Numerical Method Research Articles

Numerical Modeling and Performance Evaluation of Carbon Fiber-Reinforced Polymer-Strengthened Concrete Culverts against Water-Induced Corrosion

Numerical Modeling and Performance Evaluation of Carbon Fiber-Reinforced Polymer-Strengthened Concrete Culverts against Water-Induced Corrosion

Error estimates for a mixed finite element method for the Maxwell’s transmission eigenvalue problem

In this paper, we analyze a numerical method combining the Ciarlet-Raviart mixed finite element formulation and an iterative algorithm for the Maxwell’s transmission eigenvalue problem. The eigenvalue problem is first written as a nonlinear quad-curl eigenvalue problem. Then the real transmission eigenvalues are proved to be the roots of a non-linear function. They are the generalized eigenvalues of a related linear self-adjoint quad-curl eigenvalue problem. These generalized eigenvalues are computed by a mixed finite element method. We derive the error estimates using the spectral approximation of compact operators, the theory of mixed finite element method for quad-curl problems, and the derivatives of eigenvalues.

Efficient Modeling of Water Adsorption in MOFs Using Interpolated Transition Matrix Monte Carlo.

With the specter of accelerating climate change, securing access to potable water has become a critical global challenge. Atmospheric water harvesting (AWH) through metal-organic frameworks (MOFs) emerges as one of the promising solutions. The standard numerical methods applied for rapid and efficient screening for optimal sorbents face significant limitations in the case of water adsorption (slow convergence and inability to overcome high energy barriers). To address these challenges, we employed grand canonical transition matrix Monte Carlo (GC-TMMC) methodology and proposed an efficient interpolation scheme that significantly reduces the number of required simulations while maintaining accuracy of the results. Through the example of water adsorption in three MOFs: MOF-303, MOF-LA2-1, and NU-1000, we show that the extrapolation of the free energy landscape allows for prediction of the adsorption properties over a continuous range of pressure and temperature. This innovative and versatile method provides rich thermodynamic information, enabling rapid, large-scale computational screening of sorbents for adsorption, applicable for a variety of sorbents and gases. As the presented methodology holds strong applicative potential, we provide alongside this paper a modified version of the RASPA2 code with a ghost swap move implementation and a Python library designed to minimize the user's input for analyzing data derived from the TMMC simulations.

Examining the contact problem of a functionally graded layer supported by an elastic half‐plane with the analytical and numerical methods

This study offers a comparative study of the analytical and numerical methods for investigating a contact problem. The contact problem comprises a functionally graded layer supported by a half‐plane and loaded with a distributed load from the top surface. First, the analytical and numerical solutions to the problem are acquired by utilizing a theory of elasticity and finite element method, respectively. The problem is transformed into a system of integral equations in which the contact stress is an unknown function. The solution of the integral equation was achieved with Gauss–Jacobi integration formulation. The finite element model of the problem is created using ANSYS software, and the two‐dimensional analysis of the problem is performed. Results were obtained from the samples for different material properties and loading conditions. The distributed load width and non‐homogeneity parameters significantly impact on contact mechanics. The results indicate that the contact area and the contact stress obtained from finite element method (FEM) are close to the analytical results. As a result, acceptable error rates were obtained. Finally, this study provides evidence of a good agreement between the two methods.

Research on the factors influencing the width of hydraulic fractures through layers

AbstractThe method of segmented hydraulic fracturing in the coal seam roof has proven to be an efficient technique for coalbed methane exploitation. However, the behavior of hydraulic fractures in multilayer formations with significant differences in mechanical properties is still unclear. This paper studied the variation in hydraulic fracture width at the coal-rock interface by employing experimental method with a true triaxial hydraulic fracturing experimental system and numerical simulation method. Results revealed that the hydraulic fracture more likely to expanded along the coal-rock interface instead of break through it with the small horizontal stress difference and low flow rate injection condition. And improving the injection flow rate lager than a critical value, the hydraulic fracture tends to break through the coal-rock interface. Hydraulic fractures in both mudstone and coal beds exhibited a trend of increasing and then decreasing of fracture width at the interface. Since the strength of the coal seam was lower compared to that of the mudstone, maintaining high pressure was no longer necessary when the hydraulic fracture crossed the interface and entered the coal seam, leading to a reduction in fracture width within the mudstone. During the later stages of fracturing, the entry of proppant into the coal seam became challenging, resulting in a phenomenon characterized by excessive fluid but insufficient sand. The time required for the fracture width to traverse the proppant was found to be inversely proportional to the difference in horizontal ground stress and the flow rate of the fracturing fluid. And it was directly proportional to the modulus of elasticity, permeability of the coal seam, and interface strength. The interface strength has the greatest influence on the width of hydraulic fractures. In conclusion, this study provides valuable insights into the behavior of hydraulic fractures in multilayer formations with varying mechanical properties. The findings contribute to a better understanding of the factors affecting hydraulic fracture width within coal seams, which can ultimately enhance the efficiency of coalbed methane exploitation.

An Efficient Replacement for Schrödinger's Partial Differential Equation

The classical finite difference method for solving time-dependent partial differential equations has become quite tedious and requires the use of off-the-shelf algorithms such as those in MATLAB. The treatment by finite difference method then solution of the n resulting first order algebraic equations is quite difficult since the underlying matrix is singular. We propose an alternative revolutionary statistical technique using Bmatrix chains, which are a product of the Cairo techniques. This technique is valid for both classical macroscopic physics such as the heat diffusion equation and modern microscopic quantum mechanics such as Schrödinger's PDE. He completely neglects partial differential equations as if they never existed. The numerical results of the proposed numerical statistical method show stability, accuracy and superiority over conventional PDE methods.

Analysis of the influence of the metal wheel radial stiffness on traction characteristics

BACKGROUND: The traction characteristic of a wheel mover depends both on its type and rigidity properties, and on the physico-mechanical soil properties. The combined use of the discrete element method to describe the soil and the finite element method to model the wheel makes it possible to specify and expand the existing empirical models of the interaction of the mover with the ground. The application of this method will reduce the amount of full-scale testing required to verify the interaction model. AIMS: Development the traction characteristic of a metal wheel by varying its design parameters. METHODS: To develop a mathematical model of a metal wheel and determine traction characteristics, numerical methods of discrete and finite elements are used. RESULTS: In this paper, a metal wheel mathematical model with ability to vary the thickness of the elastic sidewall was developed. Radial stiffness characteristics were obtained for three wheel samples. The developed mathematical model of the interaction of a wheel mover with a ground is based on the application of discrete and finite element methods. In this paper, a proportional controller was used to application of forces to the wheel mover. The dependences of the longitudinal reaction coefficient on the slip coefficient were obtained and a comparative analysis of the radial stiffness influence on traction characteristics was carried out. CONCLUSIONS: The combined application of the discrete and finite element methods will make it possible to determine the traction characteristics of the movers of various designs when interacting with a deformable soil and to evaluate the influence of its design parameters on it.

Similar Solutions for Changing Characteristics of Natural Convection Laminar Flow around a Vertical Rectangular Inclined Plane Surface

The study investigates laminar natural convection flow around a vertical rectangular inclined plane surface, specifically focusing on the effects of viscous and pressure stress work. Previous research primarily addressed these effects in two-dimensional natural convection flow scenarios, while this study extends the analysis to encompass three exterior situations, accounting for variations in fluid properties outside compressible boundary layers. Employing numerical methods, the study aims to predict essential flow parameters including Prandtl’s number (Pr), controlling parameter (C), and additional parameters (A, B, D, E, ∅). The investigation yields velocity profiles (F'(0), S'(0)), temperature profiles , skin frictions (F''(0), S''(0)), and heat transfer coefficients θ'(0). Numerical results are presented to illustrate the impact of different parameters on these flow characteristics. Additionally, tabulated data in Tables-2 and Tables-3 offer further insights into the predicted flow parameters and their variations under varying conditions.

APPLICATION OF HYDROGELS FOR WATER SHUTOFF TREATMENTS. Message No. 2

The article analyzes the use of hydrogels with nanoparticle additives for well water shutoff, as well as the development of a mathematical apparatus for hydrodynamic modeling of water shutoff operations. One of the most significant trends in the development of gel forming compounds for well water shutoff in the last 10 years has been the use of nanocomposites. The base polymers for nanocomposites used for water shutoff operations are either synthetic or biopolymer origin. The article highlights the novelty and prospects of using nanoparticles in sealing compositions. Various nanocomponent additives are used to increase the success of the use of hydrogel polymer systems in order to limit water inflow and expand the scope of their application in complicated reservoir conditions. These include carbon and mineral nanoparticles, which increase the stability and strength of crosslinked gels in formation conditions.In this paper, we consider the optimization of the repair and insulation operations design using gels for well water shutoff using mathematical modeling, which helps to justify the volume of hydrogel injection and calculate the necessary pressure gradients at which the sealing screen remains stable. The paramount importance of determining the source of well flooding is emphasized, depending on which the processing design is already being built, and appropriate materials are selected; trends in the development of repair and insulation operations at the present stage are traced. Based on the results of the implementation of the proposed model by numerical methods, the authors constructed diagrams of the stability of the waterproofing screen depending on the fracture width, screen size, gel injection rate and reservoir permeability. The technique proposed in the work allows to correctly select and optimize the technological parameters of the operation to maintain the stability of the screen in specific geological conditions.Mathematical modeling allows us to strictly justify the volume of injection of the gel screen, increase the technological and economic efficiency of the process, and in large fields — to rank wells according to the priority of processing. Oilfield practice in various regions of the country fully confirms the main conclusions made in this review article. Preliminary mathematical modeling and the introduction of microdispersions into gel formulations can significantly increase the efficiency of water shutoff operations. The next step in the development of water insulation technologies is the use of nanodispersions, which look very promising in laboratory modeling and are no longer exotic materials with unrealistic cost.

Tunneling Probability of Quantum Wavepacket in Time-Dependent Potential Well

Quantum tunneling of particles plays an important role in many chemical reactions. Studying quantum tunneling in time-dependent potential wells is tricky since most of the available solutions of time-dependent potential wells are coupled to specific properties of the Hamiltonian. Here, we investigate the tunneling probability of a quantum wavepacket in time-dependent potential well by using the split operator method. This numerical method can give us an overview of the tunneling probability of a quantum wavepacket for any temporal change in the shape of the potential well. We study a time-dependent potential well model evolving from symmetric to asymmetric quartic double well since quartic potential wells resemble certain practically available potential well models.Quanta 2024; 13: 11–19.

Influence of a Long Flexible Fiber on the Transport Capability of a Non-Clogging Pump

During the operation of non-clogging pumps, the flexible long fiber is prone to clogging and winding during the flow process, which can result in damage to the non-clogging pump, so a numerical simulation method of a solid–liquid two-phase flow in a non-clogging pump with a flexible long fiber is proposed in this paper. The unsteady numerical simulation of the two-phase flow of a single flexible fiber with different densities, lengths and diameters in a double-blade non-clogging pump was carried out to study the influence of fiber parameters on fiber transport capability. The results show that at a density of 920 kg/m3, 300 kg/m3 and 732 kg/m3, the transport capability of flexible fibers decreases successively, and the transport time T0 is 0.32 s, 0.36 s and 0.48 s, respectively. The transport capability of flexible fibers with a length of 150 mm, 200 mm and 250 mm decreases successively, and the transport time T0 is 0.34 s, 0.48 s and 0.96 s, respectively. The transport time T0 is 0.48 s when the fiber diameter dp is 5 mm. When the fiber diameter dp is 7.5 mm, the transport time T0 is 0.51 s. When the fiber diameter dp is 10 mm, the fiber transport capability of the non-clogging pump decreased significantly, and the transport time T0 is 0.68 s. The fiber length has the most obvious effect on fiber transport capability, followed by the fiber diameter and fiber density.

A bootstrap study of minimal model deformations

For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional CFTs, focusing on deformations of the tricritical and ordinary Ising model. We provide non-perturbative constraints for the boundary correlation functions of these flows and compare them with conformal perturbation theory in the vicinity of the fixed points. We also reproduce a completely general constraint on the sign of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T\\overline{T }$$\\end{document} deformation in two dimensions.

Joint InSAR and discrete element numerical simulation method for landslide identification and monitoring: a case study of the Gongjue landslide, Jinsha River, China

Joint InSAR and discrete element numerical simulation method for landslide identification and monitoring: a case study of the Gongjue landslide, Jinsha River, China

Numerical comprehensive optimization and evaluation on ballistic behavior of ceramic/FRP composites based on AHP model

Numerical comprehensive optimization and evaluation on ballistic behavior of ceramic/FRP composites based on AHP model

Analyzing magnetic dipole impact in fluid flow with endothermic/exothermic reactions: neural network simulation

The consequence of exothermic/endothermic chemical reactions and Arrhenius activation on the heat and mass transport of the liquid flow past a cylinder in the incidence of a magnetic dipole is considered in the current investigation. Magnetic dipoles are used in medical applications such as magnotherapy and spectroscopy, to produce static magnetic fields. Scientists and engineers can improve the effectiveness of chemical reactions or heat transfer operations by analyzing the impact of reactions on flow and building systems with optimized flows. The modelled equations are converted into non-dimensional ordinary differential equations (ODEs) by using similarity variables. The resultant equations are solved by employing the physics-informed neural network (PINN) technique. Additionally, the comparison of PINN with the numerical method Runge–Kutta Fehlberg’s fourth-fifth order (RKF-45) is studied. The effects of different parameters on the temperature, concentration, and velocity profiles for endothermic/exothermic instances are shown graphically. The thermal, velocity, and concentration profiles get stronger as the curvature parameter values increase for both endothermic and exothermic cases. The influence of activation energy parameters, chemical reaction parameters, and endothermic/exothermic reaction parameters on the thermal and concentration is also depicted.

Matrix numerical method for probability densities of stochastic delay differential equations

Abstract Stochastic processes with time delay are invaluable for modeling in science and engineering when finite signal transmission and processing speeds can not be neglected. However, they can seldom be treated with sufficient precision analytically if the corresponding stochastic delay differential equations (SDDEs) are nonlinear. This work presents a numerical algorithm for calculating the probability densities of processes described by nonlinear SDDEs. The algorithm is based on Markovian embedding and solves the problem by basic matrix operations. We validate it for a broad class of parameters using exactly solvable linear SDDEs and a cubic SDDE. Besides, we show how to apply the algorithm to calculate transition rates and first passage times for a Brownian particle diffusing in a time-delayed cusp potential.

Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations

We construct a positivity-preserving Lie--Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of semilinear stochastic heat equations with multiplicative space-time white noise. We prove that this explicit numerical scheme converges in the mean-square sense, with rate $1/4$ in time and rate $1/2$ in space, under appropriate CFL conditions. Numerical experiments illustrate the superiority of the proposed numerical scheme compared with standard numerical methods which do not preserve positivity. p, li { white-space: pre-wrap; }

A new efficient two-step iterative method for solving absolute value equations

PurposeThis study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method.Design/methodology/approachWe present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method.FindingsThe paper provides empirical insights into how to solve a system of absolute value equations.Originality/valueThis paper fulfills an identified need to study absolute value equations.

Introduction to Theoretical and Experimental aspects of Quantum Optimal Control

Abstract Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum principle, in a physicist-friendly way. An analogy with classical Lagrangian and Hamiltonian mechanics is proposed to present the main results used in this field. Emphasis is placed on the different numerical algorithms to solve a quantum optimal control problem. Several examples ranging from the control of two-level quantum systems to that of Bose-Einstein Condensates (BEC) in a one-dimensional optical lattice are studied in detail, using both analytical and numerical methods. Codes based on shooting method and gradient-based algorithms are provided. The connection between optimal processes and the quantum speed limit is also discussed in two-level quantum systems. In the case of BEC, the experimental implementation of optimal control protocols is described, both for two-level and many-level cases, with the current constraints and limitations of such platforms. This presentation is illustrated by the corresponding experimental results.

Numerical investigations on heat transfer of supercritical RP-3 flowing in circular tube

This study aims to develop a reliable numerical model for predicting the supercritical heat transfer of aviation kerosene RP-3 in a tube under heating conditions, thereby providing a reference for revealing the mechanism behind the experimental phenomena. Based on validation studies between seven turbulence models and experiments, a numerical method using the Yang-Shih turbulence model is proposed. A detailed prediction of the turbulent flow process is obtained, and the heat transfer characteristics of RP-3 are analyzed. The evolution of parameters and properties in axial and radial directions is demonstrated, followed by investigations of the effects of system pressure, fuel inlet temperature, and mass flow rate. The drastic change in the specific heat of the fuel when its temperature is close to the pseudocritical value and the temperature difference between the area near the wall and the center of the tube are the main causes of the enhancement and deterioration of the heat exchange. A higher inlet temperature increases the heat transfer coefficient, but due to its different effects on decreasing the density and the viscosity, it increases the pressure drop. In addition, larger mass flow rates can promote turbulence intensity and heat transfer, but cause a higher pressure drop across the tube.