Homogenization of Richardsʼ equation of van Genuchten–Mualem model

This paper is devoted to the homogenization of Richards? equation of van Genuchten–Mualem model, which is a nonlinear degenerate parabolic differential equation. It is usually used to model the motion of saturated–unsaturated water flow in porous media. We firstly apply the Kirchhoff transformation to the equation and obtain a simpler equivalent equation with a linear oscillated diffusion term. Then under the real assumption for van Genuchten–Mualem model, we obtain the homogenized equation based on the two-scale convergence theory. Some results on the first order corrector are also presented.     

Analytical analysis of buckling and post-buckling of fluid conveying multi-walled carbon nanotubes

In this work, buckling and post-buckling analysis of fluid conveying multi-walled carbon nanotubes are investigated analytically. The nonlinear governing equations of motion and boundary conditions are derived based on Eringen nonlocal elasticity theory. The nanotube is modeled based on Euler–Bernoulli and Timoshenko beam theories. The Von Karman strain–displacement equation is used to model the structural nonlinearities. Furthermore, the Van der Waals interaction between adjacent layers is taken into account. An analytical approach is employed to determine the critical (buckling) fluid flow velocities and post-buckling deflection. The effects of the small-scale parameter, Van der Waals force, ends support, shear deformation and aspect ratio are carefully examined on the critical fluid velocities and post-buckling behavior.     

Synchronization of self-sustained oscillators inertially coupled through common damped system

We study the dynamics of two self-oscillating systems inertially coupled to a linear oscillator. This interaction mechanism results in various types of synchronous motions such as in-phase, anti-phase and phase synchronization. We demonstrate the existence of mono-stable regimes and multi-stable behavior with two or more coexisting attractors. We present the bifurcational analysis revealing transition mechanisms between these regimes. In the multi-stable case, we examine the role of coupling parameter and shape of oscillations (the parameter indicating nonlinearity and strength of the damping) in various structure formations of attraction basins.     

Axisymmetric vibration of single-walled carbon nanotubes in water

A double shell-Stokes flow model is developed to study the axisymmetric vibration of single-walled carbon nanotubes (SWCNTs) immerged in water. In contrast to macroscopic solid-liquid system, a submerged SWCNT is coupled with surrounding water via the van der Waals interaction. It is shown that this unique feature substantially reduces viscous damping of the axisymmetric radial, longitudinal and torsional vibrations and significantly up-shifts the frequency of the radial vibration of an SWCNT. The study offers a theoretical explanation for the experimental observation and molecular dynamics simulations available in particular cases, and provides an efficient modelling tool and useful guidance for the study of the general dynamic behaviour of SWCNTs in a fluid.     

Discontinuous synchrony in an array of Van der Pol oscillators

We show the phenomenon of complete synchronization in an network of coupled oscillators. We confirm that non-diagonal coupling can lead to the appearance or disappearance of synchronous windows (ragged synchronizability phenomenon) in the coupling parameter space. We also show the appearance of clusters (synchronization in one or more group) between coupled systems. Our numerical studies are confirmed by an electronic experiment.     

Structural joining method for the solution of the model Lighthill equation with a regular singular point

Using the structural joining method, we construct a uniformly valid explicit asymptotics of the solution of a perturbed model Lighthill equation with a regular singular point.     

LIMIT CYCLES OF CUBIC VAN DER POL EQUATION WITH ONE FINITE CRITICALPOINT

ItiswellknownthatavarietyofsignificantpracticalproblemsleadtoVanderPciequation'Equation(l)canalsobewritteninitsequivalentformItisacubicdifferentialsystemiff(x,y)y h(x)isacubicpolynomial,correspondingly,equation(1)issaidtobecubicVanderPciequation.Inthispap…     

A theoretical study of the dihydrogen molecule confined inside carbon nanotubes

The aim of this work is to better understand the interaction between the confined dihydrogen molecule and armchair (2,2), (3,3) (4,4), (5,5), and (6,6) single‐walled carbon nanotubes (SWNT) using Restricted Hartree–Fock (RHF) and Density Functional Theory (DFT) methods using B3LYP and CAM‐B3LYP functionals. Depending on the calculation method and its orientation inside the nanotube, H₂ binds differently. We found that H? H bond length increases when H₂ is trapped in CNT (2,2) and decreases for CNT (3,3) and (4,4). The characteristics of confined H₂ in (5,5) and (6,6) nanotubes are similar to H₂ in a free state. © 2013 Wiley Periodicals, Inc.