Translation-rotation Coupling Research Articles

Energy-harvesting tile incorporating an origami coupling mechanism.

We present the design and evaluation of a simple, compact and efficient electromagnetic energy harvesting tile that can be used to harness energy from footsteps. The proposed harvester incorporates a translational-rotational origami-inspired coupling mechanism to transform the axial loads exerted by human footsteps into a localized rotation of an electromagnetic generator. The coupling mechanism employs a non-rigid tunable Kresling spring, the restorative behaviour of which is tunable to maximize energy transduction from the applied load to the generator. A computational model is developed to optimize the design parameters of the mechanism, which are then utilized to fabricate a prototype of the energy harvester. The tile is tested under loading conditions that mimic a human step, where it is demonstrated that it is capable of generating 4.18 W of electrical power per step with a surface power density of 2609 μW cm-2.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Boltzmann's H-function for molecules with orientational degrees of freedom: Emergence of unique features.

Boltzmann's H-function H(t), often regarded as an analog of time-dependent entropy, holds a venerable place in the history of science. However, accurate numerical evaluation of H(t) for particles other than atoms is rare. To remove this lacuna, we generalize Boltzmann's H-function to a gas of molecules with orientational degrees of freedom and evaluate H(t) from the time-dependent joint probability distribution function f(p, L, t) for linear (p) and angular (L) momenta, evolving from an initial nonequilibrium state, by molecular dynamics simulations. We consider both prolate- and oblate-shaped particles, interacting via the well-known Gay-Berne potential and obtain the relaxation of the generalized molecular H(t) from initial (t = 0) nonequilibrium states. In the long-time limit, the H function saturates to its exact equilibrium value, which is the sum of translational and rotational contributions to the respective entropies. Both the translational and rotational components of H(t) decay nearly exponentially with time; the rotational component is more sensitive to the molecular shape that enters through the aspect ratio. A remarkable rapid decrease in the rotational relaxation time is observed as the spherical limit is approached, in a way tantalizingly reminiscent of Hu-Zwanzig hydrodynamic prediction with the slip boundary condition. In addition, we obtain H(t) analytically by solving the appropriate translational and rotational Fokker-Planck equation and obtain a modest agreement with simulations. We observe a remarkable signature of translation-rotation coupling as a function of molecular shape, captured through a physically meaningful differential term that quantifies the magnitude of translation-rotation coupling.

Decoupling of rotation and translation at the colloidal glass transition.

In dense particle systems, the coupling of rotation and translation motion becomes intricate. Here, we report the results of confocal fluorescence microscopy where simultaneous recording of translational and rotational particle trajectories from a bidisperse colloidal dispersion is achieved by spiking the samples with rotational probe particles. The latter consist of colloidal particles containing two fluorescently labeled cores suited for tracking the particle's orientation. A comparison of the experimental data with event driven Brownian simulations gives insights into the system's structure and dynamics close to the glass transition and sheds new light onto the translation-rotation coupling. The data show that with increasing volume fractions, translational dynamics slows down drastically, whereas rotational dynamics changes very little. We find convincing agreement between simulation and experiments, even though the simulations neglect far-field hydrodynamic interactions. An additional analysis of the glass transition following mode coupling theory works well for the structural dynamics but indicates a decoupling of the diffusion of the smaller particle species. Shear stress correlations do not decorrelate in the simulated glass states and are not affected by rotational motion.

CO2 inside sI clathrate-like cages: Automated construction of neural network/machine learned guest-host potential and quantum spectra computations.

We present new results on the underlying guest-host interactions and spectral characterization of a CO2 molecule confined in the cages of the sI clathrate hydrate. Such types of porous solids raise computational challenges, as they are of practical interest as gas storage/capture materials. Accordingly, we have directed our efforts toward addressing their modeling in a proper manner, ensuring the quality of the input data and the efficiency of the computational approaches. The computational procedure for spectral simulations, within the multi-configurational time-dependent Hartree framework, involves the development of a fully coupled Hamiltonian, including an exact kinetic energy operator and a many-body representation of the potential, along with dipole moment surfaces, both obtained through neural network machine learning techniques. The resulting models were automatically trained and tested on extensive datasets generated by PW86PBE-XDM calculations, following the outcome of previous benchmark studies. Our simulations enable us to explore various aspects of the quantized dynamics upon confinement of CO2@D/T, such as constrained rotational-translational quantum motions and the averaged position/orientation of the CO2 guest in comparison to the experimental data available. Particularly notable are the distinct energy patterns observed in the computed spectra for the confined CO2 in the D and T cages, with a considerably high rotational-translational coupling in the CO2@T case. Leveraging reliable computations has proved instrumental, highlighting the sensitivity of the spectral features to the shape and strength of the potential interactions, with the explicit description of many-body contributions being significant.

Fault-tolerant control for satellite autonomous rendezvous with quality characteristics and actuator uncertainties

An autonomous fault detection and fault-tolerant control solution combining Model Predictive Control (MPC) and Label Distributed Learning (LDL) is developed for the position tracking and attitude synchronization problems in autonomous satellite rendezvous and docking. The proposed algorithm can deal with center of mass (CM) variations and time-varying mass characteristics due to satellite fuel consumption, actuator saturation and fault, and external disturbances. Firstly, a six-degree-of-freedom (6-DOF) satellite translation-rotation coupling model was established to express the relative motion between the satellite and the target, taking the above factors into account. Subsequently, an on-board autonomous closed-loop fault-tolerant control algorithm using MPC is proposed, in which an LDL-based fault detection mechanism is embedded. The scheme specifies that propulsion faults are estimated by calculating the difference between the MPC's prediction of the satellite's future state and the measured change in the actual state. And the mapping matrix between the commanded force/torque and the actual force of the propulsion system is updated in real time to achieve autonomous fault detection and compensation on board the satellite. Among them, the LDL-based fault detection scheme is trained offline. It requires only simple matrix operations for on-orbit use, which is low-cost and suitable for resource-limited space environments. The additional creation of a time-varying disturbance observer allows the estimation and compensation of unmodelled errors and external disturbances. The stability of the proposed fault-tolerant control algorithm is rigorously demonstrated using Lyapunov analysis. Finally, numerical simulations show that the proposed method can successfully achieve autonomous satellite docking under different combinations of thruster faults.

Ionic Conductivity of a Lithium-Doped Deep Eutectic Solvent: Glass Formation and Rotation-Translation Coupling.

Deep eutectic solvents with admixed lithium salts are considered as electrolytes in electrochemical devices, such as batteries or supercapacitors. Compared to eutectic mixtures of hydrogen-bond donors and lithium salts, their raw-material costs are significantly lower. Not much is known about glassy freezing and rotational-translation coupling of such systems. Here, we investigate these phenomena by applying dielectric spectroscopy to the widely studied deep eutectic solvent glyceline, to which 1 and 5 mol % LiCl were added. Our study covers a wide temperature range, including a deeply supercooled state. The temperature dependences of the detected dipolar reorientation dynamics and ionic direct current (dc) conductivity reveal the signatures of glassy freezing. In comparison to pure glyceline, the lithium admixture leads to a reduction of ionic conductivity, which is accompanied by a reduction of the rotational dipolar mobility. However, this reduction is much smaller than that for deep eutectic solvents (DESs), where one main component is lithium salt, which we trace back to the lower glass-transition temperatures of lithium-doped DESs. In contrast to pure glyceline, the ionic and dipolar dynamics become increasingly decoupled at low temperatures and obey a fractional Debye-Stokes-Einstein relation, as previously found in other glass-forming liquids. The obtained results demonstrate the relevance of decoupling effects and glass transition to the enhancement of the technically relevant ionic conductivity in such lithium-doped DESs.

Curvature induces and enhances transport of spinning colloids through narrow channels.

The effect of curvature and how it induces and enhances the transport of colloidal particles driven through narrow channels represent an unexplored research avenue. Here we combine experiments and simulations to investigate the dynamics of magnetically driven colloidal particles confined through a narrow, circular channel. We use an external precessing magnetic field to induce a net torque and spin the particles at a defined angular velocity. Due to the spinning, the particle propulsion emerges from the different hydrodynamic coupling with the inner and outer walls and strongly depends on the curvature. The experimental findings are combined with finite element numerical simulations that predict a positive rotation translation coupling in the mobility matrix. Further, we explore the collective transport of many particles across the curved geometry, making an experimental realization of a driven single file system. With our finding, we elucidate the effect of curvature on the transport of microscopic particles which could be important to understand the complex, yet rich, dynamics of particle systems driven through curved microfluidic channels.

Understanding dynamics in coarse-grained models. III. Roles of rotational motion and translation-rotation coupling in coarse-grained dynamics.

This paper series aims to establish a complete correspondence between fine-grained (FG) and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I). While Paper II successfully captured translational motions in CG systems using a hard sphere mapping, the absence of rotational motions in single-site CG models introduces differences between FG and CG dynamics. In this third paper, our objective is to faithfully recover atomistic diffusion coefficients from CG dynamics by incorporating rotational dynamics. By extracting FG rotational diffusion, we unravel, for the first time reported to our knowledge, a universality in excess entropy scaling between the rotational and translational diffusion. Once the missing rotational dynamics are integrated into the CG translational dynamics, an effective translation-rotation coupling becomes essential. We propose two different approaches for estimating this coupling parameter: the rough hard sphere theory with acentric factor (temperature-independent) or the rough Lennard-Jones model with CG attractions (temperature-dependent). Altogether, we demonstrate that FG diffusion coefficients can be recovered from CG diffusion coefficients by (1) incorporating "entropy-free" rotational diffusion with translation-rotation coupling and (2) recapturing the missing entropy. Our findings shed light on the fundamental relationship between FG and CG dynamics in molecular fluids.

Description of bandgaps opening in chiral phononic crystals by analogy with Thomson scattering

Chiral phononic crystals (PnCs) provide unique properties not offered by conventional metamaterial based on classic Bragg scattering and local resonance. However, it is insufficient to only consider the inertial amplification effect to describe its bandgap mechanism due to the absence of the bandgap caused by the chirality in some specific chiral structures. Here, we theoretically and experimentally introduce an analogy with Thomson scattering in electromagnetic waves to characterize the bandgap phenomena in chiral PnCs with translation–rotation coupling. Another phononic structures with translation–translation coupling are proposed to illustrate the universality of the analogy. We evidence that the coupling motion in chiral unit cells is similar to the result of Thomson scattering, which quantitatively formulizing as inertial amplification in theory and, twice elastic Thomson scattering allows the waves in the same polarization mode to superpose in antiphase, which is essence of the bandgap formation. This finding sheds a new light on the physics of the elastodynamic wave manipulation in chiral PnCs, thus opening a definite route for the pragmatic exploitation of chiral PnCs as well as other structures with motion coupling in achieving low-frequency and broad bandgaps.

Analysis of the effect of the translational-rotational coupling on the pseudo-diffusion along the molecular axes of meta-cresol: A molecular dynamics analysis

We investigate the dynamical properties (translation and rotation) of the glass-forming liquid meta-cresol by molecular dynamics simulations. This system is investigated at 9 temperatures between 230 K and 400 K, encompassing the liquid and glassy states of meta-cresol. In order to get insight into the coupling between the translational and rotational motions, the centre of mass velocity autocorrelation function is calculated along the principal axes of meta-cresol. We show that the time behaviour of the velocity and angular velocity is connected to the change in the local structure occurring upon the glass transition. Indeed, the long-time negative region in the velocity autocorrelations is associated with a caging effect while the occurrence of a short time negative region in these functions is considered as a signature of hydrogen bonding interactions. By studying, the centre of mass velocity of meta-cresol in the molecular frame, the translation and rotation coupling was directly evidenced. The time evolution of the translational-rotational coupling is evaluated from the difference ΔαRTC(t) between the velocity autocorrelation function calculated with respect to the molecular frame (where α stands for the three axes of the local cartesian frame fixed to the individual molecule, x, y, and z) of the meta-cresol molecule and that of the same function calculated in the frame of the hypothesis that there is no statistical correlation between the translational and rotational motions. The positive regions of ΔαRTC(t) indicate an occurrence of a cooperative effect, which means that the each of the two motions is realized in the favour of the other. Conversely, negative regions indicate that the rotation and translation motions are anti-cooperative. Our results show that a strong coupling between translation and rotation occurs along the × axis that is perpendicular to the ring of meta-cresol molecule, and also along which the hydrogen bond is established.

Translation-rotation coupling and the kinematics of non-slip boundary conditions: A rough sphere between two sliding walls.

A non-slip constraint between a particle and a wall is applied at the microscopic level of collision dynamics using the rough sphere model. We analyze the consequences of the translation-rotation coupling of a rough sphere confined between two parallel planar walls and establish that shearing the walls past each other (i) preferentially deposits energy into the rotational degree of freedom and (ii) results in a bounded oscillation of the energy of the confined particle.

2H NMR studies on the dynamics of supercooled water in a metal-organic framework.

We use 2H nuclear magnetic resonance (NMR) to study water (D2O) reorientation and diffusion in the metal-organic framework MFU-4l, which features a regular three-dimensional network of nearly spherical pores with diameters of 1.2 and 1.9nm. We observe that the rotational correlation times follow Vogel-Fulcher-Tammann and Arrhenius (Ea = 0.48eV) relations above ∼225K and below ∼170K, respectively, whereas the temperature dependence continuously evolves from one to the other behavior in the broad crossover zone in between. In the common temperature range, the present NMR results are fully consistent with previous broadband dielectric spectroscopy (BDS) data on water (H2O) in a very similar framework. Several of our observations, e.g., rotational-translational coupling, indicate that a bulk-like structural (α) relaxation is observed above the crossover region. When cooling through the crossover zone, a quasi-isotropic reorientation mechanism is retained, while 2H spin-lattice relaxation evolves from exponential to nonexponential, implying that the water dynamics probed at low temperatures does no longer fully restore ergodicity on the time scale of this experiment. We discuss that the latter effect may result from bulk-like and/or confinement-imposed spatially heterogeneous water properties. Comparison with previous NMR and BDS results for water in other confinements reveals that, for confinement sizes around 2nm, water reorientation depends more on the pore diameter than on the pore chemistry, while water diffusion is strongly affected by the connectivity and topology of the pores.

Cohesive and Thermal Properties of Sodium Cyanide-Halide Mixed Crystals

In order to analyse the cohesive and thermal properties of sodium cyanide-halide mixed crystals an Extended Three Body Force Shell Model (ETSM) has been applied by incorporating the effect of translational-rotational (TR) coupling. We have conducted theoretical research on cohesive and thermal properties, such as cohesive energy (, molecular force constant (f), compressibility (), Restrahlen frequency (, Debye temperature (D), Gruneisen parameter (), Moelwyn Hughes constants (F1) and the ratio of volume thermal expansion coefficient (v) to volume specific heat (Cv), as a function of temperature within the temperature range 50K T 300K at concentration x=0, 0.27, 0.58 and 1. The current model computations and the findings of the available experiments are in good agreement. The ETSM is a sufficiently realistic model and may be applied to a variety of other mixed crystals in this family.

Slender body theories for rotating filaments

Slender fibres are ubiquitous in biology, physics and engineering, with prominent examples including bacterial flagella and cytoskeletal fibres. In this setting, slender body theories (SBTs), which give the resistance on the fibre asymptotically in its slenderness $\epsilon$ , are useful tools for both analysis and computations. However, a difficulty arises when accounting for twist and cross-sectional rotation: because the angular velocity of a filament can vary depending on the order of magnitude of the applied torque, asymptotic theories must give accurate results for rotational dynamics over a range of angular velocities. In this paper, we first survey the challenges in applying existing SBTs, which are based on either singularity or full boundary integral representations, to rotating filaments, showing in particular that they fail to consistently treat rotation–translation coupling in curved filaments. We then provide an alternative approach which approximates the three-dimensional dynamics via a one-dimensional line integral of Rotne–Prager–Yamakawa regularized singularities. While unable to accurately resolve the flow field near the filament, this approach gives a grand mobility with symmetric rotation–translation and translation–rotation coupling, making it applicable to a broad range of angular velocities. To restore fidelity to the three-dimensional filament geometry, we use our regularized singularity model to inform a simple empirical equation which relates the mean force and torque along the filament centreline to the translational and rotational velocity of the cross-section. The single unknown coefficient in the model is estimated numerically from three-dimensional boundary integral calculations on a rotating, curved filament.

Optimal formation control for multiple rotation-translation coupled satellites using reinforcement learning

In this paper, the model-free formation control problem is addressed for multiple satellites, whose dynamics involves rotation-translation coupling and nonlinearities. A two-step adaptive control strategy is proposed based on the reinforcement learning theory to iteratively solve the optimal formation control problem without knowledge of each satellite dynamics. The resulted controller is composed of an attitude controller to achieve the desired attitude, and a relative position controller to construct the satellite formation. The proposed global closed-loop control system is proven to be asymptotically stable. Simulation results on rotation-translation coupled satellite system confirm the effectiveness of the proposed adaptive optimal formation control strategy.

A three-dimensional twisted phononic crystal with omnidirectional bandgap based on inertial amplification by utilizing translation-rotation coupling

This work presents the design, manufacture, and experimental testing of a three-dimensional twisted phononic crystal made of a single-phase material. A broad, omnidirectional bandgap with continuously strong attenuation from 601 to 1504 Hz has been achieved, yet the filling ratio of the unit cell is just 22.4%. The theoretical study demonstrates that the inertial amplification based on the translation-rotation coupling is the cause of the bandgap. The translation-rotation coupling enables this phononic crystal to possess two stages of amplification. The tunability of the bandgap can be achieved in the first stage by intelligently regulating the contour of the lumped masses under the limitations of the quasi-constant stiffness and constant mass of the unit cell. The second stage allows the tilt angle of the ligaments to become a constantly tunable variable of the bandgap. This research comprehensively illuminates the 3D twisted phononic crystal based on inertial amplification and the approaches for tuning the bandgap in this class of phononic crystals.

Dynamics of a Non-Ideal Gyroscopic Rotor System with Translational-Rotational Coupling Effect of External and Internal Damping

Dynamics of a Non-Ideal Gyroscopic Rotor System with Translational-Rotational Coupling Effect of External and Internal Damping

Chirality-induced spin filtering in pseudo Jahn-Teller molecules

Chirality-induced spin selectivity (CISS) refers to an ability to induce a spin polarization of an electron transmitted through chiral materials. An important experimental observation is that incredibly large spin polarization is realized at room temperature even for organic molecules that have weak spin-orbit coupling (SOC), although SOC is the only interaction that can manipulate the electrons' spins in the setups. Therefore the mechanism of the CISS needs to be constructed in a way insensitive to or enhancing the magnitude of the SOC strength. In this paper, we describe a theoretical study of CISS with a model chiral molecule that belongs to the point group ${\mathrm{C}}_{3}$. In this molecule, electronic translational and rotational degrees of freedom for an injected electron are coupled to one another via the nuclear vibrational mode with a pseudo Jahn-Teller effect. By properly taking the molecular symmetry as well as the time-reversal symmetry into account and classifying the molecular ground states by their angular- and spin-momentum quantum numbers, we show that the chiral molecule can act as an efficient spin filter. The efficiency of this spin filtering can be nearly independent of the SOC strength in this model, while it well exceeds the spin polarization relying solely on the SOC. The nuclear vibrations turned out to have the role of not only mediating the translation-rotation coupling, but also enhancing the spin-filtering efficiency.

Rotranslational dynamics of confined water. II. Spectroscopic evidence of confinement effects on the far-infrared spectra of water isotopologues in argon and krypton matrices.

Water molecules trapped in rare gas matrices exhibit conspicuous shifts in their far-infrared (FIR), rotranslational spectral features compared with the corresponding transitions observed in the gas phase. These confinement-induced perturbations have been related not only to the quantization of translational motion but also to the coupling between the orientational and positional degrees of freedom: the rotation-translation coupling (RTC). As the propensity displayed by the nuclear spin isomers (NSI) of water to undergo interconversion in confinement is intimately related to how its nuclear spin degrees of freedom are coupled with those for intra- and intermolecular motions, confinement-induced RTC should also strongly impact the NSI interconversion mechanisms and rates. Insight into the rotranslational dynamics for H2 16O, H2 17O, and H2 18O, confined in argon and krypton matrices, is provided here based on the evolution of rotranslational spectra induced by NSI interconversion while a definitive assignment is provided from the transition energies and intensities calculated using the confined rotor model [Paper I, Wespiser et al., J. Chem. Phys. 156, 074304 (2021)]. In order to build a complete rotranslational energy diagram of confined water, which is fundamental to understand the NSI interconversion rates, the energy difference between the ground ortho and para rotranslational states is derived from the temperature dependence of the intensity ratio of mid-infrared lines emerging from these states. These investigations should provide deeper insight of the factors that control NSI interconversion of water isotopologues under extreme confinement.

Ro-translational dynamics of confined water. I. The confined asymmetric rotor model.

Confinement effects on the ro-translational (RT) dynamics of water, trapped in rare gas matrices or within endofullerenes (i.e., H2O@C60), can be experimentally assessed using rotationally resolved far-infrared, or mid-infrared, spectroscopy [Putaud et al., J. Chem. Phys. 156, 074305 (2022) (Paper II)]. The confined rotor model is used here to reveal how the quantized rotational and frustrated translational energy levels of confined water interact and mix by way of the confinement-induced rotation-translation coupling (RTC). An eccentric but otherwise isotropic 3D harmonic effective potential is used to account for confinement effects, thereby allowing the dependence of the magnitude of the RTC on the topology of the model confinement potential, the resulting intricate mixing schemes, and their impact on the RT energy levels to be examined in detail. The confined rotor model thus provides a convenient framework to investigate the matrix and isotope effects on the RT dynamics of water under extreme confinement probed spectroscopically, thereby potentially providing insight into the mechanisms and rates for ortho-H2O ↔ para-H2O nuclear spin isomer interconversion in confined water.