Free Rotation Research Articles

Investigation of buckling of rectilinear beams with additional constraint at an arbitrary internal point

Summary The problems of stability and instability (buckling) of compressed rectilinear beams are considered. The beams are treated as one-dimensional elastic bodies possessing stiffnesses of two kinds: the stiffness with respect to extension–compression and the stiffness with respect to bending. The ends of beams are hinged, but along with traditional setting of a problem, characterized by one movable hinge and a given compressive load, the problem with both immovable end hinges fixing the ends of a beam in a compressed state, is considered. In addition to the ends, the beams are assumed to be constrained in a certain way at some internal point located at an arbitrary specified distance from one of the ends. These constraints are supposed to prohibit either lateral displacements with free rotation (a hinge), or rotation with free lateral displacements. Analytical solutions for all four types of problems regarding the onset of instability are obtained and examined with respect to the position of additional constraint. It turned out that results for the cases of one movable end hinge with given compressive load and of fixed end hinges, coincide. In the case of additional hinge, its middle position provides maximal value of the critical force, whereas its limiting end position corresponds to its minimal value. As for the case of additional constraint prohibiting rotation, its middle position corresponds to minimal value of the critical force, whereas its maximal value is attained at a certain internal point of a beam located approximately at the distance of one-sixth of its length from one of the ends.

Analysis of Conformational Preferences in Caffeine.

High level DLPNO–CCSD(T) electronic structure calculations with extended basis sets over B3LYP–D3 optimized geometries indicate that the three methyl groups in caffeine overcome steric hindrance to adopt uncommon conformations, each one placing a C–H bond on the same plane of the aromatic system, leading to the C–H bonds eclipsing one carbonyl group, one heavily delocalized C–N bond constituent of the fused double ring aromatic system, and one C–H bond from the imidazole ring. Deletion of indiscriminate and selective non-Lewis orbitals unequivocally show that hyperconjugation in the form of a bidirectional –CH aromatic system charge transfer is responsible for these puzzling conformations. The structural preferences in caffeine are exclusively determined by orbital interactions, ruling out electrostatics, induction, bond critical points, and density redistribution because the steric effect, the allylic effect, the Quantum Theory of Atoms in Molecules (QTAIM), and the non-covalent interactions (NCI), all predict wrong energetic orderings. Tiny rotational barriers, not exceeding 1.3 kcal/mol suggest that at room conditions, each methyl group either acts as a free rotor or adopts fluxional behavior, thus preventing accurate determination of their conformations. In this context, our results supersede current experimental ambiguity in the assignation of methyl conformation in caffeine and, more generally, in methylated xanthines and their derivatives.

On the free rotation of a polarized spinning-top as a test of the correct radiation reaction torque

The formula for dipole radiation reaction torque acting on a system of charges, and the Larmor-like formula for the angular momentum loss by this system, differ in the time derivative term which is the analogue of the Schott term in the energy loss problem. In the well-known textbooks this discrepancy is commonly avoided via neglect of the Schott term, and the Larmor-like formula is preferred. In the present paper both formulae are used to derive two different equations of motion of a polarized spinning-top. Both equations are integrable for the symmetric top and lead to quite different solutions. That one following from the Larmor-like formula is physically unplausible, in contrast to another one. This result is accorded with the reinterpretation of Larmor’s formula discussed recently in the pedagogical literature. It is appeared, besides, that the Schott term is of not only academic significance, but it may determine the behavior of polarized micro- and nanoparticles in nature or future experiments.

Dynamics of Hydrogen in Silicon at Finite Temperatures from First Principles

Hydrogen defects in silicon still hold unsolved problems, whose disclosure is fundamental for future advances in Si technologies. Among the open issues is the mechanism for the condensation of atomic hydrogen into molecules in Si quenched from above to room temperature. Based on first‐principles calculations, the thermodynamics of hydrogen monomers and dimers is investigated at finite temperatures within the harmonic approximation. Free energies of formation indicate that the population of cannot be neglected when compared to that of at high temperatures. The results allow us to propose that molecular formation occurs during cooling processes, in the temperature window , above which the molecules collide with Si—Si bonds and dissociate, and below which the fraction of becomes negligible. The formation of and most notably of a fast‐diffusing neutral species can also provide an explanation for the apparent accelerated diffusivity of atomic hydrogen at elevated temperatures in comparison to the figures extrapolated from measurements carried out at cryogenic temperatures. Finally, it is shown that the observed diffusivity of molecules is better described upon the assumption that they are nearly free rotors, all along the migration path, including at the transition state.

Elucidating structure and dynamics of crystalline α-zirconium phosphates intercalated with water and methanol by multinuclear solid-state MAS NMR: A comprehensive NMR approach.

Solid-state NMR experiments on 2 H, 31 P, 13 C, and 1 H nuclei, including 31 P T1 , 1 H T1 , and 1 H T1ρ measurements, as well as on the kinetics of proton-phosphorus cross-polarization have been performed to characterize the crystalline and amorphous α-zirconium phosphates, which were intercalated with D2 O and/or CD3 OD. The 13 C{1 H} CP MAS NMR experiment performed for compound 1-CD3 OD (Zr (HPO4 )2. 0.2CD3 OD) with carbon cross-polarization via protons of phosphate groups has provided a prove that the methanol was intercalated into the interlayer spaces of this compound. The variable-temperature 2 H solid-echo MAS NMR spectra of intercalated compounds demonstrated that the methanol molecules, in contrast to the mobile water, were immobile, keeping, however, free CD3 rotations around the C3 -axis. It has been demonstrated that the intercalated species, D2 O and CD3 OD, do not affect the high-frequency motions of the phosphate groups. By utilizing local structural models that satisfy the constraints of the experimental data, it has been suggested that the immobile methanol molecules are located in the cavity between two neighboring layers of the zirconium phosphates. Thus, the present work illustrates the reliable criteria in a comprehensive NMR approach to structural and dynamic studies of such systems.

The Network Global Optimal Mapping Approach Utilizing a Discrete Firefly Optimization Algorithm

The three methods, agent-based model (ABM), product life cycle management (PLM), and discrete firefly optimization algorithm (DFOA), used herein rely on local infrastructure functions after reviewing the local and global functions. Then, a resolution of the multi-layered neural network is proposed. A resolution has been saved at all levels of the structure. A global approximation function that keeps learning samples stored is employed. The local map is converted using a set having a respective free rotation. Then, the translation is reflected by a global map of each local map using the affine transformation. The differences of the conversion that the optimal global map uses by minimizing the common sensor nodes are shared by the discovery of different local maps. The optimal conversion is found by running a discrete firefly optimization algorithm (DFOA). Thus, local map registration can resolve the merged map-based approach for each of several pairs and can achieve better performance. Therefore, it provides a systematic approach to building a global map from a local map. A computer simulation was conducted to verify the performance and efficiency of the algorithm.

Theoretical Model of Bending Moment for Straight Mortise-and-Tenon Joints with Wooden Pegs Involving a Gap.

The stress mechanism of a straight mortise-and-tenon joint with wooden pegs in traditional residential wooden structures was analyzed, and a theoretical moment-rotation model of the joint was derived. To verify the model, three full-scale joint specimens were fabricated and subjected to low-cycle reversed loading tests. All specimens showed tensile cracking parallel to the grain at the top or bottom of the tenon neck. The theoretical calculation results are consistent with the experimental results. The results of the parametric analysis based on the theoretical model show the following: the rotational stiffness and bending moment of the joint increase as the beam width increases; as the beam height increases, the moment increases, but the initial stiffness of the joint is only slightly impacted; as the column diameter increases, the initial stiffness and moment increase, and the free rotation of the joint decreases; as the gap between the mortise and tenon increases, the initial stiffness and moment decrease; as the sliding friction coefficient increases, both the rotational stiffness and moment of the joint increase, and the increase is greater after the joint yields than before.

Characterization of Multifunctional and Non‐stereoselective Oxidoreductase RubE7/IstO, Expanding the Functional Diversity of the Flavoenzyme Superfamily

AbstractFlavin‐dependent enzymes enable a broad range of redox transformations and generally act as monofunctional and stereoselective catalysts. Herein, we report the investigation of a multifunctional and non‐stereoselective FMN‐dependent oxidoreductase RubE7 from the rubrolone biosynthetic pathway. Our study outlines a single RubE7‐catalysed sequential reduction of three spatially distinct bonds in a tropolone ring and a reversible double‐bond reduction and dehydrogenation. The crystal structure of IstO (a RubE7 homologue) with 2.0 Å resolution reveals the location of the active site at the interface of two monomers, and the size of active site is large enough to permit both flipping and free rotation of the substrate, resulting in multiple nonselective reduction reactions. Molecular docking and site mutation studies demonstrate that His106 is oriented towards the substrate and is important for the reverse dehydrogenation reaction.

Characterization of Multifunctional and Non-stereoselective Oxidoreductase RubE7/IstO, Expanding the Functional Diversity of the Flavoenzyme Superfamily.

Flavin-dependent enzymes enable a broad range of redox transformations and generally act as monofunctional and stereoselective catalysts. Herein, we report the investigation of a multifunctional and non-stereoselective FMN-dependent oxidoreductase RubE7 from the rubrolone biosynthetic pathway. Our study outlines a single RubE7-catalysed sequential reduction of three spatially distinct bonds in a tropolone ring and a reversible double-bond reduction and dehydrogenation. The crystal structure of IstO (a RubE7 homologue) with 2.0 Å resolution reveals the location of the active site at the interface of two monomers, and the size of active site is large enough to permit both flipping and free rotation of the substrate, resulting in multiple nonselective reduction reactions. Molecular docking and site mutation studies demonstrate that His106 is oriented towards the substrate and is important for the reverse dehydrogenation reaction.

Modeling of Molten Metal Flows in a Continuous-Casting Machine Mold at Free Rotation of the Floating Closed-Bottom Nozzle

Currently, mathematical modeling applying numerical methods is widely used in the study of metallurgical processes, including metal casting processes in continuous-casting machines. The authors developed a new technology and device for casting metal into a continuous-casting machine mold and metal mixing using the effect of a rotating closed-bottom submerged nozzle with eccentric holes. The theoretical study of processes of mold filling with molten metal was carried out applying a proven numerical method and a special software package. A calculation program was developed based on the numerical schemes and algorithms. The results of calculating metal casting into a rectangular mold are presented as an example. The calculation results are provided in the form of molten metal flow patterns in various sections of the mold.

Free Rotation of Simple Molecules and Characteristic Temperatures in Glassy Polymers

Free Rotation of Simple Molecules and Characteristic Temperatures in Glassy Polymers

Surgical assistant manipulator with diagonal joints and multi-stage telescopic screws for laparoscopic solo surgery.

A surgeon in a sterilized area can perform robotically assisted laparoscopic solo surgery while controlling a laparoscope-holding robot for view stabilization and a forceps robot for pulling organs. At present, no locally operated surgical assistant manipulator with a mechanical remote center of motion (RCM) is available to operate within a small space while providing a wide range of movement. The present study describes a new locally operated detachable end-effector manipulator (LODEM) with diagonal joints and multi-stage telescopic screws. A forceps manipulator attached to commercial surgical forceps was developed. This manipulator uses RCM diagonal joints for the yaw and pitch axes, providing an intuitive pivot point and free rotation, and telescopic nested screws with multiple sliders clamp the commercial forceps for the axis of insertion. The manipulator placed above the abdominal wall using a fixed arm connected to a bed rail is motor controlled by a handheld interface with button switches for precise traction and is controlled manually for easy rough positioning. Positional accuracy at the tip with a load of 5N was under 0.5mm. Mechanical deflection was under 2.1mm. The manually controlled force was under 4.4N. Successful simulated laparoscopic cholecystectomy using the prototype manipulator to handle the target and maintain stability was performed on a surgically realistic gallbladder model. A LODEM with diagonal joints and multi-stage telescopic screws was developed to facilitate minimally invasive, robotically assisted laparoscopic solo surgery by a surgeon working near the patient. This electric motor-controlled laparoscopic instrument holder by the surgeon in the surgical field could be used for such applications.

Air-Stable Thermoluminescent Carbodicarbene-Borafluorenium Ions.

Borenium ions, originally synthesized as fundamentally important laboratory curiosities, have attracted significant attention due to their applications in catalysis and frustrated Lewis pair chemistry. However, investigations of the materials properties of these types of compounds are exceptionally rare. Herein, we report the synthesis, molecular structures, and optical properties of a new class of air-stable borenium ions, stabilized by the strongly donating carbodicarbene (CDC) ligand (2, 3, 6). Notably, CDC-borafluorenium ions exhibit thermoluminescence in solution, a result of a twisted intramolecular charge transfer process. The temperature responsiveness, which is observable by the naked eye, is assessed over a 20 to -60 °C range. Significantly, compound 2 emits white light at lower temperatures. In the solid state, these borocations exhibit increased quantum yields due to aggregation-induced emission. CDC-borafluorenium ions with two different counteranions (Br-, BPh4-) were investigated to evaluate the effect of anion size on the solution and solid-state optical properties. In addition, CDCs containing both symmetrical and unsymmetrical N-heterocycles (bis(1-isopropyl-3-methylbenzimidazol-2-ylidene)methane and bis(1,3-dimethyl-1,3-dihydro-2H-benzo[d]imidazol-2-ylidene)methane) were tested to understand the implications of free rotation about the CDC ligand carbon-carbon bonds. The experimental work is complemented by a comprehensive theoretical analysis of the excited-state dynamics.

Control Signal Analysis of Four Ring Space Stabilized Platform

In order to build a four ring space stable platform using free rotor gyroscope, the spatial layout of gyroscope and frame axis should be briefly analyzed, and the installation shafting should be orthogonal or perpendicular to each other to facilitate control and decoupling. On this basis, through the sensitive angle analysis of gyro and frame shafting, the control signals acting on each frame are deduced. Finally, through the physical design of the control loop of the space stability platform, the correctness of the research method and design form is demonstrated, which has theoretical guiding significance for the design of the space stability control loop.

Optimization of two-dimensional irregular bin packing problem considering slit distance and free rotation of pieces

In this paper, we present a two-dimensional irregular bin packing problem (2DIBPP) that takes into account the slit distance and allows the pieces to rotate freely. The target is to arrange a specified collection of pieces with irregular shapes into a minimal number of bins. Firstly, we develop a mathematical model for the 2DIBPP that considers slit distance and free rotation of the pieces, and an equidistant edge expansion approach is then proposed to handle the slit distance. Secondly, a two-stage method is implemented to get a finite collection of promising rotation angles, effectively decreasing the search neighbourhood. Thirdly, we decompose the 2DIBPP into two sub-problems: piece assignment and packing. The Partial Bin Packing (PBP) strategy is employed in the allocation stage, and we adopt an overlap minimization method to pack the pieces into an individual bin. Finally, we use a local search (LS) algorithm to advance the quality of the solutions by adjusting the piece assignment across bins. Experimental evidence exhibits that our approach is competitive in most instances of the literature, with four better results in five benchmark instances.

B-O-B bridged BOPPY derivatives: synthesis, structures, and acid-catalyzed cis-trans isomeric interconversion.

A new class of BOPPY derivatives has been facilely synthesized by a two-step reaction of coupling 3,5-dimethylpyrrole-2-carbaldehyde with 2,3-dihydrazinoquinoxaline (QDH) followed by coordinating with BF3·OEt2. The reaction mainly produces a triboron complex 3 within 1 h, while a pair of B-O-B bridged trans-cis isomers 4 and 4' are formed as the reaction time elongates to 8 h. Moreover, two bromide products 4Br and 4Br' are prepared almost quantitatively by the bromination of 4 and 4', respectively. The coordinated B-N bonds impede the free rotation of the B-O-B bridge, resulting in a high-energy polytopal rearrangement that makes the diastereomers 4, 4' and 4Br, 4Br' separable and stable under ambient conditions. Interestingly, these two diastereomeric pairs undergo feasible cis-trans interconversion in the presence of weak acid due to the acid-catalyzed B-N bond cleavage followed by rotational isomerism. In addition, optical, electrochemical and theoretical results suggest that the conformational differences in the (BF)O(BF) part have little effect on the photophysical and electronic properties of such compounds.

ON DIFFUSE INSTABILITY OF ORTHOTROPIC VISCOPLASTIC PLATES

Elastic strain is covered by the effective medium homogenization method inside a representative volume element (RVE). It has an incremental quasi rate-independent (QRI) form obtained by the endochronic concept of thermodynamic time. The rate dependence takes place by means of stress rate dependent value of the initial yield stress. Free meso rotations and constrained micro rotations within a representative volume element (RVE) are assumed. A comparison between QRI and J2 diffuse instability equations is presented for orthotropic materials. A new QRI nonlinear evolution equation for orthotropic materials is derived by tensor function representation with Spencer-Boehler structural tensors.

Cyclic Trinuclear Copper(I) Complex Exhibiting Aggregation-Induced Emission: A Novel Fluorescent Probe for the Selective Detection of Gold(III) Ions.

Coordination complexes with aggregation-induced-emission (AIE) behavior has drawn much attention because of their promising applications. Conventionally, the AIE-active metal-organic complexes are prepared from an AIE-active organic ligand, and the construction of such coordination complexes from aggregation-caused-quenching (ACQ) ligands is still challenging. Herein, we have synthesized two new cyclic trinuclear complexes (CTCs), namely, 1 and 2, from copper(I) and silver(I) and a ACQ ligand [4-(3,5-dimethyl-1H-pyrazol-4-yl)benzaldehyde, HL]. (1) exhibited AIE behavior, and the emission intensity is enhanced ∼20 times when it aggregates, which can be attributed to its tight packing and multiple intermolecular hydrogen bonds that restrained the intramolecular rotation, as confirmed by single-crystal X-ray diffraction analysis. On the other hand, (2) displayed ACQ effects, and the emission intensity is decreased ∼5 times when it aggregates. This ACQ behavior of 2 is related to its loose packing and free rotation of the ligand in crystals, resulting in nonradiative decay and fluorescence quenching. Interestingly, the CTCs 1 and 2 both exhibited a good affinity to gold(III) ions, allowing selective detection and sensing of gold ions. More importantly, the 2 shows a good limit of detection (3.28 μmol/L) and an ultrafast responsive time (∼2 s). Our studies pave a new route to designing novel AIE-active coordination complexes and further exploring the functionality of CTCs.

Breathing Room: Restoring Free Rotation in a Schiff-Base Macrocycle through Endoperoxide Formation.

Macrocyclization is a popular method for preparing hosts, but it can have unintended effects, like limiting molecular free rotation to yield mixtures of inseparable isomers. We report a [3 + 3] Schiff-base macrocycle (1) with anthracene bridges. Restricted rotation about the phenyl-anthracene bonds leads 1 to exist as a mixture of conformations (1Cs and 1C3v). Macrocycle 1 was photooxidized to tris(endoperoxide) adduct 4, alleviating restricted rotation. These results were supported by spectroscopic, structural, and computational analyses.

GA and GWO algorithm for the special bin packing problem encountered in field of aircraft arrangement

This paper addresses a special case of irregular bin packing problem which the irregular pieces with free rotation have to fill a large irregular stock sheet with defective regions while satisfying the special boundary constraint, i.e., the piece can protrude from the sheet so long as the key points in the piece’s interior lie within the container. The objective of this problem is to maximize the number of filled pieces. To our best knowledge, the piece must be placed completely inside the sheet for all packing problem tackled by published literature. Thus, existing approaches are not good solutions to this special packing problem. To achieve the goal of automated arrangement of pieces and maximize the space utilization, the genetic algorithm and grey wolf optimization algorithm are designed to solve it. The genetic algorithm adopts the elitism strategy for maintaining the portion of the best chromosomes. A new method of updating the main controlling parameter is applied for reinforcing the exploration ability of the grey wolf optimization. These two algorithms use a vector of pieces as the solution representation, and a novel heuristic algorithm decodes it to produce a layout. The proposed heuristic algorithm divides the process of packing into two stages with the objective of satisfying constraints and achieving good space utilization of sheet. Computational experiments show that the presented methods can solve this new kind of the packing problem very well.