Rotational Degrees Of Freedom Research Articles

Entropy of different phases formed by soft rods.

The computation of entropy in liquids and liquid crystal (LC) phases is a big challenge in statistical physics. In this work, we extend the two-phase thermodynamic model (2PT) to shape anisotropic soft repulsive spherocylinders (SRSs) and report the absolute values of entropy for different LC phases for a range of aspect ratios L/D = 2 - 5. We calculate the density of states for different LC phases and decompose it into contributions arising from translational and rotational degrees of freedom. The translational and rotational modes are further partitioned into diffusive, gas-like, and non-diffusive, solid-like components using a fluidicity factor. In the dilute limit, the entropy values obtained from the 2PT method match exactly those of an ideal rigid rotor. We find that, for a given packing fraction, the magnitude of the total entropy is roughly equal regardless of the different LC phases associated with different aspect ratios. We also compute the excess entropy (for L/D = 5) and compare those with the values obtained using the standard integration approach of MD or Monte Carlo equation of state of SRS. The values obtained using both approaches match very well. The rotational and translational fluidicity factors are further used to determine the phase boundaries of different LC phases.

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.

Nucleation of transition waves via collisions of elastic vector solitons

In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of elastic vector solitons, another type of nonlinear wave, in a multistable mechanical system with coupling between translational and rotational degrees of freedom. We experimentally observe the nucleation of a phase transformation arising from colliding waves, and we numerically investigate head-on and overtaking collisions of solitary waves with vectorial properties (i.e., elastic vector solitons). Unlike KdV-type solitons, which maintain their shape despite collisions, our system shows that collisions of two vector solitons can cause nucleation of a new phase via annihilation of the vector solitons, triggering the propagation of transition waves. The propagation of these depends both on the amount of energy carried by the vector solitons and on their respective rotational directions. The observation of the initiation of transition waves with collisions of vector solitons in multistable mechanical systems is an unexplored area of fundamental nonlinear wave interactions and could also prove useful in applications involving reconfigurable structures.

Simple Physical Model for the Estimation of Irreversible Dissociation Rates for Bimolecular Complexes.

In this article, we propose a simple method of estimating dissociation rates of bimolecular van der Waals complexes ("wells"), rooted in rigid body dynamics, requiring as input parameters only the bimolecular binding energy, together with the intermolecular equilibrium distance and moments of inertia of the complex. The classical equations of motion are solved for the intermolecular and rotational degrees of freedom in a coordinate system considering only the relative motion of the two molecules, thus bypassing the question of whether the energy of the complex is statistically distributed. Well-escaping trajectories are modeled from these equations, and the escape rate as a function of relative velocity and angular momentum is fitted to an empirical function, which is then integrated over a probability distribution of said quantities. By necessity, this approach makes crude assumptions on the shape of the potential well and neglects the impact of energy quantization, and, more crucially, the coupling between the degrees of freedom included in the equations of motion with those that are not. We quantify the error caused by the first assumption by comparing our model potential with a quantum chemical potential energy surface (PES) and show that while the model does make several compromises and may not be accurate for all classes of bimolecular complexes, it is able to produce physically consistent dissociation rate coefficients within typical atmospheric chemistry confidence intervals for triplet state alkoxyl radical complexes, for which the detailed balance approach has been shown to fail.

Translational and rotational non-Gaussianities in homogeneous freely evolving granular gases.

The importance of roughness in the modeling of granular gases has been increasingly considered in recent years. In this paper, a freely evolving homogeneous granular gas of inelastic and rough hard disks or spheres is studied under the assumptions of the Boltzmann kinetic equation. The homogeneous cooling state is studied from a theoretical point of view using a Sonine approximation, in contrast to a previous Maxwellian approach. A general theoretical description is done in terms of d_{t} translational and d_{r} rotational degrees of freedom, which accounts for the cases of spheres (d_{t}=d_{r}=3) and disks (d_{t}=2,d_{r}=1) within a unified framework. The non-Gaussianities of the velocity distribution function of this state are determined by means of the first nontrivial cumulants and by the derivation of non-Maxwellian high-velocity tails. The results are validated by computer simulations using direct simulation Monte Carlo and event-driven molecular dynamics algorithms.

A thermodynamics-based micro-macro elastoplastic micropolar continuum model for granular materials

A micro–macro elastoplastic micropolar continuum model for granular materials in the dry and pendular states is proposed on the basis of thermodynamics. The independent rotational degrees of freedom are considered besides the translational degrees of freedom for particles among the discrete particle system, which is described by the equivalent micropolar continuum. In the framework of the micropolar continuum, the elastic part and yield locus at macroscale are firstly rigorously deduced from the general elastic constitutive relation and Coulomb-type yield criterion at inter-particle contacts, respectively. Furthermore, the micro–macro elastoplastic micropolar continuum model is proposed, in which the model parameters have clear physical meanings. Subsequently, a return mapping algorithm for the integration of the micropolar elastoplastic model is presented. Finally, the proposed model, coded into ABAQUS software, is validated by comparisons of test and discrete element method results in terms of the stress–strain relation and strain localization phenomenon. The stress–strain relation and shear band modes are well reproduced, and the effects of the confining pressure and the partially saturated state on granular materials can also be correctly predicted by the proposed model.

Fluorescent Properties of Cyanine Dyes As a Matter of the Environment.

In non-viscous aqueous solutions, the cyanine fluorescent dyes Cy3 and Cy5 have rather low fluorescence efficiency (the fluorescence quantum yields of Cy3 and Cy5 are 0.04 and 0.3, respectively [1, 2]) and short excited state lifetimes due to their structural features. In this work, we investigated the effect of solubility and rotational degrees of freedom on the fluorescence efficiency of Cy3 and Cy5 in several ways. We compared the fluorescence efficiencies of two cyanine dyes sCy3 and sCy5 with the introduction of a sulfonyl substituent in the aromatic ring as well as covalently bound to T10 oligonucleotides. The results show that because of the different lengths of the polymethine chains between the aromatic rings of the dyes, cis-trans-isomerization has a much greater effect on the Cy3 molecule than on the Cy5 molecule, while the effect of aggregation is also significant.

Does joint impedance improve dynamic leg simulations with explicit and implicit solvers?

The nervous system predicts and executes complex motion of body segments actuated by the coordinated action of muscles. When a stroke or other traumatic injury disrupts neural processing, the impeded behavior has not only kinematic but also kinetic attributes that require interpretation. Biomechanical models could allow medical specialists to observe these dynamic variables and instantaneously diagnose mobility issues that may otherwise remain unnoticed. However, the real-time and subject-specific dynamic computations necessitate the optimization these simulations. In this study, we explored the effects of intrinsic viscoelasticity, choice of numerical integration method, and decrease in sampling frequency on the accuracy and stability of the simulation. The bipedal model with 17 rotational degrees of freedom (DOF)-describing hip, knee, ankle, and standing foot contact-was instrumented with viscoelastic elements with a resting length in the middle of the DOF range of motion. The accumulation of numerical errors was evaluated in dynamic simulations using swing-phase experimental kinematics. The relationship between viscoelasticity, sampling rates, and the integrator type was evaluated. The optimal selection of these three factors resulted in an accurate reconstruction of joint kinematics (err < 1%) and kinetics (err < 5%) with increased simulation time steps. Notably, joint viscoelasticity reduced the integration errors of explicit methods and had minimal to no additional benefit for implicit methods. Gained insights have the potential to improve diagnostic tools and accurize real-time feedback simulations used in the functional recovery of neuromuscular diseases and intuitive control of modern prosthetic solutions.

Automated Orientation Control of Motile Deformable Cells

Automated manipulation of deformable objects is challenging due to the object&#x2019;s deformation behavior. Different from still deformable objects such as wires and cloth, biological organisms such as sperm and worms are both deformable and motile, requiring the control of both deformation and motion. This paper reports automated orientation control of live sperm, as an example of motile deformable cells. Robotic manipulation of human sperm was performed by using a glass micropipette, which is a standard clinical tool, to rotate individual motile sperm. Sperm rotation must be performed before immobilization, as required in clinical cell surgery for infertility treatment. To control tail deformation during sperm rotation, a path planner was designed based on kinematic analysis and manipulation point update. To deal with the intrinsic motion of a motile sperm, a motorized stage was controlled to compensate for sperm swimming motion, and an observer was designed to decouple sperm orientation from its wiggling motion. A sliding mode controller was designed to cope with stiffness variances along the sperm tail and among different sperm. Deep neural networks were developed for robust sperm tail detection, and Kalman filter was used to predict tail motion. Experimental results demonstrated that automated sperm manipulation achieved an orientation error of 0.8<inline-formula> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> and operation time of 6.8 s, both significantly less than those of manual operation. The designed observer was effective to reduce sperm orientation error by reducing the disturbance from sperm wiggling motion. The developed sliding mode controller outperformed the PID controller in operation time, reducing the time of oocyte exposure to the ambient environment. <i>Note to Practitioners</i>&#x2014;This work tackled the challenge of rotating a fast-swimming and deformable sperm in clinical cell surgeries. Automated manipulation of deformable objects has wide applications in industrial and service settings such as manipulating wires and folding cloth. However, the intrinsic motion of a motile sperm and the lack of a rotational degree of freedom in standard micromanipulators pose difficulties to automated sperm manipulation. In this paper, we propose automation techniques for sperm orientation control. For sperm tail detection, deep learning was used to handle the variances of shape and length among different sperm. A path planning strategy and a controller were designed to achieve automated rotation of motile sperm, with its deformation and motion both controlled. The developed methods can be generalized to the manipulation of other deformable objects such as wires, cables and cloth. These objects exhibit significant variance of mechanical properties, and calibration is often time-consuming. The designed controller can be used to manipulate deformable objects with robustness to varied mechanical parameters. Path planning was designed by updating the manipulation point based on the object&#x2019;s deformation behavior, and is suitable in manipulation where constraints are imposed such as the object&#x2019;s strain.

Robust acoustic trapping and perturbation of single-cell microswimmers illuminate three-dimensional swimming and ciliary coordination

We report a label-free acoustic microfluidic method to confine single, cilia-driven swimming cells in space without limiting their rotational degrees of freedom. Our platform integrates a surface acoustic wave (SAW) actuator and bulk acoustic wave (BAW) trapping array to enable multiplexed analysis with high spatial resolution and trapping forces that are strong enough to hold individual microswimmers. The hybrid BAW/SAW acoustic tweezers employ high-efficiency mode conversion to achieve submicron image resolution while compensating for parasitic system losses to immersion oil in contact with the microfluidic chip. We use the platform to quantify cilia and cell body motion for wildtype biciliate cells, investigating effects of environmental variables like temperature and viscosity on ciliary beating, synchronization, and three-dimensional helical swimming. We confirm and expand upon the existing understanding of these phenomena, for example determining that increasing viscosity promotes asynchronous beating. Motile cilia are subcellular organelles that propel microorganisms or direct fluid and particulate flow. Thus, cilia are critical to cell survival and human health. The unicellular alga Chlamydomonas reinhardtii is widely used to investigate the mechanisms underlying ciliary beating and coordination. However, freely swimming cells are difficult to image with sufficient resolution to capture cilia motion, necessitating that the cell body be held during experiments. Acoustic confinement is a compelling alternative to use of a micropipette, or to magnetic, electrical, and optical trapping that may modify the cells and affect their behavior. Beyond establishing our approach to studying microswimmers, we demonstrate a unique ability to mechanically perturb cells via rapid acoustic positioning.

Observation of Chirality‐Induced Roton‐Like Dispersion in a 3D Micropolar Elastic Metamaterial

AbstractA theoretical paper based on chiral micropolar effective‐medium theory suggested the possibility of unusual roton‐like acoustical‐phonon dispersion relations in 3D elastic materials. Here, as a first novelty, the corresponding inverse problem is solved, that is, a specific 3D chiral elastic metamaterial structure is designed, the behavior of which follows this effective‐medium description. The metamaterial structure is based on a simple‐cubic lattice of cubes, each of which not only has three translational but also three rotational degrees of freedom. The additional rotational degrees of freedom are crucial within micropolar elasticity. The cubes and their degrees of freedom are coupled by a chiral network of slender rods. As a second novelty, this complex metamaterial is manufactured in polymer form by 3D laser printing and its behavior is characterized experimentally by phonon‐band‐structure measurements. The results of these measurements, microstructure finite‐element calculations, and solutions of micropolar effective‐medium theory are in good agreement. The roton‐like dispersion behavior of the lowest phonon branch results from two aspects. First, chirality splits the transverse acoustical branches as well as the transverse optical branches. Second, chirality leads to an ultrastrong coupling and hybridization of chiral acoustical and optical phonons at finite wavevectors.

Isogeometric degenerated shell formulation for post-buckling analysis of composite variable-stiffness shells

Variable-stiffness (VS) laminated shells with curved fibers have gradually become a promising lightweight structural concept in the aerospace field. However, as the complexity of the shell geometry and the fiber angle increases, the traditional finite element method (FEM) requires mesh refinement to guarantee accurate discretization, which significantly increases the computational cost, especially in the post-buckling analysis with multiple solving requirements. In this study, a non-uniform rational B-Splines (NURBS)-based degenerated solid shell formulation in the total Lagrangian framework is proposed for the post-buckling analysis of VS laminated shells. Since the nonlinear function related to the rotational degrees of freedom (DOFs) is additionally introduced into the displacement field expression, the restriction on the magnitude of the nodal rotations is effectively eliminated. In addition, the paper adopts the NURBS surface reconstruction technology based on the point-line-surface features to build B-spline CAD models from the point cloud with geometric imperfect features. Then, an integrated modeling-analysis framework for predicting the post-buckling behavior of VS structures with geometric imperfections is proposed. A series of numerical examples systematically demonstrate that the framework can effectively conduct the post-buckling analysis of shell structures with geometric imperfections. Meanwhile, the accuracy and robustness of the solutions by IGA are proved to be better than FEM.

Planar In-Hand Manipulation Using Primitive Rotations Based on Isometric Transformations

Achieving in-hand manipulation of a grasped object is challenging in robotic communities. This article proposes a planar intrinsic in-hand manipulation approach based on isometric transformation. We demonstrate that the isometric transformation (excluding reflections) can be reduced to rotations with two fixed centers, if more than two rotations around two different centers are performed. Furthermore, this article applies this theory to reposition and reorient a grasped object by performing three or more primitive rotations sequentially. We further analyze the feasible manipulation space, where the desired position and orientation of a grasped object can be attained. The theoretical results have been verified through simulations and experiments. In addition, we performed several real-world tasks using a novel robotic hand with two rotational degrees of freedom at each finger, demonstrating that the proposed in-hand manipulation method can reposition and reorient different grasped objects in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{SE}(2)$</tex-math></inline-formula> .

Entropy Scaling of Molecular Dynamics in a Prototypical Anisotropic Model near the Glass Transition.

Dynamics and thermodynamics of molecular systems in the vicinity of the boundary between thermodynamically nonequilibrium glassy and metastable supercooled liquid states are still incompletely explored and their theoretical and simulation models are imperfect despite many previous efforts. Among them, the role of total system entropy, configurational entropy, and excess entropy in the temperature-pressure or temperature-density dependence of global molecular dynamics (MD) timescale relevant to the glass transition is an essential topic intensively studied for over half of a century. By exploiting a well-known simple ellipsoidal model recently successfully applied to simulate the supercooled liquid state and the glass transition, we gain a new insight into the different views on the relationship between entropy and relaxation dynamics of glass formers, showing the molecular grounds for the entropy scaling of global MD timescale. Our simulations in the anisotropic model of supercooled liquid, which involves only translational and rotational degrees of freedom, give evidence that the total system entropy is sufficient to scale global MD timescale. It complies with the scaling effect on relaxation dynamics exerted by the configurational entropy defined as the total entropy diminished by vibrational contributions, which was earlier discovered for measurement data collected near the glass transition. Moreover, we argue that such a scaling behavior is not possible to achieve by using the excess entropy that is in excess of the ideal gas entropy, which is contrary to the results earlier suggested within the framework of simple isotropic models of supercooled liquids. Thus, our findings also warn against an excessive reliance on isotropic models in theoretical interpretations of molecular phenomena, despite their simplicity and popularity, because they may reflect improperly various physicochemical properties of glass formers.

Elucidation of rotational-interaction coupling and collision-induced effects in rovibrational transitions of β-N2O isotopologue at 7.8 µm mid-infrared region by cavity ring-down spectroscopy

High-sensitive cavity ring-down spectroscopy (CRDS) coupled with a cw-quantum cascade laser operating at 7.8 μm mid-infrared (MIR) region has been employed to investigate the rovibrational interaction coupling for various MIR rotational transitions of the P-and R-branches in the ν1 fundamental vibrational band (1000 ← 0000) of the β-site-specific isotopologue of nitrous oxide (β-N2O) i.e., 15N14N16O. The coupled rotational interaction was experimentally quantified from the high-resolution CRDS data and a data-driven approach was taken for the approximation of the Herman-Wallis series. Moreover, J-dependent pressure-broadened absorptions and their collision lifetimes in response to foreign-perturbing gas molecules were investigated to understand the collision-induced rotational quantum effect in β-N2O molecule. This study reveals an experimental elucidation of the fundamental infrared physics underlying rovibrational interaction and its coupling to the vibrational and rotational degrees of freedom for a non-centrosymmetric linear polyatomic molecule possessing a permanent dipole moment. Moreover, the experimentally probed interference-free spectral lines of β-N2O molecule attributing different spectroscopic signatures in the MIR region may drive new applications in environmental monitoring, biological and biomedical diagnostics in the future.

Controlling Optomechanical Libration with the Degree of Polarization.

Control of the potential energy and free evolution lie at the heart of levitodynamics as key requirements for sensing, wave function expansion, and mechanical squeezing protocols. Here, we experimentally demonstrate versatile control over the optical potential governing the libration motion of a levitated anisotropic nanoparticle. This control is achieved by introducing the degree of polarization as a new tool for rotational levitodynamics. We demonstrate thermally driven free rotation of a levitated anisotropic scatterer around its short axis and we use the rotational degrees of freedom to probe the local spin of a strongly focused laser beam.

Path following using velocity-based approach in quasi-static analysis

In the present work, we propose a novel implementation of arc-length method for the computation of equilibrium paths for frame-like structures. We exploit the advantages of velocity-based beam formulations and adapt it to quasi-static analysis with path following control. We show that such formulation allows the arc-length control constraint equation to be directly employed in its originally defined differential form, while the arc-length parameter is replaced by time in our adaptation. This simplifies the treatment of the extended system of equations and its solution procedure. Our approach also enables the rotational degrees of freedom to be members of control parameters. The ability of the proposed method to successfully and efficiently compute complex equilibrium paths in post-buckling regime is demonstrated by several numerical examples.

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.

An iterative identification method of joint properties and its applications in an end-toothed connection structure

Accurate identification of mechanical connections plays a significant role in predicting the dynamic behaviors of assembled structures. Traditional identification methods based on frequency response function (FRF) decoupling may not be suitable for the joints with many interface degrees of freedom (DOFs), especially in the case of insufficient measured FRF data and large experimental noise. In this paper, a new iterative method is proposed to solve this problem. First, the incremental basic formulas on the measured DOFs and pseudo-measured DOFs are derived, respectively. The former avoids the measurements of rotational or interface DOFs whereas the latter is suitable for the identification of the joint with many interface DOFs. Then, the joint properties expressed in terms of mass, stiffness and damping matrices are updated from the solution of the linear equation system combined with the iterative basic identification equations at different frequencies. Thus, the original problem is transformed into estimating the parameters iteratively by minimizing the differences between predicted responses and measured ones, which effectively improves the identification accuracy and numerical stability. Moreover, the iterative method is extended to the identification of nonlinear joints based on describing function theory. The validity and superiority of the proposed method are verified by a simple lumped parameter system. Then, a numerical example of a structure connected with bolted joints, which has a large number of interface DOFs, is simulated to verify the convergence and the robustness of the method to noise. Finally, the joint dynamic properties of an end-toothed connection under different contact states are identified, and the assembly responses are also accurately predicted. The effectiveness and the applicability of the proposed iterative identification method to the real structures are well validated.

Molecular Rotations, Multiscale Order, Hyperuniformity, and Signatures of Metastability during the Compression/Decompression Cycles of Amorphous Ices.

We model, via large-scale molecular dynamics simulations, the isothermal compression of low-density amorphous ice (LDA) to generate high-density amorphous ice (HDA) and the corresponding decompression extending to negative pressures to recover the low-density amorphous phase (LDAHDA). Both LDA and HDA are nearly hyperuniform and are characterized by a dynamical HBN, showing that amorphous ices are nonstatic materials and implying that nearly hyperuniformity can be accommodated in dynamical networks. In correspondence with both the LDA-to-HDA and the HDA-to-LDAHDA phase transitions, the (partial) activation of rotational degrees of freedom activates a cascade effect that induces a drastic change in the connectivity and a pervasive reorganization of the HBN topology which, ultimately, break the samples' hyperuniform character. Key to this effect is the rapid rate at which changes occur, and not their magnitude. The inspection of structural properties from the short- to the long-range shows that signatures of metastability are present at all length-scales, hence providing further solid evidence in support of the liquid-liquid critical point scenario. LDA and LDAHDA differ in terms of HBN and structural properties, implying that they are distinct low-density glasses. Our work unveils the role of molecular rotations in the phase transitions between amorphous ices and shows how the unfreezing of rotational degrees of freedom generates a cascade effect that propagates over multiple length-scales. Our findings greatly improve our basic understanding of water and amorphous ices and can potentially impact the field of molecular network-forming materials at large.