Journal of Engineering Mathematics最新文献

The Internet of Things (IoT), which has had a revolutionary influence on human existence, has become a topic of significant attention among the scientific and industrial communities. Smart healthcare, smart cities, smart devices, smart industry, smart grid, and smart cities are just a handful of the many IoT ideas that have altered human life due to the rapid progress of this IoT technology. Security issues involving IoT devices have come up as a significant issue in recent years with special emphasis on the healthcare sector. This increased emphasis is mostly due to the exposure of serious vulnerabilities in IoT security with recent hacking activities. There is significant proof that conventional methods of protecting networks are effective. Still, the use of conventional security protocols for protection of IoT gadgets and networks from hacking is not feasible due to the constrained resources associated with IoT devices and the distinct characteristics observed in IoT protocols. To improve the privacy of the IoT, researchers will need a unique collection of resources, techniques, and datasets in IoT field. To address the earlier described issues, CatBoost is an innovative ensemble approach that combines many tree techniques and optimizes for performance. This model aims to accurately and automatically detect instances of assaults and anomalies in IoT sensors within the healthcare domain. For the successful creation of a security-based model, the hyperparameters are tuned with self-adaptive memetic firefly algorithm (SAMFA) optimization. The primary advantages of this study include (i) The development of an improved ensemble learning CatBoost model-based security system for IoT healthcare network intrusion detection, (ii) the SAMFA optimization method has been implemented for determining the ideal set of hyperparameters for the CatBoost algorithm, and (iii) Assessing the model's performance with a novel dataset of real-life observations (IoT Healthcare Security Dataset). The suggested model outperforms several previous state-of-the-art techniques, with experimental findings indicating outstanding anomaly identification accuracy of 99.99%.

The objective of this work is to present a numerical solution to a system of higher fractional-order differential equations with initial value problems. In order to achieve this objective, we develop a novel theoretical result aimed to reduce these higher fractional-order systems to (alpha )-fractional systems, where (0<alpha le 1), and then apply a recent numerical approach called modified fractional Euler method, which is regarded a numerical modification of the fractional Euler Method (FEM). Finally, we will give numerical applications to illustrate our results using MATLAB procedures.

In this paper we present numerical solutions for thermal boundary layers that are developed during forced convection in a porous medium located above a flat plate. The basic feature of such layers is that they are nonsimilar. In our study we consider thermal nonequilibrium between the two phases. Accordingly, each phase is endowed with its own energy equation. The boundary-layer equations are solved with the local nonsimilarity method. We examine convection of air and liquid water, while the solid matrix is supposed to be made of cast iron. According to our computations, there are significant differences between the temperature distributions of the two phases, especially at short and moderate distances from the edge of the flat plate. Also, due to the high conductivity of the solid matrix, the thermal boundary layers are much thicker than the hydrodynamic one. The profile of the local Nusselt number is quite sensitive on the Prandtl number and only far downstream it scales with the square root of the distance. Finally, the validity of the local thermal equilibrium assumption is assessed via a comparative study. According to it, this assumption leads to significant inaccuracies in the temperature profiles but yields reasonable estimates for the thickness of the thermal boundary layer of the fluid.

The equilibrium of a structure is characterized by either Euler’s equations completed with boundary and some internal conditions, or by variational equations of a stationary point of the total potential energy defined in a set of admissible functions. Generally this set is defined as a reciprocal image of a constraint function defined between two Banach spaces E and F; and has a manifold structure. Test functions of the variational formulation belong to the Banach tangent space of this set at the stationary point. Though variational equations are suitable for numerical methods through finite elements, the restriction of test functions only in the tangent space is source of some difficulties during numerical implementation. Lagrange multipliers, when they exist, offer the best way to bypass these obstacles. In this paper we present some conditions that guarantee the existence of Lagrange multipliers and establish the links between the new variational equations obtained and the initial variational formulation. We show how it has been applied in incompressible fluid or incompressible elastic solid mechanics. The Lagrange multipliers appear as the hydrostatic pressure which modifies their constitutive laws. We also show the efficiency of the Lagrange multipliers in the limit analyses of problems encountered in the homogenization process and particularly on junction of multistructures. In recent works on junction of elastic multi-dimensional structures, the limit final coupled equations are obtained studiously after some complex calculations. The Lagrange multiplier approach on junction of multistructures herein, which is the main result of this paper, substantially simplifies the analysis, without using any ad-hoc assumption as in previous work and paves the way to treat nonlinear junction equations.

Gas flow through layers of porous materials plays a crucial role in technical applications, geology, petrochemistry, and space sciences (e.g., fuel cells, catalysis, shale gas production, and outgassing of volatiles from comets). In many applications the Knudsen regime is predominant, where the pore size is small compared to the mean free path between intermolecular collisions. In this context common parameters to describe the gas percolation through layers of porous media are the probability of gas molecule transmission and the Knudsen diffusion coefficient of the medium. We show how probabilistic considerations on layer partitions lead to the analytical description of the permeability of a porous medium to gas flow as a function of layer thickness. The derivations are made on the preconditions that the molecule reflection at pore surfaces is diffuse and that the pore structure is homogenous on a scale much larger than the pore size. By applying a bi-hemispherical Maxwell distribution, relations between the layer transmission probability, the half-transmission thickness, and the Knudsen diffusion coefficient are obtained. For packings of spheres, expressions of these parameters in terms of porosity and grain size are derived and compared with former standard models. A verification of the derived equations is given by means of numerical simulations, also providing evidence that our analytical model for sphere packing is more accurate than the former classical models.

The linear stability of plane Couette flow subject to one rigid boundary and one flexible boundary is considered at both finite and asymptotically large Reynolds number. The wall flexibility is modelled using a very simple Hooke-type law involving a spring constant K and is incorporated into a boundary condition on the appropriate Orr–Sommerfeld eigenvalue problem. This problem is analyzed at large Reynolds number by the method of matched asymptotic expansions and eigenrelations are derived that demonstrate the existence of neutral modes at finite spring stiffness, propagating with speeds close to that of the rigid wall and possessing wavelengths comparable to the channel width. A large critical value of K is identified at which a new short wavelength asymptotic structure comes into play that describes the entirety of the linear neutral curve. The asymptotic theories compare well with finite Reynolds number Orr–Sommerfeld calculations and demonstrate that only the tiniest amount of wall flexibility is required to destabilize the flow, with the linear neutral curve for the instability emerging as a bifurcation from infinity.

In this article, a mathematical model describing the unsteady adiabatic flow of spherical shock waves in a self-gravitating, non-ideal radiating gas under the influence of an azimuthal magnetic field is formulated and similarity solutions are obtained. The ambient medium is assumed to be at rest with uniform density. The effect of thermal radiation under an optically thin limit is included in the energy equation of the governing system. By applying the Lie invariance method, the system of PDEs governing the flow in the said medium is transformed into a system of non-linear ODEs via similarity variables. All the four possible cases of similarity solution are obtained by selecting different values for the arbitrary constants involved in the generators. Among these four cases, only two possess similarity solutions, one by assuming the power-law shock path and other by exponential-law shock path. The set of non-linear ODEs obtained in the case of the power-law shock path is solved numerically using the Runge–Kutta method of 4th order in the MATLAB software. The effects of variation of various parameters such as non-ideal parameter ((overline{b })), adiabatic index of the gas ((gamma )), Alfven-Mach number (({M}_{a}^{-2})), ambient magnetic field variation index ((phi )), and gravitational parameter (({G}_{0})) on the flow quantities are discussed in detail and various results are portrayed in the figures. Furthermore, the article includes a detailed comparison made between the solutions obtained for cases with and without gravitational effects in the presence of magnetic field.

Inspired by recent research interest in metasurfaces, an effective medium model is presented to study anti-plane (Love) surface waves of an elastic half-space coated with an elastic metasurface thin layer filled with coated or uncoated hard spheres. Explicit formulas are derived for phase velocity and attenuation coefficient, and the general implications of the derived results are discussed with specific examples without or with damping effect on local resonance of embedded hard spheres. Emphasis is placed on the effects of the metasurface and damping on the structure of bandgap for Love waves, with detailed comparison to the known results on Love waves of an elastic half-space coated with a thin elastic layer or elastic plate. The derived results and conclusions may offer new insights into the study of surface elastic waves in locally resonant metacomposites.

In the dynamics of linear structures, the impulse response function is of fundamental interest. In some cases one examines the short term response wherein the disturbance is still local and the boundaries have not yet come into play, and for such short-time analysis the geometrical extent of the structure may be taken as unbounded. Here we examine the response of slender beams to angular impulses. The Euler–Bernoulli model, which does not include rotary inertia of cross sections, predicts an unphysical and unbounded initial rotation at the point of application. A finite length Euler–Bernoulli beam, when modeled using finite elements, predicts a mesh-dependent response that shows fast large-amplitude oscillations setting in very quickly. The simplest introduction of rotary inertia yields the Rayleigh beam model, which has more reasonable behavior including a finite wave speed at all frequencies. If a Rayleigh beam is given an impulsive moment at a location away from its boundaries, then the predicted behavior has an instantaneous finite jump in local slope or rotation, followed by smooth evolution of the slope for a finite time interval until reflections arrive from the boundary, causing subsequent slope discontinuities in time. We present a detailed study of the angular impulse response of a simply supported Rayleigh beam, starting with dimensional analysis, followed by modal expansion including all natural frequencies, culminating with an asymptotic formula for the short-time response. The asymptotic formula is obtained by breaking the series solution into two parts to be treated independently term by term, and leads to a polynomial in time. The polynomial matches the response from refined finite element (FE) simulations.

This article presents a study on surface gravity wave scattering by a rectangular (box-type) breakwater with thin side plates in the situation of oblique incident waves in deep water. Applying the continuity of fluid pressure and velocity to Havelock’s expansion of velocity potentials, the problem is converted to an integral equation of the Fredholm type, whose solution is the horizontal component of fluid velocity. The integral equation is solved by employing Galerkin’s approximation with polynomials as basis functions multiplied by suitable weight functions. The wave reflection and transmission coefficients are calculated numerically to find the breakwater’s performance on wave scattering. The accuracy of the results is verified through numerical convergence and checking of the energy balance equation. The rectangular breakwater reflects long waves to some extent in water of infinite depth, in contrast to a thin breakwater. The thin plates attached to the rectangular breakwater show a reduction in wave transmission. Furthermore, the attachment of thin plates leads to an increment in horizontal force and a reduction in vertical force.