Analytical solution of three-dimensional Navier–Stokes equations for the flow near an infinite rotating disk

In this letter, we will consider variational iteration method (VIM) and Padé approximant, for finding analytical solutions of three-dimensional viscous flow near an infinite rotating disk. The solutions is compared with the numerical (fourth-order Runge–Kutta) solution. The results illustrate that VIM–Padé is an appropriate method in solving the systems of nonlinear equations. It is predicted that VIM–Padé can have wide application in engineering problems (especially for boundary-layer and natural convection problems).     

Neumann-like integrable models

A countable class of integrable dynamical systems, with four-dimensional phase space and conserved quantities in involution (Hn,In)$(H_n,I_n)$ are exhibited. For n=1$n=1$ we recover Neumann system on T^∗S²$T^{\ast }{S}^2$. All these systems are also integrable at the quantum level.     

Nonlinear Mechanical Response of Polymer Matrix Composites: A Review

Abstract

The present article provides a review on the nonlinear mechanical behavior of polymer matrix composites (PMCs). Initially, essential mechanisms driving the nonlinear response of PMCs under different loading conditions are discussed. Rate-dependence, tension-compression asymmetry, viscous behavior, unloading characteristics, interaction between stress components and effects of environmental factors on mechanical properties are briefly reviewed. This is followed by a review of major approaches and constitutive models for predicting stress–strain behavior of PMCs. Following an increasing degree of complexity, models are categorized into four major classes: nonlinear elasticity models, elastic-plastic models, elastic-plastic-viscous models and Damage-Plasticity models. The vast number of existing models is mainly due to the anisotropy and inhomogeneity of PMCs. In brief, this review focuses on informing the reader of major frameworks, rather than addressing all the models in detail.     

Supercontinuum generation with femtosecond optical pulse compression in silicon photonic crystal fibers at 2500 nm

In this paper, femtosecond optical pulses compression and supercontinuum generation in a triangular silicon photonic crystal fiber at 2500 nm are investigated. A region of large minimum anomalous group velocity dispersion, negligible higher order dispersions and unique nonlinearity of silicon are used to demonstrate compression of 100 fs initial input optical pulses to 2.5 fs and ultra-broadband supercontinuum generation with very low input pulse energy over short distances of the fiber.     

Synthesis and characterization of PEGylated iron and graphene oxide magnetic composite for curcumin delivery

Nowadays, nanostructures have been given significant attention in medical and biological fields. Among these nanostructures, graphene oxide (GO) has been widely used in drug delivery systems, because of its unique properties, and the ability to connect to other nanostructures such as magnetic nanoparticles (NPs) as well as polymers by its functional groups. In this research, first, GO was prepared by exfoliating graphite according to the modified Hummer’s method, and then the Fe₃O₄ NPs were synthesized by a simple co-precipitation method on GO nanosheets. In the next step, with the help of the ethyl-3-(3-dimethylaminopropyl) carbodiimide/N-hydroxysuccinimide coupling reagents, the polyethylene glycol (PEG) polymer was bonded to the GO-Fe₃O₄ nanocomposite. Finally, anti-cancer drug, curcumin (Cur) was loaded onto the nanocomposite and the Cur loading ratio was measured at about 8%. The samples were evaluated using Fourier transform-infrared, differential scanning calorimtery, vibrating-sample magnetometry, atomic force microscopy and dynamic light scattering techniques. The results show that the prepared nanocomposite is an appropriate candidate for biomedical applications.     

Modeling and active control of chatter vibrations of piezoelectric stacked machining arm in micro-turning process

Self-excited vibrations known as chatter are considered as the most detrimental issue in micro-turning processes. Occurring unpredictably, they adversely affect the tool life, productivity rate and surface quality of the machining processes. In this paper, a novel machining arm is modeled as a piezoelectric stacked rod which is subjected to a chatter force in the orthogonal micro-turning process. Due to the fact that machining processes are affected by various sources of uncertainties, H_∞ robust control approach is used to suppress the chatter vibrations of the machining arm in the presence of tool wear and dynamic model parameter variations. Also, input control force of the system is provided by exciting the input voltage of piezoelectric layers of the rod. In order to be certain that the designed controller succeeds in suppressing vibrations of the effective structural modes, behavior of the first three modes of vibrations are considered in the final response of the machining arm. In the following, performance of the robust H_∞ controller is compared with a modified PID controller. Simulation results show that the H_∞ controller improves the robustness and performance of the system against uncertainties. The PID controller extends the stability region of the sharp tool and fails to achieve this purpose for the worn tool although its performance is acceptable in suppressing chatter vibrations.

     

A study on spatially extended phase objects using speckle photography

We present an application of an improved speckle photography technique for spatially extended phase objects. A contour mapping of a thin lens displaying its phase variation is presented. A theoretical analysis is investigated followed by the experimental presentation. Reasonable interference fringes are obtained and compared with the fringes obtained for hot air. The phase information of the object is extracted using the point-by-point technique.     

Nonlinear resonant behavior of microbeams over the buckled state

The present study investigates the nonlinear resonant behavior of a microbeam over its buckled (non-trivial) configuration. The system is assumed to be subjected to an axial load along with a distributed transverse harmonic load. The axial load is increased leading the system to lose the stability via a pitchfork bifurcation; the postbuckling configuration is obtained and the nonlinear resonant response of the system over the buckled state is examined. More specifically, the nonlinear equation of motion is obtained employing Hamilton’s principle along with the modified couple stress theory. The continuous system is truncated into a system with finite degrees of freedom; the Galerkin scheme is employed to discretize the nonlinear partial differential equation of motion into a set of ordinary differential equations. This set of equations is solved numerically employing the pseudo-arclength continuation technique; first a nonlinear static analysis is performed upon this set of equations so as to obtain the onset of buckling (supercritical pitchfork bifurcation) and the buckled configuration of the microbeam. The frequency-response and force-response curves of the system are then constructed over the buckled configurations. A comparison is made between the frequency-response curves obtained by means of the modified couple stress and the classical theories. The effect of different system parameters on the frequency-response and force-response curves is also examined.     

Observation of chimera patterns in a network of symmetric chaotic finance systems

The economic and financial systems consist of many nonlinear factors that make them behave as the complex systems. Recently many chaotic finance systems have been proposed to study the complex dynamics of finance as a noticeable problem in economics. In fact, the intricate structure between financial institutions can be obtained by using a network of financial systems. Therefore, in this paper, we consider a ring network of coupled symmetric chaotic finance systems, and investigate its behavior by varying the coupling parameters. The results show that the coupling strength and range have significant effects on the behavior of the coupled systems, and various patterns such as the chimera and multi-chimera states are observed. Furthermore, changing the parameters' values, remarkably influences on the oscillators attractors. When several synchronous clusters are formed, the attractors of the synchronized oscillators are symmetric, but different from the single oscillator attractor.     

Application of elastically supported single-walled carbon nanotubes for sensing arbitrarily attached nano-objects

The potential application of SWCNTs as mass nanosensors is examined for a wide range of boundary conditions. The SWCNT is modeled via nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The added nano-objects are considered as rigid solids, which are attached to the SWCNT. The mass weight and rotary inertial effects of such nanoparticles are appropriately incorporated into the nonlocal equations of motion of each model. The discrete governing equation pertinent to each model is obtained using an effective meshless technique. The key factor in design of a mass nanosensor is to determine the amount of frequency shift due to the added nanoparticles. Through an inclusive parametric study, the roles of slenderness ratio of the SWCNT, small-scale parameter, mass weight, number of the attached nanoparticles, and the boundary conditions of the SWCNT on the frequency shift ratio of the first flexural vibration mode of the SWCNT as a mass sensor are also discussed.