Order Scheme Research Articles

Application of machine learning for ‘what if?’ stress analysis

Analysis of stresses in components of even modestly complex geometries often require the use of finite element analysis (FEA). For testing a large number of design options quickly, FEA can be time consuming and provides more accuracy than required. In this project, a machine learning-based system is developed to provide quick and approximate solutions to stress analysis problems in parametrised compressor disc geometries. Simple mechanics problems were completed preliminarily to test the practicality of machine learning approaches for this application. This included applying instance selection by the [Formula: see text]-medoids algorithm to a 2D FEA problem. A parametrised compressor disc geometry was designed and defined by eight dimensions. Stress fields were produced from two superimposed loading schemes: the rotational body force and the force exerted on the disc by the blades 495,338 samples of training data were collected from 4374 FEA simulations. Four networks were trained to predict stresses caused by each loading scheme in order to produce stress fields. The best network was of the structure 9/20/20/2 and used normalised training data. For the geometry tested, it predicted stresses with a root-mean-square error of 1.51%. The code took 0.7 s to run in total, from start-up to completion of a stress plot. The importance of the inputs in the training data set were scored with a feature selection algorithm to aid further optimisation of the system. The low computation time makes this system suitable for the early stages in a design process.

The mixed displacement method to avoid shear locking in problems in elasticity

AbstractThe mixed displacement (MD) method was initially developed to mitigate geometrical locking effects in beams, plates, and shells with the intention of having intrinsically locking‐free characteristics while using equal‐order interpolation for all degrees of freedom. In other words, it is an unlocking scheme that works independent of the element shape, polynomial order, and discretization scheme. It includes additional degrees of freedom that adhere to a carefully designed differential relation that can be interpreted as a kinematic law, incorporated in a mixed sense. Certain constraints are to be enforced on these additional degrees of freedom to obtain a well‐posed system of equations. In this work, the MD method is extended for problems in solid mechanics. We present the underlying variational formulation, followed by its application to 2D solid elements. Additionally, we showcase an idea to enforce the additional constraints in a general sense. Various numerical examples, within the framework of the finite element method and isogeometric analysis, are outlined to demonstrate the performance of the MD method in the geometrically linear and geometrically nonlinear cases.

Temporal second-order two-grid finite element method for semilinear time-fractional Rayleigh-Stokes equations

In this paper, we have developed a temporal second-order two-grid FEM to solve the semilinear time-fractional Rayleigh-Stokes equations. The proposed two-grid FEM uses the L2-1σ scheme and second order scheme to approximate the Caputo fractional derivative and the time first-order derivative in temporal direction and the standard FEM in spatial direction. The L2-norm and H1-norm stability and error estimates for the standard finite element solution and the two-grid solution are derived. The results shown that as long as the mesh sizes satisfy H=h12 and H=hr2r+2 respectively, the two-grid algorithm can achieve asymptotically optimal approximation. Furthermore, the non-uniform L2-1σ scheme was applied for temporal discretization to handle the weak singularity of the solution. Finally, the theoretical findings were confirmed by numerical results, and the effectiveness of the two-grid algorithm was demonstrated.

Combined fluid and ferrofluid buoyancy force, heat absorption and non linear ferro-viscosity effects on ferro- hydrodynamics fluid flow in orthogonal porous surface

Mixed convection incompressible ferro-hydrodynamic (FHD) boundary layer fluid flow on vertical porous curvilinear orthogonal surfaces is examined in our present study in presence of combined fluid and ferro-fluid buoyancy force, nonlinear ferro-viscosity parameter, and heat absorption/generation effects. Design/Methodology/Approach: Types of Prandtl momentum and thermal boundary layer partial differential equations in a curvilinear system are converted into non-dimensional ordinary nonlinear differential equations (ODE) by introducing dimensionless velocities, temperature functions and similarity variable. Missing initial conditions are found by shooting method and solving the system of nonlinear ODEs by Runge-Kutta integration scheme of order six. With the help of MATLAB, the numerical solutions are graphically displayed in the forms of primary velocity profile, secondary velocity profile, and temperature profile. Three types of magnetic nano-ferrofluid are considered such as water-based ferrofluid (Taiho W-40), Hydrocarbon based ferrofluid (EMG-901) and kerosene-based ferrofluid (C1-20B) whose Prandtl numbers are 44.3, 79.3 and 128 respectively shown in Table 1. For kerosene based ferro-fluid, Table 3 presents the coefficient of skin friction and heat flux. Finding: The effects of combined fluid and ferrofluid buoyancy forces, nonlinear ferro-viscosity parameter, suction/injection, and heat absorption/generation parameters on the velocity and temperature profiles are investigated. Our physical interest is to calculate the local shearing stresses and the local heat flux at the surface. Finally, we have made comparisons of the results which are highlighted the validity of our numerical calculations adopted for the presence study.

Infrared gluon propagator in the refined Gribov-Zwanziger scenario at one-loop order in the Landau gauge

The refined Gribov-Zwanziger (RGZ) action in the Landau gauge provides a local and renormalizable framework to account for the existence of infinitesimal Gribov copies in the path integral together with other relevant infrared effects such as the formation of condensates. The properties of the tree-level gluon propagator obtained in this setup have been thoroughly investigated over the past decade. It accommodates important properties seen in lattice simulations such as a finite value at vanishing momentum and positivity violation. Yet a comprehensive study about the stability of such properties against quantum corrections was lacking. In this work, we compute the gluon propagator in the RGZ scenario at one-loop order and implement an appropriate renormalization scheme in order to compare our findings with lattice data. Remarkably, the qualitative properties of the tree-level gluon propagator are preserved. In particular, the fits with lattice data show evidence for positivity violation and the existence of complex poles for SU(2) and SU(3) gauge groups. We comment on the results for the ghost propagator as well. Published by the American Physical Society 2024

Towards coordinating self-healing instances: Policy-based and non-cooperative game theory-based approaches with location awareness

Self-healing is an essential functionality in Self-Organizing cellular Network (SON). It aims to ensure service continuity by detecting, diagnosing, and compensating network outage after triggering appropriate Cell Outage Compensation (COC) functions according to the outage case. The role of self-healing is increasingly become indispensable, especially in high density network as in 5 G and beyond, in order to maintain the availability and retainability of mobile service and save revenues. However, the essence of COC entails modifications of different Network Control Parameters (NCP) which are under control of SON Functions (SONF) that are related to other self-x functionalities. In addition, it can request different types of compensation functions according to the outage case. Moreover, it requires to harmonize the objectives of the requested stand-alone SONFs over the involved Candidate Cells (CC) in order to re-build a consistent coverage model. Thus, the need for self-coordination is mandatory to guarantee conflict-free outage compensation procedure. In this paper, we propose a novel integrated coordination scheme in order to coordinate Antenna Tilt (AT)-based and Transmission Power (TXP)-based COC functions. Beside their primary targets of conflict avoidance and resolution, we prove that our location-aware coordination mechanisms, which are based on policies and Non-Cooperative Zero-Sum Game (NCZSG) theory, can collaboratively guide greedy stand-alone single-objective COC functions to reach a stable coverage model. The coordination is done even when there is no prior knowledge of the environment or the compensatory algorithms themselves. The choice of optimal Network Control Parameters Values (NCV) is determined according to the function after the coordinator's verification.

Fully-Discrete Lyapunov Consistent Discretizations for Parabolic Reaction-Diffusion Equations with r Species

AbstractReaction-diffusion equations model various biological, physical, sociological, and environmental phenomena. Often, numerical simulations are used to understand and discover the dynamics of such systems. Following the extension of the nonlinear Lyapunov theory applied to some class of reaction-diffusion partial differential equations (PDEs), we develop the first fully discrete Lyapunov discretizations that are consistent with the stability properties of the continuous parabolic reaction-diffusion models. The proposed framework provides a systematic procedure to develop fully discrete schemes of arbitrary order in space and time for solving a broad class of equations equipped with a Lyapunov functional. The new schemes are applied to solve systems of PDEs, which arise in epidemiology and oncolytic M1 virotherapy. The new computational framework provides physically consistent and accurate results without exhibiting scheme-dependent instabilities and converging to unphysical solutions. The proposed approach represents a capstone for developing efficient, robust, and predictive technologies for simulating complex phenomena.

On the viscoelastic-electromagnetic-gravitational analogy

The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun–Earth and Earth–Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.

A reliable Bayesian regularization neural network approach to solve the global stability of infectious disease model

The purpose of this study is to perform the numerical results of the global stability of infectious disease mathematical model by using the stochastic computing scheme. The design of proposed solver is presented by one of the efficient and reliable schemes named as Bayesian regularization neural network (BRNN). The global stability of infectious disease mathematical nonlinear model is categorized into susceptible, infected, recovered and vaccinated. The construction of dataset is performed through the Runge-Kutta scheme in order to lessen the mean square error (MSE) by dividing the statics as training 74 %, while 13 % for both testing and endorsement. The proposed stochastic process contains log-sigmoid merit function, twenty neurons and optimization through RBNN for the numerical solutions of the global stability of infectious disease mathematical system. The best training values for each model's case are performed around 10–11. The scheme's correctness is performed by the matching of the results and the minor calculated absolute error performances. Moreover, the regression, state transmission, error histogram and MSE indicate the trustworthiness of the designed solver.

General boundary conditions for a Boussinesq model with varying bathymetry

AbstractThis paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq–Abbott system in the presence of topography. We propose a procedure that allows one to handle very general linear or nonlinear boundary conditions. It consists in reducing the problem to a system of conservation laws with nonlocal fluxes and coupled to an ordinary differential equation. This reformulation is used to propose two hybrid finite volumes/finite differences schemes of first and second order, respectively. The possibility to use many kinds of boundary conditions is used to investigate numerically the asymptotic stability of the boundary conditions, which is an issue of practical relevance in coastal oceanography since asymptotically stable boundary conditions would allow one to reconstruct a wave field from the knowledge of the boundary data only, even if the initial data are not known.

Affine Projection Algorithms with Novel Schemes of Variable Projection Order

Affine Projection Algorithms with Novel Schemes of Variable Projection Order

A bound preserving cut discontinuous Galerkin method for one dimensional hyperbolic conservation laws

In this paper we present a family of high order cut finite element methods with bound preserving properties for hyperbolic conservation laws in one space dimension. The methods are based on the discontinuous Galerkin framework and use a regular background mesh, where interior boundaries are allowed to cut through the mesh arbitrarily. Our methods include ghost penalty stabilization to handle small cut elements and a new reconstruction of the approximation on macro-elements, which are local patches consisting of cut and un-cut neighboring elements that are connected by stabilization. We show that the reconstructed solution retains conservation and order of convergence. Our lowest order scheme results in a piecewise constant solution that satisfies a maximum principle for scalar hyperbolic conservation laws. When the lowest order scheme is applied to the Euler equations, the scheme is positivity preserving in the sense that positivity of pressure and density are retained. For the high order schemes, suitable bound preserving limiters are applied to the reconstructed solution on macro-elements. In the scalar case, a maximum principle limiter is applied, which ensures that the limited approximation satisfies the maximum principle. Correspondingly, we use a positivity preserving limiter for the Euler equations, and show that our scheme is positivity preserving. In the presence of shocks additional limiting is needed to avoid oscillations, hence we apply a standard TVB limiter to the reconstructed solution. The time step restrictions are of the same order as for the corresponding discontinuous Galerkin methods on the background mesh. Numerical computations illustrate accuracy, bound preservation, and shock capturing capabilities of the proposed schemes.

Continuous finite elements satisfying a strong discrete Miranda–Talenti identity

Abstract This article introduces continuous $H^{2}$-nonconforming finite elements in two and three space dimensions that satisfy a strong discrete Miranda–Talenti inequality in the sense that the global $L^{2}$ norm of the piecewise Hessian is bounded by the $L^{2}$ norm of the piecewise Laplacian. The construction is based on globally continuous finite element functions with $C^{1}$ continuity on the vertices (2D) or edges (3D). As an application, these finite elements are used to approximate uniformly elliptic equations in nondivergence form under the Cordes condition without additional stabilization terms. For the biharmonic equation in three dimensions, the proposed methods has less degrees of freedom than existing nonconforming schemes of the same order. Numerical results in two and three dimensions confirm the practical feasibility of the proposed schemes.

Optimization of calculations in modeling the breaking of plasma oscillations

The proposed method of optimization of calculations is of a combined nature. First, using a piecewise uniform grid, a difference scheme of the second order of accuracy of the McCormack type is constructed, and then — to weaken the stability condition — an implicit version of the scheme is used, which even in the nonlinear case allows an iteration-free implementation. When constructing a grid, a preliminary study is required, which is based on the analytical properties of the solution of the differential problem. Based on the calculations carried out, it can be concluded that the potential reduction in the amount of calculations is dozens of times without a noticeable loss of accuracy.

Digital Dental Biometrics for Human Identification Based on Automated 3D Point Cloud Feature Extraction and Registration.

Intraoral scans (IOS) provide precise 3D data of dental crowns and gingival structures. This paper explores an application of IOS in human identification. We propose a dental biometrics framework for human identification using 3D dental point clouds based on machine learning-related algorithms, encompassing three stages: data preprocessing, feature extraction, and registration-based identification. In the data preprocessing stage, we use the curvature principle to extract distinguishable tooth crown contours from the original point clouds as the holistic feature identification samples. Based on these samples, we construct four types of local feature identification samples to evaluate identification performance with severe teeth loss. In the feature extraction stage, we conduct voxel downsampling, then extract the geometric and structural features of the point cloud. In the registration-based identification stage, we construct a coarse-to-fine registration scheme in order to realize the identification task. Experimental results on a dataset of 160 individuals demonstrate that our method achieves a Rank-1 recognition rate of 100% using complete tooth crown contours samples. Utilizing the remaining four types of local feature samples yields a Rank-1 recognition rate exceeding 96.05%. The proposed framework proves effective for human identification, maintaining high identification performance even in extreme cases of partial tooth loss.

Numerical analysis of the Maxwell-Cattaneo-Vernotte nonlinear model

In the literature, one can find numerous modifications of Fourier’s law, the first of which is the Maxwell–Cattaneo–Vernotte heat equation. Although this model has been known for decades and successfully used to model low-temperature damped heat wave propagation, its nonlinear properties are rarely investigated. This paper aims to present the functional relationship between the transport coefficients and the consequences of their temperature dependence, particularly focusing on thermal conductivity. These are the consequences of the second law of thermodynamics. Furthermore, we introduce a particular implicit numerical scheme in order to solve such nonlinear heat equations reliably, free from artificial numerical errors. We investigate the scheme’s stability, dissipation, and dispersion attributes. We demonstrate the effect of temperature-dependent thermal conductivity on two different initial-boundary value problems, including time-dependent boundaries and heterogeneous initial conditions, for which we discuss the nontrivial constraints following irreversible thermodynamics.

Two-level implicit high-order compact scheme in exponential form for 3D quasi-linear parabolic equations

We discuss a new high accuracy compact exponential scheme of order four in space and two in time to solve the three-dimensional quasi-linear parabolic partial differential equations. The derived half-step discretization based scheme is implicit in nature and demands only two levels for computation. The generalization of the proposed exponential scheme for the system of the quasi-linear parabolic PDEs is also represented. We generate unconditionally stable alternating direction implicit scheme for the linear parabolic equation in general form. The accuracy and the theoretical results of the proposed scheme are verified for high Reynolds number by several numerical problems like linear and non-linear convection-diffusion equation, coupled Burgers' equations, Navier-Stokes equations, quasi-linear parabolic equation, etc.

Computational analysis of nanoparticles and waste discharge concentration past a rotating sphere with Lorentz forces

Abstract As industries rely more and more on magnetohydrodynamic (MHD) systems for different uses in power, production, and management of the environment, it becomes essential to optimize these operations. The study seeks to improve the effectiveness and productivity of cooling structures, chemical reaction reactors, and contaminant control methods by investigating these intricate interconnections. Because of this, the work scrutinizes the endothermic/exothermic (EN/EX) chemical processes, convective boundary conditions, and pollutant concentration impacts on MHD nanofluid circulation around a rotating sphere. The governing equations based on the above assumptions are reduced into a system of ordinary differential equations and solved numerically with Runge–Kutta Fehlberg’s fourth- and fifth- order schemes. The obtained numerical outcomes from the numerical scheme are presented with the aid of graphs, and the results show that the rate of mass transfer decreases with an increase in the external pollutant local source and solid volume percentage. For changes in the values of the activation energy parameter and solid fraction, the rate of thermal dispersion drops for the EN case and upsurges for the EX case. The concentration profile shows increment with the addition of the external pollutant source variation parameter and local pollutant external source parameter. The outcomes of the present work can be helpful in cooling equipment, developing advanced methods for controlling pollution, environmental management, MHD generators, and various industrial contexts.

P adé: A Code for Protoplanetary Disk Turbulence Based on Padé Differencing

The Padé code has been developed to treat hydrodynamic turbulence in protoplanetary disks. It solves the compressible equations of motion in cylindrical coordinates. Derivatives are computed using nondiffusive and conservative fourth-order Padé differencing, which has higher resolving power compared to both dissipative shock-capturing schemes used in most astrophysics codes, as well as nondiffusive central finite-difference schemes of the same order. The fourth-order Runge–Kutta method is used for time stepping. A previously reported error-corrected Fargo approach is used to reduce the time step constraint imposed by rapid Keplerian advection. Artificial bulk viscosity is used when shock capturing is required. Tests for correctness and scaling with respect to the number of processors are presented. Finally, efforts to improve efficiency and accuracy are suggested.

Influence of heat source/sink on a rotating cone in a rotating nanofluid with magnetic field impact: Application of Hosoya polynomial‐based collocation method

AbstractThe present analysis considers the angular velocities of the free flow and the arbitrarily fluctuating cone over time, leading to an unsteady stream over a rotating cone in a rotating nanofluid. The effects of heat source/sink and magnetic field on an unsteady flow past a rotating cone in a rotating nanoliquid are considered in this examination. The dimensional governing equations are transformed into nondimensional ordinary differential equations (ODEs) using the similarity variables. The nonlinear system of ODEs has been solved using the Hosoya polynomial‐based collocation method (HPBCM), and the obtained values are compared with the numerical method Runge Kutta Fehlberg's fourth‐fifth order (RKF‐45) scheme. The effects of numerous factors on the momentum and thermal distributions are shown graphically. Results reveal that the ratio of the cone angular velocity to the free stream angular velocity increases the velocity profile but converse trend is seen for the thermal profile. The upsurge in the values of the magnetic parameter intensifies the velocity profile. The rise in the values of the heat source/sink parameter upsurges the thermal profile. As the unsteady parameter increases temperature profile declines.