Prediction of frequency band gaps in one-dimensional endohedral fullerene and carbon nano-onion chains.

CONTEXT: Acoustics have always played a central role in contemporary engineering, especially in the fields of communication, sensing, and even in more extraordinary applications such as non-invasive high-intensity focused ultrasound surgery. The rapid development of nano-scale-based technologies makes imperative the need for novel acoustic devices that take advantage of nanomaterials as well as their extraordinary physical properties. The successful design of such acoustic components requires the implementation of efficient nanostructures accompanied by fast and accurate modeling. Here, endohedral fullerene and carbon nano-onion one-dimensional nano-chains are explored as possible candidate nanodevices that generate unique frequency band gaps. METHODS: The wave propagation in chains of fullerene-based molecules is predicted by representing them as infinite one-dimensional mass-in-mass chains properly assembled by the use of springs whose coefficients are expressed according to the van der Walls (vdW) atomistic interactions. Based on Bloch's theorem, interesting elastic wave dispersion curves are obtained and illustrated, characterized by distinctive frequency ranges that waves cannot propagate, revealing the unique vibroacoustic behavior of the proposed nano-systems.

Tracking ankle joint movements during gait cycle via control of functional electrical stimulation.

Functional electrical stimulation (FES) is an effective method to induce muscle contraction and to improve movements in individuals with injured central nervous system. In order to develop the FES systems for an individual with gait impairment, an appropriate control strategy must be designed to accurate tracking performance. The goal of this study is to present a method for designing proportional-derivative (PD) and sliding mode controllers (SMC) for the FES applied to the musculoskeletal model of an ankle joint to track the desired movements obtained by experiments on two healthy individuals during the gait cycle. Simulation results of the developed controller on musculoskeletal model of the ankle joint illustrated that the SMC is able to track the desired movements more accurately than the PD controller and prevents oscillating patterns around the experimentally measured data. Therefore, the sliding mode as the nonlinear method is more robust in face to unmodeled dynamics and model errors and track the desired path smoothly. Also, the required control effort is smoother in SMC with respect to the PD controller because of the nonlinearity.

Torsional Characteristics of Carbon Nanotubes: Micropolar Elasticity Models and Molecular Dynamics Simulation.

Efficient application of carbon nanotubes (CNTs) in nano-devices and nano-materials requires comprehensive understanding of their mechanical properties. As observations suggest size dependent behaviour, non-classical theories preserving the memory of body's internal structure via additional material parameters offer great potential when a continuum modelling is to be preferred. In the present study, micropolar theory of elasticity is adopted due to its peculiar character allowing for incorporation of scale effects through additional kinematic descriptors and work-conjugated stress measures. An optimisation approach is presented to provide unified material parameters for two specific class of single-walled carbon nanotubes (e.g., armchair and zigzag) by minimizing the difference between the apparent shear modulus obtained from molecular dynamics (MD) simulation and micropolar beam model considering both solid and tubular cross-sections. The results clearly reveal that micropolar theory is more suitable compared to internally constraint couple stress theory, due to the essentiality of having skew-symmetric stress and strain measures, as well as to the classical local theory (Cauchy of Grade 1), which cannot accounts for scale effects. To the best of authors' knowledge, this is the first time that unified material parameters of CNTs are derived through a combined MD-micropolar continuum theory.

Computational modeling of the effective Young's modulus values of fullerene molecules: a combined molecular dynamics simulation and continuum shell model.

Estimating the Young's modulus of a structure in the nanometer size range is a difficult task. The reliable determination of this parameter is, however, important in both basic and applied research. In this study, by combining molecular dynamics (MD) simulations and continuum shell theory, we designed a new approach to determining the Young's modulus values of different spherical fullerenes. The results indicate that the Young's modulus values of fullerene molecules decrease nonlinearly with increasing molecule size and understandably tend to the Young's modulus of an ideal flat graphene sheet at large molecular radii. To the best of our knowledge, this is first time that a combined atomistic-continuum method which can predict the Young's modulus values of fullerene molecules with high precision has been reported.

Persistence length of collagen molecules based on nonlocal viscoelastic model.

Persistence length is one of the most interesting properties of a molecular chain, which is used to describe the stiffness of a molecule. The experimentally measured values of the persistence length of the collagen molecule are widely scattered from 14 to 180 nm. Therefore, an alternative approach is highly desirable to predict the persistence length of a molecule and also to explain the experimental results. In this paper, a nonlocal viscoelastic model is developed to obtain the persistence length of the collagen molecules in solvent. A new explicit formula is proposed for the persistence length of the molecule with the consideration of the small-scale effect, viscoelastic properties of the molecule, loading frequency, and viscosity of the solvent. The presented model indicates that there exists a range of molecule lengths in which the persistence length strongly depends on the frequency and spatial mode of applied loads, small-scale effect, and viscoelastic properties of the collagen.

A computational modeling of Raman radial breathing-like mode frequencies of fullerene encapsulated inside single-walled carbon nanotubes.

Raman radial breathing-like mode (RBLM) frequencies of an infinite nanopeapods are calculated within the framework of a continuum-molecular based model. The nanotube-fullerene interaction is modeled via the Lennard-Jones interatomic potential. An analytical formulation is developed and is justified due to its good agreement with the experimental and atomistic-based results. Furthermore, we propose new relationships for the van der Waals (vdW) interaction coefficients between the atoms of this hybrid nanostructure. Numerical results are also obtained for various nanopeapods on the basis of the present formulation. The RBLM frequency upshifts are predicted for small single-walled carbon nanotubes (SWCNTs). The frequency shifts can be adequately explained by the vdW intermolecular interactions acting between the fullerene and the SWCNTs atoms. To the best of our knowledge, a simple theoretical method which can predict the Raman RBLM frequencies of the nanopeapods with high precision has not been provided hitherto. We believe that the present study is likely to fill the gap.

Radial vibration of free anisotropic nanoparticles based on nonlocal continuum mechanics.

Radial vibration of spherical nanoparticles made of materials with anisotropic elasticity is theoretically investigated using nonlocal continuum mechanics. The anisotropic elastic model is reformulated using the nonlocal differential constitutive relations of Eringen. The nonlocal differential equation of radial motion is derived in terms of radial displacement. Cubic, hexagonal, trigonal and tetragonal symmetries of the elasticity are discussed. The suggested model is justified by a good agreement between the results given by the present model and available experimental data. Furthermore, the model is used to elucidate the effect of small scale on the vibration of several nanoparticles. Our results show that the small scale is essential for the radial vibration of the nanoparticles when the nanoparticle radius is smaller than 1.5 nm.

Wave propagation in protein microtubules modeled as orthotropic elastic shells including transverse shear deformations.

Wave propagation along the microtubules is one of the issues of major concern in various microtubule cellular functions. In this study, the general wave propagation behavior in protein microtubules is investigated based on a first-order shear deformation shell theory for orthotropic materials, with particular emphasis on the role of strongly anisotropic elastic properties of microtubules. According to experimental observation, the first-order shear deformation theory is used for the modeling of microtubule walls. A general displacement representation is introduced and a type of coupled polynomial eigenvalue problem is developed. Numerical examples describe the effects of shear deformation and rotary inertia on wave velocities in orthotropic microtubules. Finally, the influences of the microtubule shear modulus, axial external force, effective thickness and material temperature dependency on wave velocities along the microtubule protofilaments, helical pathway and radial directions are elucidated. Most results presented in the present investigation have been absent from the literature for the wave propagation in microtubules.

Prediction of bending stiffness and deformed shape of non-axially compressed microtubule by a semi-analytical approach.

The bending stiffness of a microtubule is one of the most important parameters needed in the analysis of microtubule deformation. In this study, a semi-analytical approach is developed to predict the bending stiffness and deformed shape of a non-axially compressed microtubule in an explicit closed form. By using the solution presented in this paper and the experimentally observed values given in the literature, both the deformed configuration and bending stiffness of a single microtubule are determined. The proposed method is validated by comparing the obtained results with available data in the literature. The comparison shows that the present semi-analytical formulation provides the same accuracy with reduced numerical effort.