Discrete Approach Research Articles

Innovation Discrete Approach Based on Arabic Language Test Assessment

Innovation Discrete Approach Based on Arabic Language Test Assessment

On Discrete Frechet Distribution : Estimation and Application

A discrete two-parameter distribution corresponding to the continuous distribution is introduced and derived by using the approach of discretization of continuous distribution functions . The Survival and Hazard functions of the proposed distribution were also found and examined . Two methods were discussed to estimate the parameters , Maximum Likelihood and the Bayesian method , and then compare the performance using the simulation method . In addition, the compatibility of the proposed distribution was investigated through real data , and then the estimates of the survival and Hazard functions were reached . The superiority of the Bayesian method in data modelling was shown .

Improving Effectiveness of the Safety Service Patrol Programs: A Discrete Event-Based Simulation Approach

Safety service patrols (SSPs) play an important role in incident management on highways. It is critical to respond to incidents in a timely manner as this can significantly reduce nonrecurrent congestion and improve safety. Therefore, it is essential to allocate available SSP vehicles to highway segments such that their effectiveness is maximized. This study aimed to develop a simulation-based framework to assist with SSP service optimization. More specifically, a discrete event-based simulation tool (i.e., SSP-OPT) with customizable parameters was developed to help plan the optimum patrol routes based on available SSP resources and predicted incidents. The developed tool was tested with roadway traffic and incident data from the Virginia highway network. After model calibration, the simulation results showed that the developed SSP-OPT tool could replicate the patrol routes with similar performance to the field observations, validating the tool. Further, adopting the tool for corridor-level optimization could help to identify the best patrol plan to minimize SSP response time and maximize SSP response rates for a given number of SSP vehicles. The SSP-OPT tool requires minimal user input (e.g., segment lengths, annual average daily traffic) and has the flexibility to be easily applied to any highway corridor once calibrated. The tool generates various performance metrics to enable more informed decision making in SSP route planning.

Finite element analysis of a generalized rotating FGM vessel subjected to thermo-mechanical loadings: Effect of Poisson ratio and inhomogeneity parameters

Cylinders and thick walled cylindrical shells are commonly utilized in several industries to transport and store fluids under certain pressure and temperature conditions. In the present paper, a numerical solution is developed in order to investigate displacement, temperature and stress fields in a rotating pressure vessel made of generalized functionally graded material (FGM) subjected to different thermo-mechanical boundary conditions. The aim is to investigate the effect of Poisson ratio, internal pressure and temperature and inhomogeneity parameters on the stress and deformation distributions of the rotating pressure vessel. The material is considered isotropic nonhomogeneous and linearly elastic with its properties varying along the radial direction. Additionally, certain conditions, such as exterior or interior problems where r → ∞ or r → 0, respectively, are impossible to resolve using the variation of attributes as a power-law distribution. An approach to the spatial Young modulus distribution that is more broad has been suggested in the literature which can be applied to such physical challenges. The rotation of the pressure vessel is considered in the analysis, and the temperature distribution is assumed to be non-uniform. Since an analytical solution to the differential equation is not accessible, the conventional Galerkin discretization approach of the Finite Element Method (FEM) is applied, nowadays is considered one of the main numerical tools for solving Boundary Value Problems (BVP). It is addressed how stress, strain, and displacement are affected by the inhomogeneity parameter, rotation speed, pressure, temperature, and Poisson ratio. The examination of the various findings indicates that changes in the temperature profile, rotation, and inhomogeneity parameter on the thermoelastic field have a substantial impact on the stress and strain in the FGM cylinder. The findings indicate that the Poisson ratio and inhomogeneity parameters have a significant impact on the stress and deformation distributions. According to the results, the above-mentioned parameters can be adapted to control the thermoelastic filed in a FGM cylinder. The present research offers significant perspectives on the development and enhancement of rotating FGM pressure vessels intended for high-temperature applications.

Population structure and history of Mycobacterium bovis European 3 clonal complex reveal transmission across ecological corridors of unrecognized importance in Portugal.

Efforts to strengthen surveillance and control of animal tuberculosis (TB) are ongoing worlwide. Here, we developed an eco-phylodynamic framework based on discrete phylogenetic approaches informed by M. bovis whole-genome sequence data representing a multi-host transmission system at the livestock-wildlife interface, within a rich ecological landscape in Portugal, to understand transmission processes and translate this knowledge into disease management benefits. We find evidence for the co-circulation of several M. bovis clades, with frequent transmission of the Eu3 lineage among cattle and wildlife populations. Most transition events between different ecological settings took place toward host, climate and land use gradients, underscoring animal TB expansion and a potential corridor of unrecognized importance for M. bovis maintenance. Results stress that animal TB is an established wildlife disease without ecological barriers, showing that control measures in place are insufficient to prevent long-distance transmission and spillover across multi-host communities, demanding new interventions targeting livestock-wildlife interactions.

Coarse graining with control points: a cubic-Bézier based approach to modeling athermal fibrous materials

Fibrous materials continue to be of central importance to modern life, including traditional materials, such as textiles and paper, modern materials, such as polymeric materials and glass fiber, and emerging materials, such as carbon nanotube yarns. Developing constitutive laws for the mechanical behavior of such materials can be challenging owing to the often non-periodic microstructure, resulting in fairly large and computationally intractable representative volume elements. Therefore, it is imperative to design novel coarse-grained models that can bridge the computational gap and capture accurate physics associated with the mechanical behavior of fibrous materials. In this work, cubic-Béziers are used to represent fiber-segments, allowing for up to C 2(curvature)-continuous representation of curved fibers. Equations of motion are derived in terms of the control points, which allow for minimization and time integration strategies with the Lagrangian and Hamiltonian formalism. This coarse-grained model promises faster and more accurate computational performance compared to discrete approaches.

An analysis of high order FEM and IGA for explicit dynamics: Mass lumping and immersed boundaries

SummaryWe investigate the behavior of different shape functions for the discretization of hyperbolic problems. In particular, we consider classical Lagrange polynomials and B‐splines. The studies focus on the performance of the these functions as a spatial discretization approach combined with an explicit time marching scheme. In this regard, a major concern is the maximum eigenvalue that imposes restrictions on the critical time step size and suitable lumping techniques that yield a diagonal mass matrix. The accuracy of the discretization methods is assessed in an asymptotic manner in terms of the convergence of eigenvalues and eigenvectors. Further, the global accuracy is investigated in terms of the full spectrum. The results show that B‐spline discretization with a consistent mass matrix are more accurate than those based on Lagrange shape functions, which holds true in the boundary‐fitted as well as in the immersed setting. On the other hand, Lagrange shape functions are more robust with respect to standard lumping techniques, which cannot be directly applied for B‐splines without loss of accuracy. In general, we observe that none of the standard lumping schemes yields optimal results for B‐splines, even in the boundary‐fitted setting. For the immersed setting, also Lagrange shape functions show a drop in accuracy which depends on the position of the boundary that cuts the element. Several remedies are considered in order to overcome these issues, including interpolatory B‐spline bases as well as eigenvalue stabilization methods. While accuracy and stability can be improved using these remedies, we conclude from our study that it is still an open question, how to design a discretization method that achieves large critical time step sizes in combination with a diagonal mass matrix and high accuracy in the immersed setting. We note that these considerations primarily relate to linear structural dynamics applications, such as for example, structural acoustics. In nonlinear problems, such as automotive crash dynamics, other considerations predominate. An example of a one‐dimensional elastic‐plastic bar impacting a rigid wall is illustrative.

Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator

In this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and the endemic point. The examination of the system’s local and global stability is provided in terms of the basic reproductive number Rp°. The global stability analysis has been carried out using an appropriate Lyapunov function and the LaSalle invariant principle. The results demonstrate that in the infection model, if Rp°<1, then the solution converges to the disease-free equilibrium, which is both locally and globally asymptotically stable. Whilst Rp°>1, the endemic equilibrium is considered to exist. Simulations are implemented via a finite difference method with Grünwald-Letnikov discretization approach for Caputo derivative operator to define how changes in parameters impact the dynamic behavior of the system using Matlab.

Numerical method for second order singularly perturbed delay differential equations with fractional order in time via fitted computational method

The numerical solution of time fractional parabolic differential equations with singular perturbations and delay is the subject of this article. An arbitrarily small perturbation parameter ɛ(0<ɛ<<1) is multiplied the highest order derivative term. The problem’s solution shows an exponential boundary layer on the right side of the spatial domain for small values of ɛ. The solution and its derivatives are discussed together with their properties and bounds. The Crank–Nicolson approach for time discretization and the fitted operator non-standard finite difference method for space discretization are used to solve the time fractional singularly perturbed time delay problem under consideration. The comparison principle and solution bound are used to examine and analyze the scheme’s stability. The scheme’s uniform convergence is examined and demonstrated. The proposed scheme has a uniform convergence order of Mx−1+(Δt)2−γ. Two numerical illustrations for various values of ɛ are taken into consideration to validate the theoretical analysis of the scheme. The constructed scheme provides a better order of convergence and more accurate results than methods found in the literature.

Preliminary investigation of the sea-rail intermodal system's efficiency using a simulation approach: case of the Port of Trois-Rivieres

Sea-rail intermodal transportation around the globe faces complex challenges that affect the satisfaction of shippers' needs. An efficient cargo flow between the port and its hinterland depends particularly on efficient connectivity between the seaport and rail. Sea-rail intermodal can be a cost-efficient and green alternative to unimodal road transportation. Inefficient sea-rail connectivity in the seaport slows cargo flow and affects port capacity. Various factors could affect the system's efficiency and create bottlenecks in the system. A case study adopts a discrete event-based simulation approach to assess bottlenecks in the sea-rail connection that affect cargo flow and generate congestion. The data were collected from the Port of Trois-Rivières, the focus of our investigation. Our objective is to identify bottlenecks in the sea-rail intermodal system in the port, identify strategies to mitigate bottlenecks and accelerate cargo flow. To this end, we examined various scenarios, including an increase in the share of trains for cargo transportation and an increase in the number of daily train convoys. The findings underscore that elevating the train share to 40% and introducing two daily train services yield significant enhancements in key performance indicators. Noteworthy advantages encompass a reduction in the average time ships spend in the port, a decrease in the average waiting time for trains to depart from the port, an overall improvement in cargo handling efficiency within the port, and a notable alleviation of bottlenecks within the system.

Enhancing the trustworthiness of chaos and synchronization of chaotic satellite model: a practice of discrete fractional-order approaches

Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.

Multiparticle collision dynamics simulations of hydrodynamic interactions in colloidal suspensions: How well does the discrete particle approach do at short range?

The multiparticle collision dynamics (MPCD) simulation method is an attractive technique for studying the effects of hydrodynamic interactions in colloidal suspensions because of its flexibility, computational efficiency, and ease of implementation. Here, we analyze an extension of the basic MPCD method in which colloidal particles are discretized with a surface mesh of sensor nodes/particles that interact with solvent particles (MPCD + Discrete Particle or MPCD + DP). We use several situations that have been described analytically to probe the impact of colloidal particle mesh resolution on the ability of the MPCD + DP method to resolve short-ranged hydrodynamic interactions, which are important in crowded suspensions and especially in self-assembling systems that create high volume fraction phases. Specifically, we consider (A) hard-sphere diffusion near a wall, (B) two-particle diffusion, (C) hard-sphere diffusion in crowded suspensions, and (D) the dynamics of aggregation in an attractive colloidal suspension. We show that in each case, the density of sensor nodes plays a significant role in the accuracy of the simulation and that a surprisingly high number of surface nodes are needed to fully capture hydrodynamic interactions.

Cascade control algorithm for slip rate in a brake-by-wire system based on direct drive valve

To achieve a rapid response and precise control of braking hydraulic pressure, a brake-by-wire electro-hydraulic braking system based on a direct drive valve was designed. This system employs an electromagnetic linear actuator to drive the valve core directly, achieving swift adjustment of brake wheel cylinder hydraulic pressure. Given the strong coupling and non-linearity of the electromagnetic linear actuator, solely using a single-loop controller to control the slip rate can easily lead to weakened system performance. Hence, we proposed a cascade control algorithm for the brake-by-wire system, with an outer loop for slip rate control and an inner loop for direct drive valve position. The outer loop adopted a fuzzy PID control, while the inner loop adopted a model-free adaptive sliding mode control. By combining model-free adaptive control with a novel discrete exponential approach, we addressed the system’s non-linearity and unknown disturbances. A braking system test platform was constructed to verify the superior hydraulic tracking performance of this brake-by-wire system and to perform slip rate control performance analysis under different road conditions. Results demonstrated that compared to the fuzzy PID-MFAC algorithm, the proposed fuzzy PID-MFASMC control enhanced car slip rate control precision, and reduced both braking time and distance.

Error analysis for discontinuous Galerkin method for time‐fractional Burgers' equation

The primary goal of this paper is to suggest a fully discrete numerical solution approach for the time‐fractional Burgers' equation. This paper will consider the fractional derivative in the Caputo sense. The time derivative of this equation will be discretized using the L2‐type discretization formula. The spatial variable is approximated by using the nonsymmetric interior penalty discontinuous Galerkin method. The proposed method is globally and unconditionally stable. The accuracy of the solution is evaluated using a convergence analysis. Computational experiments further confirm the accuracy and stability of the suggested strategy.

Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at cross-links to form a network. Assuming that the inter-cross-link distance is much shorter than the length scale of the cell, we upscale the discrete force balance to form a continuum system of governing equations and deduce the corresponding macroscopic stress tensor. We use these discrete and continuum models to analyse the imposed displacement of a bead placed in the domain, characterizing the cell rheology through the force–displacement curve. We further derive an analytical approximation to the stress and strain fields in the limit of small bead radius, predicting the net force required to generate a given deformation and elucidating the dependency on the microscale properties of the filaments. We apply these models to networks of the intermediate filament vimentin and demonstrate good agreement between predictions of the discrete, continuum and analytical approaches. In particular, our model predicts that the network stiffness increases sublinearly with the filament pre-stress and scales logarithmically with the bead size.

Investigating the dark matter halo of NGC 5128 using a discrete dynamical model

Context. As the nearest accessible massive early-type galaxy, NGC 5128 presents an exceptional opportunity to measure dark matter halo parameters for a representative elliptical galaxy. Aims. Here we take advantage of rich new observational datasets of large-radius tracers to perform dynamical modeling of NGC 5128 Methods. We used a discrete axisymmetric anisotropic Jeans approach with a total tracer population of nearly 1800 planetary nebulae, globular clusters, and dwarf satellite galaxies extending to a projected distance of ∼250 kpc from the galaxy center to model the dynamics of NGC 5128. Results. We find that a standard Navarro-Frenk-White (NFW) halo provides an excellent fit to nearly all the data, except for a subset of the planetary nebulae that appear to be out of virial equilibrium. The best-fit dark matter halo has a virial mass of Mvir = 4.4−1.4+2.4 × 1012 M⊙, and NGC 5128 appears to sit below the mean stellar mass–halo mass and globular cluster mass–halo mass relations, which both predict a halo virial mass closer to Mvir ∼ 1013 M⊙. The inferred NFW virial concentration is cvir = 5.6−1.6+2.4, which is nominally lower than cvir ∼ 9 predicted from published cvir–Mvir relations, but within the ∼30% scatter found in simulations. The best-fit dark matter halo constitutes only ∼10% of the total mass at one effective radius but ∼50% at five effective radii. The derived halo parameters are consistent within the uncertainties for models with differing tracer populations, anisotropies, and inclinations. Conclusions. Our analysis highlights the value of comprehensive dynamical modeling of nearby galaxies and the importance of using multiple tracers to allow cross-checks for model robustness.

Study on flow behavior of fresh concrete in elbow using the dense discrete phase approach

The presence of an elbow in the pipe during pumping can cause serious problems such as separation and clogging of the concrete. It is difficult to accurately and intuitively observe the internal information of the pump tube. This work used the Dense Discrete Phase Model (DDPM) to investigate the flow behavior of fresh concrete in the elbow. Firstly, the accuracy of the simulation model is verified. Then, the DDPM is used to research the flow behavior of fresh concrete in the elbow at different inlet velocities, and the changing rules of flow velocity, pressure loss, and particle migration are revealed. This work provides a solution to ensure the normal pumping process and effectively predict the pump pressure loss.

A discrete approach for modelling the permeability evolution of granite under triaxial and true-triaxial stress conditions

In deep underground engineering, modelling the seepage characteristics of rock masses under complex stress conditions is crucial for the safe construction and stable operation of a project. The permeability of the rock mass is not only controlled by its internal pore structure but is also closely related to the deformation and fracturing of the rock. Although discrete methods offer advantages in describing the formation and development of fractures, these methods still face challenges due to the difficulties in establishing microscopic seepage models. This paper introduces a new hydro-mechanical coupled numerical model. In this model, a simple method is proposed to couple the Rigid-Body-Spring Method (RBSM) for rock deformation and fracturing simulation and the Equivalent Matrix-Fracture Network (EMFN) for seepage simulation. Subsequently, the model is employed to simulate the permeability of granite under three-dimensional stress conditions. The simulation results show that under hydrostatic stress conditions, the model accurately captures the decrease in permeability due to pore compression and collapse. Additionally, under deviatoric stress conditions, it reveals the stage-wise increase in permeability caused by granite fracturing. Finally, the model is applied to study the permeability evolution behaviour of rocks under true triaxial stress conditions. The results unveiled the significant impact of the intermediate principal stress on permeability evolution and revealing the microscopic mechanisms underpinning these effects. This paper paves a way for enhancing the application of discrete methods in forecasting the permeability evolution behaviour of intricate rock masses.

Discrete heat equation for a periodic layered system with allowance for the interfacial thermal resistance: General formulation and dispersion analysis.

Discrete heat equations for the multilayered periodic systems with allowance for the thermal resistance between the layers and corresponding dispersion relations in ω-k space have been derived and analyzed. The discrete equations imply a finite velocity of thermal disturbances and guarantee the positiveness of the solutions. Analytical expressions for the attenuation distance, and phase and group velocities have been obtained as functions of frequency and thermal resistance between the discrete layers. These functions demonstrate unusual behavior at high frequency compared to the continuum case. Furthermore, the maximum allowed frequency and wave number for the discrete heat equation are limited, whereas there are no such limits in a continuum. The discrete equation contains an infinite hierarchy of continuous partial differential equations, which starts with the Fourier law, proceeds with the hyperbolic equation, the Guyer-Krumhansl (or Jeffreys type) equation, and then with higher-order equations. The partial differential equations with a finite number of terms are only approximations of the discrete equation, which implies that on the ultrashort space and timescales the discrete approach is preferable. This work provides a relatively simple, easy-to-adopt, conceptual tool, together with analytical expressions allowing one to study ultrafast wavelike heat conduction regimes in periodic multilayered metamaterials.

APPLICATION OF TRANSPORTATION MODEL TO SOLVE TANKERS’ – ROUTING PROBLEM

The problem of selecting minimum cost routes for tankers in distributing petroleum products and satisfying customers’ requirement without scarcity in Nigeria remains a huge challenge to major marketers in the oil industries. The cost of transporting petroleum products from sources to destinations matters a lot to oil marketers because of the direct impact it has on their profits. The means of distributing petroleum products from refineries to depots or filling stations are tankers’ routing and pipelines. In this research, we extended some existing tankers’-routing models in literature which use a discrete integer programming approach to determine efficient and effective distribution of petroleum products. Consequently, we developed a new transportation linear programming algorithm to determine minimum cost routes in the delivery of petroleum product from their supply centers (refinery) to demand centers (filling stations). The significance of the application we adopted in this research lies in the modified distribution approach to tackle the complexity involved when transportation problems are formulated as linear programming problem having several variables and constraints. In this research, we formulate a new version of transportation model of tankers’ routing with the aim of reducing the cost of petroleum products delivery. The proposed transportation linear programming model was applied to a numerical example alongside other existing transportation algorithms. It is observed that, the new algorithm produced approximately the same total cost obtained by using other existing algorithms