Numerical Differentiation Research Articles

A cell-centered implicit finite difference scheme to study wave propagation in acoustic media: A numerical modeling

In the present paper, we present a Cell-Centered Implicit Finite Difference (CCIFD) operator-based numerical scheme for the propagation of acoustic waves that is very effective, accurate, and small in size. This scheme requires fewer estimation points than the traditional central difference derivative operator. Any numerical simulation is significantly impacted by the precision of a numerical derivative. Long stencils can deliver excellent accuracy while also minimizing numerical anisotropy error. However, a long stencil requires a lot of computational resources, and as these derivatives get bigger, they could start to look physically unrealistic due to contributions from nodes located extremely far, wherein the derivative is local in nature. Furthermore, using such lengthy stencils at boundary nodes may result in errors. The present article investigates a cell-centered fourth order finite difference scheme to model acoustic wave propagation which utilizes a lesser number of nodes in comparison to the traditional Central Difference (CD) operator. However, in general the implicit derivative operator has high computational cost and therefore despite its significant advantages it is generally avoided to be implemented in applications. This serves as a motivation for the present paper to explore a technique called CCIFD that significantly decreases the computational expense by nearly fifty percent. Additionally, spectral characterization of the CCIFD derivative operator has been analyzed and discussed. Finally, the wave propagation has been numerically simulated in 2-dimensional homogeneous and Marmousi model using CCIFD scheme to validate the applicability and stability of the scheme.

Urinary miRNAs: Technical Updates.

Due to its non-invasive nature and easy accessibility, urine serves as a convenient biological fluid for research purposes. Furthermore, urine samples are uncomplicated to preserve and relatively inexpensive. MicroRNAs (miRNAs), small molecules that regulate gene expression post-transcriptionally, play vital roles in numerous cellular processes, including apoptosis, cell differentiation, development, and proliferation. Their dysregulated expression in urine has been proposed as a potential biomarker for various human diseases, including bladder cancer. To draw reliable conclusions about the roles of urinary miRNAs in human diseases, it is essential to have dependable and reproducible methods for miRNA extraction and profiling. In this review, we address the technical challenges associated with studying urinary miRNAs and provide an update on the current technologies used for urinary miRNA isolation, quality control assessment, and miRNA profiling, highlighting both their advantages and limitations.

Cattle colours with a dendrological component as an ethnolinguistic phenomenon

In Slavic languages, a large number of colour designations are derived from the names of trees; these designations are not only formed morphologically, but also in a lexico-semantic way. This mainly concerns the name of the birch tree, which is noticeable primarily in numerous Pol-ish derivatives, some of which can be built up into Proto-Slavic prototypes. However, a similar phenomenon can be observed in other languages around the world. Generally speaking, these coloratives are of both narrow linguistic (etymological) and ethnolinguistic interest. They reflect the view of the Slavic peoples on the importance of dendroflora in material and spiritual life and help shed light on the worldview of the ancient Slavs.

Research progress in biosynthesis-related enzymes of coumarin compounds and their bioactivities

Coumarins are natural products with benzopyran ring as the parent nucleus. Numerous coumarin derivatives exhibit a variety of pharmacological activities, including antibacterial, anti-inflammatory, antitumor, anti-coagulant, anti-osteoporotic, and insecticidal activities. Therefore, they play an important role in both medicine and agriculture. The development and utilization of coumarin derivatives have attracted increasing attention. The advancement of gene sequencing technology and the rapid progress in synthetic bio-logy have led to significant advancement in the biosynthesis of coumarin derivatives, and has received increasing attention from global researchers. This paper presents a comprehensive overview of the key biosynthesis-related enzymes of coumarin derivatives, such as cytochrome P450 enzyme(CYP450), prenyltransferase(PT), UDP-glucosyltransferase(UGT). Additionally, the pharmacological activities of these enzymes, including anti-tumor, anti-inflammatory, antioxidant, and antibacterial activities, are systematically summarized. This review aims to provide a valuable reference for the biosynthesis of coumarin derivatives and further exploration of their medicinal potential.

Numerical derivation of pressure-impulse (P-I) diagrams of prefabricated RC columns with steel joints subjected to blast loads

In recent decades, terrorist attacks and accidental explosions have occurred frequently. The casualties are not only caused by the shock wave, but also by the structural collapse initialed from the failure of structural columns. In this paper, the dynamic response and damage mechanism of prefabricated reinforced concrete (RC) columns with steel joints (PRC) subjected to blast loads are numerically investigated. By comparing the numerical results with the experimental results, the accuracy of the finite element (FE) model is firstly verified. Then, dynamic responses and damage of PRC under blast loads induced by the TNT explosions and vapor cloud explosions (VCEs) are investigated and compared with each other. The results indicated that PRC damage under VCEs with 9.3 MPa is larger than that under TNT explosions. Conversely, the damage under VCEs with 7 MPa is smaller than that under TNT explosions, and the blast-induced damage and dynamic behavior of PRC under two types of explosions is different. Subsequently, parametric studies are further carried out to investigate the influence of key parameters of PRC, including longitudinal and transverse reinforcement ratio, column dimensions, concrete strength, steel sleeve dimensions on PRC damage. It is revealed that different parameters affect the damage for PRC column in different load regions of P-I diagrams, including the impulsive load region, dynamic load region and quasi-static load region. Increasing the sleeve length, sleeve ratio and transverse reinforcement ratio improves the shear-resistant performance of PRC, and these parameters more easily affected PRC damage in the impulsive load region. Increasing the concrete strength and column depth can increase the blast-resistant performance of PRC in three load regions. Based on parametric studies, pressure-impulse (P-I) diagrams for damage evaluation of PRC under VCEs and TNT explosions are proposed and verified. Finally, Blast-resistant design procedure of PRC based on P-I diagram is developed.

Fast Cable-Force Measurement for Large-Span Cable-Stayed Bridges Based on the Alignment Recognition Method and Smartphone-Captured Video

The accurate measurement of cable force plays an important role in the structural form, structural behavior, and safety evaluation of large-span cable-stayed bridges. A fast cable-force estimation method is proposed based on the alignment recognition method and smartphone-captured video. This method can realize real-time, non-contact, and non-destructive force measurements. Videos of bridge cables were collected using a portable smartphone, and an alignment recognition method was employed to obtain the lateral displacement along the cable, followed by numerical differentiation of the lateral displacement of the cable to acquire the acceleration time history. Based on the fundamental dynamic equation of beam elements, a unified explicit formula for cable-force calculation considering service characteristics was established in the frequency method. Finally, the method was applied to the cable-force measurement during the operation and maintenance stage of the Gengcun Dou Bridge. The measured cable forces were compared with the values obtained from the on-site monitoring system. The results show that the proposed method can accurately identify the acceleration time history at different positions of the cable, and the corresponding frequency components are essentially consistent. The average relative deviation of the measured cable forces from the reference method is within 3%. The proposed cable-force measurement method is simple as regards equipment, convenient for operation, and high in efficiency, providing a new method for the measurement of cable forces in large-span cable-stayed bridges, which can offer reliable measured cable-force data for structural analysis during bridge operation and the maintenance stage.

Static force from generalized Wilson loops on the lattice using the gradient flow

The static QCD force from the lattice can be used to extract ΛMS¯, which determines the running of the strong coupling. Usually, this is done with a numerical derivative of the static potential. However, this introduces additional systematic uncertainties; thus, we use another observable to measure the static force directly. This observable consists of a Wilson loop with a chromoelectric field insertion. We work in the pure SU(3) gauge theory. We use gradient flow to improve the signal-to-noise ratio and to address the field insertion. We extract ΛMS¯nf=0 from the data by exploring different methods to perform the zero-flow-time limit. We obtain the value 8t0ΛMS¯nf=0=0.629−26+22, where t0 is a flow-time reference scale. We also obtain precise determinations of several scales: r0/r1, 8t0/r0, 8t0/r1, and we compare these to the literature. The gradient flow appears to be a promising method for calculations of Wilson loops with chromoelectric and chromomagnetic insertions in quenched and unquenched configurations. Published by the American Physical Society 2024

Lagrange Interpolation in Matrix Form for Numerical Differentiation and Integration

Numerical differentiation has been widely applied in engineering practice due to its remarkable simplicity in the approximation of derivatives. Existing formulas rely on only three-point interpolation to compute derivatives when dealing with irregular sampling intervals. However, it is widely recognized that employing five-point interpolation yields a more accurate estimation compared to the three-point method. Thus, the objective of this study is to develop formulas for numerical differentiation using more than three sample points, particularly when the intervals are irregular. Based on Lagrange interpolation in matrix form, formulas for numerical differentiation are developed, which are applicable to both regular and irregular intervals and can use any desired number of points. The method can also be extended for numerical integration and for finding the extremum of a function from its samples. Moreover, in the proposed formulas, the target point does not need to be at a sampling point, as long as it is within the sampling domain. Numerical examples are presented to illustrate the accuracy of the proposed method and its engineering applications. It is demonstrated that the proposed method is versatile, easy to implements, efficient, and accurate in performing numerical differentiation and integration, as well as the determination of extremum of a function.

Estimating the first and second derivatives of discrete audio data

A new method for estimating the first and second derivatives of discrete audio signals intended to achieve higher computational precision in analyzing the performance and characteristics of digital audio systems is presented. The method could find numerous applications in modeling nonlinear audio circuit systems, e.g., for audio synthesis and creating audio effects, music recognition and classification, time-frequency analysis based on nonstationary audio signal decomposition, audio steganalysis and digital audio authentication or audio feature extraction methods. The proposed algorithm employs the ordinary 7 point-stencil central-difference formulas with improvements that minimize the round-off and truncation errors. This is achieved by treating the step size of numerical differentiation as a regularization parameter, which acts as a decision threshold in all calculations. This approach requires shifting discrete audio data by fractions of the initial sample rate, which was obtained by fractional delay FIR filters designed with modified 11-term cosine-sum windows for interpolation and shifting of audio signals. The maximum relative error in estimating first and second derivatives of discrete audio signals are respectively in order of 10-13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-13}$$\\end{document} and 10-10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-10}$$\\end{document} over the entire audio band, which is close to double-precision floating-point accuracy for the first and better than single-precision floating-point accuracy for the second derivative estimation. Numerical testing showed that this performance of the proposed method is not influenced by the type of signal being differentiated (either stationary or nonstationary), and provides better results than other known differentiation methods, in the audio band up to 21 kHz.

A comparative study of sensitivity computations in ESDIRK-based optimal control problems

This paper compares the impact of iterated and direct approaches to sensitivity computation in fixed step-size explicit singly diagonally implicit Runge–Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We strictly use the principle of internal numerical differentiation (IND) for the iterated approach, i.e., reusing iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of these sensitivity computations in OCPs for the quadruple tank system (QTS). We discretize the OCPs using multiple shooting and solve these with a sequential quadratic programming (SQP) solver. We benchmark the iterated and direct approaches against a base case. This base case applies the ESDIRK methods with exact Newton schemes and a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and evaluate the performance based on the number of SQP and QPs iterations, KKT violations, function evaluations, Jacobian updates, and iteration matrix factorizations. We also provide examples using the continuous-stirred tank reactor (CSTR), and the IPOPT algorithm instead of the SQP. For OCPs solved using SQP, the QTS results show the direct method converges only once, while the iterated approach and base case converges in all situations. Similar results are seen with the CSTR. Using IPOPT, both the iterated approach and base case converge in all cases. In contrast, the direct method only converges in all cases regarding the CSTR.

Robust inverse parameter fitting of thermal properties from the laser-based Ångstrom method in the presence of measurement noise using physics-informed neural networks (PINNs)

The two-dimensional laser-based Ångstrom method measures the in-plane thermal properties for anisotropic film-like materials. It involves periodic laser heating at the center of a suspended film sample and records its transient thermal response by infrared imaging. These spatiotemporal temperature data must be analyzed to extract the unknown thermal conductivity values in the orthotropic directions, an inverse parameter fitting problem. Previous demonstration of the metrology technique used a least-squares fitting method that relies on numerical differentiation to evaluate the second-order partial derivatives in the differential equation describing transient conduction in the physical system. This fitting approach is susceptible to measurement noise, introducing high uncertainty in the extracted properties when working with noisy data. For example, when noise of a signal-to-noise ratio of 10 is added to simulated amplitude and phase data, the error in the extracted thermal conductivity can exceed 80%. In this work, we introduce a new alternative inverse parameter fitting approach using physics-informed neural networks (PINNs) to increase the robustness of the measurement technique for noisy temperature data. We demonstrate the effectiveness of this approach even for scenarios with extreme levels of noise in the data. Specifically, the PINN-approach accurately extracts the properties to within 5% of the true values even for high noise levels (a signal-to-noise ratio of 1). This offers a promising avenue for improving the robustness and accuracy of advanced thermal metrology tools that rely on inverse parameter fitting of temperature data to extract thermal properties.

The Method of Direct and Reverse Phase Portraits as a Tool for Systematizing the Results of Studies of Phase Transitions in Solutions of Thermosensitive Polymers.

It is shown that a more than significant amount of experimental data obtained in the field of studying systems based on thermosensitive hydrophilic polymers and reflected in the literature over the past decades makes the issue of their systematization and classification relevant. This, in turn, makes relevant the question of choosing the appropriate classification criteria. It is shown that the basic classification feature can be the number of phase transition stages, which can vary from one to four or more depending on the nature of the temperature-sensitive system. In this work, the method of inverse phase portraits is proposed for the first time. It was intended, among other things, to identify the number of phase transition stages. Moreover, the accuracy of this method significantly exceeds the accuracy of the previously used method of direct phase portraits since, for the first time, the operation of numerical differentiation is replaced by the operation of numerical integration. A specific example of the application of the proposed method for the analysis of a previously studied temperature-sensitive system is presented. It is shown that this method also allows for a quantitative comparison between the results obtained by the differential calorimetry method and the turbidimetry method. Issues related to increasing the resolution of the method of direct phase portraits are discussed.

Numerical simulations and theoretical analysis of the forward shock wave in a non-premixed air-breathing rotating detonation combustor

The forward shock wave induced by the detonation wave propagates in the inlet and restrains the air from being injected into the rotating detonation engine, and the stable continuous propagation of the detonation wave is affected. Numerical simulation and theoretical derivation of air flow velocity and detonation wave height were carried out in a rotating detonation combustor. The influence of the forward shock wave on air flow velocity and air flow velocity on detonation wave height was analyzed. A non-premixed air-breathing rotating detonation combustor was numerically simulated with the two-dimensional Navier–Stokes equations and a kerosene/air reaction model based on the RYrhoCentralFoam solver. Analytical equations were derived and validated to calculate the air flow velocity across the forward shock wave and the height of the detonation wave. The results show that the air flow velocity across the forward shock wave is inversely proportional to the detonation wave velocity, incoming flow temperature, and pressure ratio at the forward shock wave. In addition, the angle of the forward shock wave is inversely proportional to the velocity of the detonation wave and incoming flow and is proportional to the incoming flow temperature and the pressure ratio. The forward shock wave leads to a blocked zone of injection in the combustor, as the inflow velocity decreases or even reverses across the shock wave. As a result, the forward shock wave induced by the detonation wave restrains the recovery of the reactant fill zone, which has an influence on the height of the detonation wave.

Formulas for Numerical Differentiation on a Uniform Mesh in the Presence of a Boundary Layer

Formulas for Numerical Differentiation on a Uniform Mesh in the Presence of a Boundary Layer

Stabilization of SIMPLE-like RANS solvers for computing accurate gradients using the complex-step derivative method

The Reynolds-averaged Navier-Stokes (RANS) approach in Computational Fluid Dynamics (CFD) is increasingly vital for aerodynamic design across wind turbines, gas turbines, aircraft, and rotorcraft. Enhancing the process through CFD-based design optimization requires numerous design variables, favoring gradient-based methods for better scalability than gradient-free methods. This research uses numerical differentiation techniques, particularly the complex-step derivative method, to compute gradients. Challenges arise during aerodynamic shape optimization when unconventional shapes disrupt RANS solver assumptions, causing convergence failures. These failures undermine optimization, prompting the need to enhance solver convergence for robust optimization. The modified-Boostconv method is a residual recombination method bolstering unstable eigenvalues to stabilize convergence of iterative solvers for nonlinear systems of equations. This study extends the modified-Boostconv method to combine it with the complex-step derivative technique, creating robust optimizations via RANS-CFD with accurate gradients, even for these numerically unstable cases. The main issue encountered during the complexification of the modified-Boostconv method is how to correctly ensure that the model reduction leading to the least-squares problem satisfies the complex-step derivative method. We test whether the dot product operation involved in the model reduction should be a Hermitian or non-Hermitian inner product. The problem is first tested for a simple analytical case using the logistic equation in combination with the modified-Boostconv method. It shows that the non-Hermitian inner product should be used. This is also confirmed with a similar study using the RANS solver.

Introducing Ph.D. students to asymptotic inference for two‐stage M‐estimators: Easing analytic and coding demands via the use of numerical derivatives

AbstractApplications of two‐stage M‐estimators (2SMEs) abound in empirical economics. Asymptotic theory for 2SMEs (correct formulation of the asymptotic standard errors [ASE]) has been available for decades. Nevertheless, due to the daunting nature of the requisite matrix formulations, when conducting statistical inference based on two‐stage estimates, applied researchers often implement bootstrapping methods or ignore the two‐stage nature of the estimator and report the uncorrected second‐stage outputs from packaged statistical software. In the present paper, we offer teachers of econometrics a pedagogical approach for introducing Ph.D. students to asymptotic inference for 2SMEs, with a view toward easier software implementation and empirical application. We seek to demonstrate to students (and their teachers) that the analytic and coding demands for calculating correct ASEs for the 2SME need not be burdensome (or prohibitive). The main instructional (and practical) innovation that we offer in this regard is our suggested use of numerical derivative (ND) software for calculating the most challenging components of the ASE formulations. An exercise demonstrates to the student that, by implementing ND software, one can overcome the analytic and coding impediments to conducting inference based on 2SMEs, without abandoning rigor.

Stress concentration factor estimation for corroded steel plates using the surface gradient method

Pitting corrosion occurs in steel components as a stress-accumulating surface irregularity that is vulnerable to fatigue crack nucleation. In this study, stress distribution in sinusoidal surfaces was investigated to devise an estimation method for the stress concentration factor (SCF) fluctuations of corroded steel. An SCF equation for sinusoidal surfaces was developed from empirical data based on three parameters: wavelength, thickness, and position. For corroded surfaces, successive numerical differentiations can be performed on each point to determine the sinusoidal surface having a point sharing the same gradient information. Notably, the SCFs of corresponding points are comparable; SCF estimation is made feasible for irregular surfaces through sinusoidal surfaces. In two-dimensional sections, maximum error was below 5% at pits and 15% for the surface. In three-dimensional models, maximum error was below 20% at pits for wide-ranging corroded specimens. Therefore, the proposed method effectively estimates SCF for identifying areas at risk of fatigue cracking.

Coumarin as an Elite Scaffold in Anti-Breast Cancer Drug Development: Design Strategies, Mechanistic Insights, and Structure-Activity Relationships.

Breast cancer is the most common cancer among women. Currently, it poses a significant threat to the healthcare system due to the emerging resistance and toxicity of available drug candidates in clinical practice, thus generating an urgent need for the development of new potent and safer anti-breast cancer drug candidates. Coumarin (chromone-2-one) is an elite ring system widely distributed among natural products and possesses a broad range of pharmacological properties. The unique distribution and pharmacological efficacy of coumarins attract natural product hunters, resulting in the identification of numerous natural coumarins from different natural sources in the last three decades, especially those with anti-breast cancer properties. Inspired by this, numerous synthetic derivatives based on coumarins have been developed by medicinal chemists all around the globe, showing promising anti-breast cancer efficacy. This review is primarily focused on the development of coumarin-inspired anti-breast cancer agents in the last three decades, especially highlighting design strategies, mechanistic insights, and their structure-activity relationship. Natural coumarins having anti-breast cancer efficacy are also briefly highlighted. This review will act as a guideline for researchers and medicinal chemists in designing optimum coumarin-based potent and safer anti-breast cancer agents.

A multi-stage framework for coordinated scheduling of networked microgrids in active distribution systems with hydrogen refueling and charging stations

Due to the increase in electric energy consumption and the significant growth in the number of electric vehicles (EV) at the level of the distribution network, new networks have started using new fuels such as hydrogen to improve environmental indicators and at the same time better efficiency from the excess capacity of renewable resources. In this article, the services that can be provided by hydrogen refueling stations and charging electric vehicles in the optimal performance of microgrids have been investigated. The model proposed in this paper includes a two-stage stochastic framework for scheduling resources in microgrids, especially hydrogen refueling stations and electric vehicle charging. In this model, two main goals of cost minimization and greenhouse gas emissions are considered. In the proposed framework and in the first stage, the service range of microgrids is determined precisely according to the electrical limitations of distribution systems in emergency situations. Then, in the second stage, the problem of energy management in each microgrid will be solved centrally. In this situation, various indicators including the output energy of renewable sources, smart charging of hydrogen and electric vehicle charging stations (EV/FCV) and flexible loads (FL) are evaluated. The final mathematical model is implemented as a multivariate integer multiple linear problem (MILP) using the GUROBI solver in GAMS software. The simulation results on the modified IEEE 118-Bus network show the positive effect of the presence of flexible loads and smart charging strategies by charging stations. Also, the numerical derivation shows that the operating costs of the entire system can be reduced by 4.77% and the use of smart charging strategies can reduce greenhouse gas emissions by 49.13%.

2-(4-Nitrophenyl)isothiazol-3(2H)-one: A Promising Selective Agent against Hepatocellular Carcinoma Cells.

Liver cancer ranks among the most prevalent malignancies globally and stands as a leading cause of cancer-related mortality. Numerous isothiazolone derivatives and analogues have been synthesized and investigated for their potential as anticancer agents; however, limited data exist regarding their efficacy against liver cancer. In the present study, two nitrophenyl-isothiazolones, the 5-benzoyl-2-(4-nitrophenyl)isothiazol-3(2H)-one (IsoA) and the 2-(4-nitrophenyl)isothiazol-3(2H)-one (IsoB), were preliminarily investigated for their cytotoxicity against hepatoma human (Huh7) cells as a liver cancer model and Immortalized Human Hepatocytes (IHHs) as a model of non-cancerous hepatocytes. IsoB, derived from IsoA after removal of the benzoyl moiety, demonstrated the highest cytotoxic effect against Huh7 cells with CC50 values of 19.3 μΜ at 24 h, 16.4 μΜ at 48 h, and 16.2 μΜ at 72 h of incubation, respectively. IsoB also exhibited selective toxicity against the liver cancerous Huh7 cells compared to IHH cells, reinforcing its role as a potent and selective anticancer agent. Remarkably, the cytotoxicity of IsoB was higher when compared with the standard chemotherapeutical agent 5-fluorouracil (5-FU), which also failed to exhibit higher toxicity against the liver cancerous cell lines. Moreover, IsoB-treated Huh7 cells presented a noteworthy reduction in mitochondrial membrane potential (ΔΨm) after 48 and 72 h, while mitochondrial superoxide levels showed an increase after 24 h of incubation. The molecular mechanism of the IsoB cytotoxic effect was also investigated using RT-qPCR, revealing an apoptosis-mediated cell death along with tumor suppressor TP53 overexpression and key-oncogene MYCN downregulation.