Numerical Analysis Approach Research Articles

Advances in Topological Methods for Solving Nonlinear Partial Differential Equations

Higher order nonlinear partial differential equations (PDEs) are very difficult to compare or analyze and therefore there is restriction towards analytical or numerical appraisal. The following research aims at solving the problem of the solutions of Nonlinear PDEs through the application of topological fixed-point theory and degree theory, as well as the application of variational methods towards improving the existence, uniqueness, and stability of solutions to PDEs under all possible boundary conditions. The purpose of the study is to investigate the effectiveness of these methods in multifaceted and multi-grained systems. We used both fixed-point analyses to check the convergence of solutions and degree-theoretic methods for checking multiplicity of solutions, and variational structure for critical points of solutions. Newton-Raphson and finite element techniques were used in solving solutions with much ease for increased efficiency. A selection of findings shows that topological techniques are an efficient means of handling nonlinearity in PDEs; degree theory uncovers the multiplicity of solutions while variational techniques unveil the stability characteristics. This research advances the field of nonlinear analysis beyond the prior art by broadening the scope of topology in new domains and providing enhanced methods of computation of PDEs where it matters most: where traditional linear methods fail to apply. In the context of physics, engineering, and environmental studies nonlinear modeling is vital and the practical implication highlighted herein is useful for all. Possible future work might apply these methods to more general boundary conditions as well as combined analytical-numerical approaches.

A New CDM-Based Approach for the Nonlinear Numerical Structural Analysis of Flax Fiber Reinforced Plastic

Fibre-reinforced polymers based on natural fibers, such as flax fibers, exhibit pronounced nonlinear orthotropic material behavior. This presents a significant challenge in finite element analysis (FEA) simulations, as the nonlinear constitutive models available in commercial FEA tools are difficult to apply and fail to capture all the material’s specific characteristics. Relying on initial or reduced secant moduli in linear quasi-static analyses of deformations or stress states can result in inaccurate outcomes and overly optimistic strength predictions, particularly in compression-dominated cases. However, with appropriate modifications, classical laminate theory (CLT) can be adapted for nonlinear analysis. This involves iteratively updating the components of the stiffness matrix for the unidirectional (UD) ply during the calculation process based on the current strain state and stress interactions. This study presents and discusses a computational algorithm for the FEA software ABAQUS/CAE 2019, which incorporates material-related orthotropic nonlinearities and stress-dependent interactions within the CLT framework. The algorithm represents a single-scale material model at the meso level (UD ply) and is based on the concept of orthotropic elasto-damage within the framework of continuum damage mechanics (CDM) theory. Numerical implementation is achieved through a user-defined field (USDFLD) subroutine, accompanied by a pre-processing Python script for managing experimental data, computing data fields, and calculating parameters. As shown below, this type of implementation appears justified compared to a user material subroutine (UMAT) subroutine in terms of computational efficiency and practicality.

An Analytical Approach to Solving Partial Differential Equations in Mathematical Modeling

Partial Differential Equations (PDEs) are quite central in the applied mathematical modeling, and bring out the essence of yielding solution insights of physics, civil and mechanical engineering, biology and even financial related systems. This study focuses on putting into practice first fundamentals of PDEs such as separation of variables, Fourier, transforms, Green’s functions as well as series expansions. The analytical techniques for solving problems of heat conduction, wave propagation and fluid dynamics are derived and applied and various problems are solved. Comparisons to other methods with numbers bring into light primary and secondary advantages and disadvantages of analytical solutions and their computational complexity. The work focuses on the stability/ convergence/ applications/ potential of these techniques and the author suggests mixed analytical-numerical approaches in further research. This work links abstract theories to real-life problems and ensures better prediction as well as innovations for a variety of fields.

Assessment of the Stability of Some Landslide Bodies in Georgia Using a Numerical-analytical Approach

Assessment of the Stability of Some Landslide Bodies in Georgia Using a Numerical-analytical Approach

On Non-Linear Differential Systems with Mixed Boundary Conditions

For the constructive analysis of locally Lipschitzian system of non-linear differential equations with mixed periodic and two-point non-linear boundary conditions, a numerical-analytic approach is developed, which allows one to study the solvability and construct approximations to the solution. The values of the unknown solution at the two extreme points of the given interval are considered as vector parameters whose dimension is the same as the dimension of the given differential equation. The original problem can be reduced to two auxiliary ones, with simple separable boundary conditions. To study these problems, we introduce two different types of parametrized successive approximations in analytic form. To prove the uniform convergence of these series, we use the appropriate technique to see that they form Cauchy sequences in the corresponding Banach spaces. The two parametrized limit functions and the given boundary conditions generate a system of algebraic equations of suitable dimensions, the so-called system of determining equations, which give the numerical values of the introduced unknown parameters. We prove that the system of determining equations define all possible solutions of the given boundary value problems in the domain of definition. We established also the existence of the solution based on the approximate determining system, which can always be produced in practice. The theory was presented in detail in the case of a system of differential equations consisting of two equations and having two different solutions.

Identifying crowdfunding storytellers who deliver successful projects: a machine learning approach

Crowdfunding plays a key role in financial technology to provide individuals and enterprises with funding opportunities to establish start-ups and/or new business ventures. It is mainly used to link projects’ creators and backers, collect money and plan fundraising projects via social networks. This paper proposes a machine learning-enabled approach to analyse Kickstarter numerical and textual data and predict the successful funding and delivery of crowdfunding projects. It offers crowdfunding stakeholders benefits including creator credibility assessment, project risk reduction, and backer confidence enhancement. This research proposes a data preprocessing approach to prepare the dataset and extract the relevant features for the predictions. Besides, it trains and compares five numerical machine learning classification models and three text-mining methods to find the best-fitted numerical and textual analysis approaches. According to the results, the proposed SVM model outperforms the numerical benchmarks in terms of Accuracy, Precision, Recall, F1 score, and model Training latency. Moreover, BERT gives the best results if the dataset is complex, while Word2vec works better with simple features in textual analysis.

Parametric study of the apparent modal parameters of crowd-footbridge systems

The modal parameters of footbridges are time-variant as pedestrians walk along them, resulting in a new dynamic system comprising the isolated structure and the walking persons. This phenomenon is known as human-structure interaction (HSI) and is particularly significant for lightweight footbridges, where the effective damping ratio of the combined system is significantly higher than that of the isolated structure. This paper proposes an analytical-numerical approach to address the effects of HSI on the modal parameters of the coupled system. The effective damping ratios and natural frequency are determined by solving the eigenvalue problem of a two-degree-of-freedom mass-spring-damper system, with one degree of freedom representing the isolated structure and the other representing the equivalent model of the walking persons. The obtained results are compared with experimental measurements from the literature, illustrating the effectiveness of the proposed approach while also demonstrating its computational cost-effectiveness in comparison to existing methods.

Threshold Condition of Energy Splitting for Some Classes of Symmetric Double Well Potential

The double-well potential (DWP) is a prevalent mathematical model for systems with 2 force centers, widely applied in quantum physics. Often expressed as a function with multiple parameters, the DWP can exhibit either single-well or double-well behavior depending on these parameters. Within the tunneling regime, optical properties are primarily characterized by the energy difference resulting from energy splitting (ES). Thus, formulating boundary conditions for the DWP and quantifying ES are critical but understudied areas. This research explores the threshold conditions for the existence of DWPs and ES in 2 common classes of symmetric DWPs: The extensively studied Razavy potentials and the more recently introduced Dong potentials. Utilizing quasi-exact solutions for Razavy potentials and the filter method for Dong potentials, we analyze the dependence of ES on DWP parameters. Our findings align well with existing numerical data, eigenfunction analysis and energy difference approaches. This innovative methodology allows for the examination of threshold conditions for higher ES, and provides an opportunity to control ES in DWPs by adjusting structural parameters. HIGHLIGHTS For symmetric-hyperbolicus double well potentials there are some threshold condition,.i.e.: (i) threshold for existence DWP, (ii) threshold for existence DWP with first-level energy splitting rE12 characterized by ε2 = Vmax, and (iii) Threshold for existence DWP with higher-level energy splitting rEij characterized by εj = Vmax. The method has been applied in the Razavy and Dong class potentials. The eigen-energies are determined through quasi-exact solutions for Razavy potentials and numerically using the filter method for Dong potentials. We find the the critical condition as a function od structural parameters. Our findings are in good agreement with the eigenfunction and energy difference approaches. GRAPHICAL ABSTRACT

Design of a crash energy absorber for a composite aircraft fuselage using a combined analytical–numerical approach

Design of a crash energy absorber for a composite aircraft fuselage using a combined analytical–numerical approach

Stability and convergence computational analysis of a new semi analytical-numerical method for fractional order linear inhomogeneous integro-partial-differential equations

Abstract The motive behind this research work, is to originate a semi-analytical-numerical approach for the solution of fractional order linear integro partial differential equations (FOLIPDEs), especially in-homogeneous FOLIPDEs of different types, like fractional version of Fredholm and Volterra type IEs etc. To attain the said purpose, we will study some fractional formulations of linear model integral equations from the existing literature. Then we will describe the proposed semi analytical-numerical procedure alongwith its stability analysis and convergence properties. We will then prove with the aid of some particular numerical examples that the said approach is not only lucid and efficient but also precise. The outcomes of the proposed technique will show that this scheme has notable prospectives for solving a large class of FOLIEs. At the end, the contribution of this work in the advancements of semi analytical-numerical approaches for
the solution of fractional order linear integro partial differential equations will be laid down and discussion for future research in this field.

A steady-state numerical approach for the thermo-structural analysis of a cryogenic piston pump

Abstract The process of liquefaction of gaseous fuels, such as natural gas or hydrogen, is an essential technology that helps reduce transportation costs over long distances. Cryogenic piston pumps play a critical role in these systems, as they compress the fuel up to 700 bar before vaporization and storage in high-pressure vessels. Due to the extreme temperatures and pressures involved, the design of these machines poses a significant challenge from the thermal and structural point of view. This work presents the application of a simplified numerical approach for evaluating the thermally induced stresses and deformations through a de-coupled thermo-structural three-dimensional analysis of a prototype cryogenic piston pump. Thermal simulations of the solid domain are carried out to assess the steady-state temperature distribution of the pump. The heat transfer between the pump and cryogenic liquid is computed using three-dimensional steady-state CFD simulations of the suction and discharge phases. Heat generated by friction during the working cycle of the pump and external natural convection are calculated and imposed as a heat source in the simulations. The steady-state temperature distribution is imposed in a finite-element steady-state three-dimensional structural simulation to evaluate the combined effect of thermal loads induced by the cryogenic temperatures and loads induced by the high working pressures. Results show how the proposed methodology can assist in the design of cryogenic piston pumps by offering valuable insights into the most critical aspects of these machines.

Nonlinear vibration analysis of multi-support oil-tank system in aero-engine based on asymptotic methods

This article is primarily focused on the complicated nonlinear vibration behavior of an aero-engine lubricating oil-tank system with multiple nonlinear pedestals. First, the rubber damping ring’s nonlinear factors are introduced into a cubic nonlinear dynamic model of lubricating oil-tank system. The nonlinear system parameters are identified by testing a simplified aero-engine lubricating oil-tank structure. Then, the nonlinear dynamic model is solved via asymptotic approach, and results are confirmed using Runge-Kutta numerical analysis approach. The system’s vibration responses and amplitude-frequency curves are also acquired, and influence of system parameters on nonlinearity is analyzed. Finally, an experimental investigation on the simplified oil-tank is performed. The nonlinear vibration characteristics of the rubber damping ring and its vibration reduction mechanism are verified using vibration transmissibility. The experimental results are consistent with numerical results. This paper’s recommended analysis approach has engineering significance for vibration and noise reduction design of aero-engine components.

Thrombogenic Risk Assessment of Transcatheter Prosthetic Heart Valves Using a Fluid-Structure Interaction Approach

Background and ObjectiveProsthetic heart valve interventions such as TAVR have surged over the past decade, but the associated complication of long-term, life-threatening thrombotic events continues to undermine patient outcomes. Thus, improving thrombogenic risk analysis of TAVR devices is crucial. In vitro studies for thrombogenicity are typically difficult to perform. However, revised ISO testing standards include computational testing for thrombogenic risk assessment of cardiovascular implants. We present a fluid-structure interaction (FSI) approach for assessing thrombogenic risk of transcatheter aortic valves. MethodsAn FSI framework was implemented via the incompressible computational fluid dynamics multi-physics solver of the ANSYS LS-DYNA software. The numerical modeling approach for flow analysis was validated by comparing the derived flow rate of the 29 mm CoreValve device from benchtop testing and orifice areas of commercial TAVR valves in the literature to in silico results. Thrombogenic risk was analyzed by computing stress accumulation (SA) on virtual platelets seeded in the flow fields via ANSYS EnSight. The integrated FSI-thrombogenicity methodology was subsequently employed to examine hemodynamics and thrombogenic risk of TAVR devices with two approaches: 1) engineering optimization and 2) clinical assessment. ResultsSimulated effective orifice areas for commercial valves were in reported ranges. In silico cardiac output and flow rate during the positive pressure differential period matched experimental results by approximately 93 %. The approach was used to analyze the effect of various TAVR leaflet designs on hemodynamics, where platelets experienced instantaneous stresses reaching around 10 Pa. Post-TAVR deployment hemodynamics in patient-specific bicuspid aortic valve anatomies revealed varying degrees of thrombogenic risk with the highest median SA around 70 dyn·s/cm2 - nearly double the activation threshold - despite those being clinically classified as “mild” paravalvular leaks. ConclusionsOur methodology can be used to improve the thromboresistance of prosthetic valves from the initial design stage to the clinic. It allows for unparalleled optimization of devices, uncovering key TAVR leaflet design parameters that can be used to mitigate thrombogenic risk, in addition to patient-specific modeling to evaluate device performance. This work demonstrates the utility of advanced in silico analysis of TAVR devices that can be utilized for thrombogenic risk assessment of other blood recirculating devices.

Price optimization in supply chain agreements: a comparative analysis of buyback and put option contracts for inventory risk management

AbstractThis paper aims to provide a model of a supply chain in the integrated system and obtain its optimal decision variables. The paper introduces buyback and put option contracts to reduce inventory risk. These contracts were compared in three different cases via a numerical analysis approach. In the first case, the holding cost (h) of a retailer for surplus orders in the buyback contract is equal to the option price (o) in the put option model. The relationship between exercise price (e) in the put option model and buyback price (b) in the buyback contract was obtained by comparing the optimal values in the models. This study found that the exercise price in the put option contract will be greater than the buyback price. Furthermore, it is more likely that the retailer gave more benefits under the buyback agreement than the time the retailer chooses the put option contract. Therefore, it can be concluded that if the retailer chooses the buyback agreement in this situation, can gain more benefits. The study provides essential managerial insights to compare agreements and presents recommendations to choose a suitable contract.

Noise analysis of variable-speed rotor technology on the coaxial lift-offset helicopter

The impact of variable-speed rotor technology on the aerodynamic and aeroacoustic characteristics of a coaxial lift-offset helicopter was investigated using a numerical analysis approach. The free wake vortex lattice method was utilized to predict aerodynamic performance, while the Ffowcs-Williams Hawkings acoustic analogy was employed to evaluate the noise impact. The Harrington coaxial rotor was used as the baseline configuration. Results show that reducing the rotational speed, in combination with lift-offset, leads to a decrease in overall power required during forward flight by lowering both collective and cyclic pitch. This is primarily due to a reduction in profile power across the speed range. However, excessive rotor deceleration can lead to an expanded reverse flow region, increasing induced power at high forward speeds. From an acoustics perspective, the reduced rotor speed mitigated loading noise radiated toward the ground, especially in the region 40-60 degrees below the rotor plane, achieving a maximum 2.6 dB reduction at the evaluated observer location. This study indicates that the technology can offer advantages for both performance and noise in forward flight conditions.

Contribution of rolling resistance to the drag coefficient of spheres freely rolling on a rough inclined surface

The drag coefficient (CD) of a sphere freely rolling without slipping on a rough plane is presented in this study. Increasing panel roughness has been found to increase CD, although lubrication theory predicts that the larger gap imposed by the rougher panel should yield a smaller drag. We propose that this increase in drag is due to the effects of rolling resistance, which increases with panel roughness. The total drag on a sphere is decomposed into fluid drag and drag due to rolling resistance, where the fluid drag is predicted using a combined analytical–numerical approach. It is shown that rolling resistance can be modeled as a resistive torque opposing the sphere motion, generated by the offset contact normal force from the sphere center plane. This coefficient of rolling resistance (μr) can be predicted using the root mean square roughness (Rq) of the panel. Additionally, μr is observed to increase with sphere down-slope velocity and an empirical relationship between μr, Rq, and non-dimensional velocity (U∗) is given. A comparison of the drag predicted by the proposed model with measured data indicates good agreement for all the four panels considered. Consistent with previous literature, a non-linear relationship between μr, Rq, and U∗ is proposed. Although increasing panel roughness leads to a smaller fluid drag due to the larger gap imposed by rougher panels, the drag due to rolling resistance increases more rapidly. This leads to an increase in total drag with increase in the panel roughness. Additionally, increasing panel roughness is observed to have a significant effect on the sphere wake, leading to irregular wake shedding and increase in the Strouhal number.

Numerical analysis approach to twin primes conjecture

This paper provides a better approximation of the functions presented in the article “Numerical Analysis Approach to Twin Primes Conjecture” (see [3]). The new estimates highlight the approximations used in the previous article and the validity of Theorems 1 and 2 through the use of the false hypothesis based on the distribution of primes punctually following the Logarithmic Integral Li(x) (see [4] and [7], pp. 174–176) will be re-evaluated.

Investigation of numerical solution approaches for the cavitating flow analysis of twisted hydrofoils

In this study, geometrical parameters such as twist, section thickness, and angle of attack are numerically investigated for their influence on lift and drag coefficients, as well as cavitation development. The Delft 11 Hydrofoil, a twisted version of the NACA0009 foil with a −2° angle of attack, is used as the benchmark geometry for validation studies under both non-cavitating and cavitating flow conditions. After the validation studies, the geometries of the NACA0009 and NACA0015 hydrofoils were redesigned as half-twisted and twisted. These redesigned hydrofoils, along with the original no-twist versions, were analyzed under cavitating flow conditions within an angle of attack range of −2<AoA<5°. In the study, three-dimensional, unsteady, cavitating flow is modelled by two different solution approaches, RANS and DES, with the SST Menter k-omega turbulence model. The Schnerr-Sauer cavitation model is employed to obtain cavitation formation. The same physical conditions with RANS simulations are performed using a refined mesh with the DES method, focusing particularly on accurately and precisely obtaining cavitation development, especially cavitation cycles. Additionally, DES analyses were performed for various time step values, demonstrating the specific influence of the time step on cavitation cycles. The results show that while the RANS method effectively predicts the lift and drag forces of the hydrofoil, the DES method is crucial for capturing cavitation dynamics with greater precision, particularly for obtaining cavitation cycles. The results also indicate that twisted hydrofoil geometries produce more lift and drag force than half-twisted and no-twist geometries for both NACA0009 and NACA0015 hydrofoils. In addition, the cavitation formation around the hydrofoil generally increases with the twistiness.

Flame stabilization and emission reduction: a comprehensive study on the influence of swirl velocity in hydrogen fuel-based burner design

PurposeThis study aims to numerically analyse a full-scale burner across a wide range of operating pressure conditions and determine the effect of swirl velocity on flame stabilization, flame holding and combustion performance.Design/methodology/approachThis study uses a numerical analysis approach to investigate a three-dimensional full-scale burner. Modified governing equations are used to determine the effect of swirl velocity on flame stabilization and flame holding. The GR-Mech 3.0 chemical reaction mechanism is used to predict the combustion process. To validate the model, a grid independence study is performed.FindingsThe study reveals that swirl velocity enhances flame stability, resulting in better combustion rates. As the swirl velocity increases, higher flame temperatures are observed due to high convective heat recirculation. The heat transfer coefficient and high radiative extinction coefficient are found to vary based on fuel swirl velocity. The mass fraction of CH4 and CO emphasizes the role of swirl velocity on flame structure. Increasing velocity potentially improves combustion by delaying the process, leading to better combustion and lower emissions.Originality/valueThe findings of this study contribute to the understanding of swirl-stabilized combustion and can guide the development of advanced combustion technologies, making it a valuable addition to the existing combustion field.

Titanium Complex with New Schiff Base 4-(N, N-dimethylaminobenzylidene)-1- phenylsemicarbazide: Synthesis, Thermal, XRD, and Antibacterial properties

4-(N, N-dimethylaminobenzylidene) 1-phenylsemicarbazide Schiff base (SB) was synthesized from 1-phenylsemicarbazide and 4-(N,N-dimethylaminobenzaldehyde). Numerous analytical approaches, such as ele-mental analysis, 1HNMR, 13CNMR, electronic spectra, and FT-IR spectroscopy were utilized to analyze the newly synthesized Schiff base. The Ti (IV) Schiff base complex was produced, and its electrolytic nature, stability, and octahedral structural properties were determined by elemental, IR, UV-Vis spectral, conductivity, and thermal studies (TGA-DTA). From XRD results, the practical size of Schiff base and its complex were in the nano range with crystallinity structure. To evaluate the antibacterial activity, the free ligand and its complex were assessed in vitro against Pseudomonas aeruginosa, Escherichia coli, and Staphylococcus aureus. These results show that the metal complex has stronger antibacterial action than the Schiff base ligand.