Free Rotation Research Articles

On injectivity of quantum finite automata

We consider notions of freeness and ambiguity for the acceptance probability of Moore-Crutchfield Measure Once Quantum Finite Automata (MO-QFA). We study the injectivity problem of determining if the acceptance probability function of a MO-QFA is injective over all input words, i.e., giving a distinct probability for each input word. We show that the injectivity problem is undecidable for 8 state MO-QFA, even when all unitary matrices and the projection matrix are rational and the initial state vector is real algebraic. We also show undecidability of this problem when the initial vector is rational, although with a huge increase in the number of states. We utilize properties of quaternions, free rotation groups, representations of tuples of rationals as linear sums of radicals and a reduction of the mixed modification of Post's correspondence problem, as well as a new result on rational polynomial packing functions which may be of independent interest.

Rotation of CH3+ Cations in Helium Droplets.

Observation of the free rotation of molecules in helium droplets enabled microscopic study of interaction of quantum rotors with a superfluid environment at T = 0.4 K. This work extends studies of rotation in helium to molecular cations, such as methenium, CH3+. The spectrum of the v3 band of CH3+ around 3130 cm-1 has three prominent peaks assigned to the rotational structure of the band. While the free CH3+ is an oblate top, in helium it behaves as a prolate top. This effect is ascribed to the strong binding of two He atoms along the figure axis of the ion. Our results indicate that the other He atoms within the first solvation shell remain fluxional and in disparity with the widely accepted model of a rigid He "snowball" surrounding ions.

A control-orientated analytical model for a cyclorotor wave energy device with N hydrofoils

We present a new analytical model from which a model-based controller can be derived for a cyclorotor-based wave energy converter (WEC). Few cyclorotor-based WEC concepts and models have previously been studied and only one control strategy for the entire wave cancellation has been tested. Our model is derived for a horizontal cyclorotor with N hydrofoils and is suitable for the application of various control algorithms and the calculation of various performance metrics. The mechanical model is based on Newton’s second law for rotation. The cyclorotor operates in two dimensional potential flow. This paper modeled the velocity field in detail around the turbine with N hydrofoils by explaining each velocity term and estimated the generated torque using two methods (point source method and thin-chord method). The developed model is very convenient for control design, using the power take off torque and hydrofoil pitch angles as control inputs. The authors of this work have derived new, exact analytic functions for the free surface perturbation and induced fluid velocity field caused by hydrofoil rotation. These new formulae significantly decrease the model calculation time and increase the accuracy of the results. The new equations also provide useful insight into the nature of the associated variables, and are successfully validated against the results of physical experiments and numerical calculations previously published by two independent research groups. Representation of hydrofoils as both a point source and a thin chord were analysed, with both models cross-validated for the case of free rotation in monochromatic waves.

Cholesteric layers with tangential-conical surface anchoring for an electrically controlled polarization rotator

The voltage dependences of polarization characteristics of light passed through the cholesteric layers with tangential-conical boundary conditions have been investigated. It has been shown that such layers allow turning the polarization azimuth more than 70 ∘ because of the unique untwisting effect of the cholesteric helix, due to free azimuthal rotation of the director on the substrate with conical anchoring. Optical cells under study have some advantages (low control voltage, smooth variation of polarization azimuth, simplicity of design) and can be used as an electrically controlled polarization rotator of white light.

Water Switched Reversible Thermochromism in Organic Salt of Sulfonated Anil

We report concomitant stoichiomorphs [(4,4′-BPY-2H)2+(SA-SY-H)−2·4H2O] 1 and [(4,4′-BPY-H)+(SA-SY-H)−·4H2O] 2 formed in the same reaction vessel, with formation of 2 following 1. The expeditious formation of 1 with half equivalent of bipyridyl former, attributed to 2-fold bifurcated methoxy assisted hydroxyl-pyridinium synthon, leaves behind the solution with an excess of bipyridyl, resulting in the formation of 2. Organic salts 1 and 2 crystallize as triclinic (P̅1) and monoclinic (P21/c) tetrahydrates, with D3 acyclic non-branched and branched lattice water clusters. Hirshfeld and fingerprint studies reveal reciprocal O–H···H–O and weak dispersive H···H contacts are the major intermolecular interactions responsible for supramolecular aggregation. Interestingly, 1 exhibits reversible thermochromism switched by lattice water, while 2 is not thermochromic. Photochromism in both sulfonated anil based organic salts 1 and 2 is ruled out due to the significantly lower Vfree value than required for the free rotation about the imine bond to generate cis–trans isomers. Keto–enol prototropism-triggered thermochromism is also ruled out because of the intramolecular sulfonate proton shift to the imine nitrogen as well as the position of absorption curves in the Kubelka–Munk plots. The lattice water switched mechanism for reversible thermochromism in 1 is proposed and substantiated by FT-IR, TGA-DTA, DR-UV, and P-XRD studies and further validated by the Tauc plots. To the best of our knowledge, 1 represents the first example of water-triggered all-organic reversible thermochromic material and has been utilized as a thermal sensor for the reflux reactions in low boiling solvents.

Unseating of single-span bridges with skew angles out of the limit range for free rotation

Past researches have indicated that skewed bridges can rotate around the obtuse corners upon gap closure and the bridge deck can rotate freely when the skew angle is within a limit range. Beyond this range, the rotation of the bridge deck could be locked against the abutments. For these bridges, girder unseating can be avoided either by geometric constraint of the deck or by providing adequate support length to account for seismic demands. In this paper, the unseating of single-span bridges is studied for skew angles out of the limit range for free rotation. To begin, the skew angle limit range for free rotation was derived for bridges with and without expansion gaps. It was found that the expansion gap has a slight influence on the skew angle limit range for free rotation. The minimum support length (N) of skewed bridges to reach geometric constraint (when locked against the abutments) was then derived step-by-step based on geometry. It is found that the N to reach geometric constraint increases with skew angles approximately in an exponential manner. Finally, a parametric study was performed on prototype skewed bridges using a shake table experiment-validated nonlinear model to compute the support length demands during design-level earthquakes. Nonlinear analysis was performed under seven historical near-fault records scaled to the design-level earthquakes. Comparison was made between the support length to reach geometric constraint and those from numerical analysis. The results indicate that it is very likely that a single-span bridge of any skew angle could rotate freely during the design-level earthquakes even when its geometry could allow it to be blocked by the abutments. Therefore, the minimum support length of single-span bridges should be designed based on seismic demands rather than geometric constraint when the skew angles are out of the limit range. In addition, it was also found that the Japan Road Association (JRA) is unreasonable to assume zero skew effect on the minimum support length requirements and current codes and specifications underestimate the skew factor when the skew angles fall out of the limit range.

The mobile phone as a free-rotation laboratory

Modern mobile phones contain a three-axis microelectromechanical system (MEMS) gyroscope, capable of taking accurate measurements of the angular velocity along the three principal axes of the phone with a sampling rate of 100 Hz or better. If the phone is tossed in the air, then, neglecting air resistance, it is in free rotation (rotation in the absence of a torque) with respect to its centre of mass, and the phone's gyroscope can be used to record the rotational dynamics. This enables experimental investigation of free rotation. In this paper, we use a mobile phone to demonstrate the steady states for rotation of the phone about two of its principal axes, and the instability in rotation about the third corresponding to the intermediate moment of inertia. We also show the approximate conservation of angular momentum and rotational kinetic energy during motion in the air, and compare the data with numerical solution of Euler's equations for free rotation. Our results demonstrate the capability of smartphones for investigating free rotation, and should be of interest to college and university teachers developing “at home” physics labs for remote learning.

BACKLASH-FREE POWER DRIVE OF MACHINES

Thebacklash-freepower drive of the machines ensures that the working shaft does not move freely when changing the direction of rotation. As a backlash-freegapless power drive, a single-stage planetary gearbox is proposed, containing two Central wheels, a carrier, and satellites, which are blocks of two gears, each of which is mounted on the carrierʼs axis by means of a rolling bearing and a freerunning Cam clutch. At the same time, the couplings are placed so as to ensure free rotation of the wheels in different directions. The gears are connected to each other by a pre-twisted cylindrical torsion spring. The proposed design will ensure reliable operation of the drive when the specified requirements are met.

Synthesis and Evaluation of Charge Transport Property of Ethynylene‐Bridged Anthracene Oligomers

AbstractA set of ethynylene‐bridged anthracene oligomers from monomer to tetramer is synthesized and characterized. The red‐shifts in the UV–vis absorption and fluorescence spectra indicate the π‐extension with elongation of the linear chain. Cyclic voltammetric measurements suggest that their highest occupied molecular orbitals are located lower than –5.0 eV, indicating high air stability. Single‐crystal X‐ray analysis of a trimer needle crystal indicates that anthracene units display a twisted arrangement, adopting a face‐to‐face packing structure. The dip‐coating method with a very slow pulling rate provides crystalline films of dimer and trimer. The top‐contact bottom‐gate organic field‐effect transistor devices reveal that trimer shows better charge transport property (8.0 × 10–3 cm2 V–1 s–1) than dimer (8.9 × 10–4 cm2 V–1 s–1). Furthermore, the single‐crystal field‐effect transistor of trimer shows mobility up to 0.14 cm2 V–1 s–1, which is higher than that of tetramer (3.3 × 10–2 cm2 V–1 s–1). This is likely due to the larger amount of defects in tetramer crystals that are caused by the free rotation of ethynylene units, while the trimer achieves a good balance between the effective π‐conjugation and defectless crystal formation.

Supramolecular Copolymerization of Bichromophoric Chiral and Achiral Perylenediimide Dyes

Propagation and amplification of chirality are considered to play an important role in the chemical evolution of biological homochirality. Stereochemical communications have been demonstrated to have a significant effect on the formation of chiral hierarchical structures in helical polymers, surface assemblies and supramolecular polymers. The formation of supramolecular copolymers based on chiral and achiral bichromophoric perylenediimide (PDI) dyes having a binaphtyl- and biphenyl-core-bridging unit, respectively, was investigated in terms of chiral amplification and propagation. The biphenyl-bridged PDI dye was expected to perform as a prochiral component to adopt both right- and left-handed twisting structures with the free rotation over the phenyl-phenyl linkage upon partnered with the chiral binaphtly PDI dye in the coassemblies. The coassemblies between the chiral and achiral PDI dyes with dissimilar core units demonstrated the composition dependent control in the length of supramolecular nanofibers as well as amplification of optical activity.

Hold that pose

Macrocycles Within proteins, individual peptide bonds have free rotation but typically keep to a narrow conformational space. Macrocycles are already conformationally hindered and provide an interesting venue for pushing peptide bonds into uncharted territory. Diaz et al. prepared a series of small macrocycles using so-called dominant rotors, peptide-like units that are kinetically locked in a particular conformation. Structural analysis revealed unusual conformations of the peptide backbone beside the dominant rotor, perhaps indicative of the kinds of fleeting intermediates expected during peptide folding. Nat. Chem. 13 , 218 (2021).

Aggregation-Induced Emission: From Small Molecules to Polymers-Historical Background, Mechanisms and Photophysics.

The enhancement of photoluminescence through formation of molecular aggregates in organic oligomers and conjugated organic polymers is reviewed. A historical contextualization of aggregation-induced emission (AIE) phenomena is presented. This includes the loose bolt or free rotor effect and J-aggregation phenomena, and discusses their characteristic features, including structures and mechanisms. The basis of both effects is examined in key molecules, with a particular emphasis on the AIE effect occurring in conjugated organic polymers with a polythiophene (PT) skeleton with triphenylethylene (TPE) units. Rigidification of the excited state structure is one of the defining conditions required to obtain AIE, and thus, by changing from a flexible ground state to rigid (quinoidal-like) structures, oligo and PTs are among the most promising emerging molecules alongsidewith the more extensively used TPE derivatives. Molecular structures moving away from the domination of aggregation-caused quenching to AIE are presented. Future perspectives for the rational design of AIEgen structures are discussed.

Chemical Bonding in Homoleptic Carbonyl Cations [M{Fe(CO)5 }2 ]+ (M=Cu, Ag, Au).

Syntheses of the copper and gold complexes [Cu{Fe(CO)5}2][SbF6] and [Au{Fe(CO)5}2][HOB{3,5‐(CF3)2C6H3}3] containing the homoleptic carbonyl cations [M{Fe(CO)5}2]+ (M=Cu, Au) are reported. Structural data of the rare, trimetallic Cu2Fe, Ag2Fe and Au2Fe complexes [Cu{Fe(CO)5}2][SbF6], [Ag{Fe(CO)5}2][SbF6] and [Au{Fe(CO)5}2][HOB{3,5‐(CF3)2C6H3}3] are also given. The silver and gold cations [M{Fe(CO)5}2]+ (M=Ag, Au) possess a nearly linear Fe‐M‐Fe’ moiety but the Fe‐Cu‐Fe’ in [Cu{Fe(CO)5}2][SbF6] exhibits a significant bending angle of 147° due to the strong interaction with the [SbF6]− anion. The Fe(CO)5 ligands adopt a distorted square‐pyramidal geometry in the cations [M{Fe(CO)5}2]+, with the basal CO groups inclined towards M. The geometry optimization with DFT methods of the cations [M{Fe(CO)5}2]+ (M=Cu, Ag, Au) gives equilibrium structures with linear Fe‐M‐Fe’ fragments and D 2 symmetry for the copper and silver cations and D 4d symmetry for the gold cation. There is nearly free rotation of the Fe(CO)5 ligands around the Fe‐M‐Fe’ axis. The calculated bond dissociation energies for the loss of both Fe(CO)5 ligands from the cations [M{Fe(CO)5}2]+ show the order M=Au (D e=137.2 kcal mol−1)>Cu (D e=109.0 kcal mol−1)>Ag (D e=92.4 kcal mol−1). The QTAIM analysis shows bond paths and bond critical points for the M−Fe linkage but not between M and the CO ligands. The EDA‐NOCV calculations suggest that the [Fe(CO)5]→M+←[Fe(CO)5] donation is significantly stronger than the [Fe(CO)5]←M+→[Fe(CO)5] backdonation. Inspection of the pairwise orbital interactions identifies four contributions for the charge donation of the Fe(CO)5 ligands into the vacant (n)s and (n)p AOs of M+ and five components for the backdonation from the occupied (n‐1)d AOs of M+ into vacant ligand orbitals.

Research on 3D virtual simulation of geology based on GIS

A simplified method based on GIS combined with virtual reality modeling language (VRML) to achieve real time and fast 3D geological modeling is proposed. By calling the borehole rock and soil information stored in the GIS database, it is automatically created using spatial interpolation technology. The spatial interpolation technology is used to automatically create the side map of the model, and automatically output this information as a VRML script according to the standard format. The created model can be displayed independently without relying on the modeling software platform and can realize functions such as free rotation, flying, and zooming. Successfully developed a 3D geological modeling system based on the introduced design ideas, and used the system to achieve 3D geological modeling of a certain bridge site. This method has the characteristics of simple operation, fast modeling speed, less manual intervention, and visual interactive operation and can be used as an auxiliary decision-making method for engineering surveys.

ANCHORING PERFORMANCES ANALYSIS OF TENSION-TORSION GROUTED ANCHOR UNDER FREE AND NON-FREE ROTATING CONDITIONS

For the failure mechanism of the anchor cable lags behind the practice demand for theoretical models, Abaqus technique was used to analyze the anchoring performances of the grouted anchor under the conditions of free and non-free rotating. The tension-torsion coupling characteristics and the progressive failure mechanism of the anchorage segment were studied during the pull-out test. The torsion response of the anchorage segment and the internal horizontal and vertical strain changes in the anchoring concrete were also analyzed. Results show that the proposed calculation model of the anchor cable is verified. With the increase of the pulling-out displacement, the load response of the anchored section is gradually transferred from the inside to the outside. The anchoring stress in the concrete undergoes the evolution process of rod shape-bell shape-aquarium shape-spear shape. As an intermediate transition layer, the anchoring agent breaks before the concrete and at the same time that plays a buffering effect. Under the action of tension-torsion coupling, the anchoring agent is prone to tensile-shear composite failure. There are two different ways of transmitting force for the grouted anchor under rotating and non-rotating conditions, and the anchoring force of the anchor cable will be reduced in the state of free rotation. The obtained conclusions can provide a reference for the similar anchoring practice. Keywords: Grouted anchor, Tension-torsion coupling, Numerical simulation, Failure mechanism, Anchoring force

3D Simulation with Flow-Induced Rotation for Non-Deformable Tidal Turbines

The overall potential for recoverable tidal energy depends partly on the tidal turbine technologies used. One of problematic points is the minimum flow velocity required to set the rotor into motion. The novelty of the paper is the setup of an innovative method to model the fluid–structure interactions on tidal turbines. The first part of this work aimed at validating the numerical model for classical cases of rotation (forced rotation), in particular, with the help of a mesh convergence study. Once the model was independent from the mesh, the numerical results were tested against experimental data for both vertical and horizontal tidal turbines. The results show that a good correspondence for power and drag coefficients was observed. In the wake, the vortexes were well captured. Then, the fluid drive code was implemented. The results correspond to the expected physical behavior. Both turbines rotated in the correct direction with a coherent acceleration. This study shows the fundamental operating differences between a horizontal and a vertical axis tidal turbine. The lack of experiments with the free rotation speed of the tidal turbines is a limitation, and a digital brake could be implemented to overcome this difficulty.

CGRP monoclonal antibody prevents the loss of diffuse noxious inhibitory controls (DNIC) in a mouse model of post-traumatic headache.

Determine the role of calcitonin-gene related peptide in promoting post-traumatic headache and dysregulation of central pain modulation induced by mild traumatic brain injury in mice. Mild traumatic brain injury was induced in lightly anesthetized male C57BL/6J mice by a weight drop onto a closed and unfixed skull, which allowed free head rotation after the impact. We first determined possible alterations in the diffuse noxious inhibitory controls, a measure of net descending pain inhibition called conditioned pain modulation in humans at day 2 following mild traumatic brain injury. Diffuse noxious inhibitory control was assessed as the latency to a thermally induced tail-flick that served as the test stimulus in the presence of right forepaw capsaicin injection that provided the conditioning stimulus. Post-traumatic headache-like behaviors were assessed by the development of cutaneous allodynia in the periorbital and hindpaw regions after mild traumatic brain injury. We then determined if intraperitoneal fremanezumab, an anti-calcitonin-gene related peptide monoclonal antibody or vehicle administered 2 h after sham or mild traumatic brain injury induction could alter cutaneous allodynia or diffuse noxious inhibitory control responses on day 2 post mild traumatic brain injury. In naïve and sham mice, capsaicin injection into the forepaw elevated the latency to tail-flick, reflecting the antinociceptive diffuse noxious inhibitory control response. Periorbital and hindpaw cutaneous allodynia, as well as a loss of diffuse noxious inhibitory control, was observed in mice 2 days after mild traumatic brain injury. Systemic treatment with fremanezumab blocked mild traumatic brain injury-induced cutaneous allodynia and prevented the loss of diffuse noxious inhibitory controls in mice subjected to a mild traumatic brain injury. Sequestration of calcitonin-gene related peptide in the initial stages following mild traumatic brain injury blocked the acute allodynia that may reflect mild traumatic brain injury-related post-traumatic headache and, additionally, prevented the loss of net descending inhibition within central pain modulation pathways. As loss of conditioned pain modulation has been linked to multiple persistent pain conditions, dysregulation of descending modulatory pathways may contribute to the persistence of post-traumatic headache. Additionally, evaluation of the conditioned pain modulation/diffuse noxious inhibitory controls response may serve as a biomarker of vulnerability for chronic/persistent pain. These findings suggest that early anti-calcitonin-gene related peptide intervention has the potential to be effective both for the treatment of mild traumatic brain injury-induced post-traumatic headache, as well as inhibiting mechanisms that may promote post-traumatic headache persistence.

Devising quality control criteria for manufacturing control valves of the type «nozzle-flap»

This paper is a continuation of research into the causes and ways to eliminate the generation of self-oscillations in the system of automatic regulation of rotations of the free turbine in the turboshaft gas turbine engines of helicopters. The study of dynamic processes in the system of automatic regulation of free turbine’s rotations in a turboshaft GTE has shown that one of the reasons for the development of self-oscillations is the poor performance of the control valve of the type «nozzle-flap» in the rotation regulator’s hydraulic drive. At a pump-regulator plant, the criterion for the quality of control valve execution or repair implies that the geometric size of the valve parts and the flow rate of working fluid through the valve when the flap is closed meet the technical requirements. As practice shows, this is not enough. With this approach, valve defects manifest themselves only during the tests of assemblies as part of the engine. This paper proposes a method to examine the characteristics of control valves such as «nozzle-flap», as well as criteria for assessing the quality of their execution. Experimental characteristics of control valves such as «nozzle-flap» for an actual regulator of free turbine rotation frequency are given. New data on the outflow of liquid from the nozzle with a flap have been obtained. It is shown that the destruction of the stagnation zone in the nozzle tip could result in that the valve flow rate increases, which negatively affects the characteristics of the hydraulic drive and regulator in general. A technique has been proposed to improve the stability of the valve’s performance by increasing the relative length of the nozzle. It is shown that the most informative characteristic of the valve is the dependence of flow rate on the position of the flap. Based on this characteristic, it is possible to determine the criteria for rejecting valves without testing them as part of the assembly

Loop-mediated fluorescent probes for selective discrimination of parallel and antiparallel G-Quadruplexes

Herein we report simple pyridinium (1–3) and quinolinium (4) salts for the selective recognition of G-quadruplexes (G4s). Among them, the probe 1, interestingly, selectively discriminated parallel (c-KIT-1, c-KIT-2, c-MYC) G4s from anti-parallel/hybrid (22AG, HRAS-1, BOM-17, TBA) G4s at pH 7.2, through a switch on response in the far-red window. Significant changes in the absorption (broad 575 nm → sharp 505 nm) and emission of probe 1 at 620 nm, attributed to selective interaction with parallel G4s, resulted in complete disaggregation-induced monomer emission. Symmetrical push/pull molecular confinements across the styryl units in probe 1 enhanced the intramolecular charge transfer (ICT) by restricting the free rotation of CC units in the presence of sterically less hindered and highly accessible G4 surface/bottom tetrads in the parallel G4s, which is relatively lower extent in antiparallel/hybrid G4s. We confirm that the disaggregation of probe 1 was very effective in the presence of parallel G4–forming ODNs, due to the presence of highly available free surface area, resulting in additional π-stacking interactions. The selective sensing capabilities of probe 1 were analyzed using UV–Vis spectroscopy, fluorescence spectroscopy, molecular dynamics (MD)–based simulation studies, and 1H NMR spectroscopy. This study should afford insights for the future design of selective compounds targeting parallel G4s.

Synthesis, crystal structures and solid-state acidochromism of multiaryl-substituted pyridine derivatives with aggregation-induced emission property

Pyridine derivatives have been widely reported as fluorescent sensors in solution phase, but they are rarely used in solid state due to aggregation-caused quenching effect. Herein, two new multiaryl-substituted pyridine derivatives with benzofuran (ABFP) and benzothiophene (ABTP) at 6-position were synthesized to study solid-state emissions and fluorescence stimulus-responsive properties. These two compounds have highly twisted molecular conformations, as revealed by the single-crystal structure analyses. They emit slight fluorescence in pure organic solutions due to the free rotations of peripheral aromatic rings, whereas show strong blue/cyan emissions in aggregated state because of the restriction of intramolecular rotation, revealing typical aggregation-induced emission (AIE) characteristic. These compounds adopt loose stacking arrangements and have weak intermolecular interactions, which are advantageous to strong solid-state emissions. Upon the stimulation of trifluoroacetic acid-ethylenediamine, the ABFP and ABTP solid-state samples exhibit a transformation in fluorescence colour between blue and green/yellow-green, revealing reversible acidochromic activities. Furthermore, the protonation of the nitrogen atom on the pyridine ring is unambiguously confirmed to be responsible for the acidochromic activities in solid state by the single-crystal structure analyses. The work provides important information for the design of the fluorescent molecules with AIE and solid-state acidochromism based on the traditional pyridine skeleton.