This paper investigates the bending vibration of rotating single-walled carbon nanotubes (SWCNTs) based on nonlocal theory. To this end, the rotating SWCNTs system modeled as a beam with a circular cross section and the Euler-Bernoulli beam theory (EBT) is applied with added effects such as rotary inertia, gyroscopic effect and rotor mass unbalance. Using nonlocal theory, two coupled sixth orde...

We study the effective reduction for a nonlocal stochastic partial differential equation with oscillating coefficients. The operator in this is generator of non-Gaussian Levy processes, either integrable or non-integrable jump kernels. examine limiting behavior as scaling parameter tends to zero, and derive reduced (local nonlocal) equation. In particular, work leads an data assimilation system...

We present a theory of orientational order in nematic liquid crystals which interpolates between several distinct approaches based on the director field (Oseen and Frank), order parameter tensor (Landau and de Gennes), and orientation probability density function (Onsager). As in density-functional theories, the suggested free energy is a functional of spatially-dependent orientation distributi...

The low-energy scattering of ortho positronium (Ps) by H, He, Ne, and Ar atoms has been investigated in the coupled-channel framework by using a recently proposed timereversal-symmetric nonlocal electron-exchange model potential with a single parameter C. For H and He we use a three-Ps-state coupled-channel model and for Ar and Ne we use a static-exchange model. The sensitivity of the results i...

We examine saturation properties of a quark-based picture of nuclear matter. Soliton matter consisting of nonlocal confining solitons is used to model nuclear matter. Each composite nucleon is described by a non-topological soliton as given by the Global Color Model. We apply techniques and concepts from the description of crystal lattices. In particular, the Wigner-Seitz approximation is used ...

In this article we analyze the minimization of the so-called nonlocal isoperimetric problem (NLIP) posed on the flat 2-torus. After establishing regularity of the free boundary of minimizers, we show that when the parameter controlling the influence of the nonlocality is small, there is an interval of values for the mass constraint such that the global minimizer is exactly lamellar; that is, th...

We study dynamical ordering of rods. In this process, rod alignment via pairwise interactions competes with diffusive wiggling. Under strong diffusion, the system is disordered, but at weak diffusion, the system is ordered. We present an exact steady-state solution for the nonlinear and nonlocal kinetic theory of this process. We find the Fourier transform as a function of the order parameter, ...

By using the Krasnoselskii’s fixed point theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundary value problem with variable parameter u 4 t B t u′′ t λf t, u t , u′′ t , 0 < t < 1, u 0 u 1 ∫1 0 p s u s ds, u ′′ 0 u′′ 1 ∫1 0 q s u ′′ s ds is considered, where p, q ∈ L1 0, 1 , λ > 0 is a parameter, and B ∈ C 0, 1 , f ∈ C 0, 1 × 0,∞ × −∞, ...

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and b...

In the present study, nonlinear vibration of coupled carbon nanotubes (CNTs) in presence of surface effect is investigated based on nonlocal Euler-Bernoulli beam (EBB) theory. CNTs are embedded in a visco-elastic medium and placed in the uniform longitudinal magnetic field. Using von Kármán geometric nonlinearity and Hamilton’s principle, the nonlinear higher order governing equations are deriv...