Stable multistep schemes based on Caputo fractional derivative approximation are presented for solving 1D and 2D nonlinear fractional model arising from dielectric media. We approximate Caputo fractional derivatives in time with a multistep scheme of order O(τ3−α) & O(τ3−β),1<β<α<2, spatial Laplacian operator with a central difference scheme, and nonlinear source term g(B) by using Taylor series. The

Most of the recent epidemic outbreaks in the world have as a trigger, a strong migratory component as has been evident in the recent Covid-19 pandemic. In this work we address the problem of migration of human populations and its effect on pathogen reinfections in the case of Dengue, using a Markov-chain susceptible-infected-susceptible (SIS) metapopulation model over a network. Our model postulates

This study deals with free, forced undamped vibration and the random, damped vibration of an inhomogeneous beam composed of two materials with significantly different elastic moduli and material densities. Exact solution is obtained for natural frequencies and the mode shapes using Krylov-Duncan functions, along with the comparison with the results furnished by the Galerkin's method. Random vibrations

A nonlinear reaction cross-diffusion predator-prey system under Neumann boundary condition is considered. Negative diffusion coefficients with local accumulation effect of prey are introduced. Firstly, the criteria for local asymptotic stability of the positive homogeneous steady state with or without cross-diffusion are discussed. Moreover, the conditions for diffusion-driven instability are obtained

The morphodynamic evolution of the shape of dunes and piles of granular material is largely dictated by avalanching phenomena, acting when the local slope gets steeper than a critical repose angle. A class of degenerate parabolic models are proposed closing a mass balance equation with several viscoplastic constitutive laws to describe the motion of the sliding layer. Comparison among them is carried

In this work, the rheological behavior of power-law fluids on the flow dynamics is studied numerically. Studied cases include confined and non-confined problems that involve a single and two cylinders in tandem for 2-D and 3-D. For 2-D cases, the critical Reynolds numbers that define the Hopf bifurcation and its relation between the blockage ratio and the nature of the fluid are analyzed, including

In the crosswind environment, the flow field around a bridge pylon is complex and variable so that the vehicles are prone to side slip when passing by this region. In this situation, safety and comfort are severely affected. In this study, a dynamic coupling method that uses computational fluid dynamics (CFD) coupled with multibody dynamics was adopted to investigate the aerodynamic performance and

The vertical, rocking and horizontal vibrations of a rigid disk on multi-layered soils are studied by using a coupled approach of stiffness matrix method and “integral equation method”. Considering groundwater level, the layered soils consist of a number of dry layers and saturated layers, and a bedrock at the bottom. To allow the assembly of a global equation of this layered system, the stiffness

A robot supported by two points on a supporting rough plane is considered. The robot is driven by displacement of internal masses and friction against the surface of the support. The robot body contains two motors that rotate one unbalanced rotor (eccentric weight) and one flywheel. A mathematical model of a plane-parallel robot motion is constructed. Friction is modeled using Coulomb's law. The angular

With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using active load-bearing elements integrated into the structure. Such adaptive structures are of high complexity and very heterogeneous in nature. Port-Hamiltonian systems

This work presents results on the simulation of the generation and propagation of ship-borne waves, using an advanced nonlinear dispersive wave model based on the higher order Boussinesq-type equations. The model includes a single frequency dispersion term, expressed through convolution integrals; it is adapted to represent ship-borne waves by adopting the approach for wave generation by a moving local

This article presents a fractional-order mathematical model of the biological phenomena that occur in cancer therapy. The formulation generalizes the one proposed by Soto-Ortiza and Finley that consists of eighteen integer order differential equations and intends to serve as a platform for cancer treatment design. The fractional model is used to test the hypothesis that a combination of anti-Vascular

Space deployable structures are widely used in aerospace engineering, which have been addressed new folding methods, such as spatial overconstrained linkages and origami structures. This paper proposes a novel kirigami-inspired space cylindrical surface deployable structure with a large deployment ratio and a few degrees of freedom, as well as its optimization design method. Based on the thick panel

A blade with an adjustable stagger angle is a type of blade that is able to partially rotate around its long axis. In fact, while a hub rotates, simultaneously the angle of the blade root section can change. The objective of this research is to develop and analyze a model of rotating cantilever orthotropic blade with adjustable stagger angle. Using Hamilton's principle, the governing partial differential

The Journal of Applied Mathematical Modelling (AMM) is a leading international journal in the field of mathematics and engineering focused on research related to mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems, whose first issue was published in 1976. Motivated by the 40th anniversary in 2016, this study aims to develop a bibliometric overview

In this paper, responses of the stochastic energy harvesting systems with bilateral rigid stoppers are studied, in which the Newton’s impact model is adopted to describe the impact force between the proof mass and stoppers. To the best knowledge of the authors, the dynamical characteristics of the vibro-impact energy harvesting system have been scarcely investigated by utilizing the stochastic averaging

A method for isogeometric structural shape optimization using a multilevel approach and automated sensitivity analysis is presented in this work. The analysis mesh is obtained after carrying out successive refinements using the knot insertion and/or degree elevation algorithms, while retaining the coarse geometry for the domain design. Even though analytical sensitivities can be derived and implemented

This paper presents a frequency domain spectral finite element model (SFEM) for studying wave propagation in laminated composite shell panels. The SFEM formulation is derived using two different theories: (i) the first order shear deformation theory (FSDT) that takes shear deformation into consideration, and (ii) the classical shell theory (CST) that neglects shear deformation. The spectral approach

Classical fisheries biology aims to optimise fisheries-level outcomes, such as yield or profit, by controlling the fishing effort. This can be adjusted to allow for the effects of environmental stochasticity, or noise, in the population dynamics. However, when multiple fishing entities, which could represent countries, commercial organisations, or individual vessels, can autonomously determine their

In this paper, the unsteady natural cavitation and ventilated cavitation are investigated with the large eddy simulation method. The predicted cavity morphology and evolution process before and after ventilation agree well with the available experimental data. The results indicate that in natural cavitation, the formation of a U-type cavity is closely related to the separation of a re-entrant jet and

Based on tumor radiobiologic mechanisms, this paper develops a new tumor growth dynamic model with radiotherapy. It investigates how the reoxygenation of hypoxic cells and the radiosensitivity of radiotherpy influence the effect of tumor radiotherapy. The existence of the positive periodic solution, the asymptotic stabilities of the tumor-free equilibrium and the hypoxic tumor cell-free periodic solution

In this paper, the Petrov-Galerkin finite element interface method is modified to the vectorial form and applied to compute the band structure of phononic crystals with complicated scatterer geometry. Value-periodic subspace and projective grid are employed in this method. Complete mathematical model together with the continuity and equilibrium conditions on the scatterer interface as well as the Bloch-periodic

The feed-in tariff is a policy instrument designed to drop off the investment cost of solar energy, which has been thriving in Europe for many years. Similarly, tax-rebate regulation also aims to spur the diffusion of renewable technologies applied in America. However, it’s not clear that which policy is better off from the perspective of the members in the whole solar photovoltaic supply chain. To

The symplectic approach is used to establish the unified framework for solving governing equations of some thin plate problems in elasticity. By introducing appropriate functions, the given partial differential equation is first transferred into a separable Hamiltonian system. The completeness of the system of generalized eigenvectors of corresponding Hamiltonian operator matrix is proved, which serves

In this paper, we investigate the capabilities of the unsteady Reynolds-averaged Navier–Stokes (URANS) equations for capturing the helical structures found in a three-dimensional, incompressible and isothermal annular swirling jet undergoing vortex breakdown. The flow topology is representative of a bluff-body combustor operating at a Reynolds number Re = 8500 and swirl number S = 0.39. As a turbulence

The paper deals with a drive concept that uses the controllable mechanical properties of a magnetorheological fluid (MRF). The biologically inspired operating principle is based on crawling using anisotropic friction, as of worms, and non-Newtonian fluids, as of snails. The MRF located between a slider and two slide-blocks is functionally relevant for the drive system to generate a translational motion

NP-hard scheduling problems with the criterion of minimizing the maximum penalty, e.g. maximum lateness, are considered. For such problems, a metric which delivers an upper bound on the absolute error of the objective function value is introduced. Taking the given instance of some problem and using the introduced metric, the nearest instance is determined for which a polynomial or pseudo-polynomial

The subject of the paper is a simply supported circular plate with symmetrically varying mechanical properties in the thickness direction. In extreme cases of this variability, the plate becomes a single-layer or three-layer structure. The main goal of the study is to develop a mathematical description of both a single-layer and three-layer structure using one formula. The mathematical model also includes

In this paper we present recent evolvements of three robust numerical models for the simulation of the evolution of wave fields and hydrodynamic circulation in gulfs and coastal areas with large harbours and significant urban port facilities. The models are integrated into a single software suite for the development of a decision support tool to provide reliable forecasts of sea states prevailing at

This work outlines on the three dimensional motion of a rigid body about a fixed point according to Lagrange’s case under the action of a gyrostatic moment and a Newtonian force field. It is considered that the center of mass of the body is shifted slightly with respect to the principal axis of dynamic symmetry. Equations of motion are derived using the principal equation of the angular momentum and

This paper studies the characteristics of the large natural satellites in the solar system using clustering techniques. A variety of distances such as the Canberra, Arc-Cosine, Jaccard, Euclidean, Lorentzian and Manhattan are used to unravel the relationships between the moons emerging from their attributes. In a first phase, 19 large moons are selected and measured under the light of 9 orbital and

This paper presents complete steps for the construction and solution algorithm for a projection-based reduced order model coupled with an artificial neural net model. The reduced model is constructed based on the Galerkin projection of the equations governing the physical processes on reduced subspaces obtained by the Proper Orthogonal Decomposition method. The projection is done using numerical discretisation

In previous papers, the authors introduced a new formulation of the flow equations, involving friction and gravity effects, in gas transportation networks. They also proposed finite element methods combined with Newton-like algorithms for numerical solution. The main goal of the present paper is to include into the above formulation the usual devices existing in a gas transmission network other than

An unconditionally stable cone complementary formulation is established in this study for modeling frictional and cohesive contact problems. In order to simulate continuous and discontinuous media within a unified framework, the proposed cone complementary formulation is further integrated into the high-order numerical manifold method (NMM), which is based on six-node triangular meshes and is free

Almost all flows of polymers are accompanied by evolution of the molecular configuration, which has a great influence on material properties. However, the existing molecular configuration evolution models are mainly limited to the configuration evolution of a single molecular chain in a dilute solution ignoring intermolecular forces; it is impossible to predict the evolution of the molecular configuration

Deterministic mathematical models are frequently used to represent the predator-prey interaction for a deeper understanding of population dynamics. This approach, however, always has some limitations as it does not capture the environmental noise or demographic stochasticity which are important features of any natural system. In this paper, we study a minimal deterministic model of phytoplankton-zooplankton

Honest signals and cues have been observed as part of interspecific and intraspecific communication among animals. Recent theories suggest that existing signaling systems have evolved through natural selection imposed by predators. Honest signaling in the interspecific communication can provide insight into the evolution of anti-predation techniques. In this work, we introduce a deterministic three-stage

On the basis of an interesting and tractable parametric family of distributions, which figures prominently as an empirical model for asymmetric and heavy-tailed data, we introduce a novel parametric regression model that is quite simple and may be very useful to model many types of real data which occurs frequently in practice. The unknown parameters are estimated using the maximum likelihood estimation

The pre-positioning problem is an important part of emergency supply. Pre-positioning decisions must be made before disasters occur under high uncertainty and only limited distribution information. This study proposes a distributionally robust optimization model for the multi-period dynamic pre-positioning of emergency supplies with a static pre-disaster phase and a dynamic post-disaster phase. In

Thermoelectric materials can harvest heat and turn it into electricity and vice versa, which could lead to more cost-effective devices and appliances. This article investigates the problem of electrical and thermal rigid punch acting on thermoelectric materials. Some full-field quantities are given in a closed form. Importantly, some useful formulas for measuring the thermoelectric parameters by the

The structural stability of a column with rectangular and circular cross-section under axial compression is studied based on various higher-order shear deformation beam theories. This paper has two-fold objectives. One is to introduce a transition parameter to describe the direction of axial load from Engesser’s hypothesis to Haringx’s one, then a unified method is presented to determine the critical

We consider the Economic Order Quantity (EOQ) model for exponentially deteriorating items in which the items deteriorate at a rate proportional to the inventory level per unit time, which leads to an exponentially decreasing inventory level function over time. The coexistence of the exponential and polynomial terms in the total cost function makes closed-form exact solutions impossible, so approximations

A new stochastic isogeometric analysis method based on reduced basis vectors (SRBIGA) is proposed for engineering structures with random field material properties and external loads. Based on the Galerkin isogeometric functions, the proposed SRBIGA applies the Karhunen–Loève expansion to discretize the random field uncertainties. Inspired by the stochastic Krylov subspace theory, the structural responses

The Kawahara equation is a model of capillary-gravity water wave and plasma waves. In this paper, a direct method based on the Jacobi elliptic functions is presented to get analytical solutions of the space-time fractional Kawahara equation. Moreover, new exact solutions are obtained for a nonlinear ordinary differential equation (dF/dξ)2 = PF4(ξ) + QF2(ξ) + R, which appears as an auxiliary equation

Considering the complex product working circumstances under severe conditions, this paper first specifies the shock processes that a product experiences. The multi-stage description of competing failure processes is accomplished by considering various factors affecting the performance degradation process as well as by introducing the soft failure threshold in order to effectively illustrate the overall

Analytic solutions on twin tunnelling at great depth in viscoelastic geomaterial considering three-dimensional effects of tunnel faces are presented using the complex variable methods. According to the time interval between twin tunnel faces, the proposed solutions can be divided into two cases: A) newly constructing twin tunnels; and B) newly constructing single tunnel influencing an existing one

The present paper aims to incorporate nonlinear amplitude dispersion effects in parabolic and hyperbolic approximation models. First, an explicit and analytical method for considering nonlinearities in parabolic approximation models is investigated. This method follows the concept of calculating spatially and temporally varying wave phase celerities within the simulation. The nonlinear dispersion relation

Atom search optimization is a newly developed metaheuristic algorithm inspired by molecular basis dynamics. The main changes of premature convergence and poor balance between exploration and exploitation still persist, which cannot yet do well in solving some complex optimization problems. To solve the above problems and get better performance, an improved atom search optimization with nonlinear inertia

Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct

Seasonal forcing and contact patterns are two key features of many disease dynamics that generate periodic patterns. Both features have not been ascertained deeply in the previous works. In this work, we develop and analyze a non-autonomous degree-based mean field network model within a Susceptible-Infected-Susceptible (SIS) framework. We assume that the disease transmission rate being periodic to

The present research deals with thermal buckling and postbuckling of sigmoid functionally graded material (S-FGM) plates with porosities resting on elastic foundation based on the popular third-order shear deformation theory and the well-known von Kármán large deflection assumption. Special attention is paid to scrutinize the secondary instability that occurs during postbuckling regime. In addition

In this study, semi-global practical asymptotic stability of a class of nonlinear cascade systems with upper triangular configuration has been investigated. In particular, using general results presented on stabilization of the discrete-time systems, a semi-global practical asymptotic stabilizing controller has been designed and the essential conditions for the semi-global asymptotic stability of this

The efficiency and reliability of the bulb turbine can be influenced by the crack fault of the blade in the actual hydropower engineering. To explore this problem, this work is employed to mainly study the effects of the crack fault on the dynamic characteristics of the blade under different external excitations. Firstly, a displacement function of the cracked blade is innovatively proposed as the

In the present paper a thorough probabilistic methodology is presented, aiming at estimating the reliability of coastal structures, such as rubble mound breakwaters during their lifetime, based on the probabilistic representation of load environmental and resistance parameters. One of the innovative points and main objectives of this study is the estimation of the failure probability of a coastal structure

Soil-water characteristic curve is an essential constitutive relationship required for modelling unsaturated soil behaviour. Earlier supposed to be characteristic or unique for a particular soil, it is now well established that there are various sources of uncertainty which lead to different curves for the same soil. Hence it becomes necessary to probabilistically characterize soil-water characteristic

For tunnels located at shallow depths, the adjacent surcharge loadings caused by new building constructions or overloading on the ground surface significantly influence the stability of the tunnel and lining. This study presents a new rigorous analytical solution for the stress and displacement around lined circular tunnels at a shallow depth, fully considering the interaction between the ground and

In this paper, we consider optimal control problem involving a time-varying state-delay system arising in 1,3-propanediol microbial batch process. The dynamic system in this problem includes unknown time-varying delay function and unknown kinetic parameters. To optimally determine the unknown delay function and unknown kinetic parameters in the system, the weighted least-squares error between the computed

The mathematical model and non-smooth dynamics of a two-segment articulated pipe conveying fluid with the upper segment subjected to a one-sided rigid stop is investigated. To determine the effect of the one-sided rigid stop on the impacting behaviors of the articulated pipe under various geometrical and physical parameters, the nonlinear equations of motion combined with the rigid impacting condition

The fractional reaction-diffusion equation has an important physical and theoretical meaning, but its analytical solution poses considerable problems. This paper develops an efficient numerical process, the local radial basis function generated by the finite difference (named LRBF-FD) method, for finding the approximation solution of the time-fractional fourth-order reaction-diffusion equation in the

Structural model updating (SMU) by sensitivity analysis is a reliable and successful approach to adjusting finite element models of real structures by modal data. However, some challenging issues, including the incompleteness of measured modal parameters, the presence of noise, and the ill-posedness of the inverse problem of SMU may cause inaccurate and unreliable updating results. By deriving a hybrid