Translational Degrees Of Freedom Research Articles

Disentangling the formation, mechanism, and evolvement of the covalent methanesulfonyl fluoride acetylcholinesterase adduct: Insights into an aged-like inactive complex susceptible to reactivation by a combination of nucleophiles.

Chemical warfare nerve agents and pesticides, known as organophosphorus compounds inactivate cholinesterases (ChEs) by phosphorylating the serine hydroxyl group located at the active site of ChEs. Over the course of time, phosphorylation is followed by loss of an organophosphate-leaving group and the bond with ChEs becomes irreversible, a process known as aging. Differently, structurally related irreversible catalytic poisons bearing sulfur instead of phosphorus convert ChEs in its aged form only by covalently binding to the key catalytic serine. Kinetic and crystallographic studies of the interaction between Torpedo californica acetylcholinesterase (TcAChE) and a small organosulfonate, methanesulfonyl fluoride (MSF), indeed revealed irreversibly methylsulfonylated serine 200, to be isosteric with the bound aged sarin/soman analogues. The potent bulky reversible inhibitor 7-bis-tacrine (BTA) adopts, in the active site of the crystal structure of the MSF-enzyme adduct, a location and an orientation that closely resemble the one being found in the crystal structure of the BTA-enzyme complex. Remarkably, the presence of BTA accelerates the rate of methanesulfonylation by a factor of two. This unexpected result can be explained on the basis of two facts: i) the steric hindrance exerted by BTA to MSF in accessing the active site and ii) the acceleration of the MSF-enzyme adduct formation as a consequence of the lowering of the rotational and translational degrees of freedom in the proximity of the catalytic serine. It is well known that pralidoxime (2-Pyridine Aldoxime Methyl chloride, 2-PAM) alone or in the presence of the substrate acetylcholine cannot reactivate the active site serine of the TcAChE-MSF adduct. We show that the simultaneous presence of 2-PAM and the additional neutral oxime, 2-[(hydroxyimino)methyl]-l-methylimidazol (2-HAM), triggers the reactivation process of TcAChE within the hour timescale. Overall, our results pave the way toward the likely use of a cocktail of distinctive oximes as a promising recipe for an effective and fast reactivation of aged cholinesterases.

Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom.

This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ2, where κ = (m/M)1/4 is the usual Born-Oppenheimer parameter. The lowest order term is the usual Born-Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born-Oppenheimer theory. We show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born-Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

Anti-galloping analysis of iced quad bundle conductor based on compound damping cables

Based on the strain displacement relationship of spatial curved beam theory, a nonlinear dynamic equation for a hybrid model of iced bundle conductor galloping analysis with three translational degrees of freedom and one rotational degree of freedom was established. The element independence is numerically studied, and the impact of modal truncation on the galloping response is analyzed to verify the accuracy of the model. In addition, the compound damping cable is applied to transmission lines for the first time to prevent galloping, and a corresponding nonlinear vibration control finite element equation for the iced quad bundle conductor with a compound damping cable structure under wind load is developed. The study also examines the influence of various parameters on galloping amplitude. The results show that the hybrid model accurately predicts the galloping response of transmission lines. The compound damping cable can effectively suppress the galloping of the quad bundle conductor, and the vibration reduction effect reaches more than 85%. Increasing the installation height of the compound damping cable improves its damping effect. At the same installation height, when the horizontal installation position is close to the mid-span of the conductor, the damping effect first increases and then decreases, suggesting an optimal installation position exists. Moreover, properly increasing the stiffness of the primary cable and reducing the stiffness of the return spring can improve the vibration reduction effect of the compound damping cable. Additionally, if the damping coefficient and the mass of the primary cable are properly increased, the vibration reduction effect of the compound damping cable will be better.

Translational eigenstates of He@C60 from four-dimensional abinitio potential energy surfaces interpolated using Gaussian process regression.

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two abinitio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

Compliance Modeling and Kinetostatic Analysis of a Generalized 3-PSS Compliant Parallel Micro-Motion Platform.

In order to expand the range of motion performance of the 3-PSS-compliant parallel micro-motion platform, a variable inclination angle of the mechanism's guide rails was introduced to construct a category of generalized 3-PSS compliant parallel micro-motion platforms with distinct configurations (exhibiting different motion performances) but identical motion patterns (three translational degrees of freedom). The compliance and kinetostatics of such micro-motion platform are modeled and analyzed. Firstly, the compliance model is established based on the coordinate transformation method. Then, simplifying the micro-motion platform into a spring system, the kinetostatic model in terms of input force-output displacement is established based on the compliance model using the compliance matrix method. For practical application considerations, the kinetostatic model in terms of input displacement-output displacement is further derived based on the input force-output displacement model. Then, the correctness of the established compliance model and kinetostatic model is successively verified through finite element simulation. Finally, using two specified motion trajectories (spatial spiral trajectory and planar circular trajectory) as examples, an analysis is conducted on the influence of guide rail inclination angle variations on the kinetostatic performance of the micro-motion platform. This analysis serves as guidance for the rational design of such micro-motion platforms.

Atomic-Scale Time-Resolved Imaging of Krypton Dimers, Chains and Transition to a One-Dimensional Gas.

Single-atom dynamics of noble-gas elements have been investigated using time-resolved transmission electron microscopy (TEM), with direct observation providing for a deeper understanding of chemical bonding, reactivity, and states of matter at the nanoscale. We report on a nanoscale system consisting of endohedral fullerenes encapsulated within single-walled carbon nanotubes ((Kr@C60)@SWCNT), capable of the delivery and release of krypton atoms on-demand, via coalescence of host fullerene cages under the action of the electron beam (in situ) or heat (ex situ). The state and dynamics of Kr atoms were investigated by energy dispersive X-ray spectroscopy (EDS), electron energy loss spectroscopy (EELS), and X-ray photoelectron spectroscopy (XPS). Kr atom positions were measured precisely using aberration-corrected high-resolution TEM (AC-HRTEM), aberration-corrected scanning TEM (AC-STEM), and single-atom spectroscopic imaging (STEM-EELS). The electron beam drove the formation of 2Kr@C120 capsules, in which van der Waals Kr2 and transient covalent [Kr2]+ bonding states were identified. Thermal coalescence led to the formation of longer coalesced nested nanotubes containing more loosely bound Krn chains (n = 3-6). In some instances, delocalization of Kr atomic positions was confirmed by STEM analysis as the transition to a one-dimensional (1D) gas, as Kr atoms were constrained to only one degree of translational freedom within long, well-annealed, nested nanotubes. Such nested nanotube structures were investigated by Raman spectroscopy. This material represents a highly compressed and dimensionally constrained 1D gas stable under ambient conditions. Direct atomic-scale imaging has revealed elusive bonding states and a previously unseen 1D gaseous state of matter of this noble gas element, demonstrating TEM to be a powerful tool in the discovery of chemistry at the single-atom level.

Effect of anisotropic interactions on the heat conduction of one-dimensional chains

One-dimensional (1D) chain models are frequently employed to investigate heat conduction in various systems. Despite their widespread use, there has been limited exploration of 1D chain models with anisotropic interactions. In this study, we examine heat conduction in a 1D chain model with orientation–position coupled interaction, namely the compressible XY model, and compare it with isotropic Fermi-Pasta-Ulam-Tsingou β (FPUT-β) systems. At low temperatures, the local temperatures in the translational and rotational degrees of freedom differ due to the difference in the contact thermal resistance in the two degrees of freedom. The system maintains orientational order, and the orientation–position-coupling effect lowers thermal conductivity in translational degrees of freedom. As the temperature rises above a transition point, the rotation of particles switches from oscillation to diffusion, leading to a solid-like to fluid-like transition in the rotational degree of freedom. The anisotropic interactions become negligible under time averaging, making the system’s properties similar to those of isotropic FPUT-β systems. Additionally, we investigate the system’s orientational structure to elucidate this transition. These findings will enhance our understanding of the dynamics of nanoscale anisotropic systems, such as the heat conduction of spin chains.

Jumping Platonic Solids on a Vibrating Plate

AbstractThe mechanical excitation of solid bodies by a vibrating plate is not only an interesting fundamental problem, but also has relevance in many mechanical systems, for example, in the preparation of granular gases in microgravity. Herein, the energy input by an oscillating plate is numerically investigated as a function of the excitation parameters for selected Platonic solids and their behavior compared to that of a jumping sphere. The most important additional features, not relevant for spheres, are the excitation of body rotations and a permanent energy exchange between the rotational and translational degrees of freedom during the collisions with the plate. The distribution of kinetic energies is analyzed by a numerical simulation of the dynamics, using structures which emulate the mechanical behavior of regular polyhedra.

Local Rotational Jamming and Multi-Stage Hyperuniformities in an Active Spinner System

An active system consisting of many self-spinning dimers is simulated, and a distinct local rotational jamming transition is observed as the density increases. In the low density regime, the system stays in an absorbing state, in which each dimer rotates independently subject to the applied torque; while in the high density regime, a fraction of the dimers become rotationally jammed into local clusters, and the system exhibits microphase-separation like two-phase morphologies. For high enough densities, the system becomes completely jammed in both rotational and translational degrees of freedom. Such a simple system is found to exhibit rich and multiscale disordered hyperuniformities among the above phases: the absorbing state shows a critical hyperuniformity of the strongest class and subcritically preserves the vanishing density fluctuation scaling up to some length scale; the locally jammed state shows a two-phase hyperuniformity conversely beyond some length scale with respect to the phase cluster sizes; the totally jammed state appears to be a monomer crystal, but intrinsically loses large-scale hyperuniformity. These results are inspiring for designing novel phase-separation and disordered hyperuniform systems through dynamical organization.

Design and kinematical performance analysis of a novel reconfigurable parallel mechanism with three remote center-of-motion modes

In view of the demands for variability and safety in surgical procedures, this paper presents a novel reconfigurable parallel mechanism (RPM) capable of performing three remote center-of-motion (RCM) modes: 1R1T, 2R1T, and 3R1T. One of the RCM modes can transform into two distinct configurations from the switch configuration, in which one configuration offers a rotational degree-of-freedom (DOF) and a translational DOF in the YOZ plane, and the other configuration provides identical DOFs in the XOZ plane. A novel device is introduced for switching between the active and passive modes of the revolute joint, which serves as the basis for the RPM reconfiguration process. Utilizing screw theory, the mobility and actuation scheme of the RPM in each configuration are analyzed. Inverse kinematic analysis and Jacobian matrices are then carried out. Subsequently, kinematical performances, such as singularity, workspace, and dexterity, are studied. All results indicate that the proposed RPM has the ability to switch motion modes without requiring reassembly and can effectively meet the diverse demands of surgical procedures based on specific minimally invasive surgery (MIS) requirements.

Design and Analysis of a Reconfigurable Hybrid Robot for Machining of Large Workpieces

Abstract Large workpieces are important components of core equipment in aerospace and other fields, where the machining mainly focuses on the surfaces and inner cavities. However, it may be unsuitable for existing machining robots to directly achieve integrated machining, that is, not only the high-precision surface machining but also the machining of different inner cavities in a limited space. To satisfy these machining requirements, a new reconfigurable hybrid robot (RHR) is proposed, called the 3PRR-3PSS-UPU RHR, for machining the surface and inner cavity of large workpieces (where P, P, R, S, and U stand for the actuated prismatic joint, passive prismatic joint, revolute joint, spherical joint, and universal joint, respectively). The proposed RHR consists of two parallel manipulators (PMs), in which one is a spatial 3PRR PM with one translational degree-of-freedom (DOF) and the other is a 3PSS-UPU reconfigurable PM (RPM) with different configurations of two rotational and one translational (2R1T) DOFs using locking equipment, which is the main advantage of the designed robot. The inverse kinematics and singularities of two PMs are analyzed. The stiffness performance of the spatial 3PRR PM is compared with that of a moving slider with one translational DOF. By evaluating the workspace and motion/force transmissibility, the kinematic performance of two PMs is presented using several local and global indices, followed by the dimensional optimization of link parameters. Based on the structural characteristics and excellent performance, it can be inferred that the 3PRR-3PSS-UPU RHR has great potential for machining large workpieces.

LevCube: A six-degree-of-freedom magnetically levitated nanopositioning stage with centimeter-range XYZ motion

Among various types of precision stages, magnetically levitated precision positioning stages offer unique capabilities including frictionless motion, vacuum compatibility, and contamination-free operation, making them highly attractive for various applications such as photolithography scanners, micro-machining tools, and microscopes. However, today’s magnetically levitated stages often only offer long-stroke motion in the planar directions, and typically have a limited motion range in the vertical axis. This fact limits their applicability in machines and instruments that require precision motion in all translational degrees of freedom (DOFs). Aiming to address this challenge, this paper presents the design, modeling, prototyping, and experimental evaluations for a novel magnetically levitated nanopositioning stage, which we call the LevCube, that can provide nano-precision positioning with a motion stroke of 10 mm in all translational DOFs. The LevCube prototype stage was successfully levitated with a positioning control bandwidth of 100 Hz in the translational DOFs and 70 Hz in the rotational DOFs. The maximum force of the stage is 25.5 N under 3.5 A current amplitude, which generates a maximum stage acceleration of 2.5 times the gravitational acceleration. These performances show the potential of the proposed stage to provide all-axis long-stroke precision positioning capability for future microscopes and manufacturing machines.

On the nature of the Schottky anomaly in endohedral water.

In this work, we study the heat capacity contribution of a rigid water molecule encapsulated in C60 by performing six-dimensional eigenstate calculations with the inclusion of its quantized rotational and translational degrees of freedom. Two confinement model potentials are considered: in the first, confinement is described using distributed pairwise Lennard-Jones interactions, while in the second, the water molecule is trapped within an eccentric but isotropic 3D harmonic effective confinement potential [Wespiser et al., J. Chem. Phys. 156, 074304 (2022)]. Contributions to the heat capacity from both the ortho and para nuclear spin isomers of water are considered to enable the effects of their interconversion to be assessed. By including a symmetry-breaking quadrupolar potential energy term in the Hamiltonian, we can reproduce the experimentally observed Schottky anomaly at ∼2K [Suzuki et al., J. Phys. Chem. Lett. 10, 1306 (2019)]. Furthermore, our calculations predict a second Schottky anomaly at ∼0.1K resulting from the H configuration, a different orientational arrangement of the fullerene cages in crystalline solid C60. Contributions from the H configuration to CV also explain the second peak observed at ∼7K in the experimentally measured heat capacity.

Design of a novel hybrid cable-constrained parallel leg mechanism for biped walking machines

AbstractIn this paper, a novel cable-constrained parallel mechanism is presented as a lightweight, low-cost leg mechanism design for walking machines to be used on flat surfaces. The proposed leg mechanism has three translational degrees of freedom. It is based on two specific hybrid kinematic topologies being herewith proposed. The paper reports the kinematic analysis formulation and a position performance evaluation to confirm the main characteristics of the proposed solutions. A 3D CAD model and simulations are carried out to demonstrate the feasibility of the proposed design for performing a human-like gait trajectory. A prototype has been built, and preliminarily tests have been conducted to confirm the motion capabilities of the proposed mechanism design. Then a second, enhanced prototype has been designed and built. An experimental validation is carried out for tracking a planar walking trajectory with the built prototypes by using a real-time PCI controller. Results are presented to validate the operation characteristics of the proposed mechanism and to prove its feasibility for legged walking machines.

Multi-Objective Design Optimization of Multiple Tuned Mass Dampers for Attenuation of Dynamic Aeroelastic Response of Aerospace Structures

This paper proposes a design procedure to determine the optimal configuration of multi-degrees of freedom (MDOF) multiple tuned mass dampers (MTMD) to mitigate the global dynamic aeroelastic response of aerospace structures. The computation of the aerodynamic excitations is performed considering two models of atmospheric disturbances, namely, the Power Spectral Density (PSD) modelled with the Davenport Spectrum (DS) and the Tuned Discrete Gust (TDG) with the one-minus cosine profile. In order to determine the optimum sets of MTMD, a Multi-objective design Optimization considering Genetic Algorithm (MOGA) is implemented, where the selected fitness functions for the analysis are the minimization of the total mass of the resonators as well as the concurrent minimization of the peak displacements of a specified structural node in all translational degrees of freedom. A case study is presented to demonstrate the proposed methodology, where the optimal sets of MTMD are determined for the concurrent minimization of the pointing error of a truss-like antenna structure as well as the mass of the considered MTMD. It is found that the placement of the MTMD in the primary reflector of the antenna structure provided a maximum reduction in the pointing error of 62.0% and 39.2%, considering the PSD and the TDG models, respectively. Finally, this paper presents an advanced framework to estimate optimal parameters of MTMD control devices under convoluted loading cases as an initial step towards the use of such passive systems in applications that commonly employ active or semi-active solutions.

Microfluidic rotating-target device capable of three-degrees-of-freedom motion for efficient in situ serial synchrotron crystallography.

There is an increasing demand for simple and efficient sample delivery technology to match the rapid development of serial crystallography and its wide application in analyzing the structural dynamics of biological macromolecules. Here, a microfluidic rotating-target device is presented, capable of three-degrees-of-freedom motion, including two rotational degrees of freedom and one translational degree of freedom, for sample delivery. Lysozyme crystals were used as a test model with this device to collect serial synchrotron crystallography data and the device was found to be convenient and useful. This device enables in situ diffraction from crystals in a microfluidic channel without the need for crystal harvesting. The circular motion ensures that the delivery speed can be adjusted over a wide range, showing its good compatibility with different light sources. Moreover, the three-degrees-of-freedom motion guarantees the full utilization of crystals. Hence, sample consumption is greatly reduced, and only 0.1 mg of protein is consumed in collecting a complete dataset.

Impact of Limited Degree of Freedom Drag Coefficients on a Floating Offshore Wind Turbine Simulation

The worldwide effort to design and commission floating offshore wind turbines (FOWT) is motivating the need for reliable numerical models that adequately represent their physical behavior under realistic sea states. However, properly representing the hydrodynamic quadratic damping for FOWT remains uncertain, because of its dependency on the choice of drag coefficients (dimensionless or not). It is hypothesized that the limited degree of freedom (DoF) drag coefficient formulation that uses only translational drag coefficients causes mischaracterization of the rotational DoF drag, leading to underestimation of FOWT global loads, such as tower base fore-aft shear. To address these hydrodynamic modeling uncertainties, different quadratic drag models implemented in the open-source mid-fidelity simulation tool, OpenFAST, were investigated and compared with the experimental data from the Offshore Code Comparison Collaboration, Continued, with Correlation (OC5) project. The tower base fore-aft shear and up-wave mooring line tension were compared under an irregular wave loading condition to demonstrate the effects of the different damping models. Two types of hydrodynamic quadratic drag formulations were considered: (1) member-based dimensionless drag coefficients applied only at the translational DoF (namely limited-DoF drag model) and (2) quadratic drag matrix model (in dimensional form). Based on the results, the former consistently underestimated the 95th percentile peak loads and spectral responses when compared to the OC5 experimental data. In contrast, the drag matrix models reduced errors in estimates of the tower base shear peak load by 7–10% compared to the limited-DoF drag model. The underestimation in the tower base fore-aft shear was thus inferred be related to mischaracterization of the rotational pitch drag and the heave motion/drag by the limited-DoF model.

A novel magnetically levitated tip/tilt motion platform

This paper presents the mechatronic system design and control of a tip/tilt motion platform with a magnetically levitated mover tailored for dynamic rotational scanning operation. It employs a Lorentz force-based actuation system with five degrees of freedom and four spherical Halbach arrays on a fully passive mover. The system includes highly integrated optical proximity sensors for sensing the mover position in all degrees of freedom and a passive magnetic bearing for restraining the non-actuated degree of freedom. The actuation system enables a mechanical angular range of ±1° in both axes, with first structural modes of the 3D printed mover occurring at 1 kHz. A control system is designed for the five actively controlled degrees of freedom for obtaining a robustly stable and precise motion system. The resulting closed-loop system has a bandwidth of 200 Hz in the rotational and 100 Hz in the translational degrees of freedom and a small positioning uncertainty of 0.02% of the full motion range.

The outflow of gas mixture into vacuum, periodically interrupted by bodies moving towards the jet

The problem about the unsteady outflow of a mixture of gases into a vacuum, periodically interrupted by bodies moving toward the jet, was studied. This problem was considered as a possible gas separation technique. The unsteady flow of the gas mixture was simulated using the event-driven molecular dynamics (EDMD) approach under the following conditions: (1) moving boundaries, (2) a wide range of Knudsen number, (3) a wide range of Mach number, (4) violation of equilibrium between rotational and translational degrees of freedom. The problem of periodically interrupted flow was solved as close to reality as possible, taking into account the finite gap between the stator and the moving runner blades. The dependences of the molar fraction and flow rate of the resulting mixture on the system parameters were obtained. As a result, a number of practically important recommendations for the design of such systems have been formulated.

On the contribution of phonons to electrochemical potential of Li-ion metal-organic frameworks

According to Nernst equation, the prediction of equilibrium voltage in electrochemical cells involve the calculation of all contributions of the free energy, corresponding to electronic, vibrational and translational degrees of freedom. Most simulations are restricted to the electronic energy computed in the frame of DFT, mainly because accurate ab-initio investigations of electronic structure usually provides a useful approximation, while the calculations of properties for periodic structures typically involve massive computational resources. In this paper we propose a methodology that allows for the calculation of vibrational contributions to Nernst equation and show that in the case of organic materials (i.e. Li2-Mn-DOBDC electrodes) they represent an important contribution to the total electrode potential that cannot be neglected for the correct understanding of the redox mechanism.