A computationally-efficient method for evaluating friction in molecular rotary bearings is presented. This method estimates drag from fluctuations in molecular dynamics simulations via the fluctuation–dissipation theorem. This is effective even for simulation times short compared to a bearing's energy damping time and for rotation speeds comparable to or below typical thermal values. We apply this method to two molecular rotary bearings of similar size at 300 K: previously studied nested (9,9) (14,14) double-walled carbon nanotubes and a hypothetical rotary joint consisting of single acetylenic bonds in a rigid diamondoid housing. The acetylenic joint has a rotational frictional drag coefficient of 2 × 10−35 kg m2 s−1. The friction for the nested nanotubes is 120 times larger, comparable to values reported by previous studies. This fluctuation-based method could evaluate dissipation in a variety of molecular systems with similarly rigid and symmetric bearings.
In @cite_66 , four different MD simulation configurations using the LAMMPS code and AIREBO force field were used to obtain consistent friction estimates for a rotating nested nanotube bearing. Other dissipation estimates for rotating nested nanotube bearings have been determined using intralayer interactions based on the Brenner potential @cite_47 with interlayer interactions based on the Kolmogorov-Crespi registry-dependent potential @cite_3 , and with the COMPASS force field @cite_24 . Dissipation estimates for sliding nested nanotube bearings have been determined using a custom force field and custom numerical simulator in @cite_27 @cite_69 , and a custom force field based on @cite_60 and the r-RESPA integrator in @cite_56 .
@cite_69 @cite_60 @cite_3 @cite_56 @cite_24 @cite_27 @cite_47 @cite_66
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We use a molecular dynamics simulation to investigate the properties and design space of molecular gears fashioned from carbon nanotubes with teeth added via a benzyne reaction known to occur with C60. Brenner's reactive hydrocarbon potential is used to model interatomic forces within each molecular gear. A Lennard-Jones 6-12 potential or the Buckingham (exp +6) potential plus electrostatic interaction terms are used for intermolecular interactions between gears. A number of gear and gear shaft configurations are simulated on parallel computers. One gear is powered by forcing the atoms near the end of the nanotube to rotate, and a second gear is allowed to rotate by keeping the atoms near the end of its nanotube constrained to a cylinder. The meshing aromatic gear teeth transfer angular momentum from the powered gear to the driven gear. Results suggest that these gears can operate at up to 50-100 GHz in a vacuum at room temperature. The failure mode involves tooth slip, not bond breaking, so failed gears can be returned to operation by lowering the temperature and or rotation rate. M This article features multimedia enhancements available from the abstract page in the online journal; see http: www.iop.org. Atomistic simulations of double-walled carbon nanotubes (DWCNTs) as rotational bearings were performed. Molecular mechanics (MM) calculations show that the interlayer energy surface of the bearings is nearly flat. Thermal effects on the bearings were studied with molecular dynamics (MD) simulations at finite temperature. These simulations show that the interlayer corrugation against rotation, and hence the interlayer friction coefficient, is extremely small, suggesting the possible application of DWCNTs as wearless bearings. Extreme operational conditions of the bearings for which the bearings disintegrate are also reported. Abstract Simulation of friction in carbon nanotube (CNT) bearing systems has been a popular topic, yet many questions remain open. For example, quantitative estimates of friction reported to date range by as much as eight orders of magnitude, and simulation techniques employ a variety of disparate simulation paradigms and parameters. This paper presents a new suite of consistently implemented but complementary and independent molecular simulations of rotary CNT bearing systems, which span the approaches reported to date, yet agree quantitatively within the error margin, or about one order of magnitude. A comparison between these new results, existing simulation results, and one experimental friction datum is presented. Furthermore, quantitative relationships between friction and the system operating parameters are determined. Friction is found to vary linearly with rotating speed and system temperature, while system length and mean diameter do not have a strong effect. Finally, based on phonon energy spectrum computations, we show that friction is a broadband phenomenon, which does not depend strongly on a specific vibrational mode, but rather appears to occur from the aggregate interactions of many modes at different frequencies. This work reports an in-depth analysis of the mechanics of CNT friction and shows that it can be simulated using complementary approaches, while still obtaining the same result. The analysis reveals the underlying mechanism causing friction and how the governing parameters affect its behavior. We report on a study of the translational sliding motion and dynamic friction in systems of double-walled carbon nanotubes using molecular dynamics simulations combined with theoretical analysis. The sliding motion is described by a one-dimensional analytical model which includes the van der Waals force between the nanotubes, a dynamic friction force, and a small Langevin-type fluctuating force. The dynamic friction force is shown to be linear in the velocity over a large domain of initial conditions in armchair-armchair, zigzag-armchair, and zigzag-zigzag double-walled nanotubes. Beyond this domain, evidence is obtained for nonlinear effects which increase friction. In armchair-armchair systems, the dynamic friction is observed to be nonlinearly enhanced by the excitation of internal modes. In the linear domain, the coefficient of proportionality between the dynamic friction force and the velocity is shown to be given by Kirkwood's formula in terms of the force autocorrelation function. The mechanical properties of sliding carbon nanotubes have been investigated by classical molecular dynamics simulations in the canonical ensemble. In particular we have studied damped oscillations in the separation between the centres of mass of the inner and outer tubes of double-walled carbon nanotubes (DWCN). Incommensurate DWCNs forming (7, 0)@(9, 9) structures were simulated for systems at 298.15 K with axial lengths from 12.21 to 98.24 nm. The oscillations exhibited frequencies in the range of gigahertz with the frequency decreasing as the length of the system increases. The time until oscillations become negligible exhibited a nearly linear dependence on the length of the system. Two macroscopic models were developed in order to understand the forces involved in terms of macroscopic properties like friction and shear. The first model considered constant restoring forces during the whole event, while in the second the value of these constant restoring forces depended on the initial conditions of each oscillation. Both models reproduced the oscillations quite well, while the second model allows us to predict the dynamic shear strength in terms of the axial length of the system for tubes with the same diameters. The calculated dynamic shear strength exhibited monotonic behaviour with an inverse dependence on the length of the system. For systems with unequal axial lengths, the restoring force, which drives the oscillation, is reduced compared to the system with equal lengths, regardless of whether the outer nanotube is longer or shorter. M This article contains online multimedia enhancements This is the second in a series of papers in which we derive a @math -expansion for the two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In this model, two phases appear, which interact via a nonlocal Coulomb type energy. Here we focus on the sharp interface version of this energy in the regime where one of the phases has very small volume fraction, thus creating small "droplets" of the minority phase in a "sea" of the majority phase. In our previous paper, we computed the @math -limit of the leading order energy, which yields the averaged behavior for almost minimizers, namely that the density of droplets should be uniform. Here we go to the next order and derive a next order @math -limit energy, which is exactly the Coulombian renormalized energy obtained by Sandier and Serfaty as a limiting interaction energy for vortices in the magnetic Ginzburg-Landau model. The derivation is based on the abstract scheme of Sandier-Serfaty that serves to obtain lower bounds for 2-scale energies and express them through some probabilities on patterns via the multiparameter ergodic theorem. Without thus appealing to the Euler-Lagrange equation, we establish for all configurations which have "almost minimal energy" the asymptotic roundness and radius of the droplets, and the fact that they asymptotically shrink to points whose arrangement minimizes the renormalized energy in some averaged sense. Via a kind of @math -equivalence, the obtained results also yield an expansion of the minimal energy for the original Ohta-Kawasaki energy. This leads to expecting to see triangular lattices of droplets as energy minimizers. This paper demonstrates the fabrication, characterization, and experimental imaging results of a 62+62 element λ 2-pitch row-column-addressed capacitive micromachined ultrasonic transducer (CMUT) array with integrated apodization. A new fabrication process was used to manufacture a 26.3 mm by 26.3 mm array using five lithography steps. The array includes an integrated apodization, presented in detail in Part I of this paper, which is designed to reduce the amplitude of the ghost echoes that are otherwise prominent for row-column-addressed arrays. Custom front-end electronics were produced with the capability of transmitting and receiving on all elements, and the option of disabling the integrated apodization. The center frequency and -6-dB fractional bandwidth of the array elements were 2.77 ± 0.26 MHz and 102 ± 10 , respectively. The surface transmit pressure at 2.5 MHz was 590 ± 73 kPa, and the sensitivity was 0.299 ± 0.090 V Pa. The nearest neighbor crosstalk level was -23.9 ± 3.7 dB, while the transmit-to-receive-elements crosstalk level was -40.2 ± 3.5 dB. Imaging of a 0.3-mm-diameter steel wire using synthetic transmit focusing with 62 single-element emissions demonstrated axial and lateral FWHMs of 0.71 mm and 1.79 mm (f-number: 1.4), respectively, compared with simulated axial and lateral FWHMs of 0.69 mm and 1.76 mm. The dominant ghost echo was reduced by 15.8 dB in measurements using the integrated apodization compared with the disabled configuration. The effect was reproduced in simulations, showing a ghost echo reduction of 18.9 dB. Reproducible positioning of the patient during fractionated external beam radiation therapy is imperative to ensure that the delivered dose distribution matches the planned one. In this paper, we expand on a 2D-3D image registration method to verify a patient’s setup in three dimensions (rotations and translations) using orthogonal portal images and megavoltage digitally reconstructedradiographs (MDRRs) derived from CT data. The accuracy of 2D-3D registration was improved by employing additional image preprocessing steps and a parabolic fit to interpolate the parameter space of the cost function utilized for registration. Using a humanoid phantom, precision for registration of three-dimensional translations was found to be better than 0.5 mm (1 s.d.) for any axis when no rotations were present. Three-dimensional rotations about any axis were registered with a precision of better than 0.2 ° (1 s.d.) when no translations were present. Combined rotations and translations of up to 4 ° and 15 mm were registered with 0.4 ° and 0.7 mm accuracy for each axis. The influence of setup translations on registration of rotations and vice versa was also investigated and mostly agrees with a simple geometric model. Additionally, the dependence of registration accuracy on three cost functions, angular spacing between MDRRs, pixel size, and field-of-view, was examined. Best results were achieved by mutual information using 0.5 ° angular spacing and a 10 × 10 cm 2 field-of-view with 140 × 140 pixels . Approximating patient motion as rigid transformation, the registration method is applied to two treatment plans and the patients’ setup errors are determined. Their magnitude was found to be ⩽ 6.1 mm and ⩽ 2.7 ° for any axis in all of the six fractions measured for each treatment plan.