Independent Degrees Of Freedom Research Articles

Steady as they hover: kinematics of kestrel wing and tail morphing during hovering flights.

Wind-hovering birds exhibit remarkable steadiness in flight, achieved through the morphing of their wings and tail. We analysed the kinematics of two nankeen kestrels (Falco cenchroides) engaged in steady wind-hovering flights in a smooth flow wind tunnel. Motion-tracking cameras were used to capture the movements of the birds as they maintained their position. The motion of the birds' head and body, and the morphing motions of their wings and tail were tracked and analysed using correlation methods. The results revealed that wing sweep, representing the flexion/extension movement of the wing, played a significant role in wing motion. Additionally, correlations between different independent degrees of freedom (DoF), including wing and tail coupling, were observed. These kinematic couplings indicate balancing of forces and moments necessary for steady wind hovering. Variation in flight behaviour between the two birds highlighted the redundancy of DoF and the versatility of wing morphing in achieving control. This study provides insights into fixed-wing craft flight control from the avian world and may inspire novel flight control strategies for future fixed-wing aircraft.

Focus tunable vector autofocusing Airy vortex beams resist atmospheric turbulence.

The rapid increase in orbital angular momentum (OAM) mode size with increasing modal order, given the limited-size of the receiver, is a major impediment to high-capacity OAM mode multiplexing in practice. Based on the Pancharatnam-Berry (PB) phase theory, we correlate the change of the polarization state with the curvature of the wavefront isophase line in the source plane and manipulate the focusing ability of vector autofocusing Airy vortex beam (AAVB) by combining the isophase line curvature and the intensity gradient of the beam, which are two independent degrees of freedom. The present method enables flexible on-demand focusing of vector AAVBs in free space and is more effective in focusing higher order OAM modes, which can reduce the full-width at half maximum (FWHM) of the AAVB with topological charge l= 25 to 1/5 of that of the conventional scalar type. And the modulated vector AAVB is superior to the conventional scalar one in terms of mitigating atmospheric turbulent disturbance. The work provides a potentially useful basis for improving the capability of future free-space OAM systems for large-scale dense communications.

Inflationary initial conditions for the cosmological gravitational wave background

The initial conditions on the anisotropies of the stochastic gravitational-wave background of cosmological origin (CGWB) largely depend on the mechanism that generates the gravitational waves. Since the CGWB is expected to be non-thermal, the computation of the initial conditions could be more challenging w.r.t. the Cosmic Microwave Background (CMB), whose interactions with other particles in the early Universe lead to a blackbody spectrum. In this paper, we show that the initial conditions for the cosmological background generated by quantum fluctuations of the metric during inflation deviate from adiabaticity. These primordial gravitational waves are indeed generated by quantum fluctuations of two independent degrees of freedom (the two polarization states of the gravitons). Furthermore, the CGWB plays a negligible role in the Einstein's equations, because its energy density is subdominant w.r.t. ordinary matter. Therefore, the only possible way to compute the initial conditions for inflationary gravitons is to perturb the energy-momentum tensor of the gravitational field defined in term of the small-scale tensor perturbation of the metric. This new and self-consistent approach shows that a large, non-adiabatic initial condition is present even during the single-field inflation. Such a contribution enhances the total angular power spectrum of the CGWB compared to the standard adiabatic case, increasing also the sensitivity of the anisotropies to the presence of relativistic and decoupled particles in the early Universe. In this work we have also proved that our findings are quite general and apply to both single-field inflation and other scenarios in which the CGWB is generated by the quantum fluctuations of the metric, like the curvaton.

Transmissive reconfigurable metasurface enabling independent control of active and passive modules through weak coupling

Metasurfaces have demonstrated rich electromagnetic control capabilities and degrees of freedom in past years. As is well known, for passive metasurfaces, their functionalities cannot be further expanded accordingly once prototypes are established. Therefore, reconfigurable metasurfaces, utilizing active devices to replace geometric changes in passive structures, have received widespread attention, especially with the development of wireless communication recently. In reconfigurable metasurfaces, artificial meta-atoms are composed of active devices and passive structures combined together. However, these two modules are usually utilized as a whole due to the tight coupling of the active devices and the passive structures, which results in passive structures not receiving sufficient attention and being utilized as independent degrees of freedom. In this article, we propose the concept of weakly coupled reconfigurable metasurfaces in transmissive systems, enabling independent control of active and passive modules through weak coupling. As the proof of concept, a simple weakly coupled system is proposed, which can realize the transmission wavefront engineering through the geometric changes of meta-structures in passive mode, while achieving switching between transmission and reflection states in active mode, respectively. Our exploration lies in making use of the physical structure, which is easily neglected in traditional reconfigurable metasurface design, emphasizing the collaborative work of active and passive modules, exploring more available variables within the same aperture, and providing a potential solution for balancing functionality and resource consumption in practical applications.

A deep-learning model for the density profiles of subhaloes in IllustrisTNG

ABSTRACT We present a machine-learning-based model for the total density profiles of subhaloes with masses $M \gtrsim 7\times 10^8\, h^{-1}{\rm M}_\odot$ in the IllustrisTNG100 simulation. The model is based on an interpretable variational encoder (IVE) which returns the independent factors of variation in the density profiles within a low-dimensional representation, as well as the predictions for the density profiles themselves. The IVE returns accurate and unbiased predictions on all radial ranges, including the outer region profile where the subhaloes experience tidal stripping; here its fit accuracy exceeds that of the commonly used Einasto profile. The IVE discovers three independent degrees of freedom in the profiles, which can be interpreted in terms of the formation history of the subhaloes. In addition to the two parameters controlling the normalization and inner shape of the profile, the IVE discovers a third parameter that accounts for the impact of tidal stripping on to the subhalo outer profile; this parameter is sensitive to the mass loss experienced by the subhalo after its infall on to its parent halo. Baryonic physics in the IllustrisTNG galaxy formation model does not impact the number of degrees of freedom identified in the profile compared to the pure dark matter expectations, nor their physical interpretation. Our newly proposed profile fit can be used in strong lensing analyses or other observational studies which aim to constrain cosmology from small-scale structures.

Active Oxygenated Structure‐Intensified CO2 Capture Enables Efficient Electrochemical Ethylene Production Over Carbon Nanofibers

AbstractThe pursuit of high efficacy C−C coupling during the electrochemical CO2 reduction reaction remains a tremendous challenge owing to the high energy barrier of CO2 activation and insufficient coverage of the desired intermediates on catalytic sites. Inspired by the concept of capture‐coupled CO2 activation, we fabricated quinone‐grafted carbon nanofibers via an in situ oxidative carbonylation strategy. The quinone functionality of carbon nanofibers promotes the capture of CO2 followed by activation. At a current density of 400 mA cm−2, the Faradaic efficiency of ethylene reached 62.9 %, and a partial current density of 295 mA cm−2 was achieved on the quinone‐rich carbon nanofibers. The results of in situ spectroscopy and theoretical calculations indicated that the remarkable selectivity enhancement in ethylene originates from the quinone structure, rather than the electronic properties of Cu particles. The interaction of quinone with CO2 increases the local *CO coverage and simultaneously hinders the co‐adsorption of *H on Cu sites, which greatly reduces the energy barrier for C−C coupling and restrains subsequent *CO protonation. The modulation strategy involving specific oxygenated structure, as an independent degree of freedom, guides the design of functionalized carbon materials for tailoring the selectivity of desired products during the CO2 capture and reduction.

Active Oxygenated Structure-Intensified CO2 Capture Enables Efficient Electrochemical Ethylene Production Over Carbon Nanofibers.

The pursuit of high efficacy C-C coupling during the electrochemical CO2 reduction reaction remains a tremendous challenge owing to the high energy barrier of CO2 activation and insufficient coverage of the desired intermediates on catalytic sites. Inspired by the concept of capture-coupled CO2 activation, we fabricated quinone-grafted carbon nanofibers via an in situ oxidative carbonylation strategy. The quinone functionality of carbon nanofibers promotes the capture of CO2 followed by activation. At a current density of 400 mA cm-2, the Faradaic efficiency of ethylene reached 62.9 %, and a partial current density of 295 mA cm-2 was achieved on the quinone-rich carbon nanofibers. The results of in situ spectroscopy and theoretical calculations indicated that the remarkable selectivity enhancement in ethylene originates from the quinone structure, rather than the electronic properties of Cu particles. The interaction of quinone with CO2 increases the local *CO coverage and simultaneously hinders the co-adsorption of *H on Cu sites, which greatly reduces the energy barrier for C-C coupling and restrains subsequent *CO protonation. The modulation strategy involving specific oxygenated structure, as an independent degree of freedom, guides the design of functionalized carbon materials for tailoring the selectivity of desired products during the CO2 capture and reduction.

Design, Manufacturing, and Open-Loop Control of a Soft Pneumatic Arm

Soft robots distinguish themselves from traditional robots by embracing flexible kinematics. Because of their recent emergence, there exist numerous uncharted territories, including novel actuators, manufacturing processes, and advanced control methods. This research is centred on the design, fabrication, and control of a pneumatic soft robot. The principal objective is to develop a modular soft robot featuring multiple segments, each one with three degrees of freedom. This yields a tubular structure with five independent degrees of freedom, enabling motion across three spatial dimensions. Physical construction leverages tin-cured silicone and a wax-casting method, refined through an iterative processes. PLA moulds that are 3D-printed and filled with silicone yield the desired model, while bladder-like structures are formed within using solidified paraffin wax-positive moulds. For control, an empirically fine-tuned open-loop system is adopted. This paper culminates in rigorous testing. Finally, the bending ability, weight-carrying capacity, and possible applications are discussed.

Vector vortex beams sorting of 120 modes in visible spectrum

Abstract Polarization (P), angular index (l), and radius index (p) are three independent degrees of freedom (DoFs) of vector vortex beams, which have found extensive applications in various domains. While efficient sorting of a single DoF has been achieved successfully, simultaneous sorting of all these DoFs in a compact and efficient manner remains a challenge. In this study, we propose a beam sorter that simultaneously handles all the three DoFs using a diffractive deep neural network (D2NN), and demonstrate the robust sorting of 120 Laguerre–Gaussian (LG) modes experimentally in the visible spectrum. Our proposed beam sorter underscores the considerable potential of D2NN in optical field manipulation and promises to enhance the diverse applications of vector vortex beams.

Quantum remote control utilizing multiple degrees of freedom

We present protocols for remote implementation of general operators between two nodes, which are considered: the first where an arbitrary single-qubit operation acts on photon state in the polarization degree of freedom, and the second with photon state in the temporal degree of freedom. By employing simultaneous entanglement in two independent degrees of freedom, both protocols are fulfilled near deterministically in two steps. In the first step, the effective cross-Kerr interaction and X-quadrature measurements of the coherent states are main tools for achieving the goal. Together with the available existing optical elements and common single-photon detectors, the construction circuit of the second step is simple and feasible with current technologies. Our protocols are beneficial to long-distance quantum communication and quantum metrology.

Four-DOF Robotic Arm System for Goods Transport

Paper presents the design, development, and implementation of a Four-Degree-of-Freedom (Four-DOF) Robotic Arm System tailored for the purpose of efficient goods transport. The increasing demand for automation in logistics and industrial sectors has prompted the need for versatile robotic solutions capable of manipulating objects in various environments. The proposed robotic arm system addresses this need by offering four independent degrees of freedom, enabling it to perform intricate tasks involved in goods transport. The system's mechanical design incorporates four joints, each contributing to a specific movement: lifting, lowering, rotating, and extending. These movements provide the necessary flexibility to manoeuvre in complex spaces, making it suitable for applications within warehouses, factories, and distribution canters. The design process involved careful consideration of structural integrity, weight distribution, and motion optimization to ensure safe and precise operation. In conjunction with the mechanical design, the robotic arm is equipped with advanced sensing and control mechanisms. Sensor arrays, including proximity sensors and cameras, enable the arm to perceive its environment and detect objects, ensuring accurate object detection and collision avoidance. The control system, driven by a combination of microcontrollers and software algorithms, orchestrates the movement of each joint to achieve seamless coordination and efficient goods transport. Real-world implementation of the Four-DOF Robotic Arm System showcases its ability to streamline goods transport operations. By automating tasks that previously required manual intervention, the system enhances operational efficiency, reduces labour costs, and minimizes the risk of human error. Furthermore, its adaptability to diverse environments underscores its potential to revolutionize the logistics industry.

Micropolar Elasticity in Physically-Based Animation

We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material's strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We propose a new orthotropic micropolar curvature energy that allows us to make materials stiff to bending in specific directions. For the simulation of dynamic micropolar deformables we propose a novel incremental potential formulation with a consistent FEM discretization that is well suited for the use in physically-based animation. This allows us to easily couple micropolar deformables with dynamic collisions through a contact model inspired from the Incremental Potential Contact (IPC) approach. For the spatial discretization with FEM we discuss the challenges related to the rotational degrees of freedom and propose a scheme based on the interpolation of angular velocities followed by quaternion time integration at the quadrature points. In our evaluation we validate the consistency and accuracy of our discretization approach and demonstrate several compelling use cases for micropolar materials. This includes explicit control over bending and torsion stiffness, deformation through prescription of a volumetric curvature field and robust interaction of micropolar deformables with dynamic collisions.

Evolution of the wave function's shape in a time-dependent harmonic potential

Abstract An effective operational approach to quantum mechanics is to focus on the evolution of wave packets, for which the wave function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of freedom describing the shape of the wave packet and its fluctuations. These quantum dressing are independent degrees of freedom, mathematically encoded in the higher moments of the wave function. We review how to extract the effective dynamics for Gaussian wave packets evolving according to the Schrödinger equation with time-dependent potential in a 1 + 1-dimensional spacetime, and derive the equations of motion for the quadratic uncertainty. We then show how to integrate the evolution of all the higher moments for a general wave function in a time-dependent harmonic potential.

Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions

Standard relativistic hydrodynamics has been successful in describing the properties of the strongly interacting matter produced in the heavy-ion collision experiments. Recently, there has been a significant theoretical advancement in this field to explain spin polarization of hadrons emitted in these processes. Although current models have successfully explained some of the experimental data based on the coupling between spin polarization and vorticity of the medium, they still lack a clear understanding of the differential measurements. This is commonly interpreted as an indication that the spin needs to be treated as an independent degree of freedom whose dynamics is not entirely bound to flow circulation. In particular, if the spin is a macroscopic property of the system, in equilibrium its dynamics should follow hydrodynamic laws. Here, we develop a framework of relativistic hydrodynamics which includes spin degrees of freedom from the quantum kinetic theory for Dirac fermions and use it for modeling the dynamics of matter. Following experimental observations, we assume that the polarization effects are small and derive conservation laws for the net baryon current, the energy–momentum tensor and the spin tensor based on the de Groot–van Leeuwen–van Weert definitions of these currents. We present various properties of the spin polarization tensor and its components, analyze the propagation properties of the spin polarization components, and derive the spin-wave velocity for arbitrary statistics. We find that only the transverse spin components propagate, analogously to the electromagnetic waves. Finally, using our framework, we study the space–time evolution of the spin polarization for the systems respecting certain space–time symmetries and calculate the mean spin polarization per particle, which can be compared to the experimental data. We find that, for some observables, our spin polarization results agree qualitatively with the experimental findings and other model calculations.

An EFT hunter’s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes

We derive the contact terms contributing to the four-point amplitudes of the standard model particles, keeping terms with up to quartic energy growth. Imposing just the unbroken low-energy symmetry, and treating the electroweak gauge bosons and the Higgs as independent degrees of freedom, we obtain the most general four-point contact-term amplitudes, corresponding to the Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (SMEFT) predictions, via on-shell Higgsing of the massless SMEFT contact terms. We discuss several aspects of bottom-up versus top-down on-shell derivations of the HEFT and SMEFT amplitudes, highlighting in particular the simple counting of HEFT dimensions in the on-shell approach and the transparent relation between perturbative unitarity and gauge-invariance in the little-group covariant massive spinor formalism. Our results provide a formulation of Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis.

FLUTTER SPEED LIMITS OF SUBSONIC WINGS

Flutter is a phenomenon resulting from the interaction between aerodynamic and structural dynamic forces and may lead to a destructive instability. The aerodynamic forces on an oscillating airfoil combination of two independent degrees of freedom have been determined. The problem resolves itself into the solution of certain definite integrals, which have been identified as Theodorsen functions. The theory, being based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing-ection theory relating to the steady case. The mechanism of aerodynamic instability has been analyzed in detail. An exact solution, involving potential flow and the adoption of the Kutta condition, has been analyzed in detail. The solution is of a simple form and is expressed by means of an auxiliary parameter K. The use of finite element modeling technique and unsteady aerodynamic modeling with the V-G method for flutter speed prediction was used on a fixed rectangular and tapered wing to determine the flutter speed boundaries. To build the wing the Ansys 5.4 program was used and the extract values were substituted in the Matlab program which is designed to determine the flutter speed and then predicted the various effects on flutter speed. The program gave us approximately identical results to the results of the referred researches. The following wing design parameters were investigated skin shell thickness, material properties, cross section area for beams, and changing altitude. Results of these calculations indicate that structural mode shape variation plays a significant role in the determination of wing flutter boundary.

A brain-computer typing interface using finger movements.

Intracortical brain computer interfaces (iBCIs) decode neural activity from the cortex and enable motor and communication prostheses, such as cursor control, handwriting and speech, for people with paralysis. This paper introduces a new iBCI communication prosthesis using a 3D keyboard interface for typing using continuous, closed loop movement of multiple fingers. A participant-specific BCI keyboard prototype was developed for a BrainGate2 clinical trial participant (T5) using neural recordings from the hand-knob area of the left premotor cortex. We assessed the relative decoding accuracy of flexion/extension movements of individual single fingers (5 degrees of freedom (DOF)) vs. three groups of fingers (thumb, index-middle, and ring-small fingers, 3 DOF). Neural decoding using 3 independent DOF was more accurate (95%) than that using 5 DOF (76%). A virtual keyboard was then developed where each finger group moved along a flexion-extension arc to acquire targets that corresponded to English letters and symbols. The locations of these letter/symbols were optimized using natural language statistics, resulting in an approximately a 2× reduction in distance traveled by fingers on average compared to a random keyboard layout. This keyboard was tested using a simple real-time closed loop decoder enabling T5 to type with 31 symbols at 90% accuracy and approximately 2.3 sec/symbol (excluding a 2 second hold time) on average.

Analysis of flow characteristics and throttling loss of a novel high-frequency two-dimensional rotary valve

High-speed on-off valve uses its high-frequency characteristics to realize the switching effect of fast opening and closing or generate relatively continuous pressure and flow. Compared with the conventional direct acting structure, the frequency of reciprocating sliding of the valve spool is limited due to the need to overcome the large inertial force, while the valve spool of the rotary valve structure can easily achieve continuous and rapid rotary movement, which makes it easier to quickly open or close the hydraulic valve. Therefore, a novel high-frequency two-dimensional rotary valve is proposed. Through the two-dimensional rotary valve, the fluid is discretized in the form of fluid pulse width modulation to realize the flow distribution according to the demand of the system actuator. The spool has two independent degrees of freedom: the rotary motion of the spool is used to control the frequency of the fluid pulse width modulation and the axial displacement of the spool is used to control its width. Inspired by the working principle of the high-speed on-off valve to realize the instantaneous release of energy by quickly opening action, the flow characteristics and throttling loss of two-dimensional rotary valve are analyzed. The shape of the valve port of the high-frequency two-dimensional rotary valve is designed, flow field models with different valve port angle are established and the throttling loss of the valve port is obtained, which is verified by the simulation and the experiment. The working principle of two-dimensional rotary valve is similar to the high-speed on-off valve group, but compared with the high-speed on-off valve using the electric signal control mode, two-dimensional rotary valve can control the flow only by controlling the axial position of the valve spool. The high-frequency two-dimensional rotary valve using fluid pulse width modulation is expected to be used in variable system, load sensing system, distributed power source and other systems with variable and energy-saving requirements.

Pure gauge theory for the gravitational spin connection

The gravitational spin connection appears in gravity as a non-Abelian gauge field for the Lorentz group $SO(3,1)$, which is non-compact. The action for General Relativity is linear in the field strength associated to the spin connection, and its equation of motion corresponds to the standard metricity constraint. Consequently, the zero-torsion spin connection is never realized as an independent degree of freedom and is determined by the vierbein field. In this work, we take a different perspective and consider a pure Yang-Mills theory for the spin connection coupled to Dirac fermions, resulting in the former being a dynamical field. After discussing various approaches towards managing the pathologies associated with non-compact gauge theories, we compute the tree-level amplitude for fermion scattering via a spin connection exchange. In contrast to integrating out torsion in the presence of fermions, the model induces a chiral four-Fermi like term that involves a right-right current interaction, which is not present in the Standard Model.

Practically Enhanced Hyperentanglement Concentration for Polarization-Spatial Hyperentangled Bell States with Linear Optics and Common Single-Photon Detectors

Hyperentanglement, defined as the simultaneous entanglement in several independent degrees of freedom (DOFs) of a quantum system, is a fascinating resource in quantum information processing with its outstanding merits. Here we propose heralded hyperentanglement concentration protocols (hyper-ECPs) to concentrate an unknown partially less polarization-spatial hyperentangled Bell state with available linear optics and common single-photon detectors. By introducing time-delay DOFs, the schemes are highly efficient in that the success of the scheme can be accurately heralded by the detection signatures, and postselection techniques or photon-number-resolving detectors, necessary for previous experiments, are not required. Additionally, our linear optical architectures allow certain states, where concentration fails, to be recyclable, and a trick makes the success probabilities of our schemes higher than those of previous linear optical hyper-ECPs.