ON THE MECHANICS OF ELLIPSOIDAL FULLERENES INSIDE OPEN CARBON NANOCONES: A NOVEL NUMERICAL APPROACH

NANO ◽  
2014 ◽  
Vol 09 (03) ◽  
pp. 1450034 ◽  
Author(s):  
R. ANSARI ◽  
F. SADEGHI ◽  
M. FAGHIH SHOJAEI
Keyword(s):  
Potential Energy ◽  
Fullerene Molecule ◽  
Interaction Force ◽  
Numerical Approach ◽  
Continuum Approximation ◽  
Vertex Angle ◽  
Geometrical Parameters ◽  
Operational Matrices ◽  
Carbon Nanocones ◽  
Open Cnc

In this research, mechanics of concentric ellipsoidal fullerenes inside open carbon nanocones (CNCs) is investigated. To this end, using continuum approximation in conjunction with Lennard-Jones (LJ) potential function, quadruple-integral expressions associated with van der Waals (vdW) potential energy and interaction force are first derived. For determination of these expressions, it is assumed that the fullerene molecule enters the open CNC through the small end or wide end. Thereafter, an efficient approach based on the differential quadrature (DQ) method is proposed to numerically evaluate the obtained quadruple integrals. The proposed method takes advantage of computing multidimensional integrals efficiently with using appropriate number of grid points. By introducing DQ-based operational matrices of differentiation and integration, the quadruple-integral expressions are estimated over their domains. Moreover, new semianalytical expressions are introduced in terms of triple integrals to evaluate vdW interactions. The validity and accuracy of the introduced numerical method are proved by comparing the results obtained through this method with ones achieved via the semianalytical expressions. The ease of implementation and quick answer of the demonstrated numerical solution enable us to comprehensively examine the effects of different geometrical parameters such as small end radius wide end radius and vertex angle of nanocone on the distributions of vdW potential energy and interaction force. The results reveal that the ellipsoidal fullerene undergoes an asymmetrical motion along the axis of open CNC.

Continuum study on the mechanics of ion-based carbon nanocones as gigahertz oscillators

2018 ◽  
Vol 233 (9) ◽  
pp. 3259-3276 ◽  
Author(s):  
F Sadeghi ◽  
R Ansari
Keyword(s):  
Potential Energy ◽  
Functional Groups ◽  
Oscillation Frequency ◽  
Electrostatic Interactions ◽  
Chloride Ion ◽  
Interaction Force ◽  
Separation Distance ◽  
Integration Scheme ◽  
Vertex Angle ◽  
Geometrical Parameters

There is a growing interest in the development of nanomechanical oscillators operating in the gigahertz range and beyond. This paper introduces a novel nano-oscillator based on a chloride ion inside an open carbon nanocone decorated by functional groups at both small and wide ends. Assuming that the carbon atoms and the electric charges of functional groups are evenly distributed over the surface and the two ends of nanocone, respectively, a continuum-based model is presented through which potential energy and interaction force are evaluated analytically. The van der Waals interactions between ion and nanocone are modeled by the 6–12 Lennard–Jones potential, while the electrostatic interactions between ion and two functional groups are modeled by the Coulomb potential. With respect to the proposed formulations, potential energy and interaction force distribution are presented by varying sign and magnitude of functional groups charge and geometrical parameters (size of small and wide ends of nanocone and its vertex angle). Using the fourth-order Runge–Kutta numerical integration scheme, the equation of motion is also solved to arrive at the time histories of separation distance and velocity of ion. An extensive study is performed to investigate the effects of sign and magnitude of functional groups charge, geometrical parameters, and initial conditions (initial separation distance and initial velocity) on the oscillatory behavior of ion-electrically charged open carbon nanocone oscillator. Numerical results demonstrate that the oscillation frequency of chloride ion inside an uncharged nanocone is respectively lower and higher than those generated inside a nanocone whose small end is decorated by positively and negatively charged functional groups. It is further shown that oscillation frequency is highly affected by the sign of electric charges distributed at the small end of nanocone.

Oscillation of C60 Fullerene in Carbon Nanotube Bundles

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
R. Ansari ◽  
F. Sadeghi ◽  
A. Alipour
Keyword(s):  
Carbon Nanotube ◽  
Potential Energy ◽  
Oscillation Frequency ◽  
Initial Conditions ◽  
Van Der Waals ◽  
Oscillatory Behavior ◽  
C60 Fullerene ◽  
Continuum Approximation ◽  
Geometrical Parameters ◽  
Energy Potential

This paper aims to present a thorough investigation into the mechanics of a C60 fullerene oscillating within the center of a carbon nanotube bundle. To model this nanoscale oscillator, a continuum approximation is used along with a classical Lennard–Jones potential function. Accordingly, new semianalytical expressions are given in terms of single integrals to evaluate van der Waals potential energy and interaction force between the two nanostructures. Neglecting the frictional effects and using the actual van der Waals force distribution, the equation of motion is directly solved. Furthermore, a new semianalytical formula is derived from the energy equation to determine the precise oscillation frequency. This new frequency formula has the advantage of incorporating the effects of initial conditions and geometrical parameters. This enables us to conduct a comprehensive study of the effects of significant system parameters on the oscillatory behavior. Based upon this study, the variation of oscillation frequency with geometrical parameters (length of tubes or number of tubes in bundle) and initial energy (potential energy plus kinetic energy) is shown.

On the Oscillation Frequency of Ellipsoidal Fullerene–Carbon Nanotube Oscillators

2012 ◽  
Vol 3 (1) ◽  
Author(s):  
R. Ansari ◽  
F. Sadeghi
Keyword(s):  
Oscillation Frequency ◽  
Carbon Nanostructures ◽  
Initial Conditions ◽  
Interaction Force ◽  
Oscillatory Behavior ◽  
Continuum Approximation ◽  
Geometrical Parameters ◽  
System Variables ◽  
Walled Carbon Nanotubes ◽  
Analytical Expressions

There are many new nanomechanical devices created based on carbon nanostructures among which gigahertz oscillators have generated considerable interest to many researchers. In the present paper, the oscillatory behavior of ellipsoidal fullerenes inside single-walled carbon nanotubes is studied comprehensively. Utilizing the continuum approximation along with Lennard–Jones potential, new semi-analytical expressions are presented to evaluate the potential energy and van der Waals interaction force of such systems. Neglecting the frictional effects, the equation of motion is directly solved on the basis of the actual force distribution between the interacting molecules. In addition, a semi-analytical expression is given to determine the oscillation frequency into which the influence of initial conditions is incorporated. Based on the newly derived expression, a thorough study on the various aspects of operating frequencies under different system variables such as geometrical parameters and initial conditions is conducted. Based on the present study, some new aspects of such nano-oscillators have been disclosed.

Theoretical leakage equations towards liquid-phase flow in the straight-through labyrinth seal

2021 ◽  
pp. 1-44
Author(s):  
Lingsheng Han ◽  
Yongqing Wang ◽  
Kuo Liu ◽  
Ziyou Ban ◽  
Bo Qin ◽  
...  
Keyword(s):  
Liquid Phase ◽  
Numerical Approach ◽  
Labyrinth Seal ◽  
Resistance Coefficient ◽  
Cryogenic Cooling ◽  
Geometrical Parameters ◽  
Phase Flow ◽  
Labyrinth Seals ◽  
Leakage Flow Rate ◽  
Empirical Coefficients

Abstract Labyrinth seals are widely applied in turbomachinery for gas and liquid sealing. A series of labyrinth seal leakage equations so far have been proposed for compressible gas, but few equations for incompressible liquid. Based on the flow conserving governing equations, this paper originally presents semi-empirical analytic equations of the leakage flow rate and tooth-clearance pressure for liquid-phase flow in the straight-through labyrinth seal. The equations indicate that the leakage and pressure are closely related to the inlet pressure, outlet pressure, seal geometrical parameters and four empirical coefficients, whilst no relation to the temperature and compressibility effects compared to the common gas equations. The empirical coefficients include the velocity compensation coefficient, friction coefficient, jet contraction coefficient and resistance coefficient. Particularly, the velocity compensation coefficient is determined through an optimization by the genetic algorithm, while others are referred from previous research. Ultimately, taking the sealing of deeply subcooled liquid nitrogen within the spindle of the cryogenic cooling machine tool as a case, the accuracy of proposed equations is evaluated under various pressure ratios and geometry conditions using the numerical approach, whose numerical model has been validated by the experimental data in the literature. The results show that errors between calculation and simulation are generally within the limit of ±5%, except for the pressure values at the first two teeth. This work provides a theoretical basis for further studies on the liquid leakage equations in other labyrinth seal types.

The lines-of-force landscape of interactions between molecules in crystals; cohesive versus tolerant and `collateral damage' contact

2010 ◽  
Vol 66 (3) ◽  
pp. 396-406 ◽  
Author(s):  
Angelo Gavezzotti
Keyword(s):  
Crystal Structures ◽  
Structure Prediction ◽  
Crystal Packing ◽  
Minimum Energy ◽  
Lattice Energy ◽  
Interaction Force ◽  
Coordination Shell ◽  
Geometrical Parameters ◽  
Interaction Energies ◽  
Organic Salts

A quantitative analysis of relative stabilities in organic crystal structures is possible by means of reliable calculations of interaction energies between pairs of molecules. Such calculations have been performed by the PIXEL method for 1108 non-ionic and 98 ionic organic crystals, yielding total energies and separate Coulombic polarization and dispersive contributions. A classification of molecule–molecule interactions emerges based on pair energy and its first derivative, the interaction force, which is estimated here explicitly along an approximate stretching path. When molecular separation is not at the minimum-energy value, as frequently happens, forces may be attractive or repulsive. This information provides a fine structural fingerprint and may be relevant to the mechanical properties of materials. The calculations show that the first coordination shell includes destabilizing contacts in ∼ 9% of crystal structures for compounds with highly polar chemical groups (e.g. CN, NO2, SO2). Calculations also show many pair contacts with weakly stabilizing (neutral) energies; such fine modulation is presumably what makes crystal structure prediction so difficult. Ionic organic salts or zwitterions, including small peptides, show a Madelung-mode pairing of opposite ions where the total lattice energy is stabilized from sums of strongly repulsive and strongly attractive interactions. No obvious relationships between atom–atom distances and interaction energies emerge, so analyses of crystal packing in terms of geometrical parameters alone should be conducted with due care.

scholarly journals Multi-Dimensional Harmonic Balance With Uncertainties Applied to Rotor Dynamics

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
J. Didier ◽  
J.-J. Sinou ◽  
B. Faverjon
Keyword(s):  
Monte Carlo ◽  
Dynamic Systems ◽  
Harmonic Balance ◽  
Polynomial Chaos ◽  
Harmonic Balance Method ◽  
Numerical Approach ◽  
Rotor Dynamics ◽  
Geometrical Parameters ◽  
Chaos Expansion ◽  
Response Functions

This paper describes the coupling of a Multi-Dimensional Harmonic Balance Method (MHBM) with a Polynomial Chaos Expansion (PCE) to determine the dynamic response of quasi-periodic dynamic systems subjected to multiple excitations and uncertainties. The proposed method will be applied to a rotor system excited at its support. Uncertainties considered include both material and geometrical parameters as well as excitation sources. To demonstrate the effectiveness and validity of the proposed numerical approach, the results that include mean, variation of the response, envelopes of the Frequency Response Functions and orbits will be systematically compared to a classical Monte Carlo approach.

Proton transfer in acetylacetone and its α-halo derivatives

2016 ◽  
Vol 18 (1) ◽  
pp. 344-350 ◽  
Author(s):  
Fatemeh Dolati ◽  
Sayyed Faramarz Tayyari ◽  
Mohammad Vakili ◽  
Yan Alexander Wang
Keyword(s):  
Potential Energy ◽  
Proton Transfer ◽  
Bond Strength ◽  
Electronic Properties ◽  
Energy Function ◽  
Potential Energy Function ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Barrier Heights

A two-dimensional potential energy function has been applied to study the bent intramolecular H-bonds within acetylacetone and its α-halo derivatives. The theoretically predicted proton transfer barrier heights correlate very well with geometrical parameters and electronic properties related to the H-bond strength.

Continuum Modeling of van der Waals Interaction Force Between Carbon Nanocones and Carbon Nanotubes

2011 ◽  
Vol 2 (3) ◽  
Author(s):  
F. Alisafaei ◽  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Van Der Waals ◽  
Interaction Force ◽  
Van Der Waals Interaction ◽  
Continuum Modeling ◽  
Jones Potential ◽  
Carbon Nanocones ◽  
Single Walled Carbon ◽  
Lennard Jones ◽  
Walled Carbon Nanotubes

Using the Lennard–Jones potential, continuum modeling of the van der Waals potential energy and interaction force distributions are investigated for the eccentric and concentric single-walled carbon nanocones inside the single-walled carbon nanotubes. Furthermore, a new semi-analytical solution is presented to evaluate the van der Waals interaction of the nanocone located on the axis of the nanotube. Eccentric and concentric configurations of these nanostructures are also investigated to obtain the preferred position of the nanocone inside the nanotubes. Finally, the optimum radius of a carbon nanotube for which the preferred location of carbon nanocones is along the tube axis is found.

scholarly journals Statistics of work and orthogonality catastrophe in discrete level systems: an application to fullerene molecules and ultra-cold trapped Fermi gases

2015 ◽  
Vol 6 ◽  
pp. 755-766 ◽  
Author(s):  
Antonello Sindona ◽  
Michele Pisarra ◽  
Mario Gravina ◽  
Cristian Vacacela Gomez ◽  
Pierfrancesco Riccardi ◽  
...  
Keyword(s):  
Fullerene Molecule ◽  
Numerical Approach ◽  
Fermi Gases ◽  
Primary Role ◽  
Fundamental Physics ◽  
Work Distribution ◽  
Photoemission Data ◽  
Trapped Fermions ◽  
Work Done ◽  
Photo Ionization

The sudden introduction of a local impurity in a Fermi sea leads to an anomalous disturbance of its quantum state that represents a local quench, leaving the system out of equilibrium and giving rise to the Anderson orthogonality catastrophe. The statistics of the work done describe the energy fluctuations produced by the quench, providing an accurate and detailed insight into the fundamental physics of the process. We present here a numerical approach to the non-equilibrium work distribution, supported by applications to phenomena occurring at very diverse energy ranges. One of them is the valence electron shake-up induced by photo-ionization of a core state in a fullerene molecule. The other is the response of an ultra-cold gas of trapped fermions to an embedded two-level atom excited by a fast pulse. Working at low thermal energies, we detect the primary role played by many-particle states of the perturbed system with one or two excited fermions. We validate our approach through the comparison with some photoemission data on fullerene films and previous analytical calculations on harmonically trapped Fermi gases.

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