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The paper considers a discrete-time, Markov, stochastic process model of drivers' day-to-day evolving route choice, the evolving ‘state’ of such a system being governed by the traffic interactions between vehicles, and the adaptive behaviour of drivers in response to previous travel experiences. An approximating deterministic process is proposed, by approximating both the probability distribution of previous experiences—the “memory filter”—and the conditional distribution of future choices. This approximating process includes both flow means and variances as state variables. Existence and uniqueness of fixed points of this process are examined, and an example used to contrast these with conventional stochastic equilibrium models. The elaboration of this approach to networks of an arbitrary size is discussed.

The primary focus of this study is to tackle a critical industry issue concerning energy inefficiency. This is achieved through an investigation into enhancing heat transfer in solar radiation phenomena on a curved surface. The problem formulation of governing equations includes the combined effects of thermal relaxation, Newtonian heating, radiation mechanism, and Darcy-Forchheimer to enhance the uniqueness of the model. This research employs the Cattaneo–Christov heat theory model to investigate the thermal flux via utilizing the above-mentioned phenomenon with a purpose of advancing thermal technology. A mixture of silicon dioxide (SiO_2)\ and Molybdenum disulfide (MoS_2) is considered for the nanoparticle’s thermal propagation in base solvent propylene glycol. The simulation of the modeled equations is solved using the Shifted Legendre collocation scheme (SLCS). The findings show that, the solar radiation effects boosted the heating performance of the hybrid nanofluid. Furthermore, the heat transmission progress increases against the curvature and thermal relaxation parameter.

Shifted Legendre collocation scheme (SLCS) is utilized to solve the simulation of the modeled equations.

The findings show that, the solar radiation effects boosted the heating performance of the hybrid nanofluid. The heat transmission progress increase against the curvature and thermal relaxation parameter.

This research employs the Cattaneo–Christov heat theory model to investigate the thermal flux via utilizing the above-mentioned phenomenon with a purpose of advancing thermal technology.

Due to the important and extensive use of graphene in the engineering structures, the purpose of this paper is to investigate the low-velocity impact (LVI) response of a graphene-reinforced plate with a rectangular central hole.

In this paper, Halpin-Tsai theory is used to model the mechanical properties of the plate made of polymethyl methacrylate (PMMA) resin and graphene particles. First, the plate displacement field is presented, and then the strains and stresses are obtained. The motion equations are extracted using energy equations, Ritz method and generalized Lagrange equations. The verification of theoretical formulation shall be carried out using the ABAQUS finite element software suite.

The effects of graphene volume fraction, approaching the impact point to the corner of the rectangular plate, and different boundary conditions of the plate are studied for LVI of impactor with spherical tip on the rectangular central hole reinforced by graphene. Important responses of the impact, such as the contact force between the impactor and the plate as well as the displacement of the plate at the impact place, are investigated and analyzed in this research.

Considering the wide application of graphene in the engineering structures, the simulation of the LVI on the graphene-reinforced plate made of PMMA resin with a rectangular central hole is carried out in this paper using numerical and theoretical modeling.

This study aims to use fractal theory to investigate the contact mechanics of two bidirectional anisotropic surfaces, taking into account the friction coefficient of the contact interface. This study introduces a model that centers on normal contact load and contact stiffness, providing an extensive framework to elucidate the interactions between these surfaces.

The research adopts the Weierstrass–Mandelbrot (W-M) function for simulating bidirectional surface profiles. Through the application of elastic-plastic contact theory, it evaluates the contact area and load of a singular asperity across elasticity, elastoplasticity and plasticity phases. The contact load and stiffness of the rough surface are determined using a refined asperity density distribution function, and these findings are juxtaposed with extant models to validate their precision and rationality.

The study delineates the influence of fractal dimension (D), surface roughness (G), ellipse eccentricity (e) and friction coefficient (µ) on the contact area, load and stiffness. It reveals that the contact area enlarges with the fractal dimension (D) yet diminishes with increased eccentricity (e), roughness (G) and friction coefficient (µ). These elements considerably affect the contact load and stiffness, underscoring their significance in comprehending surface interactions.

This study applies fractal theory to analyze the contact mechanics of bidirectional anisotropic surfaces, considering the geometry and mechanics of ellipsoidal asperities on rough surfaces to develop a contact mechanics model. This model clarifies the deformation of an asperity in normal contact, presenting a more rational alternative to current models.

This study examined the reciprocal influence of demand learning and preference matching in the context of store brand customization. The demand-learning effect refers to the collection of market demand information through production, based on pre-order demands, enabling retailers to accurately predict and allocate product quantities, thus improving inventory management. The preference-matching effect involves engaging consumers in the production and design processes of store brands to align fully with their preferences, thereby increasing the purchase impact of store brand products and promoting consumption.

We employ game-theoretic models to analyze a two-echelon supply chain consisting of a manufacturer and a retailer. The retailer offers both national brands, manufactured by the supplier and in-house store brands. To enhance their competitive edge, the retailer can adopt a customized strategy targeting the store brand to attract a wider consumer base.

The analysis reveals that, under low commission fees, the manufacturer consistently opts for high production quantities, irrespective of the level of demand uncertainty. However, when the perceived value of a store brand is low and demand uncertainty is either low or high, the retailer should choose a minimal or zero production quantity. The decision-making process is influenced by the customization process, wherein the effects of demand learning and preference matching occasionally mutually reinforce each other. Specifically, when the perceived value of a store brand is low, or the product cost is high, along with high customization costs, the interplay between demand learning and preference matching becomes mutually inhibiting. Consequently, the significance of store brand customization diminishes.

This study enhances the current body of knowledge by providing a deeper understanding of the theoretical value of store brand customization. In addition, it offers valuable decision-making support to enterprises by assisting them in selecting appropriate inventory and customization strategies.

The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil.

First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs.

Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown.

This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper.

The purpose of this study is to evaluate and minimize the losses of alternating current (AC) in the winding of electrical machines. AC winding losses are frequently disregarded at low frequencies, but they become a significant concern at high frequencies. This is the situation where applications require a high speed. The most significant applications in this category are electrical propulsion and drive systems.

An analytical model is used to predict the AC losses in the winding of electrical machines. The process involves dividing the slot into separate layers and then calculating the AC loss factor for each layer. The model aims to calculate AC losses for two different winding arrangements involving circular conductors. This application focuses on the stator winding of a permanent magnet synchronous motor that is specifically designed for electric vehicles. The model is integrated into an optimization process that makes use of the genetic algorithm method to minimize AC losses resulting from the arrangement of conductors within the slot.

This study and its findings demonstrate that the arrangement of the conductors within the slot has a comparable effect on the AC losses in the winding as the machine's geometric and physical properties. The effectiveness of electrical machines depends heavily on optimizing the arrangement of conductors in the slot to minimize AC winding losses.

The proposed strategy seeks to minimize AC winding losses in high-speed electric machines by providing a cost-effective and precise solution to improve energy efficiency.

The paper aims to the size-dependent analysis of functionally graded materials in thermal environment based on the modified couple stress theory using finite element method.

The element formulation is developed within the framework of the penalty unsymmetric finite element method (FEM) in that the C¹ continuity requirement is satisfied in weak sense and thus, C⁰ continuous interpolation enhanced by independent nodal rotation is employed as the test function. Meanwhile, the trial function is designed based on the stress functions and the weighted residual method. Besides, the special Gauss quadrature scheme is employed for integrals of matrices in accordance with the graded variation of the material properties.

The numerical results reveal that in thermal environment, functionally graded materials exhibit better bending performance compared to homogeneous materials, Moreover, the findings also indicate that with an increase in MLSP, the natural frequencies of out-of-plane modes gradually increase, while the natural frequencies of in-plane modes show much less variation, leading to a mode switch phenomenon.

The work provides an efficient numerical tool for analyzing and designing the functionally graded structures in thermal environment in practical engineering applications.