Rotational Degrees Of Freedom Research Articles

Anisotropic active Brownian particle with a fluctuating propulsion force.

The active Brownian particle (ABP) model describes a swimmer, synthetic or living, whose direction of swimming is a Brownian motion. The swimming is due to a propulsion force, and the fluctuations are typically thermal in origin. We present a two-dimensional model where the fluctuations arise from nonthermal noise in a propelling force acting at a single point, such as that due to a flagellum. We take the overdamped limit and find several modifications to the traditional ABP model. Since the fluctuating force causes a fluctuating torque, the diffusion tensor describing the process has a coupling between translational and rotational degrees of freedom. An anisotropic particle also exhibits a mass-dependent noise-induced drift, which does not disappear in the overdamped limit. We show that these effects have measurable consequences for the long-time diffusivity of active particles, in particular adding a contribution that is independent of where the force acts.

High-resolution CH stretch spectroscopy of jet-cooled cyclopentyl radical: First insights into equilibrium structure, out-of-plane puckering, and IVR dynamics.

First, high-resolution sub-Doppler infrared spectroscopic results for cyclopentyl radical (C5H9) are reported on the α-CH stretch fundamental with suppression of spectral congestion achieved by adiabatic cooling to Trot ≈ 19(4) K in a slit jet expansion. Surprisingly, cyclopentyl radical exhibits a rotationally assignable infrared spectrum, despite 3N - 6 = 36 vibrational modes and an upper vibrational state density (ρ ≈ 40-90 #/cm-1) in the critical regime (ρ ≈ 100 #/cm-1) necessary for onset of intramolecular vibrational relaxation (IVR) dynamics. Such high-resolution data for cyclopentyl radical permit detailed fits to a rigid-rotor asymmetric top Hamiltonian, initial structural information for ground and vibrationally excited states, and opportunities for detailed comparison with theoretical predictions. Specifically, high level ab initio calculations at the coupled-cluster singles, doubles, and perturbative triples (CCSD(T))/ANO0, 1 level are used to calculate an out-of-plane bending potential, which reveals a C2 symmetry double minimum 1D energy surface over a C2v transition state. The inversion barrier [Vbarrier ≈ 3.7(1) kcal/mol] is much larger than the effective moment of inertia for out-of-plane bending, resulting in localization of the cyclopentyl wavefunction near its C2 symmetry equilibrium geometry and tunneling splittings for the ground state too small (<1MHz) to be resolved under sub-Doppler slit jet conditions. The persistence of fully resolved high-resolution infrared spectroscopy for such large cyclic polyatomic radicals at high vibrational state densities suggests a "deceleration" of IVR for a cycloalkane ring topology, much as low frequency torsion/methyl rotation degrees of freedom have demonstrated a corresponding "acceleration" of IVR processes in linear hydrocarbons.

"Awakening" of the S2 Emission of Tricarbocyanine Dyes Stimulated by Interaction with Carbon Quantum Dots.

Anti-Kasha emission (i.e., the emission from Sn (n > 1) excited levels) of infrared chromophores which possess intensive absorption and S1 emission in the near-infrared region, but which are spectrally silent in the visible, is a challenging task for relevant applications such as energy conversion, bioimaging, sensitization of solar cells, optical sensors, and so on. Here we demonstrate a dual emission of near-infrared tricarbocyanine dyes with a bright green S2 fluorescence, whose quantum yield increases by 2-4 times together with a strong enhancement of the spontaneous rate of S2 fluorescence, whereas the quantum yield of S1 emission decreases by 2-7 times, respectively, as a result of immobilization of the dye molecule via interaction with carbon quantum dots. The enhanced immobilization-induced S2 emission is shown to occur because of planarization of the molecule and freezing its rotational degrees of freedom as indicated by suppression of the dye hot-band absorption-assisted anti-Stokes S1 emission.

(Digital Presentation) Carbon Quantum Dot Assisted Enhancement of S2 Fluorescence of Near-Infrared Dyes through Immobilization-Induced Emission Effect

Aggregation-induced emission of organic dyes is a phenomenon in which organic luminophores show higher photoluminescence (PL) efficiency in the aggregated state than in a free molecule, due to the freezing rotational degrees of freedom of the luminophore which otherwise quench the PL emission. In many cases, however, coupling of molecules leads to quenching of their emission due to the concentration quenching or self-quenching (exciton-exciton annihilation) effect. Therefore, in order to realize an enhanced PL emission as a result of molecule-molecule interaction a fine balance should be achieved between freezing rotational degrees of freedom of the molecule and escaping self-quenching effect. This could be realized via immobilization of the luminophore onto the inert surface.Here, we demonstrate an enhancement of specific S2 emission of the near-infrared (NIR) dyes of tricarbocyanine family due to their immobilization on the surface of carbon nanoparticles that induce freezing a specific planar conformation of the molecule imposed by the carbon plane of the particle it interact with. Carbon quantum dots serve as inert particles that render an opposite influence on the S1 and S2 emission of the tricarbocyanine dyes. We demonstrate a dual emission of the NIR tricarbocyanine dyes with a bright green S2 fluorescence, which is relatively weak for the free dye molecule but whose quantum yield increases by 2-4 times, together with a strong enhancement of the spontaneous rate of S2 fluorescence, whereas the quantum yield of S1 emission in the NIR decreases by 2-7 times, respectively, as a result of immobilization of the dye molecule via the interaction with carbon quantum dots. The above changes are dependent on the terminal and meso-groups of the dye and the solvent used. The dye immobilization due to interaction with carbon quantum dots causes freezing rotational degrees of freedom of the molecule as indicated by suppression of the dye hot band absorption-assisted anti-Stokes S1 emission.The observed “lighting up” of an anti-Kasha emission, i.e., the emission from Sn (n>1) excited levels, of the NIR chromophores which possess intensive S1 absorption and emission in the NIR region, but which are spectrally silent in the visible, can lead to their potential applications in the fields such as energy conversion, bio-imaging and bio-sensing, sensitization of solar cells, etc.

Lack of collective motion in granular gases of rotators

The dynamics of gases made of particles interacting dissipatively—known as granular gases—can be fully described by the translational and rotational motion of the individual particles; however, most of the results in the field refer to the limit of smooth particles, which implies that the rotational degrees of freedom are suppressed. Here we investigate the opposite limit: we consider a granular gas where the translational degrees of freedom are suppressed, and the key degrees of freedom are rotational. Our results indicate that for many-particle systems of pure rotators collective effects almost completely suppressed. This is in a sharp contrast to granular gases of smooth particles and other conventional matter where the translational degrees of freedom dominate the kinetics.

Orientation-Insensitive Chipless RFID Achieved in Multiple Rotational Degrees of Freedom

Frequency-coded chipless radio frequency identification (RFID) suffers from resonant frequency detuning caused by misaligned orientations. The literature has employed topological symmetry to prevent shape variations; however, this scheme is effective only for the orientation in roll and cannot address other rotational degrees of freedom, including pitch and yaw. This study takes the first step to cope with the orientation mismatch against arbitrary roll, pitch, and yaw angles. The proposed technique requires the design of tag and new reader architecture, eliminating complex signal processing. The tag comprises resonators with the pattern of a short dipole. Two reader antennas are placed orthogonally and fed with equal power, illuminating co-polarized electromagnetic waves toward the tag. Based on the Pythagorean trigonometric identity, the sum of the backscattering power is unvarying against the rotations in pitch or yaw. The proposed technique is experimentally validated using a 6.97 bit system. When orientation mismatch in yaw appears, the proposed scheme improves the read reliability from 54.3% to 93.5%. Moreover, when mismatch in both roll and yaw occurs, the reliability is improved from 43.8% to 91.8%. Practical aspects, including various detection zones and the loading effect, are also analyzed.

Six-degrees-of-freedom simulation model for future multi-megawatt airborne wind energy systems

Currently developed airborne wind energy systems have reached sizes of up to several hundred kilowatts. This paper presents the high-level design and a six-degrees-of-freedom model of a future fixed-wing airborne wind energy system operated in pumping cycles. This framework is intended to be used as an open-source reference system. The fixed-wing aircraft has a span of 42.5 m and produces a nominal electrical power of 3 MW. The ground station is modelled as a winch with a rotational degree of freedom describing the reel-in and reel-out motion, constant drum diameter and drive train inertia. A quasi-static approach is used to model the relatively stiff tether. The tether is discretised by 16 segments with variable length to account for reeling. A tracking controller ensures the kite's flight path during the autonomous pumping cycle operation. The controller alternates between crosswind figure-of-eight manoeuvres while reeling out and gliding on an arc-shaped path towards the ground station during retraction. The operational and controller parameters are determined using a CMA-ES evolution algorithm to maximise the average cycle power of a specific kite design at different wind speeds and given operational constraints. The algorithm identifies optimised flight paths for a range of wind speeds up to 30 m s−1 leading to a power curve with a cut-in wind speed of 10 m s−1 at operating altitude.

Competition between collective and individual conical intersection dynamics in an optical cavity

Light-induced nonadiabatic phenomena arise when molecules or molecular ensembles are exposed to resonant external electromagnetic fields. The latter can either be classical laser or quantized cavity radiation fields, which can couple to either the electronic, nuclear or rotational degrees of freedom of the molecule. In the case of quantized radiation fields, the light–matter coupling results in the formation of two new hybrid light–matter states, namely the upper and lower ‘polaritons’. Light-induced avoided crossings and light-induced conical intersections (CIs) between polaritons exist as a function of the vibrational and rotational coordinates of single molecules. For ensembles of N molecules, the N − 1 dark states between the two optically active polaritons feature, additionally, so-called collective CIs, involving the coordinates of more than one molecule to form. Here, we study the competition between intramolecular and collective light-induced nonadiabatic phenomena by comparing the escape rate from the Franck–Condon region of a single molecule and of a molecular ensemble coupled to a cavity mode. In situations where the polaritonic gap would be large and the dark-state decay channels could not be reached effectively, the presence of a seam of light-induced CI between the polaritons facilitates again the participation of the dark manifold, resulting in a cooperative effect that determines the overall non-radiative decay rate from the upper into the lower polaritonic states.

Dynamic Stability of Cracked Composite Plates

In this study, the dynamic instability region of cracked composite plates subjected to periodic axial loading has been investigated numerically by using the finite element method. A composite plate based on classical lamination theory is modeled by using the finite element method. It is assumed that the boundary condition of the composite plate is fixed on one side and the other sides are free. The composite plate is divided into square plate elements, each having four nodes. Each node has one translational and two rotational degrees of freedom, therefore, the square plates have twelve degrees of freedom. Mathieu-Hill type motion equation, which is used to calculate the dynamic instability region of the plate is created by using energy expressions obtained from the Lagrange equation. The developed MATLAB finite element code is used to examine the effect of crack on dynamic instability region for composite plates.

Adjusting unit cell three-dimensional posture and mirror array: A novel lattice structure design approach

Lattice structures’ performance is directly determined by the topological structure and arrangement of cells. Here, we propose a lattice structure design approach that generates predictable mechanical properties by adjusting the three-dimensional posture and mirror arrays of cells. Specifically, the Euler angle (α β γ) is introduced to accurately control the three rotational degrees of freedom of the orthogonal unit cell. Then, a new unit cell with symmetric characteristics composed of multiple primitive rotation units is constructed by mirror operation, which is called super variable pose Octahedral Structures (SVPOS). The mathematical model of SVPOS topological structure is established, the mapping relationship between Euler Angle and relative density is deduced, and the mechanical response of structures with different Euler angles is studied. The results show that Structure of α = β = γ = 30˚ obtained the best performance, and the elastic modulus, compressive strength, and energy absorption at 50% strain of it are 553.1%, 471.9% and 529% of that of the octahedral, respectively. The new lattice structure can be obtained by adjusting the Euler Angle, its relative density and performance can be better predicted, which can provide experimental and theoretical basis for the design of lattice structures that meet different requirements.

Dynamic control of octahedral rotation in perovskites by defect engineering

Engineering oxygen octahedra rotation patterns in $ABO_3$ perovskites is a powerful route to design functional materials. Here we propose a strategy that exploits point defects that create local electric dipoles and couple to the oxygen sublattice, enabling direct actuation on the rotational degrees of freedom. This approach, which relies on substituting an $A$ site with a smaller ion, paves a way to couple dynamically octahedra rotations to external electric fields. A common antisite defect, $\mathrm{Al_{La}}$ in rhombohedral LaAlO$_3$ is taken as a prototype to validate the idea, with atomistic density functional theory calculations supported with an effective lattice model to simulate the dynamics of switching of the local rotational degrees of freedom to long distances. Our simulations provide an insight of the main parameters that govern the operation of the proposed mechanism, and allow to define guidelines for screening other systems where this approach could be used for tuning the properties of the host material.

Attitude dynamics and control of a large flexible space structure by means of a minimum complexity model

A technique for deriving a low-order model of a large, deformable space vehicle, with a configuration resembling that of the International Space Station, is proposed. The modeling approach is based on a hybrid Newtonian–Lagrangian approach, where a generalized Euler equation is written for rotational degrees of freedom, whereas the dynamics of states associated to deformation by means of a Galërkin approach is derived by means of a Lagrangian formulation. The assumed modes method is adopted, where modal characteristics of the main deformable structure are estimated on the basis of its real characteristics, estimated by means a finite element model of the actual truss configuration. A cluster of control moment gyroscopes is considered as the actuator for attitude control. Open- and closed-loop maneuvers are considered, in order to highlight coupling between rotational and deformation degrees of freedom. The modeling tools allows for a quick search of gains which minimizes structural excitations during large angle slews.

Modeling lattice metamaterials with deformable joints as an elastic micropolar continuum

Planar lattice metamaterials, such as periodic beam networks, are often considered as the micropolar continuum, where each material point has two translational degrees of freedom and one rotational degree of freedom. The joints through which bars are linked to one another are generally approximated as rigid. This study focuses on lattices with complex-structured deformable joints. The deformation field in each joint is obtained by conducting structural analyses. Once the “stiffness matrix” of the joint-centered unit cell is obtained by the finite element method, it can be used as the input for the standard procedure of calculating micropolar elastic moduli that are based on the equivalence of strain energy. As a result, effective moduli can be expressed in a semi-analytical form, meaning that only the cell structural stiffness is given numerically. The present model is validated by comparison to the FEM simulations. Particularly, the auxetic and anisotropic properties are discussed for various lattice metamaterials with deformable joints. We then take the obtained effective moduli as inputs to the in-house micropolar FEM code and obtain results agreeing well with the FEM structural simulations.

Image Based Control of 2-Dof Ball Balancing System

In this study, Ball-Plate stabilization system is designed to control with image processing algorithms. The position of the ball is aimed to control by tilting the plate on which the ball is located at certain positions and speeds. The system has two rotational degrees of freedom and is an unstable system. Accordingly, a closed-loop controller is designed using a PID controller, the error in the system response is calculated, and the communication is established with the sensors and actuators. In this way, the position of the ball can be controlled so that it converges to the center point on the plate. In the system, two DC motors are used as an actuator and a camera is used as a feedback sensor. In order to generate the transfer function, the mathematical modeling of the system is calculated. The image taken from the camera is processed and the position information of the ball is obtained. The motors are driven with the obtained position information. Maximum Overshoot and Steady State Error is calculated for both x-y axis and results are given in figures.

Probing Two Distinct Types of Topological Rainbow Concentrators Related to the Acoustic Valley Hall Insulator in Synthesized Three-Dimensional Space

Synthesized three-dimensional space provides us with a platform to explore the intriguing acoustic valley Hall insulator. In this paper, a rotational degree of freedom is introduced to construct a synthetic three-dimensional space. Based on simulations, our results show that Weyl points and Fermi arcs and topologically nontrivial edge modes appear in a synthetic space. Not only rotational operation but also boundary truncation can modulate the frequencies of nontrivial edge states, which result in two completely different edge states at the upper and lower boundaries. Using frequencies of edge states protected by Weyl points, we devise two different acoustic topological rainbow devices. The two devices are able to trap states with different frequency components at different spatial positions: one device is capable of capturing low-frequency components at close range, while the other has the ability to confine low-frequency components at long distances. This work may boost further the development of topological rainbow devices in a synthetic space related to the acoustic valley Hall insulator.

Constructing Spin Density Vector Twists With Spin Density Singularity

In this article, we propose a non-orbital angular momentum (OAM) method for constructing the spiral twists of spin density (SD) vectors in three-dimensional (3D) optical fields. This is realized by generating strings of SD singularities in a longitudinal plane of a strongly focused HG10 mode beam with circular polarization. We demonstrate that in this plane, the SD singularities manifest themselves as the Gouy phase difference. Through observing the Gouy phase difference, the strings of the SD singularities and their topological reactions are examined. It is found that the spiral twists of SD vectors are constructed in the two-dimensional (2D) space between two strings and their twisting behaviors can be adjusted by the topological reactions of the strings. This finding shows that the spiral twists can be formed in a 2D space rather than the 1D space in previous studies, which provides a more flexible way to utilize this rotational degree of freedom. Our result also clarifies that although the spiral twists of SD vectors can be a result of spin-orbital angular momentum interaction, the OAM is not a necessary condition for the generation of these twists. Our theoretical proposal for structuring SD vectors may have applications in 3D optical manipulation.

Self-adaptive 3D lattice for curved sandwich structures

The design and fabrication of curved sandwich structures with a 3D lattice core always faces the challenge of adaptability and connectivity between the core and the skins. Here, we propose a pinned method by releasing rotational degrees of freedom in the common node of the adjacent lattice cells. The design of the lattice core only needs to consider the size and number of cells rather than the shape of the skins. The pinned design demonstrates advantages in self-adaption of the 3D lattice core to skins with generalized cylindrical type and ensures to fabricate curved sandwich structures of a large scale. Lattice samples of four kinds of node-connection forms with three different strut thicknesses are fabricated to investigate the effects of pin-joint design and strut thickness on mechanical performance. Lattices with suitable collinear connection design have comparable modulus and strength to snap-fitted lattices. The proposed method has the potential for standardized production of curved 3D lattice sandwich structures with excellent mechanical performance. • We propose a pinned method by releasing rotational degrees of freedom in the common node of the adjacent lattice cells. • The pinned design demonstrates advantages in self-adaption of the 3D lattice core to generalized cylindrical skins. • Lattices with suitable collinear connection design have comparable mechanical behaviors to snap-fitted lattices.

Multi-scale dispersive gradient elasticity model with rotation for the particulate composite

Research on the characteristics of composites material has received enormous interest in recent years. The multi-scale nature of composite material leads to employing advanced techniques. Moreover, the presence of a wave with the high-frequency source adds complexity to the analysis. In this paper, a novel multi-scale elasticity model was developed to predict the wave dispersion property of particulate composites. The methodology was based on the simultaneous participation of translational and rotational degrees of freedom in motion equations. The method scheme of gaining motion equations was accomplished by using Taylor's expansion as a continualization method. The framework of the motion equations and restrictions determined the layout of the lattice. The obtained lattice was a network of polydispersive particles in three-dimensional as a unit cell. The model proposed the inertia coefficient and dimension coefficient, which reflected the heterogeneity on the particulate composite. The theoretical results were then validated with experimental results. For this aim, concrete and mortar with the various classes of heterogeneity were nominated as a sample of particulate composite material. The nominated composites were prepared with different mixture schemes from geopolymer paste. The wave dispersion behavior of geopolymer specimens was established by measuring phase velocity in various frequencies. In addition to geopolymer products, experimental results from independent literature were scrutinized for concrete and mortar with cement binder. In the end, the capability of the presented parameters was indicated for realizing the state of concrete curing and features of the binder.

A micropolar peridynamic differential operator and simulation of crack propagation

The micropolar continuum explains the size effects in the materials with microstructures by attaching micro-rotations to the material points, but it still encounters difficulties when describing discontinuities. The peridynamic theory takes its advantage in dealing with discontinuous problems. This work formulates the micropolar continuum under the peridynamic differential operator framework. The micropolar elasticity field equations with spatial derivatives are rewritten in the spatial integral form such that the discontinuities can be naturally embedded in the micropolar continuum body. To check the accuracy and effectiveness of such micropolar peridynamic differential operator formulation, the stress concentration factor of a two-dimensional square plate with a central circular hole subjected to unidirectional constant stress was simulated and compared with the results of finite element analysis. The stationary crack propagation phenomena of three modes were reproduced respectively by considering a critical stretch with rotational degrees of freedom. The impact of characteristic length on the crack propagation was investigated. It is found that characteristic length has an insignificant effect on the mode I crack while significantly affects the mode II crack. The work provides some essential references for the fracture behavior modeling of materials with microstructures.

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.