Coupling Terms Research Articles

Incremental control as an enhanced and robust implementation of gain scheduled controllers avoiding hidden coupling terms

This paper proposes a new and simple method to combine incremental control with the classical proportional-integral (PI) control in order to increase the robustness properties of the resulting control law. The proposed method avoids hidden coupling terms in a similar manner to the differential PI controller implementation (DPI) and hence allows for fast gain scheduling. The integral action is accomplished by feedback of actuator measurements and therefore avoids integrator windup without complicated anti-windup schemes. The control law obtains an increase in robust performance with a response less sensitive to variations in flight dynamic parameters when compared to the equivalent PI controller. Improvement in disturbance rejection is also obtained with a faster and more robust response. Increased robustness toward input time delay is observed by example. The trade-off between increased robustness and sensitivity to sensor noise and delay can be adjusted with an intuitive tuning parameter. The novel method, denoted incremental DPI (iDPI), is investigated in the context of fixed-wing flight control. The concept is verified as a retrofit for an industry-level PI baseline controller for the longitudinal motion of a fixed-wing aircraft using a high-fidelity simulation model.

Non-trivial solutions and their stability in a two-degree-of-freedom Mathieu–Duffing system

The Mathieu–Duffing equation represents a basic form for a parametrically excited system with cubic nonlinearities. In multi-degree-of-freedom systems, parametric resonances and the associated limit cycles take place at both principal and combination resonance frequencies. Furthermore, using asynchronous parametric excitation of coupling terms leads to a broadband destabilization of the trivial solution and the appearance of limit cycles at non-resonant frequencies. Regarding applications, the utilization of this excitation method has its significant importance in micro- and nanosystems. On the one hand, cubic nonlinearities are found to be abundant in these systems. On the other hand, parametric excitation is preferably utilized in these systems for better amplification leading to an enhanced sensitivity and for squeezing thermal noise, and thus, proved to be significantly useful in mechanical, optical and microwave systems. Therefore, this theoretical investigation should be of relevant importance to those small-scaled systems. Accordingly, a general two-degree-of-freedom Mathieu–Duffing system is studied. The non-trivial solutions are obtained at different parametric resonance conditions. A bifurcation analysis is carried out using the multiple scales method, followed by investigating the effect of the asynchronous parametric excitation on the existence of limit cycles at resonant and non-resonant frequencies.

Modified Dynamic Movement Primitives: Robot Trajectory Planning and Force Control Under Curved Surface Constraints.

Dynamic movement primitives (DMPs) have been widely applied in robot motion planning and control. However, in some special cases, original discrete DMP fails to generalize proper trajectories. Moreover, it is difficult to produce trajectories on the curved surface. To solve the above problems, a modified DMP method is proposed for robot control by adding the scaling factor and force coupling term. First, the adjusted cosine similarity is defined to assess the similarity of the generalized trajectory with respect to the demonstrated trajectory. By optimizing the similarity, the trajectories can be generated in all situations. Next, by adding the force coupling term derived from adaptive admittance control to the transformation system of the original DMP, the controller achieves the force control ability. Then, the modified DMP-based robot control system is developed. The stability and convergence of the system are proved. Finally, the high precisions of the proposed method are verified by simulations and experiments. The method is significant for trajectory learning and generalization on the curved surface.

Comprehensive quantum chemical analysis of the (ro)vibrational spectrum of thiirane and its deuterated isotopologue

The (ro)vibrational spectra of thiirane, c-C2H4S, and its fully deuterated isotopologue, c-C2D4S, have been studied by means of vibrational configuration interaction theory, VCI, its incremental variant, iVCI, and subsequent variational rovibrational calculations, RVCI, which rely on multidimensional potential energy surfaces of coupled-cluster quality including up to four-mode coupling terms. Accurate geometrical parameters, fundamental vibrational transitions and first overtones, rovibrational spectra and rotational spectroscopic constants have been determined from these calculations and were compared with experimental results whenever available. A number of tentative misassignments in the vibrational spectra could be resolved and most results for the deuterated thiirane are high-level predictions, which may guide experiments to come. Besides this, a new implementation of infrared intensities within the iVCI framework has been tested for the transitions of the title compounds and are compared with results obtained from standard VCI calculations.

A micromechanical cyclic damage model for high cycle fatigue failure of short fiber reinforced composites

This paper presents a micromechanical high cycle fatigue damage model for short fiber reinforced composite materials. Because the damage processes within such materials are influenced strongly by their microstructure, we use a mean field homogenization framework to compute the macroscopic behavior of the composite as well as the microscopic stresses and strains in the constituent phases. This allows us to account for damage phenomena related to both the fiber phase as well as in the matrix material. Fiber and fiber-interface damage is modeled using a Tsai–Wu and Weibull-based approach and the progressive damage due to cyclic loading is described by a progressive matrix damage model. The latter includes a novel coupling term in which the matrix damage progression is linked to the damage state of the reinforcing fibers. A cycle-based numerical formulation is used to overcome the computational limits of such load cases in the time domain. While the approaches are in principle applicable to different types of fiber–matrix composite, a short glass fiber reinforced polyamide 6.6 is used as an example material, for which microstructural analyses as well as tensile and fatigue tests are reported. The model’s capabilities with regard to complex fiber orientations and different fiber fractions are studied using different grades of this material class. Furthermore, the model is analyzed via benchmarks of the numerical schemes and by parameter sensitivity studies. The results show that the approach is capable of modeling the complex and microstructure-dependent fatigue damage and fatigue limits for the different material grades with limitations only becoming visible at very high fiber fractions.

Multiplicity of Positive Solutions for a Semilinear Elliptic System with Strongly Coupled Critical Terms and Concave Nonlinearities

Multiplicity of Positive Solutions for a Semilinear Elliptic System with Strongly Coupled Critical Terms and Concave Nonlinearities

Unconditionally stable, second order, decoupled ensemble schemes for computing evolutionary Boussinesq equations

In this report we present two unconditionally stable, second order, decoupled ensemble schemes for computing evolutionary Boussinesq equations: the stabilized scalar auxiliary variable Crank-Nicolson leap-frog ensemble scheme (Stab-SAV-CNLF-En) and the stabilized scalar auxiliary variable BDF2 ensemble scheme (Stab-SAV-BDF2-En). The two ensemble schemes adopt the recently developed stabilized scalar auxiliary variable (SAV) idea and ensemble timestepping to achieve both high efficiency and unconditional stability. Specifically, the stabilized SAV approach makes it possible to devise unconditionally long time stable schemes for which the nonlinear terms and coupling terms in the Boussinesq equations are made fully explicit, leading to linear systems with constant coefficient matrices to be solved after spatial discretization. The ensemble timestepping further improves the efficiency by making the coefficient matrices of all realizations the same, so that efficient block solvers can be applied to solve the corresponding one linear system with multiple right hand sides and thus greatly reduce the computational cost. We prove the proposed schemes are unconditionally stable and present implementation details. Ample numerical tests are performed to show the efficiency and effectiveness of the combined approach.

Chirality induced spin selectivity: A classical spin-off.

We demonstrate that angular momentum selectivity of particles traversing chiral environments is not limited to the quantum regime and can be realized in classical scenarios also. In our classical variant, the electron spin, which is central to the quantum chirality induced spin selectivity (CISS) effect, is replaced by the self-rotation of a finite-volume body. The latter is coupled to the center of mass orbital motion of the body through a helical tube via wall friction that acts as a dissipative spin-orbit coupling term. As a specific example, we study C60 molecules that are initially spinning in opposite senses and investigate the effect of various external control parameters on their spatial separation when driven through a rigid helical channel. We highlight resemblances and inherent differences between the quantum CISS effect and its classical variant and discuss the potential of the latter to formulate a new paradigm for enantio-separation.

Perturbation in an interacting dark Universe

In this paper we have considered an interacting model of dark energy where the dark sectors are allowed to interact among themselves through an assumed relation. By solving the perturbation equations numerically, we have studied the imprints on the growth of matter as well as dark energy fluctuations. It has been found that for higher rate of interaction strength for the coupling term, visible imprints on the dark energy density fluctuations are observed at the early epochs of evolution. In order to check the viability of the model, we have tested the interacting model with different observational datasets and have looked into the evolution of the density contrast, and the effects on the CMB temperature fluctuation as well as matter power spectrum.

Quantum Phenomena Inside a Black Hole: Quantization of the Scalar Field Iniside Horizon in Schwarzschild Spacetime

We discuss the problem of the quantization and dynamic evolution of a scalar free field in the interior of a Schwarzschild black hole. A unitary approach to the dynamics of the quantized field is proposed: a time-dependent Hamiltonian governing the Heisenberg equations is derived. It is found that the system is represented by a set of harmonic oscillators coupled via terms corresponding to the creation and annihilation of pairs of particles and that the symmetry properties of the spacetime, homogeneity and isotropy are obeyed by the coupling terms in the Hamiltonian. It is shown that Heisenberg equations for annihilation and creation operators are transformed into ordinary differential equations for appropriate Bogolyubov coefficients. Such a formulation leads to a general question concerning the possibility of gravitationally driven instability, that is however excluded in this case.

Admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties

ABSTRACT This paper investigates the admissibility and robust stabilization of fractional-order singular discrete systems with interval uncertainties. Firstly, based on the analysis of the regularity, causality and stability, novel admissibility conditions for nominal fractional-order singular discrete systems are derived including a necessary and sufficient condition in terms of spectral radius and a sufficient condition in terms of non-strict linear matrix inequalities. In order to eliminate the coupling terms and propose strict linear matrix inequality results, another novel admissibility condition is obtained, which is more tractable and reliable with the available linear matrix inequality software solver and more suitable for the controller design compared with the existing results. Secondly, the state feedback controller synthesis for the fractional-order singular discrete systems with interval uncertainties is addressed and the state feedback controller is designed. Finally, the efficiency of the proposed method is demonstrated by two numerical simulation examples.

Spin-dependent polarization and quantum Hall conductivity in decorated graphene: influence of locally induced spin–orbit-couplings and impurities

We study spin transport through graphene-like substrates in the presence of one or several, locally induced spin–orbit coupling (SOC) terms resulting from periodically placed strips, on their top and decorated with a random distribution of impurities. Intrinsic SOC, Rashba SOC and/or pseudo-spin-inversion-asymmetry coupling are considered. A systematic investigation of the spin conductance identifies the main SOC terms which lead to its energy dependence as well as the extent to which the impurity concentration and each SOC term can affect or tune it, In addition, the spin current flow is considered in the presence of different SOC impurities and their related group symmetry such C 6v , C 3v , D 6h and D 3h . Further, we show that the quantum spin-Hall effect (QSHE) related to the spin edge states depends only on the spin character when the PIA and ISO terms are not sublattice resolved, and on both the spin and sublattice character when they are. In addition, we show that the RSO term plays a major role in obtaining edge states that are either protected on both edges or only on one edge against backscattering. This Rashba term creates an anticrosing gap that affects the symmetry in the edge localizations and leads to half-topological states. The results can facilitate the experimental choice of appropriately decorated strips to (i) develop spin-transistor devices by tuning the Fermi energy, (ii) control the robustness of the QSHE against backscattering even in the presence of on-site sublattice asymmetry induced by a transverse electric field or functionalizations, and (iii) provide a strong theoretical support for spintronic quantum devices.

Defect structures and (ferro)magnetism in Zn1-xFexO nanoparticles with the iron concentration level in the dilute regime (x = 0.001 – 0.01) prepared from acetate precursors

Zn1-xFexO nanoparticles with the iron concentrations level in the dilute regime (x = 0.001–––0.01) were produced by a sol–gel route from acetate precursors along with an un-doped and 3 at.% Fe-doped reference. The X-ray diffraction of the un-doped and 0.1–1 at.% Fe-doped samples reveal the reflections for only the ZnO wurtzite structure. Fe doping enhances the a-axis lattice constant, the unit cell volume and the microstrain. Iron doping reduces the average crystallite/particle size (confirmed by Scanning Electron Microscopy), improving the surface-to-volume ratio or the concentration of defective surface sites. XPS identifies the iron in both Fe3+ and Fe2+ states. XPS and 57Fe Mossbauer spectroscopy indicate a broad distribution (distortion) of Fe3+ sites on the surface of ZnO nanoparticles. The blue shift and broadening of the UV emission, and quenching of defect-related photoluminescence in the Fe-doped samples verify the presence of iron in the ZnO lattice and surface intrinsic defects. 0.1–1 at.% Fe-doped ZnO show room temperature ferromagnetism, RTFM, characteristic of dilute magnetic semiconductors, DMS. The magnetization measurements with temperature evidence an antiferromagnetic alignment and an increase of ferromagnetic contribution with Fe doping up to 1 at.%. Zn0.97Fe0.3O reference is a superparamagnetic ZnO/ZnFe2O4 nanocomposite with a blocking temperature of 20 K; HRTEM shows (ultra)fine ZnFe2O4 particles at the surface of ZnO nanoparticles. The analysis of experimental data of 0.1–1 at.% Fe-doped ZnO was done in terms of iron coupling with intrinsic defects, which can generate surface Fe3+ states with geometries similar to the Fe3+ in inverse spinel ZnFe2O4. The superexchange interaction (resembling that in the inverse spinel ZnFe2O4) between the Fe3+ sites with distorted configuration resulting in ferrimagnetism was hypothesised as a possible mechanism of RTFM. Experimental (structural, local chemical, magnetic, optical) and interpretation results can be used to optimize the processing conditions for Fe-doped ZnO to serve as an effective DMS, e.g. for spintronic applications.

Unconditional stability and error analysis of an Euler IMEX-SAV scheme for the micropolar Navier-Stokes equations

In this paper, we consider numerical approximations for solving the micropolar Navier-Stokes (MNS) equations, that couples the Navier-Stokes equations and the angular momentum equation together. By combining the scalar auxiliary variable (SAV) approach for the convective terms and some subtle implicit-explicit (IMEX) treatments for the coupling terms, we propose a decoupled, linear and unconditionally energy stable scheme for this system. We further derive rigorous error estimates for the velocity, pressure and angular velocity in two dimensions without any condition on the time step. Numerical examples are presented to verify the theoretical findings and show the performances of the scheme.

Exchange Coupling Effects on the Magnetotransport Properties of Ni-Nanoparticle-Decorated Graphene

We characterize the effect of ferromagnetic nickel nanoparticles (size ∼6 nm) on the magnetotransport properties of chemical-vapor-deposited (CVD) graphene. The nanoparticles were formed by thermal annealing of a thin Ni film evaporated on top of a graphene ribbon. The magnetoresistance was measured while sweeping the magnetic field at different temperatures, and compared against measurements performed on pristine graphene. Our results show that, in the presence of Ni nanoparticles, the usually observed zero-field peak of resistivity produced by weak localization is widely suppressed (by a factor of ∼3), most likely due to the reduction of the dephasing time as a consequence of the increase in magnetic scattering. On the other hand, the high-field magnetoresistance is amplified by the contribution of a large effective interaction field. The results are discussed in terms of a local exchange coupling, J∼6 meV, between the graphene π electrons and the 3d magnetic moment of nickel. Interestingly, this magnetic coupling does not affect the intrinsic transport parameters of graphene, such as the mobility and transport scattering rate, which remain the same with and without Ni nanoparticles, indicating that the changes in the magnetotransport properties have a purely magnetic origin.

A stabilized divergence-free virtual element scheme for the nematic liquid crystal flows

In this work, we propose and analyze a stabilized divergence-free virtual element method (VEM) for approximating the hydrodynamics system of nematic liquid crystal flows. By adding appropriate stabilization term so that the nonlinear potential function can be treated explicitly, and using the implicit-explicit (IMEX) approach to handle the nonlinear coupling terms, we develop a linear and energy-stable fully discrete virtual element scheme. We further prove that the fully discrete scheme is uniquely solvable and energy stable in discrete sense, moreover, we obtain the optimal error estimates rigorously. Finally, numerical examples are provided to demonstrate the accuracy, stability and efficiency of the proposed scheme.

High resolution FTIR spectrum of CH2D37Cl: ν4 and ν8 fundamental bands

The high-resolution Fourier transform infrared spectrum of CH2D37Cl has been analyzed in the region of the ν4 and ν8 bands from 1170 to 1370 cm−1. The upper states of these fundamentals, separated by 0.6 cm−1, interact with each other by a-type as well as b-type Coriolis resonance, and a strong asymmetric distribution of the intensity of the rotational structure in each band is observed. The spectral analysis resulted in the assignment of 2774 and 1611 rovibrational transitions for ν4 and ν8 bands, respectively, which have been simultaneously fitted using Watson's A-reduction Hamiltonian in the Ir representation and the relevant perturbation operators. A set of spectroscopic constants for the two fundamentals as well as seven coupling terms have been determined. From spectral simulations, the dipole moment ratio |Δµa/Δµb| of ν4 has been determined to be 1.3 ± 0.1 while the intensity ratio between ν4 and ν8 has been estimated to be 5.0 ± 1.0.

Dynamical stability in presence of non-minimal derivative dependent coupling of k-essence field with a relativistic fluid

In this paper we investigate a non-minimal, space-time derivative dependent, coupling between the k-essence field and a relativistic fluid using a variational approach. The derivative coupling term couples the space-time derivative of the k-essence field with the fluid 4-velocity via an inner product. The inner product has a coefficient whose form specifies the various models of interaction. By introducing a coupling term at the Lagrangian level and using the variational technique we obtain the k-essence field equation and the Friedmann equations in the background of a spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) metric. Explicitly using the dynamical analysis approach we analyze the dynamics of this coupled scenario in the context of two kinds of interaction models. The models are distinguished by the form of the coefficient multiplying the derivative coupling term. In the simplest approach we work with an inverse square law potential of the k-essence field. Both of the models are not only capable of producing a stable accelerating solution, they can also explain different phases of the evolutionary universe.

Searching for low-mass axions using resonant upconversion

We present new results of a room temperature resonant AC haloscope, which searches for axions via photon upconversion. Traditional haloscopes require a strong applied DC magnetic background field surrounding the haloscope cavity resonator, the resonant frequency of which is limited by available bore dimensions. UPLOAD, the UPconversion Low-Noise Oscillator Axion Detection experiment, replaces this DC magnet with a second microwave background resonance within the detector cavity, which upconverts energy from the axion field into the readout mode, accessing axions around the beat frequency of the modes. Furthermore, unlike the DC case, the experiment is sensitive to a newly proposed quantum electromagnetodynamical axion coupling term $g_{aBB}$. Two experimental approaches are outlined - one using frequency metrology, and the other using power detection of a thermal readout mode. The results of the power detection experiment are presented, which allows exclusion of axions of masses between 1.12 $-$ 1.20 $\mu eV$ above a coupling strength of both $g_{a\gamma\gamma}$ and $g_{aBB}$ at $3 \times 10^{-6}$ 1/GeV, after a measurement period of 30 days, which is a three order of magnitude improvement over our previous result.

Effect of γ-Oryzanol on the LE-LC Phase Coexistence Region of DPPC Langmuir Monolayer.

We have studied the effect of relative composition of γ-Oryzanol (γ-Or) on the liquid expanded-liquid condensed phase coexistence region in the mixed Langmuir monolayer of γ-Or and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) molecules at air-water interface. The surface manometry studies at a fixed temperature show that the mixture of γ-Or and DPPC forms a stable monolayer at air-water interface. As the relative composition of γ-Or increases the range of area per molecule over which the coexistence of liquid expanded (LE)-liquid condensed (LC) phases exists reduces. Although the LE-LC phase coexistence corresponds to the first-order phase transition, the slope of the surface pressure-area per molecule isotherm is non-zero. Earlier studies have attributed the non-zero slope in LE-LC phase coexistence region to the influence of the strain between the ordered LC phase and disordered LE phase. The effect of strain on the coexistence of LE-LC phases can be studied in terms of molecular density-strain coupling. Our analysis of the liquid condensed-liquid expanded coexistence region in the isotherms of mixed monolayers of DPPC and γ-Or shows that with the increase in the mole fraction of sterol in the mixed monolayer the molecular lateral density-strain coupling increases. However, at 0.6 mole fraction of γ-Or in the mixed monolayer the coupling decreases. This is corroborated by the observation of minimum Gibb's free energy of the mixed monolayer at this relative composition of γ-Or indicating better packing of molecules.