIC in vitro and in vivo. In summary, our findings showed that the observed pharmacokinetic interactions might be attributable to the inhibition of the metabolism of DIC by SchA, which might be responsible for the protection of SchA against DIC-induced hepatotoxicity. Therefore, the development of a standardized combination of DIC and SchA may protect patients from DIC-induced liver injury.

THE QURʾĀN AND SCIENCE, PART III: MAKERS OF THE SCIENTIFIC MIRACULOUSNESS

AbstractThe last article of this three‐part series on the Qurʾān and science discusses the creation and development of the scientific miraculousness of the Qurʾān, which claims that the Qurʾān contains scientific findings and has particular scientific features, such as harmonious numerical analogies and formulae, that confirm the divine origin of the text. It became a political‐theological tool used by Muslim preachers and activists across the globe. Unlike scientific interpreters of the Qurʾān, advocates of scientific miraculousness were concerned with not only uniting Muslims and proving God's authority over the universe but also promoting the Qurʾān as a mine of modern science, archaeology, and history, the authenticity of which is unchallengeable.

Simulation Analysis and Optimization Design of Electromagnetic Fields in Coaxial Processing Cavities Based on the Theory of Electrostatic Fields

The coaxial processing cavity is an important component of high-frequency electromagnetic water treatment devices. Due to its easy installation, wide applicability, and excellent scale removal effect, it has been widely used in various factories. To study the influence of excitation source waveform, processing cavity length, and anode-cathode radius ratio on the intensity and distribution of the electromagnetic field in the coaxial processing cavity under time-varying fields, this paper derives the numerical calculation formula for electromagnetic energy in the coaxial processing cavity based on the theory of electrostatic fields. The finite element method is used to visualize the intensity and distribution of the electromagnetic field in the coaxial processing cavity. By optimizing the structure of the coaxial processing cavity, the optimal range of the anode-cathode radius ratio is determined. The research results show that, under the conditions of electrostatic field theory, square waves have the maximum electromagnetic energy, the length of the processing cavity does not affect the distribution of the electromagnetic field, and the optimal anode-cathode radius ratio range is 0.375-0.5.

A Numerical Approach for Dealing with Fractional Boundary Value Problems

This paper proposes a novel numerical approach for handling fractional boundary value problems. Such an approach is established on the basis of two numerical formulas; the fractional central formula for approximating the Caputo differentiator of order α and the fractional central formula for approximating the Caputo differentiator of order 2α, where 0&lt;α≤1. The first formula is recalled here, whereas the second one is derived based on the generalized Taylor theorem. The stability of the proposed approach is investigated in view of some formulated results. In addition, several numerical examples are included to illustrate the efficiency and applicability of our approach.

Spectrally accurate numerical quadrature formulas for a class of algebraically singular periodic Hadamard finite part integrals by regularization

We consider the numerical computation of Hadamard Finite Part (HFP) integrals Hσ(t;u)=⨎0T|sinπ(x−t)T|σu(x)dx,0<t<T,σ<−1,σ⁄∈Z,u(x) being sufficiently differentiable and T-periodic on R. Thus σ=−(m+δ), m∈{1,2,3,…}, 0<δ<1. For each such σ, we regularize Hσ(t;u), and show that Hσ(t;u)=Hσ+2r(t;Uσ),r=⌊(m+1)/2⌋, where Uσ(x)=∑k=0raku(2k)(x) for some constants ak, Hσ+2r(t;Uσ) being a regular integral. We then propose to approximate Hσ(t;u) by the quadrature formula Qσ,n(t;u)≡Hσ(t;ϕn), where ϕn(x) is the nth-order balanced trigonometric polynomial that interpolates u(x) on [0,T] at the 2n equidistant points xn,k=kT2n, k=0,1,…,2n−1. The implementation of Qσ,n(t;u) is simple, the only input needed for this being the 2n function values u(xn,k), k=0,1,…,2n−1. Using Fourier analysis techniques, we develop a complete convergence theory for Qσ,n(t;u) as n→∞ and prove that it enjoys spectral convergence when u∈C∞(R).We also show that the theoretical developments and numerical quadrature formulas developed for the HFP integrals Hσ(t;u) with σ<−1 and σ⁄∈Z apply, with no changes, to the regular singular integrals Hσ(t;u) with σ>−1 and σ⁄∈Z.We illustrate the effectiveness of Qσ,n(t;u) with numerical examples both for σ<−1 and σ>−1.Finally, we show that the HFP or regular integral ⨎0Tf(x)dx of any T-periodic integrand f(x) that has algebraic singularities of the form |x−t+kT|σ, 0<t<T, k=0,±1,±2,…, with σ⁄∈Z, but is sufficiently differentiable in x on R∖{t±kT}k=0∞, can be expressed as Hσ(t;u), where u(x) is a T-periodic and sufficiently differentiable function of x on R that can be computed from f(x). Therefore, ⨎0Tf(x)dx can be computed efficiently using our new numerical quadrature formulas Qσ,n(t;u) on the individual Hσ(t;u). Again, only 2n function evaluations, namely, u(xn,k), k=0,1,…,2n−1, are needed for the whole process.

Evolution Law of Structural Form and Heat Transfer Performance of Thermal Insulation System.

Building thermal insulation and energy conservation have become urgent problems in the field of civil engineering because they are important for achieving the goal of carbon neutralization. Thermal conductivity is an important index for evaluating the thermal insulation of materials. To study the influence of different porosity levels on the thermal conductivity of materials, this paper established a random distribution model using MATLAB and conducted a comparative analysis using COMSOL finite element software and classical theoretical numerical calculation formulas. The thermal conductivity of composite materials was determined based on a theoretical calculation formula and COMSOL software simulations, and the theoretical calculation results and simulation results were compared with the measured thermal conductivity of the composites. Furthermore, the influence of the width of the gaps between the materials on the heat transfer process was simulated in the fabricated roof structure. The results showed the following: (1) The thermal conductivity values calculated using the Zimmerman model were quite different from those calculated using the Campbell-Allen model and those calculated using the COMSOL software; (2) The thermal conductivity values calculated using the theoretical calculation formula were lower than the measured data, and the maximum relative error was more than 29%. The COMSOL simulation results were in good agreement with the measured data, and the relative error was less than 5%; (3) When the gap width was less than 60 mm, it increased linearly with the heat transfer coefficient. The heat transfer coefficient increased slowly when the gap width was greater than 60 mm. This was mainly due to the thermal bridge effect inside the insulation system. Based on these research results, a thermal insulation system was prepared in a factory.

Landslide risk evaluation method of open-pit mine based on numerical simulation of large deformation of landslide

It is of great practical significance to carry out quantitative risk assessment of landslide disaster to protect people’s lives and property safety and maintain the sustainable development of social economy. The delineation of landslide disaster range is the key link of landslide risk evaluation in open-pit mine. This study took the open-pit coal mine coal mine in Block I of Thar coal field in Pakistan as the research background, and constructed a framework for landslide risk evaluation in open-pit mines. Based on the numerical simulation method of large deformation of landslide, the disaster range of landslide in open-pit mine was delineated. The stability of stope slope was analyzed based on rigid body limit equilibrium method. The probability of landslide instability was calculated based on Monte Carlo method. And the comprehensive fuzzy evaluation model was established to calculate the total risk value of landslide. The results showed that: through numerical simulation and empirical formula calculation, the landslide disaster range was accurately delineated, and the comprehensive vulnerability of the disaster bearing body was determined to be medium vulnerability; the annual probability of landslide instability under natural conditions was 0.003, which belongs to moderate risk. The annual probability of landslide instability under rainstorm conditions was 0.024, which was highly dangerous; the annual probability of landslide instability under seismic conditions was 0.018, which was highly dangerous. Under natural conditions, the total risk value of landslide was 114,686.4 rmb, and the annual mortality rate of population was 0.0255 people/year. The total risk value of landslide under rainstorm condition was 11,707,570 rmb, and the annual mortality rate of population was 0.18375 people/year. The total risk value of landslide under earthquake condition was 43,007,400 rmb, and the annual mortality rate of population was 0.135 person/year, which was an unacceptable risk. The economic loss was a small geological disaster risk under natural conditions, and it was a medium-sized geological disaster risk under both rainstorm and earthquake conditions. Therefore, landslide prevention and control and management measures such as slope deformation monitoring were proposed to ensure the safety of personnel and property in open-pit mines.

Differences in Antegonial Index values in type II diabetes mellitus patients using panoramic radiography

Objectives: This research is aimed to analyze the value of the antegonial index in patients with type II diabetes mellitus using panoramic radiography.&#x0D; Materials and Methods: This research is using stratified random sampling study with unpaired numerical comparative formula. The research sample was patients who were visiting and diagnosed with type II diabetes mellitus for ≤ 5 years and &gt; 5 years by doctors at the Internal Diseases Polyclinic at Ulin General Hospital, Banjarmasin. Mandibular cortical thickness can be seen in the results of panoramic radiographs using radiomorphometric measurements with mandibular cortical index measurements, which is called as antegonial index. Antegonial index measurement as a screening tool can detect either the patient is positive or negative for having bone resoption. &#x0D; Results: The result showed average value of mandibular cortical thickness in patients with diabetes mellitus type II with a period of disease ≤ 5 years does not match the normal limit of &gt; 3.2 mm, which is 2.57 ± 1.41 and the average value of mandibular cortical thickness in the group of patients with long period of disease &gt; 5 years is 2.19 ± 0.76.&#x0D; Conclusion: Mandibular cortical thickness in patients with type II diabetes mellitus for ≤ 5 years and &gt; 5 years is not within normal limits.

Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation

AbstractIn this article, we propose a second‐order shifted composite numerical integral formula, which is denoted as the SCNIF2. We transform the nonlinear time fractional wave equation into a partial differential equation with a fractional integral term and use the SCNIF2 in time and the finite element algorithm in space to formulate a fully discrete scheme. In order to decrease the initial error of the numerical scheme, we add some starting parts. In addition, we prove the stability and error estimation of the algorithm. Finally, we illustrate the effect of the starting parts and the accuracy of the numerical scheme through some numerical tests.

A new second order Taylor-like theorem with an optimized reduced remainder

In this paper, we derive a variant of the Taylor theorem to obtain a new minimized remainder. For a given function f defined on the interval [a,b], this formula is derived by introducing a linear combination of f′ computed at n+1 equally spaced points in [a,b], together with f′′(a) and f′′(b). We then consider two classical applications of this Taylor-like expansion: the interpolation error and the numerical quadrature formula. We show that using this approach improves both the Lagrange P2- interpolation error estimate and the error bound of the Simpson rule in numerical integration.

Passively Maintained Closed Cavity Façade—Experimental Validation of the Mathematical Thermal Model

Although glass façades have been on the market for over a century, new improvements, following sustainable standards, are still being invented. An improvement of the actively maintained CCF has occurred in passive maintenance with natural ventilation of the cavity and insulation glass unit placed on the external side, which has served as a true motivation for further research. To develop the idea, a new type of CCF was invented, followed by the creation of the software, whose purpose is to determine optimal CCF façade components. During this research, an experimental and mathematical model was made regarding the thermal behavior, later validated by the measurements on-site in Rugvica, Croatia. Using simplified but unconventional methods, numerous formulae and variables, a simulation of climatic loads onto the CCF was conducted. Validations of the thermal model were made during winter and summer periods for southern and western façade orientation, explaining how heat transfers from the environment to close cavity façade elements. It was found from the analysis that air temperatures of the façade elements follow the outer air temperature, by constant air exchange with the outer space. The results showed great potential with up to 3 °C (5–10%) of difference in experimental and calculated results, thus creating a basis for further improvement of the software with the addition of structural and hygric behavior of the façade element, regarding climate conditions.

Asphalt concrete air void evaluation by applying infrared thermography

ABSTRACT Asphalt concrete is an essential part of infrastructure, and its quality and structural condition directly impact traffic comfort and safety. Air voids is applied for assessing its structural condition. This research aims to establish a physical relation between the thermal behaviour and air voids of asphalt concrete using infrared thermography. To ensure accuracy, calibration techniques including geometric, radiation, and emissivity calibration were applied in the experiment. Four asphalt concrete specimens with different air voids were tested in this study. The results indicated a clear and constant relationship between temperature increase and air voids, which serve as a critical indicator for evaluating the structural condition of asphalt concrete. Additionally, the empirical experiment showed that the thermal behaviour in the first minute followed a different trajectory compared to the subsequent measurements. The numerical results and empirical formula derived from this research can serve as a basis for formulating the analytical equation that connects asphalt concrete air voids to observations from infrared thermography. Once this relationship is established, the structural condition of asphalt concrete can be evaluated using regular and commonly available infrared thermal cameras instead of relying on other specialised and single-use equipment.