Algorithm For Numerical Calculation Research Articles

Neutrino oscillations in matter using the adjugate of the Hamiltonian

We revisit neutrino oscillations in constant matter density for a number of different scenarios: three flavors with the standard Wolfenstein matter potential, four flavors with standard matter potential and three flavors with non-standard matter potentials. To calculate the oscillation probabilities for these scenarios one must determine the eigenvalues and eigenvectors of the Hamiltonians. We use a method for calculating the eigenvalues that is well known, determination of the zeros of determinant of matrix (λI-H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\lambda I -H)$$\\end{document}, where H is the Hamiltonian, I the identity matrix and λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document} is a scalar. To calculate the associated eigenvectors we use a method that is little known in the particle physics community, the calculation of the adjugate (transpose of the cofactor matrix) of the same matrix, (λI-H)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\lambda I -H)$$\\end{document}. This method can be applied to any Hamiltonian, but provides a very simple way to determine the eigenvectors for neutrino oscillation in matter, independent of the complexity of the matter potential. This method can be trivially automated using the Faddeev–LeVerrier algorithm for numerical calculations. For the above scenarios we derive a number of quantities that are invariant of the matter potential, many are new such as the generalization of the Naumov–Harrison–Scott identity for four or more flavors of neutrinos. We also show how these matter potential independent quantities become matter potential dependent when off-diagonal non-standard matter effects are included.

Stepless Transmission Optimization for Green Micromobility

Small, electrified vehicles are becoming possible for urban environmental mobility due to their environmental performance, including zero-emission driving. Vehicles of this type use electric motors as sources of mechanical energy. Today, two types of transmission are most used in electrical micromobility vehicles (skateboards, scooters, tricycles, quadricycles, mopeds, motorcycles, go-karts, etc.): chain transmission and belt transmission. This transmission types provides a constant gear ratio that can only compromise between the maximum speed and the starting torque values, thus reducing the usage efficiency of the engine. This reduces vehicle manufacturers’ choice of less powerful drive and control elements, as well as balancing performance and efficiency at low and high speeds as well as on terrain.A novel design of a continuously variable transmission (CVT) for an electric go-kart is presented in this paper. The CVT consists of an inertial driving pulley mounted on an electric motor shaft, a timing V-belt, a gear wheel on the drive axle and 2 pressure rolls, which are moved by a servo motor for tensioning the V-belt. Gear ratio of a transmission can change seamlessly in the range of 1.5 - 2.2. The CVT has been tested under real conditions. The top speed of the electric go-kart with the given CVT and motor power 24.7 kW is 133km/h; time to accelerate to the top speed is 25 s. Total efficiency of the transmission (motor shaft, CVT, drive axle and wheels) is 65-72 % now, but there exist a lot of possibilities to improve it in the future. The conditions under which the novel CVT has an advantage over belt and chain transmissions with constant gear ratios have been studied. The developed mathematical model, the method for determination its constants, the algorithm for numerical calculations and the optimization criterion makes it possible to determine the optimal gear ratio for a vehicle with various CVT (not only belt) at any point in time in different racing modes. The model has been proved experimentally during acceleration and deceleration tests of the go-kart; it describes precisely the motion of the go-kart within the speed measurement error.The developed solution is applicable in urban micromobility. An optimized and stable transmission system focused on energy efficiency, resource saving, using less powerful drive and zero-emission.

The Lattice Boltzmann Method Using Parallel Computation: A Great Potential Solution for Various Complicated Acoustic Problems

This paper proposes the D2Q5 Lattice Boltzmann method (LBM) method, in two dimensions with five discrete lattice velocities, for simulating linear sound wave propagation in closed rooms. A second-order linear acoustic equation obtained from the LBM method was used as the model equation. Boundary conditions at the domain boundary use the bounce-back scheme. The LBM numerical calculation algorithm in this paper is relatively simpler and easy to implement. Parallelization with the GPU CUDA was implemented to speed up the execution time. The calculation results show that the use of parallel GPU CUDA programming can accelerate the proposed simulation 27.47 times faster than serial CPU programming. The simulation results are validated with analytical solutions for acoustic pulse reflected by the flat and oblique walls, the comparisons show very good concordance, and the D2Q5 LBM has second-order accuracy. In addition, the simulation results in the form of wavefront propagation images in complicated shaped rooms are also compared with experimental photographs, and the comparison also shows excellent concordance. The numerical results of the D2Q5 LBM are promising and also demonstrate the great capability of the D2Q5 LBM for investigating room acoustics in various complexities.

Theoretical determination of speed of sound and fourth virial coefficient by using Kihara (12–6) potential

Abstract In this paper, a new theoretical approach is suggested for the numerical calculation algorithm of the fourth virial coefficient and its components with the Kihara potential. For the first time, this study reports the results of the fourth virial coefficient over the Kihara potential. The proposed method can be used to calculate the thermodynamics properties of gases with developed correctness. The method is tested for some molecules and as an example of application, the proposed method has been performed for gases of C3H8 and SF6. The obtained calculation results have been compared with the theoretical and experimental data and the results have been found to be consistent with the literature data. It can be seen from the application that the calculation of the fourth virial coefficient with the Kihara potential can provide important results in the calculation of the thermophysical properties of other real systems.

LitzImp: A Fast Impedance Extraction Algorithm for Litz Wire Coil

Litz wire coil (LWC) is an electronic component commonly used in wireless power transfer (WPT) and heating applications. However, due to its complex twisting structure with turns, existing calculation methods such as analytical methods and finite element method (FEM) cannot extract the impedance of LWC efficiently. This paper proposes an efficient numerical calculation algorithm named LitzImp for fast impedance extraction of LWC. LitzImp provides different simplification schemes for different coil structures, reducing the resource consumption in the repeated calculation for the same structures and improving efficiency while maintaining high accuracy. Experiments with nine manufactured coils, including circular coils (CC) and rectangular coils (RC), from simple to complex, are adopted to verify the performance of LitzImp. The comparative verification compared with FEM and the analytical method shows the advantages of LitzImp in terms of efficiency and accuracy. Through the analysis of the time consumption, the proposed method is 45 times faster than the similar numerical method for a given coil structure. For highly complex coils (500 strands), the impedance is obtained in less than 5.5 hours with good agreement with the measurement. LitzImp will be a powerful tool for the optimal design of LWC due to its high efficiency.

Analysis of elastic properties of 3D-printed parts using the finite element method

This research paper presents a comparative analysis of the elastic properties of 3D-printed parts made from polymer composite materials using PLA plastic. The analysis was conducted using both the finite element method and experimental measurements. Specifically, PLA-Cg+ and PLA-CCF samples were printed with varying printing parameters, such as raster angle and print layer thickness. The study demonstrates that the employed numerical calculation algorithm provides sufficiently accurate assessment of the elastic characteristics of materials across different combinations of the investigated parameters. Moreover, the analysis of the results reveals that the accuracy of the calculations is significantly influenced by the microstructure, which is determined by the size and shape of the pores that form during the printing process.

Crack tip field analysis for thermo-mechanical fatigue loading

This study aimed to establish a computational strategy for the thermo-mechanical fatigue (TMF) simulations of crack tip fields considering both the in-phase (IP) and out-of-phase (OOP) loading histories. To this end, an algorithm for multi-physics numerical calculations was developed and implemented by incorporating Maxwell 3D, Fluent, and the transient structural modules of ANSYS 2021R1, to understand the mechanics of crack tip deformation under thermo-mechanical loading conditions. These computations are based on the coupled heat loss from magnetic field eddy currents and the forced convective air-cooling accounted for by turbulence model response, which provides the gradients of mechanical elastic–plastic deformations. The proposed algorithm was applied to replicate and analyse the crack growth test conditions of polycrystalline XH73M nickel-based alloys subjected to a triangular waveform of IP and OOP cycles and a temperature range of 400–650 °C. Further, multi-physics finite element (FE) modelling of the stress, strain, and displacement fields in uncracked and fractured single-edge-notch tension specimens was performed. The novelty of the results lies in the crack tip fields, which strongly influenced by the phase relation between mechanical loading and temperature, provided the electromagnetic and fluid dynamics characteristics and the elastic–plastic properties of the material are dependent on the current temperature and time across a particular deformation cycle. Notably, the complete three-dimensional multi-physics FE analysis presented herein is expected to contribute toward a better understanding of the different mechanisms driving TMF crack growth and also help address the related outstanding questions.

A Numerical Calculation Algorithm of the Inclination Function Based on the Representation of SO(3) Group

A Numerical Calculation Algorithm of the Inclination Function Based on the Representation of SO(3) Group

Analytical and numerical research based on one modified refined bending theory

In the article, an analytical and numerical study based on one modified refined bending theory is presented. By the finite difference method, a general numerical calculation algorithm is developed. The solution obtained by the proposed method is compared with the results of known solutions, namely, with the solution of the classical theory, the exact solution, the solution in trigonometric series, as well as with experimental data. Comparison of the results obtained by the method given in the article with the solutions determined by other methods shows sufficient accuracy, which indicates the reliability of the proposed method based on one option of the modified refined bending theory. Classical theory is not applicable to such problems under consideration.

Quantum Algorithm for Numerical Energy Gradient Calculations at the Full Configuration Interaction Level of Theory.

A Bayesian phase difference estimation (BPDE) algorithm allows us to compute the energy gap of two electronic states of a given Hamiltonian directly by utilizing the quantum superposition of their wave functions. Here we report an extension of the BPDE algorithm to the direct calculation of the energy difference of two molecular geometries. We apply the BPDE algorithm for the calculation of numerical energy gradients based on the two-point finite-difference method, enabling us to execute geometry optimization of one-dimensional molecules at the full-CI level on a quantum computer. Results of numerical quantum circuit simulations of the geometry optimization of the H2 molecule with the STO-3G and 6-31G basis sets, the LiH and BeH2 molecules at the full-CI/STO-3G level, and the N2 molecule at the CASCI(6e,6o)/6-311G* level are given.

STUDY OF BOREHOLE HEAT EXCHANGER HEAT TRANSFER ENHANCEMENT PARAMETERS

This paper discusses the study of parameters for improving the heat transfer of a borehole heat exchanger for a ground source heat pump application. The study of efficiency parameters was carried out based on an experimental prototype of a ground source heat pump developed by the authors. A mathematical model has been developed for calculating the efficiency of a ground heat exchanger based on three-dimensional equations of heat and mass transfer in a porous medium. The numerical solution was carried out using the COMSOL Multiphysics software. The numerical calculation algorithm was verified by comparison with experimental data from the created prototype. Calculations were made of the efficiency of a borehole heat exchanger with various geometric configurations of the pipes in the well. With an increase in the tube diameter, the heat transfer increases. With a tube diameter of 40 mm, the thermal efficiency of the heat exchanger was 42.4 W/m in the heat charging mode, which is 24% more with a diameter of 20 mm. With increasing well depth, the heat transfer efficiency increases. The influence of the thermal conductivity coefficients of the pipe material, grout material and various types of ground on the heat transfer efficiency was also studied. It was shown that with an increase in the thermal conductivity coefficients of grout and ground, the heat flux increases, but above 6.0 W/m K, the heat flux practically does not change. When the coefficient of thermal conductivity of the pipe material is higher than 1.0 W/m K, the heat fluxes almost do not change. In general, materials containing plastics are used for piping of ground heat exchangers, the thermal conductivity coefficients of which vary between 0.24-0.42 W/m K.

How solid–liquid adsorption affects the liquid–vapor interface in pores

AbstractThe augmented Young–Laplace (AYL) equation has been widely used to describe the liquid–vapor interfaces affected by capillarity and adsorption, particularly in nanoporous or clay minerals where strong adsorptive interaction prevails. Still, how adsorption ultimately shapes the liquid–vapor interface in pores remains elusive. All current forms of the AYL equation only consider the attractive van der Waals interaction for complete wetting surface and are mostly an extension of the general equation based on thermodynamic principles without rigorous derivation. In this paper, closed forms of the AYL equations are derived by variational calculus method for two typical pore models considering effects of capillarity and adsorption, based on the minimization of free energy for the equilibrium system. The van der Waals, electrical, and structural forces are incorporated as disjoining pressure into the proposed AYL equations to quantify effects of both attractive and repulsive interactions (hence complete and partial wetting conditions) on interfacial geometry and equilibrium matric potential. Numerical calculation algorithms are established to solve the interfacial geometric profiles and characteristics. The proposed model illustrates a transition region on the interface where geometry and physical characteristics are drastically altered under adsorption compared with sole capillarity. Different surface wettabilities are examined for interface profiles and curvature distributions. An apparent contact angle on the partial wetting surface is identified that is approaching complete wetting as the adsorption dominates when pore size reduces. Water retention and interparticle force demonstrate clear distinctions in their evolution, with different particle sizes and varying half‐filling angles under adsorptive conditions as water volume changes.

Algorithm for numerical calculation of nonlinear lenticular membrane-pneumatic systems by iterative method of parameter increments taking into account the aftereffect of air pressure

Objective. The purpose of this study is to create a static calculation algorithm to determine the maximum bearing capacity of a lenticular membrane-pneumatic system for covering large spans under the action of external force loads.Method. A numerical study of a large-span membranepneumatic structure was carried out by the step method of incrementing parameters using the finite element method and the Euler-Cauchy numerical procedure of the third order of accuracy at the step.Result. The authors have developed a technique for computer static calculation of geometrically and physically nonlinear lenticular membrane-pneumatic systems of coatings for large span structures by the iterative method of parameter increments with the phased application of the finite element method in the form of the displacement method, the universal equation of gas state and the improved Euler-Cauchy numerical procedure of the third order of accuracy.Conclusion. Ignoring the aftereffect in the calculations means the imbalance of the system due to unbalanced pneumatic forces calculated with an error of 11.2% and affecting, as the calculations showed, in the amount of approximately 7% percent on the increment of excess air pressure in the lens.

Study on Self-Excited Oscillation Suppression of Supersonic Inlet Based on Parallel Cavity

Aiming at the problem of self-excited oscillation in a supersonic inlet, the oscillation suppression of parallel cavities in a shock system is studied. Based on the shock dynamic model, the theoretical calculation model of parallel cavity under dynamic shock is established, and the effects of cavity volume and oscillation frequency on shock oscillation flow field parameters are analyzed. On this basis, an integrated numerical model including cavity and inlet and outflow fields is established, and the effects of cavity on the inlet flow field parameter distribution and parameter oscillation are compared by using unsteady numerical calculation algorithm. The theoretical calculation results show that the parallel cavity can reduce the amplitude of flow field pressure oscillation, and increasing the cavity volume is beneficial to suppress parameter oscillation. The unsteady numerical calculation of three groups of working conditions shows that the cavity changes the amplitude of parameter oscillation, and the high amplitude frequency point also decreases compared to the model without cavity. Through the alternating change of pressure between the channel and cavity during the movement of the shock wave, the cavity gas filling and overflow dampen the shock wave forward and pressure change of the mainstream, so as to suppress the self-excited oscillation.

Algorithm for numerical calculation of multicore fiber with signal gain saturation

Algorithm for numerical calculation of multicore fiber with signal gain saturation

Computing the exact distribution of a linear combination of generalized logistic random variables and its applications

We consider methods for numerical evaluation of the probability density function, cumulative distribution function and quantile function of a linear combination of n independent generalized logistic random variables. Here we derive the exact expressions for the probability density function and cumulative distribution function in terms of Fox's H-function. We also provide an algorithm for numerical calculation of Fox H- function and we compare its performance with a method based on the numerical inversion of the characteristic function. The numerical precision, efficiency and computing time of the proposed algorithm were considered. Applicability and comparison of the suggested approaches are illustrated by an application to financial returns.

Numerical solution of the problem of gas filtration in porous media by the method of coordinate splitting

The article presents a three-dimensional mathematical model and numerical calculation algorithm based on the method of coordinate splitting for analysis and forecasting the process of gas filtration in porous media. The use of the method of coordinate splitting made it possible to reduce the original problem to three locally one-dimensional problems and to reduce the computation time by reducing the number of computational operations. Developed mathematical apparatus can be successfully used to solve design problems or refinement of design solutions of gas fields, as well as production forecasting process.

A Study of $\tau^-$ and $\mu^-$ in the Field of Nuclei Using Neural Network Techniques

The rate of a heavy lepton (muon or tau) capture by nuclei as well as the heavy lepton to electron conversion rate can be calculated when the heavy lepton wavefunction is known. Analytical calculation of the wavefunction of any of these leptons around any nucleus is not feasible owning to their small Bohr radii, on the one hand, and to the finite nuclear extend on the other. A new numerical calculation algorithm is proposed hereby, which makes use of the concept of neural networks. The main advantage of this new technique is that the wave function is produced analytically as a sum of sigmoid functions.

Algorithm for Numerical Calculations of Robotic Group Movement During Transport Mission

The paper considers an algorithm for searching for the time of residential roof inspection using an unmanned aerial system, which incorporates unmanned aerial vehicles (UAV) of a multicopter type with a thermal imaging device as a transporting load. Algorithms and their implementation for the problem are considered. The problem of multicopter group movement with restrictions on load, range, roof height and other characteristics is solved. An original algorithm for the system functioning is proposed and justified. The advantage of the algorithm is a quick solution search, visibility and the ability to be verified by the user. There are some disadvantages, such as the resulting solution being suboptimal, the memory complexity growing exponentially, and the UAV charging time being out of consideration (in the absence of a replacement battery). The algorithm is implemented in the MatLab environment, and the example of calculations is presented, the computational experiment is conducted. In further research, it is planned to introduce a larger number of restrictions and conditions and also to test the dynamic change in logistics routes for UAV failures.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ И АЛГОРИТМ РАСЧЕТА ТЕПЛОВОГО СОСТОЯНИЯ РЕГЕНЕРАТОРА ДЛЯ АККУМУЛИРОВАНИЯ ТЕПЛОТЫ СЖИГАНИЯ КОНВЕРТЕРНОГО ГАЗА И НАГРЕВА ВОЗДУХА ДЛЯ КОТЛА-УТИЛИЗАТОРА

The heat of combustion of the converter gas, which is periodically formed in the oxygen-converter production at the metallurgical plant, is proposed to be used for alternate heating of the checkerwork of two regenerators (such as сowpers), and their alternate cooling by a continuous flow of air heated to a high temperature, and directed to the recovery boiler to generate steam. A mathematical model is presented that allows evaluating the thermal state of the regenerator, the temperatures of the heating gases and the heated air in the modes of heating and cooling the regenerator checkerwork. An algorithm for numerical calculation of the temperature fields of the regenerator checkerwork, gases and air is presented.