By Hashem Rafii-Tabar

Carbon nanotubes are the material of nanotechnology. research into their houses has develop into the most energetic fields of contemporary examine. This publication provides the most important computational modelling and numerical simulation instruments to enquire carbon nanotube features. specifically, tools utilized to geometry and bonding, mechanical, thermal, shipping and garage houses are addressed. the 1st part describes vintage statistical and quantum mechanical simulation options, (including molecular dynamics, Monte Carlo simulations and ab initio molecular dynamics), atomistic concept and continuum dependent tools. the second one part discusses the applying of those numerical simulation instruments to rising fields akin to nanofluidics and nanomechanics. With chosen experimental effects to assist make clear theoretical innovations, this can be a self-contained e-book that might be of curiosity to researchers in a wide variety of disciplines, together with nanotechnology, engineering, fabrics technological know-how and physics.

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**Extra info for Computational Physics of Carbon Nanotubes**

**Example text**

The postulate underlying this equality of the time-average and ensemble average is referred to as the ergodic postulate. According to this postulate, the -point of a system visits and spends equal time at all the points of its phase space before returning to the original point. To discuss the concept of an ensemble average, consider an ensemble with a large number N of members, all in different dynamical microstates. Each member follows an independent history and does not interact with others. In the course of time, the -points representing these members move along their own trajectories, and the overall motion of these points resembles the movement of a cloud of particles.

The x1 and x2 axes are respectively parallel to the zigzag and armchair directions, the primitive vectors of the unit cell are given by √ 3 1 eˆ 1 + eˆ 2 , a1 = a 2 2 √ 3 −1 eˆ 1 + eˆ 2 . 1 is given by √ 2 3a . 17) where (n, m) are a pair of integers that characterise the chiral vector, and are referred to as the chiral indices. 17) as 1 L = |Ch | = a(n2 + m2 + nm) 2 . 17), cos θ = from which it follows that sin θ = 2n + m 1 , 1 , 2(n2 + m2 + nm) 2 √ 3m 2(n2 + m2 + nm) 2 √ 3m tan θ = . e. the lattice point A, coincides with the origin O leads to the formation of an (n, m) nanotube whose circumference is the length of the chiral vector, and whose diameter dt is therefore 1 a(n2 + m2 + nm) 2 L .

P3N ; t), or F( ; t), called the time-dependent phase space probability density, or distribution function, is introduced so that F( ; t)d represents the fraction of N -points at a time t within the elemental volume d , constructed around the phase point , where d ≡ dq1 . . dq3N dp1 . . dp3N . 12) is ρ( ; t) = N F( ; t). 13) The function F( ; t), being the probability density, is normalised: ... F( ; t)d = 1. Employing F( ; t), the classical ensemble average S ( ) variable S is deﬁned as S( ) ens = ...