Volume 19, Issue 2 -

Considering the recent aspiration of experts dealing with the painting of aircraft and bonnet of cars to further understand the relevance of skin friction and heat transfer while painting all these objects that are neither horizontal nor vertical, neither a cone/wedge or cylinder but upper horizontal surface of a paraboloid of revolution; a two-dimensional electrically conducting Casson fluid flow on an upper horizontal thermally stratified surface of a paraboloid of revolution is analyzed. The influence of melting heat transfer and thermal stratification are properly accounted for by modifying classical boundary condition of temperature. Plastic dynamic viscosity and thermal conductivity of the fluid are assumed to vary linearly with temperature. In view of this, all necessary models were modified to suit the case Tm<T∞$T_m<T_\infty$. It is assumed that natural convection is driven by buoyancy; hence the suitable model of Boussinesq approximation is adopted. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically by using Runge–Kutta technique along with shooting method. Effects of the magnetic field, temperature-dependent plastic dynamic viscosity and buoyancy parameters on the velocity and temperature are showed graphically and discussed. Normal influence of Lorentz force exists on Casson fluid flow when the thickness of the surface is small. Scientists and experts are urge to note an adverse effect of this force occurs on the fluid flow when the thickness of the surface is large.

Earthquakes have underlined the need for health monitoring and safety assessment of engineering structures in general and especially historical heritage. These structures can be exposed to many different loads such as earthquake and wind that may cause the deterioration and loss of structural integrity. In this study, ambient vibration-based system identification of Zağanos Bastion is carried out for health assessment using linear and nonlinear analyses. 3D finite element analyses of the bastion are performed using relievo drawings and analytical dynamic characteristics are obtained. Ambient vibration tests are conducted on the bastion and experimental dynamic characteristics such as natural frequencies, mode shapes and damping ratios are determined. Enhanced Frequency Domain Decomposition Method in the frequency domain and Stochastic Subspace Identification Method in the time domain are used to extract the experimental dynamic characteristics. Maximum differences are minimized using some uncertain parameters to obtain the updated finite element model. Linear and nonlinear time history analyses are carried out using 1999 Kocaeli earthquake ground motion record to display the maximum displacements, stresses and local damage regions with detail. This study suggests that minor damage at the connection points and exterior surface will sustain under destructive earthquakes.

Sufficient conditions are given for the existence of solutions of anti-periodic value problems for impulsive fractional differential systems involving both Caputo and Riemann–Liouville fractional derivatives. We allow the nonlinearities p(t)f(t,x,y,z,w)$p(t)f(t,x,y,z,w)$ and q(t)g(t,x,y,z,w)$q(t)g(t,x,y,z,w)$ in fractional differential equations to be singular at t=0$t=0$ and t=1$t=1$. Both f$f$ and g$g$ may be super-linear and sub-linear. The analysis relies on some well known fixed point theorems. The initial value problem discussed may be seen as a generalization of some ecological models. An example is given to illustrate the efficiency of the main theorems. Many unsuitable lemmas in recent published papers are pointed out in order not to mislead readers. A conclusion section is given at the end of the paper.

In this article, we present a microcontroller implementation of the synchronization of two Van der Pol oscillators submitted to disturbances of the pulse-like type. Three coupling schemes are used: the classical linear proportional coupling, a power order coupling and an adaptive coupling. After obtaining the coupling coefficients for synchronization through numerical simulation, the microcontroller implementation is carried out using simulation based on Euler algorithm. Agreement is found between both simulation strategies.

We introduce a mesh-free method, i.e., MLS collocation method for the numerical solution of a kind of nonlinear fractional Fredholm integro-differential equation. An error bound is provided for the proposed method which supports its convergence. Detailed numerical experiments approve its excellency in attaining the desired accuracy for a quite low computational cost. We have also compared linear basis with quadratic basis in terms of CPU time.

When mathematically calculating the radiant heat flux during combustion, the radiant property of a gaseous mixture can be approximated as a weighted sum of the radiant properties of fictitious gases to give an equivalent effect of the actual gas mixture. This concept has been in use for many years. However, it was initially tailored to product gases in air-combustion environment. With the advent and progress in nitrogen-free combustion (particularly for environmental purposes), the chemical composition of the combustion gases is highly altered and existing models should be assessed for their suitability in these new environments. We carried out this task, which was motivated by our recent modeling work that revealed that a new model should be developed for nitrogen-free combustion environments. The model proposed here has four participating gases plus one transparent gas and its performance in predicting radiant heat transfer in 3D benchmark problems is evaluated in comparison with existing models, using the discrete-ordinate method for directional radiation domain combined with the finite-volume method of the spatial domain.

This article presents several sufficient conditions for the existence of at least one weak solution and infinitely many weak solutions for the following Neumann problem, originated from a capillary phenomena, {−div((1+|∇u|p(x)1+|∇u|2p(x))|∇u|p(x)−2∇u)+α(x)|u|p(x)−2u=λf(x,u)inΩ,∂u∂ν=0on∂Ω$$\begin{equation*} \left\{\begin{array}{ll} -{\rm div}\bigg(\bigg(1+\frac{|\nabla u|^{p(x)}}{\sqrt{1+|\nabla u|^{2p(x)}}}\bigg) |\nabla u|^{p(x)-2}\nabla u\bigg)+\alpha(x)|u|^{p(x)-2}u\\=\lambda f(x,u) \mbox{in}\,\,\Omega,\\ \frac{\partial u}{\partial \nu}=0\mbox{on}\,\,\partial \Omega \end{array}\right. \end{equation*}$$ where Ω⊂RN$\Omega \subset \mathbb{R}^N$(N≥2)$(N\geq 2)$ is a bounded domain with boundary of class C1,$C^1,$ν$\nu$ is the outer unit normal to ∂Ω,$\partial \Omega,$λ>0$\lambda>0$, α∈L∞(Ω),$\alpha\in L^{\infty}(\Omega),$f:Ω×R→R$f:\Omega\times\mathbb{R}\to\mathbb{R}$ is an L1$L^1$-Carathéodory function and p∈C0(Ω‾)$p\in C^0(\overline{\Omega})$. Our technical approach is based on variational methods and we use a more precise version of Ricceri’s Variational Principle due to Bonanno and Molica Bisci. Some recent results are extended and improved. Some examples are presented to illustrate the application of our main results.

In this paper, we investigate the synchronization problem of impulsive fractional-order neural networks with both time-varying and distributed delays. By using the fractional Lyapunov method and Mittag–Leffler function, some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks and one illustrative example is given to demonstrate the effectiveness of the obtained results.

In this paper, we deal with the existence of multiple nontrivial solutions for the following fractional p$p$-Laplacian Kirchhoff problems (∬R2N|u(x)−u(y)|p|x−y|N+psdxdy)θ−1(−Δ)psu=λ|u|θp−2u+|u|ps∗−2uin  Ω,u=0in  RN∖Ω,$$ \displaystyle\left\{ \begin{array}{ll} &\Bigr( \displaystyle\iint_{{\mathbb R}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N +ps}}\mathrm{d}x\mathrm{d}y\Bigr)^{\theta-1}(-\Delta)^s_p u = \lambda |u|^{\theta p-2}u \vspace{.2cm}\\ &\quad+ |u|^{p_s^*-2}u \hfill \hbox{in}\ \ \Omega , \vspace{.2cm}\\ &u = 0 \hfill \qquad\qquad\quad\hbox{in}\ \ {\mathbb R}^N\setminus\Omega, \end{array} \right. $$ where parameter λ>0$\lambda>0$ belongs to some left neighbourhood of the eigenvalue of the nonlocal operator (∬R2N|u(x)−u(y)|p|x−y|N+psdxdy)θ−1(−Δ)ps.$(\iint_{{\mathbb R}^{2N}}\frac{|u(x)-u(y)|^{p}}{|x-y|^{N +ps}}\mathrm{d}x\mathrm{d}y)^{\theta-1}(-\Delta)^s_p.$ The main feature and difficulty of our problems is the fact that the problem is degenerate.

We introduce a generalized version of the front tracking algorithm for the full ultra-relativistic Euler system. The construction and analysis of this algorithm are somewhat simpler than other algorithms. Moreover, this scheme leads to a more robust and efficient result. The scheme also satisfies positivity. This scheme is compared with other two schemes by two numerical test cases. Furthermore we give another application of this scheme, namely we check the explicit formula of interaction of two generalized shocks, by further numerical test case.