Non-uniform System Research Articles

Bending and vibration analyses of coupled axially functionally graded tapered beams

The nonlinear bending and vibrations of tapered beams made of axially functionally graded (AFG) material are analysed numerically. For a clamped–clamped boundary conditions, Hamilton’s principle is employed so as to balance the potential and kinetic energies, the virtual work done by the damping, and that done by external distributed load. The nonlinear strain–displacement relations are employed to address the geometric nonlinearities originating from large deflections and induced nonlinear tension. Exponential distributions along the length are assumed for the mass density, moduli of elasticity, Poisson’s ratio, and cross-sectional area of the AFG tapered beam; the non-uniform mechanical properties and geometry of the beam along the length make the system asymmetric with respect to the axial coordinate. This non-uniform continuous system is discretised via the Galerkin modal decomposition approach, taking into account a large number of symmetric and asymmetric modes. The linear results are compared and validated with the published results in the literature. The nonlinear results are computed for both static and dynamic cases. The effect of different tapered ratios as well as the gradient index is investigated; the numerical results highlight the importance of employing a high-dimensional discretised model in the analysis of AFG tapered beams.

On second-harmonic generation in nonuniformly magnetized media

This paper presents a theoretical study of new effects of double-frequency optical signal generation in magnetic media with a nonuniform magnetization distribution. The study is based on the hydrodynamic approximation of the motion of conduction electrons in the field of an electromagnetic wave and equations for the mean electron spin. Within this approach, the mechanisms of the toroidal moment effect, which was experimentally discovered earlier in a system of magnetic particles with a vertical magnetization distribution as well as in a multilayered magnetic system (which is a collinear nonuniform magnetic system), are demonstrated. A new effect that appears due to the presence of equilibrium spin currents in a nonuniform magnetic system is studied in detail. This effect was predicted from the symmetry and can occur only in noncollinearly magnetized media. It is shown that this effect has a resonance nature with a resonance at a pump frequency equal to the plasma frequency of conduction electrons. Estimates of the susceptibility at the double frequency for the parameters of nickel and the typical scale of variation in the magnetization, which is equal to 10 nm, show that the susceptibility near the frequency of the plasma resonance at the chosen parameters is on the order of 10–9 esu, which holds up a hope of the experimental detection of this effect.

Infinite-dimensional disturbance-observer-based control for an axially moving non-uniform system with input constraint

In this paper, the vibration control and input saturation constraint problem of an axially moving non-uniform system subject to unknown disturbances is investigated. The key control objectives are to control the vibration of the system and eliminate the effects of the input saturation constraint. To that end, a boundary control with an auxiliary system is designed by utilizing Lyapunov’s direct method. Additionally, a boundary disturbance observer is proposed to deal with the boundary disturbance, and an infinite-dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. With the designed boundary control, uniformly bounded stability of the controlled system is achieved through rigorous Lyapunov analysis without any model reduction. Finally, simulation results are given to show the effectiveness of the designed control scheme.

Effect of heterogeneity in a model of El Niño Southern Oscillations

The emergence of oscillations in models of the El Niño effect is of utmost relevance. Here we investigate a coupled nonlinear delay differential system modeling the El Niño/ Southern Oscillation (ENSO) phenomenon, which arises through the strong coupling of the ocean-atmosphere system. In particular, we study the temporal patterns of the sea surface temperature anomaly of the two sub-regions. For identical sub-regions we typically observe a co-existence of amplitude and oscillator death behavior for low delays, and heterogeneous oscillations for high delays, when inter-region coupling is weak. For moderate inter-region coupling strengths one obtains homogeneous oscillations for sufficiently large delays and amplitude death for small delays. When the inter-region coupling strength is large, oscillations are suppressed altogether, implying that strongly coupled sub-regions do not yield ENSO-like oscillations. Further we observe that larger strengths of self-delay coupling favours oscillations, while oscillations die out when the delayed coupling is weak. This indicates again that delayed feedback, incorporating oceanic wave transit effects, is the principal cause of oscillatory behaviour. So the effect of trapped ocean waves propagating in a basin with closed boundaries is crucial for the emergence of ENSO. Further, we show how non-uniformity in delays, and difference in the strengths of the self-delay coupling of the sub-regions, affect the rise of oscillations. The broad trends are similar to a coupled system with identical sub-regions, namely, larger delays and self-delay coupling strengths lead to oscillations, while strong inter-region coupling kills oscillatory behaviour. The difference between the uniform case and the non-uniform system, is that amplitude death and homogeneous oscillations are predominant in the former, while oscillator death and heterogeneous oscillations are commonly found in the latter. Interestingly, we also find that when one sub-region has low delay and another has high delay, under weak coupling the oscillatory sub-region induces oscillations in sub-region that would have gone to a steady state if uncoupled. Thus we find that coupling sub-regions has a very significant effect on the emergence of oscillations, and strong coupling typically suppresses oscillations, while weak coupling of non-identical sub-regions can induce oscillations, thereby favouring ENSO.

Exact ordering of energy levels for one-dimensional interacting Fermi gases with SU (N) symmetry

Based on the exact solution of one-dimensional Fermi gas systems with $SU(n)$ symmetry in a hard wall, we demonstrate that we are able to sort the ordering of the lowest energy eigenvalues of states with all allowed permutation symmetries, which can be solely marked by certain quantum numbers in the Bethe ansatz equations. Our results give examples beyond the scope of the generalized Lieb-Mattis theorem, which can only compare the ordering of energy levels of states belonging to different symmetry classes if they are comparable according to the pouring principle. In the strongly interacting regime, we show that the ordering of energy levels can be determined by an effective spin-exchange model and extend our results to the non-uniform system trapped in the harmonic potential.

Efficient chemical potential evaluation with kinetic Monte Carlo method and non-uniform external potential: Lennard-Jones fluid, liquid, and solid.

The aim of this paper is to present a method of a direct evaluation of the chemical potential of fluid, liquid, and solid with kinetic Monte Carlo simulation. The method is illustrated with the 12-6 Lennard-Jones (LJ) system over a wide range of density and temperature. A distinctive feature of the methodology used in the present study is imposing an external potential on the elongated simulation box to split the system into two equilibrium phases, one of which is substantially diluted. This technique provides a reliable direct evaluation of the chemical potential of the whole non-uniform system (including that of the uniformly distributed dense phase in the central zone of the box), which, for example, is impossible in simulation of the uniform crystalline phase. The parameters of the vapor-liquid, liquid-solid, and fluid-solid transitions have been reliably determined. The chemical potential and the pressure are defined as thermodynamically consistent functions of density and temperature separately for the liquid and the solid (FCC) phases. It has been shown that in two-phase systems separated by a flat interface, the crystal melting always occurs at equilibrium conditions. It is also proved that in the limit of zero temperature, the specific heat capacity of an LJ crystal at constant volume is exactly 3Rg (where Rg is the gas constant) without resorting to harmonic oscillators.

Data-Aware Task Dispatching for Batch Queuing System

This paper describes a scheduling method focusing on exploiting the local access of a nonuniform storage-access file system. In our approach, the file access cost is calculated and combined with the CPU load average into a comprehensive value, which will be used as the standard for scheduling. We evaluated our approach in comparison with the original Torque scheduler using three benchmarks: thput-gfpio, readgf, and BLAST benchmarks. For thput-gfpio, the read throughput showed a 3.59 times boost, whereas for readgf, the total execution time was reduced to about 1/10th of the original value. Finally, using the BLAST benchmark, the total execution time was reduced by 33%.

Characteristics of electromechanical disturbance propagation in non‐uniform power systems

A disturbance in anywhere of an interconnected power system will cause system oscillation that propagates in the entire power grid in the form of a wave. A disturbance propagation model for power systems is proposed to investigate the dispersion relation of the discrete model. Then, the reflection and transmission phenomena are discussed in the non-uniform power system model, and the influences of disturbance oscillation frequency on the reflection and transmission coefficients are analysed. Finally, a chain system and a New England benchmark test system are used to validate the correctness of the theoretical analysis. This work is meaningful to analyse the electromechanical dynamics of power systems and control the disturbance propagation.

Pure axial flow of viscoelastic fluids in rectangular microchannels under combined effects of electro-osmosis and hydrodynamics

This paper presents an analysis of the combined electro-osmotic and pressure-driven axial flows of viscoelastic fluids in a rectangular microchannel with arbitrary aspect ratios. The rheological behavior of the fluid is described by the complete form of Phan-Thien–Tanner (PTT) model with the Gordon–Schowalter convected derivative which covers the upper convected Maxwell, Johnson–Segalman and FENE-P models. Our numerical simulation is based on the computation of 2D Poisson–Boltzmann, Cauchy momentum and PTT constitutive equations. The solution of these governing nonlinear coupled set of equations is obtained by using the second-order central finite difference method in a non-uniform grid system and is verified against 1D analytical solution of the velocity profile with less than 0.06% relative error. Also, a parametric study is carried out to investigate the effect of channel aspect ratio (width to height), wall zeta potential and the Debye–Huckel parameter on 2D velocity profile, volumetric flow rate and the Poiseuille number in the mixed EO/PD flows of viscoelastic fluids with different Weissenberg numbers. Our results show that, for low channel aspect ratios, the previous 1D analytical models underestimate the velocity profile at the channel half-width centerline in the case of favorable pressure gradients and overestimate it in the case of adverse pressure gradients. The results reveal that the inapplicability of the Debye–Huckel approximation at high zeta potentials is more significant for higher Weissenberg number fluids. Also, it is found that, under the specified values of electrokinetic parameters, there is a threshold for velocity scale ratio in which the Poiseuille number is approximately independent of channel aspect ratio.

Non-uniform doping outperforms uniform doping for enhancing the photocatalytic efficiency of Au-doped TiO 2 nanotubes in organic dye degradation

Abstract Uniform doping is usually recognized as an efficient method for enhancing photocatalysis of TiO 2 , while non-uniform doping is generally supposed to be inefficient because of the inhomogeneous dispersion of dopants. However, in this study, we present the first example of non-uniform doping (with Au)-better enhanced photocatalysis of TiO 2 nanotubes, as compared to uniform doping, in terms of the photocatalytic organic dye degradation. The extent to which the non-uniform doping (achieved by liquid phase deposition (LPD)) can enhance photocatalysis is evaluated, along with a comparison with uniform doping. There exists an additional positive effect in the non-uniform doping system, that is, as generated interfaces between pure phase TiO 2 and Au-doped TiO 2 , in contrast to the uniform doping system leading to a positive “platinum island” effect. Such double beneficial effects contribute to the highest performance in the photocatalytic organic dye degradation for the Au-non-uniformly doped TiO 2 nanotubes as compared to other samples involved in this study. Both the “platinum island” and interfacial separation effects are helpful to isolate the photo-generated electrons and holes, resulting in enhanced photocatalytic activities.

Fidelity enhancement in high-data-rate digital mobile fronthaul with sample bits interleaving and unequally-spaced PAM4.

Driven by continuously growing mobile traffic, line rate of digital mobile fronthaul (MFH) network keeps surging. 4-level pulse amplitude modulation (PAM4) is a promising format to provide such high data capacity, due to its bandwidth and cost efficiency. In this paper, we propose an improved method to reduce mobile signal distortion caused by bit error of optical transmission. The concept comes from the characteristic that high order sample bit error induces far severer performance degradation to radio signal than low order one. In the solution, high order sample bits and low order sample bits are interleaved, so that they are respectively mapped to first bit (1stb) and second bit (2ndb) of PAM4 symbol. On the other hand, amplitude levels of PAM4 are set unequal to broaden the "middle eye", levering accuracy of 1stb. Hence, the total fidelity of mobile signal is enhanced. The feasibility is confirmed both theoretically and experimentally. The investigation is based on two typical digital systems, i.e., 16-bit uniform quantizing and 8-bit nonuniform quantizing. Experimental results indicate that, EVM of LTE-A like radio signal decreases by up to 13dB in uniform quantizing system, and by up to 5dB in nonuniform quantizing system, compared with conventional equally-spaced PAM4.

\u201cDeflecting elastic prism\u201d and unidirectional localisation for waves in chiral elastic systems

For the first time, a design of a “deflecting elastic prism” is proposed and implemented for waves in a chiral medium. A novel model of an elastic lattice connected to a non-uniform system of gyroscopic spinners is designed to create a unidirectional wave pattern, which can be diverted by modifying the arrangement of the spinners within the medium. This important feature of the gyro-system is exploited to send a wave from a point of the lattice to any other point in the lattice plane, in such a way that the wave amplitude is not significantly reduced along the path. We envisage that the proposed model could be very useful in physical and engineering applications related to directional control of elastic waves.

Iterative learning fault diagnosis algorithm for non-uniform sampling hybrid system

For a class of non-uniform output sampling hybrid system with actuator faults and bounded disturbances, an iterative learning fault diagnosis algorithm is proposed. Firstly, in order to measure the impact of fault on system between every consecutive output sampling instants, the actual fault function is transformed to obtain an equivalent fault model by using the integral mean value theorem, then the non-uniform sampling hybrid system is converted to continuous systems with timevarying delay based on the output delay method. Afterwards, an observer-based fault diagnosis filter with virtual fault is designed to estimate the equivalent fault, and the iterative learning regulation algorithm is chosen to update the virtual fault repeatedly to make it approximate the actual equivalent fault after some iterative learning trials, so the algorithm can detect and estimate the system faults adaptively. Simulation results of an electro-mechanical control system model with different types of faults illustrate the feasibility and effectiveness of this algorithm.

On the SNR Variability in Noisy Compressed Sensing

Compressed sensing (CS) is a sampling paradigm that allows to simultaneously measure and compress signals that are sparse or compressible in some domain. The choice of a sensing matrix that carries out the measurement has a defining impact on the system performance and it is often advocated to draw its elements randomly. It has been noted that in the presence of input (signal) noise, the application of the sensing matrix causes SNR degradation due to the noise folding effect. In fact, it might also result in the variations of the output SNR in compressive measurements over the support of the input signal, potentially resulting in unexpected non-uniform system performance. In this work, we study the impact of a distribution from which the elements of a sensing matrix are drawn on the spread of the output SNR. We derive analytic expressions for several common types of sensing matrices and show that the SNR spread grows with the decrease of the number of measurements. This makes its negative effect especially pronounced for high compression rates that are often of interest in CS.

Periodic solutions versus practical switching control for sensorless Piecewise Affine systems (PWA)

This work concerns the stabilization of general Piecewise Affine (PWA) systems without common equilibrium; the main objective consists in proposing a characterization of periodic solutions, by determining the critical parameters values of the cyclic behaviors. The proposed approach is based on the expansion of previous results on practical stabilization by switching. Due to the non-convex nature of general PWA synthesis problems, we primarily present a BMI formulation of the practical stabilization that is used to generate periodic solutions. More precisely, we characterize ω-limit sets as periodic trajectories of the global PWA system in terms of special invariant sets of the practical stabilization method. This will avoid a posteriori subset inclusion checking, since the underlying set belongs to the admissible state space part. This approach generalizes previous results to obtain invariance conditions and the set ω-limit points. A methodology and algorithms to compute periodic trajectories parameters are provided. Two illustrative examples are used for simulation, in particular the third order of Goodwin oscillator model is investigated as a non-uniform oscillatory complex system.

Dynamic Programming Model for the System of a Non-Uniform Deficit Irrigation and a Reservoir

This paper proposes two optimization models for uniform and non-uniform deficit irrigation. In the first model, the objective function consists of a benefit–cost ratio. The deficit irrigation ratio was determined by dynamic programming, according to the reservoir releases, and minimized a damage function (objective function). The second model used dynamic programming to develop an integrated optimization of non-uniform deficit irrigation and reservoir operation. The comparison between the results of the models shows that when applying the second model the cropping area, volume of water regulated by the reservoir, annual production, gross income and benefit–cost ratio increased by 48, 43, 48, 47 and 2.4%, respectively. Therefore, integrated dynamic programming of a non-uniform deficit irrigation and reservoir system can be recommended to increase the integrated productivity of a storage dam and irrigation system. Copyright © 2016 John Wiley & Sons, Ltd.

Modelling of a non-buoyant vertical jet in waves and currents

A generic numerical model using the large eddy simulation (LES) technique is developed to simulate a non-buoyant vertical jet in wave and/or current environments. The experimental data obtained in five different cases, i.e., one case of the jet in a wave only environment, two cases of the jet in a cross-flow only environment and two cases of the jet in a wave and cross-flow coexisting environment, are used to validate the model. The grid sensitivity tests are conducted based on four different grid systems and the results illustrate that the non-uniform grid system C (205×99×126 nodes with the minimum size of 1/10 jet diameter) is sufficiently fine for the modelling. The comparative study shows that the wave-current non-linear interaction should be taken into account at the inflow boundary while modelling the jet in wave and cross-flow coexisting environments. All numerical results agree well with the experimental data, showing that: (1) the jet under the influence of the wave action has a faster centerline velocity decay and a higher turbulence level than that in the stagnant ambience, meanwhile the “twin peaks” phenomenon exists on the cross-sectional velocity profiles, (2) the jet under a cross-flow scenario is deflected along the cross-flow with the node in the downstream, (3) the jet in wave and cross-flow coexisting environments has a flow structure of “effluent clouds”, which enhances the mixing of the jet with surrounding waters.

Information approach for optimizing the load distribution during steam generation in lignite gasification

Optimization of the heat recovery system for secondary steam generation in pulverized-fuel lignite gasification is considered in terms of designing systems with high degrees of organization. This represents one of the final stages in the algorithm for the synthesis of industrial chemical systems with an unspecified number of elements and undefined topology, when optimal gas generator parameters have already been determined and are fixed for the given problem. Organization criteria are analyzed in the process of increasing the complexity of the nonuniform system. Consistent functioning of the system components is taken into account.

Modelling and control for a class of axially moving nonuniform system

ABSTRACTIn this paper, we deal with the active control problem for a class of axially moving system. The system is nonuniform due to the spatial-varying mass and spatiotemporally varying tension. The infinite dimensional model of the nonuniform system represented by the hybrid partial-ordinary differential equations is derived with consideration of the spatiotemporally varying distributed disturbance. To suppress the vibration of the nonuniform system, full state feedback boundary control is developed. For the case that the system states cannot be measured, output feedback boundary control is proposed by using the high-order observers for the estimation of the unmeasurable states. The disturbance observer is introduced to mitigate the effects of the boundary disturbance. With the proposed boundary control, the stability of the closed-loop nonuniform system is achieved through rigorous analysis and the uniform boundedness of the all closed-loop signals is guaranteed. Numerical simulations are performed to validate the performance of the control scheme proposed.

3D modeling of reaction-diffusion dynamics in an electrokinetic Y-shaped microreactor

We perform a 3D numerical modeling of reaction-diffusion dynamics in a Y-shaped microreactor, considering a fully developed combined electroosmotic and pressure-driven flow. The governing equations, based on a second-order irreversible reaction, are solved invoking a finite-volume approach for a non-uniform grid system. We demonstrate that the reaction is highly position dependent: more production is observed adjacent to the horizontal walls for a favorable pressure gradient, whereas both the wall and centerline are the regions of highest production when a back pressure is applied. We further show that, to achieve the maximum production rate, the EDL should be thick enough, the pressure gradient should be unfavorable, and both the diffusiveties and the inlet concentrations of the reacting components should be identical. Although the same is true for the production efficiency, defined to be the ratio of the average production concentration to the inlet concentration of the limiting component, there is a main difference: when the inlet concentrations are the same the efficiency is minimal. Moreover, the concentration pick is inclined toward the component with either less diffusivity or less inlet concentration; the inclination is magnified when either the Debye length increases or an unfavorable pressure gradient is employed.