Extra Degree Of Freedom Research Articles

Supersymmetrizing the Pasti-Sorokin-Tonin action

In this paper the harmonic superspace action of the tensor multiplet of N = (1, 0), d = 6 supersymmetry is constructed which in the bosonic limit reduces to the known Pasti-Sorokin-Tonin action for the self-dual tensor field. The action involves, besides the potential containing the dynamical fields, also an auxiliary tensor multiplet and a set of analytic superfields with gauge PST scalar among them. For each of gauge symmetries of the PST action, a superfield analog is found. The equations of motion are calculated and it is shown that no extra degrees of freedom appear.

K-Ambiguity function in the framework of offset linear canonical transform

A new version of ambiguity function (AF) associated with the offset linear canonical transform (OLCT) is considered in this paper. This new version of AF coined as the [Formula: see text]-AF associated with the OLCT ([Formula: see text]-AFOL) is defined based on the OLCT and the fractional instantaneous auto-correlation. A natural magnification effect characterized by the extra degrees of freedom of the OLCT and by a factor [Formula: see text] on the frequency axis enables the [Formula: see text]-AFOL to have flexibility to be used in cross-term reduction. Firstly, we defined the [Formula: see text]-AF associated with the OLCT ([Formula: see text]-AFOL), and establish its relationship with the [Formula: see text]-Wigner distribution in OLCT domain. Later on, we define the basic properties including the scaling, conjugate-symmetry, shifting, marginal and Moyal’s formulae of [Formula: see text]-AFOL in depth. The results show that [Formula: see text]-AFOL can be viewed as one of the generalizations of the classical AF which has elegance, simplicity and flexibility in the frequency marginal property. The novelty of our paper lies in applications part, where we have shown how the proposed transform is used for the detection of single-component and bi-component linear frequency-modulated (LFM) signals.

Gauge symmetry of the chiral Schwinger model from an improved gauge unfixing formalism

In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain values of the α parameter, two second-class constraints, which means that this system does not possess gauge invariance. However, we know that it is possible to disclose gauge symmetries in such a system by converting the original second-class system into a first-class one. This procedure can be done through the gauge unfixing (GU) formalism by acting with a projection operator directly on the original second-class Hamiltonian, without adding any extra degrees of freedom in the phase space. One of the constraints becomes the gauge symmetry generator of the theory and the other one is disregarded. At the end, we have a first-class Hamiltonian satisfying a first-class algebra. Here, our goal is to apply a new scheme of embedding second-class constrained systems based on the GU formalism, named improved GU formalism, in the BCSM. The original second-class variables are directly converted into gauge invariant variables, called GU variables. We have verified that the Poisson brackets involving the GU variables are equal to the Dirac brackets between the original second-class variables. Finally, we have found that our improved GU variables coincide with those obtained from an improved BFT method after a particular choice for the Wess-Zumino terms.

Scaling of bi-material sandwich panels subjected to impact loadings

Scaling is a widely used concept in impact and explosion engineering which is mainly utilized to predict the response behaviour of large-scale mechanical structures by conducting experiments on scaled trial models. However, the practical application of currently available conventional scaling methodologies for impact and explosive processes are significantly restricted by their inability to properly capture the scale effects of strain rate and strain hardening. Also, they are suffering from an insufficient number of independent degrees of freedom. Furthermore, the zeroth-order finite similitude theory, which can annihilate the non-scalability of rate and hardening effects, doesn’t provide us with efficient scaling methods when the investigated structure is made out of different materials. More precisely, the zeroth-order finite similitude theory and the classical dimensional analysis, which are suffering from a limited number of independent degrees of freedom, cannot scale the elastic-plastic behaviour represented by different parts of a structure made out of different materials. In other words, classical scaling methodologies including dimensional analysis and even the zeroth-order finite similitude theory cannot fix two different features having the same unit using different degrees of freedom, which make them useless for structures made of more than one material such as bi-material sandwich panels. In the presented paper, a new scaling methodology is developed based on the recently proposed first-order finite similitude theory which for the first time enables us to capture the rate dependent plastic behaviour of an impacted structure made out of two different materials. A sandwich panel made of two different materials which is subjected to an impact loading is considered as the case study in order to investigate the efficiency of the proposed first-order based scaling technique. The numerical results are determined using Abaqus finite element software in which the Johnson-Cook constitutive equation is utilized to take into account the rate and hardening effects on the initial yield stress. The results reveal that the behaviour of impacted full-scale bi-material sandwich panels can be predicted with a high accuracy when the extra degree of freedom provided us with the first-order finite similitude (i.e. R1) is set to vary between −1 and 1 (i.e. [Formula: see text]). Furthermore, it is found that the pure mechanical and thermo-mechanical behaviour of the impacted core honeycomb are highly accurately predicted using scaled-down trial models which are made from dissimilar materials and designed based on the zeroth-order finite similitude theory.

Fractional Sliding Mode Harmonic Control of an Active Power Filter

A sliding mode control (SMC) strategy with a fractional-order scheme is developed to provide an effective way to compensate for the harmonic current and strengthen the performance of an active power filter (APF). The formulation of a fractional-order sliding mode controller (FOSMC) is incorporated in the current control of an APF control system, obtaining an extra degree of freedom over integer-order ones to improve the dynamic property. The simulation results of the APF utilizing the designed strategy confirm the satisfactory performance and smaller total harmonic distortion (THD) by comparative study.

A Bayesian approach to improving production planning

In this study, we present an efficient Bayesian framework for improving production planning decisions. The framework consists of a Bayesian modeling section that accounts for time correlation and mass balance, and an improved production planning formulation that considers the effect of model uncertainty, correlation, disturbances, process control, extra degrees of freedom and process limitations. The proposed Bayesian framework is implemented on an industrially relevant fluid catalytic cracking process model and is compared to the production planning process traditionally followed in the refining industry. Simulation results demonstrate that the proposed Bayesian model is 60% more accurate and requires half the training time of traditional industrial approaches. The resulting production planning structure has robust performance due to considering uncertainty in model predictions.

Dispersion engineering of spoof plasmonic metamaterials via interdigital capacitance structures.

This work presents an approach to realize the dispersion engineering of spoof plasmonic metamaterials with controllable cutoff frequencies. Interdigital capacitance structures are applied to construct the unit cells. Dispersion properties are firstly analyzed to investigate the effects of interdigital capacitance, and the influence of the geometrical parameters of the proposed unit cell on the cutoff frequencies is studied. Then, a spoof surface plasmon polariton (SSPP) transmission line (TL) is developed based on the proposed unit cell together with a smooth transition. The matching principles of the transition are explained by the dispersion curves and the normalized impedance of the corresponding matching unit cells. Finally, the transmission characteristics of the TL are simulated and measured to validate the feasibility of the proposed strategy. Both the lower and upper cutoff frequencies can be tuned jointly by the extra degrees of freedom provided by the interdigital capacitance structures. In comparison with designs based on a substrate-integrated waveguide (SIW), the proposed strategy can reduce the transversal dimension by a factor of two under the same conditions. This work can greatly accelerate the development of versatile microwave integrated circuits and systems based on spoof plasmonic metamaterials.

Design of a novel robust adaptive cascade controller for DC‐DC buck‐boost converter optimized with neural network and fractional‐order PID strategies

AbstractA cascade technique with two control loops is designed for a DC\DC Buck‐Boost converter that is a right half‐plane zero (RHPZ) structure called a non‐minimum phase system. This concept presents several challenging constraints for designing well‐behaved control techniques. Cascade controllers can provide various benefits compared with single loop controllers such as higher safety, higher robustness, and higher stability. This strategy assumes the system as a black‐box structure without the need for a mathematical model of the system. This benefit can decrease the computational burden and provides faster dynamics along with ease of implementation. This technique consisted of an outer Fractional‐order PID voltage controller tuned with the Antlion Optimizer (ALO) algorithm, which provides a reference current for the inner control loop of the Neural Network‐based LQR (NN‐LQR) controller. The basic principle in cascade controllers is a more rapid performance of the inner loop that has been satisfied with the NN‐LQR strategy, which optimizes and tunes the gains of the LQR controller and shows faster dynamics and higher robustness. It should be mentioned that the number of neurons is limited to 2 and 4 in each layer to decrease the computational burden with lower complexity. Also, the ALO algorithm is a modern nature‐inspired algorithm used to tune the PID gains with better results under‐constrained problems with diverse search spaces. Considering the negative impacts of various disturbances on a power converter, a Fractional‐order‐based PID (FO‐PID) control technique is a proper alternative since it shows higher robustness in load uncertainties along with better dynamical responses based on its extra degree of freedom. Moreover, to evaluate the superiority of this controller, two other controllers are designed using the PSO algorithm for PID and FO‐PID controllers. Finally, the presented cascade controller has been tested in various working conditions through simulation and experiment results.

Perspective on Meta-Boundaries

The judicious design of the electromagnetic boundary provides a crucial route to control light–matter interactions, and it is thus fundamental to basic science and practical applications. General design approaches rely on the manipulation of bulk properties of the superstrate or substrate and on the modification of boundary geometries. Due to the recent advent of metasurfaces and low-dimensional materials, the boundary can be flexibly featured with a surface conductivity, which can be rather complex but provide an extra degree of freedom to regulate the propagation of light. In this Perspective, we denote the boundary with a nonzero surface conductivity as the meta-boundary. The meta-boundaries are categorized into four types, namely, isotropic, anisotropic, biisotropic, and bianisotropic meta-boundaries, according to the electromagnetic boundary conditions. Accordingly, the latest developments for these four kinds of meta-boundaries are reviewed. Finally, an outlook on the research tendency of meta-boundaries is provided, particularly on the manipulation of light–matter interactions by simultaneously exploiting meta-boundaries and metamaterials.

Chaotic dynamics from coupled magnetic monodomain and Josephson current.

The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in the absence of an external ac drive, whereas in the superconductor-ferromagnet-superconductor Josephson junction, known as the φ_{0} junction, the magnetic layer effectively provides two extra degrees of freedom that can facilitate chaotic dynamics in the resulting four-dimensional autonomous system. In this work, we use the Landau-Lifshitz-Gilbert model for the magnetic moment of the ferromagnetic weak link, while the Josephson junction is described by the resistively capacitively shunted-junction model. We study the chaotic dynamics of the system for parameters surrounding the ferromagnetic resonance region, i.e., for which the Josephson frequency is reasonably close to the ferromagnetic frequency. We show that, due to the conservation of magnetic moment magnitude, two of the numerically computed full spectrum Lyapunov characteristic exponents are trivially zero. One-parameter bifurcation diagrams are used to investigate various transitions that occur between quasiperiodic, chaotic, and regular regions as the dc-bias current through the junction, I, is varied. We also compute two-dimensional bifurcation diagrams, which are similar to traditional isospike diagrams, to display the different periodicities and synchronization properties in the I-G parameter space, where G is the ratio between the Josephson energy and the magnetic anisotropy energy. We find that as I is reduced the onset of chaos occurs shortly before the transition to the superconducting state. This onset of chaos is signaled by a rapid rise in supercurrent (I_{S}⟶I) which corresponds, dynamically, to increasing anharmonicity in phase rotations of the junction.

Generic Modification of Gravity, Late Time Acceleration and Hubble Tension

We consider a scenario of large-scale modification of gravity that does not invoke extra degrees of freedom, but includes coupling between baryonic matter and dark matter in the Einstein frame. The total matter energy density follows the standard conservation, and evolution has the character of deceleration in this frame. The model exhibits interesting features in the Jordan frame realised by virtue of a disformal transformation where individual matter components adhere to standard conservation but gravity is modified. A generic parametrization of disformal transformation leaves thermal history intact and gives rise to late time acceleration in the Jordan frame, which necessarily includes phantom crossing, which, in the standard framework, can be realised using at least two scalar fields. This scenario is embodied by two distinguished features, namely, acceleration in the Jordan frame and deceleration in the Einstein frame, and the possibility of resolution of the Hubble tension thanks to the emergence of the phantom phase at late times.

The halo bias for number counts on the light cone from relativistic N-body simulations

We present the halo number counts and its two-point statistics, the observable angular power spectrum, extracted for the first time from relativistic N-body simulations. The halo catalogues used in this work are built from the relativistic N-body code gevolution, and the observed redshift and angular positions of the sources are computed using a non-perturbative ray-tracing method, which includes all relativistic scalar contributions to the number counts. We investigate the validity and limitations of the linear bias prescription to describe our simulated power spectra. In particular, we assess the consistency of different bias measurements on large scales, and we estimate up to which scales a linear bias is accurate in modelling the data, within the statistical errors. We then test a second-order perturbative bias expansion for the angular statistics, on a range of redshifts and scales previously unexplored in this context, that is 0.4 ≤ z̅ ≤ 2 up to scales ℓ max ∼ 1000. We find that the angular power spectra at equal redshift can be modelled with high accuracy with a minimal extension of the number of bias parameters, that is using a two-parameter model comprising linear bias and tidal bias. We show that this model performs significantly better than a model without tidal bias but with quadratic bias as extra degree of freedom, and that the latter is inaccurate at z̅ ≥ 0.7. Finally, we extract from our simulations the cross-correlation of halo number counts and lensing convergence. We show that the estimate of the linear bias from this cross-correlation is consistent with the measurements based on the clustering statistics alone, and that it is crucial to take into account the effect of magnification in the halo number counts to avoid systematic shifts in the computed bias.

Dispersion error control for underwater acoustic scattering problems using a coupled cell-based smoothed radial point interpolation method

A coupled cell-based smoothed radial point interpolation method is presented by combining the cell-based smoothed radial point interpolation method (CSRPIM) and the modified Dirichlet to Neumann boundary condition (MDtN-BC) to effectively control the dispersion error in predicting acoustic scattering. In the coupled CSRPIM, the MDtN-BC is used to satisfy the Sommerfeld radiation condition approaching infinity, and a cell-based smoothing operation together with the radial point interpolation method (RPIM) is adopted to soften the acoustic stiffness of the numerical model. The condensed RPIM shape functions are created by using real and virtual nodes, and virtual node selection schemes are studied to appropriately soften the stiffness. A major advantage of the coupled CSRPIM is that it can achieve very close-to-exact stiffness of the original model without introducing extra degrees of freedom. The properties of the proposed method are numerically studied. Simulations indicate that the six-virtual-node selection scheme performs the best. The results reveal that the developed method can significantly reduce the dispersion error and has excellent computational performance. In addition, the developed method shows good potential for practical acoustic-scattering prediction in engineering applications.

Wrist autonomy based on upper-limb synergy: a pilot study.

Incorporating an electrically powered wrist can largely improve the dexterity of a prosthetic hand when grasping various objects; however, it also intensifies the difficulty of the hand's operation due to the introduction of extra degrees of freedom (DOFs). The mechanism of multi-joint synergy in human body movements provides a new sight to solve this problem. In this paper, focusing on four typical manipulation activities of daily life (ADLs), 10 upper-limb joint angles were collected and analyzed first to verify the existence of synergy. Then, a linear regression model was established to predict the wrist rotation angle from the shoulder and elbow joints, which can be directly used as a control reference for achieving wrist autonomy. For both healthy and amputee subjects, experimental platforms were established and control tests were conducted, wherein the task completion time and compensatory movement during the four ADLs were evaluated. The results show that our synergy-based wrist autonomy method can effectively improve the completion efficiency of multiple ADLs without increasing the control complexity. Also, it can significantly reduce the compensatory movements of multiple joints compared to traditional prostheses using an idle wrist.

Quadratic-phase scaled Wigner distribution: convolution and correlation

In this paper, we propose the novel integral transform coined as the quadratic-phase scaled Wigner distribution (QSWD) by extending the Wigner distribution associated with quadratic-phase Fourier transform (QWD) to the novel one inspired by the definition of fractional bispectrum. A natural magnification effect characterized by the extra degrees of freedom of the quadratic-phase Fourier transform (QPFT) and by a factor k on the frequency axis enables the QSWD to have flexibility to be used in cross-term reduction. By using the machinery of QSWD and operator theory, we first establish the general properties of the proposed transform, including the conjugate symmetry, non-linearity, shifting, scaling and marginal. Then, we study the main properties of the proposed transform, including the inverse, Moyal’s, convolution and correlation. Finally, the applications of the newly defined QSWD for the detection of single-component and bi-component linear frequency-modulated (LFM) signal are also performed to show the advantage of the theory.

Inflationary flavor oscillations and the cosmic spectroscopy

Inflationary scenarios motivated by high-energy physics generically contain a plethora of degrees of freedom beyond the primordial curvature perturbation. The latter interacts in a simple way with what we name "inflationary flavor eigenstates", which differ, in general, from freely propagating "mass eigenstates". We show that the mixing between these misaligned states results in new striking behaviors in the squeezed limit of the curvature perturbation three-point function, depending not only on the mass spectrum but also on the "mixing angles" of the theory. These results bring about a new perspective on the cosmological collider program: contrary to a widespread belief, the primordial signal needs not be dominated by the lightest extra degree of freedom. Instead, we show that it may display either modulated oscillations, a broken power law, or a transition from oscillations to a power law, thus offering a detailed cosmic spectroscopy of the particle content of inflation.

Dynamics of diverse polarization singularities in momentum space with far-field interference

Polarization singularities in momentum space, including bound states in the continuum (BICs) and circularly polarized states (CPSs), render great potential in singular and chiral optics. As far-field topological signatures of Bloch modes in photonic crystal slab, the dynamic evolution of the polarization singularities is observed by tuning the geometric parameters of the slab itself. Here, we combine the photonic crystal slab with a reflected multilayer substrate in which interference between the reflected optical field and the upward radiation of the Bloch mode brings us an extra degree of freedom to manipulate the polarization singularities without breaking the structural symmetry. As the polarization singularities evolve with the spacing between the photonic crystal slab and the substrate, the CPSs and extrinsic BICs are both generated from charge reversal of the at-\ensuremath{\Gamma} intrinsic BIC and then collide with the off-\ensuremath{\Gamma} intrinsic BICs. Importantly, all BICs are topologically protected from splitting throughout the whole dynamic process owing to the preservation of structural symmetry. Our findings suggest an alternative route to pursue ultrahigh-$Q$ CPS resonances and merge diverse BICs, which is potentially applicable in chiral optics, topological photonics, and beam modulation.

Dielectric chiral metasurfaces for enhanced circular dichroism spectroscopy at near infrared regime.

Numerous applications of chiro-optical effects can be found in nanophotonics, including imaging and spin-selective absorption, particularly in sensing for separating and detecting chiral enantiomers. Flat single-layer metasurfaces composed of chiral or achiral sub-wavelength structures offer unique properties to manipulate the light due to their extraordinary light-matter interaction. However, at optical wavelengths, the generation of strong chirality is found to be challenging via conventional chiral metasurface approaches. This work intends to design and optimize a dielectric chiral meta-nano-surface based on a diatomic design strategy to comprehend giant chiro-optical effects in the near-infrared (NIR) regime for potential application in circular dichroism (CD) spectroscopy. Instead of using a single chiral structure that limits the CD value at optical wavelengths, the proposed metasurface used a diatomic (two meta-atoms with distinct geometric parameters) chiral structure as a building block to significantly enhance the chiro-optical effect. Combining both meta-atoms in a single periodicity of the building block introduces constructive and destructive interferences to attain the maximum circular dichroism value exceeding 75%. Moreover, using multipolar resonance theory, the physics behind the generation of giant chiro-optical effects have also been investigated. The proposed dielectric chiral meta-platform based on the extra degree of freedom can find application in compact integrated optical setups for CD spectroscopy, enantiomer separation and detection, spin-dependent color filters, and beam splitters.

LMI-Based H∞ Observer Design for Nonlinear Lipschitz System

The problem of circle criterion-based H∞ observer design for nonlinear systems is addressed in this article. An LMI-based observer is developed for the nonlinear Lipschitz systems with linear outputs under the presence of noise/disturbances. The proposed LMI condition is obtained by using reformulated Lipschitz property, standard Young's relation and a newly defined positive definite matrix multiplier. The inclusion of the matrix multiplier adds additional numbers of decision variables in the LMI, which provides extra degrees of freedom from a feasibility point of view. Further, the performance of the proposed observer is validated using numerical examples.

On trigonometric interpolation in an even number of points

In contrast to odd-length trigonometric interpolants, even-length trigonometric interpolants need not be unique; this is apparent from the representation of the interpolant in the (real or complex) Fourier basis, which possesses an extra degree of freedom in the choice of the highest-order basis function in the even case. One can eliminate this degree of freedom by imposing a constraint, but then the interpolant may cease to exist for certain choices of the interpolation points. On the other hand, the Lagrange representation developed by Gauss always produces an interpolant despite having no free parameters. We discuss the choice Gauss's formula makes for the extra degree of freedom and show that, when the points are equispaced, its choice is optimal in the sense that it minimizes both the standard and 2-norm Lebesgue constants for the interpolation problem. For non-equispaced points, we give numerical evidence that Gauss's formula is no longer optimal and consider interpolants of minimal 2-norm instead. We show how to modify Gauss's formula to produce a minimal-norm interpolant and that, if the points are equispaced, no modification is necessary.