Saturated Boundary Research Articles

Stabilization of the Kawahara equation with saturated internal or boundary feedback controls

Stabilization of the Kawahara equation with saturated internal or boundary feedback controls

Innovation-saturated Koopman Kalman filter for distribution system dynamic state estimation against measurement outliers

Sensor errors, model uncertainty, changes in the surrounding environment, data loss, or malicious network attacks can all result in outliers, which can pollute the measurement process of the distribution system. In this study, to address this problem, a dynamic state estimation method for distribution systems based on innovation-saturated Koopman Kalman filter (IS-KKF) was proposed. The Koopman Kalman filter (KKF) is model-free and data-driven, and estimates nonlinear dynamics through the conventional linear Kalman filter. To make the Koopman Kalman filter robust to measurement outliers, the innovation saturation mechanism applies a saturation function to it. To correct the state estimation, this mechanism is applied to the filtering process. When outliers occur, the distorted innovation is saturated to prevent the state estimation results from being destroyed. Adaptive adjustment of the saturated boundary is a feature of this mechanism. Extensive simulations were carried out on the IEEE 118-bus test system to verify the effectiveness and robustness of the proposed method. The simulation results demonstrate that the proposed method can effectively reject outliers with different amplitudes, types, and continuous times, has significant computational efficiency, and does not require additional measurement redundancy.

Saturated boundary feedback control of quasi-linear hyperbolic balance laws with application to LWR traffic flow stabilization

The saturated boundary stabilization problem for quasi-linear hyperbolic systems of balance laws is considered under H2-norm in this paper, where the boundary conditions of the system are subject to actuator saturations. The resulting closed-loop system is proven to be locally exponentially stable with respect to the steady states in the presence of saturations. To this end, the sector nonlinearity model is introduced to deal with the saturation term, and then sufficient conditions for ensuring the locally exponential stability are established in terms of a set of matrix inequalities by employing the Lyapunov function method along with a sector condition. Furthermore, these results are applied to the stabilization of the two-lane traffic flow dynamic represented by Lighthill–Whitham–Richards (LWR) model. By utilizing variable speed limit (VSL) devices, a saturated boundary feedback controller is designed to stabilize the two-lane traffic flow, and the exponential convergence of the quasi-linear traffic flow system in H2 sense is validated by numerical simulations.

H2O saturated phase change threshold under molecular free path scale

The distribution of droplet and crystal is a key point in space engine plume flow research. Plume flow in vacuum may have great gas molecular free path, thus resulting in non-continuum and LTE (local thermal equilibrium). To obtain understanding on more general H2O phase change threshold, this article establishes a Gibbs phase calculation method. Internal pressure is proposed as a new concept to be distinguished from static pressure. The effect of vapor transitional temperature Tg−tran, vapor rotational temperature Tg−rot, phase change surface temperature Tneu and space characteristic length L on H2O phase change threshold is investigated. According to the results, phase change is more hard for non-continuum vapor than continuum one. Under TE (thermal equilibrium), the saturated phase change boundary line for H2O deflect toward low temperature side when the vapor number density is low. Under LTE, vapor can transform to water under the vapor number density below three phase point in LTE circumstances, which is impossible under TE situation. Tg−tran, Tg−rot and Tov shows different influence degree on the H2O phase change threshold, whose degree order from large to low is: vapor thermodynamics temperature Tg−ov, vapor transitional temperature Tg−tran and vapor rotational temperature Tg−rot.

Design of saturated boundary control for hyperbolic systems with in-domain disturbances

Boundary feedback control design is studied for 1D hyperbolic systems with an in-domain disturbance and a boundary feedback controller under the effect of actuator saturation. Nonlinear semigroup theory is used to prove well-posedness of mild solution pairs to the closed-loop system. Sufficient conditions in the form of dissipation functional inequalities are derived to establish global stability for the closed-loop system and L2-stability in presence of in-domain disturbances. The control design problem is then recast as an optimization problem over linear matrix inequality constraints. Numerical results are shown to validate the effectiveness of the proposed control design.

Stability analysis of a Korteweg-de Vries equation with saturated boundary feedback

The stability analysis of the linear and nonlinear Korteweg-de Vries equations in presence of a saturated feedback actuator is studied. The well-posedness is derived by using nonlinear semigroup results, Schauder's and Banach fixed point theorems. The exponential stability is shown thanks to an observability inequality, which is obtained via contradiction and compactness arguments. Finally, an alternative proof of the asymptotic stability of the linear Korteweg-de Vries equation is presented.

Measurement and modelling of ternary solid–liquid phase equilibrium of (DL-malic acid + maleic acid + water) from 283.15 K to 333.15 K

The solid–liquid phase equilibrium data of (DL-malic acid + maleic acid + water) in binary and ternary systems were measured by high performance liquid chromatography (HPLC) method at 283.15 K, 293.15 K, 303.15 K, 313.15 K, 323.15 K and 333.15 K under atmospheric pressure, and then six isothermal ternary phase diagrams were established. Each isothermal ternary phase diagram included one co-saturated point (invariant), two saturated boundary curves, and three crystallization regions (DL-malic acid, maleic acid, and mixture of both). For extending the application of measured solid–liquid phase equilibrium data, the Wilson model and NRTL model were used for correlation and prediction, and the relative average deviation (RAD) and root-mean-square deviation (RMSD) were applied to assess the calculation precision. The maximum values of RAD and RMSD were 2.61 × 10−2 and 1.87 × 10−3 with Wilson model, 3.31 × 10−2 and 1.86 × 10−3 with NRTL model, respectively, which demonstrated that the calculated data were close to the experimental data, and accurate theoretical data under other experimental conditions were able to acquire through the two models in DL-malic acid + maleic acid + water system. The study provided reliable and accurate data for separating the mixture of DL-malic acid and maleic acid in water.

Approximate analytical solution and parameter estimation for one‐dimensional horizontal absorption based on the van Genuchten–Mualem model

AbstractThe van Genuchten–Mualem (VGM) model is used to describe the absorption of water by soil. The model is highly nonlinear, so developing a simple analytical or approximate method to predict the movement of soil water via the VGM model then estimating the model parameters is necessary. We present a approximate functional extremum solution (FES) for the problem of one‐dimensional horizontal absorption (1DHA) of water in soil under constant saturated boundary conditions and uniform initial conditions based on the least action and the variational principles. Simple linear relationships between the infiltration characteristics (distribution of soil water content, cumulative infiltration, infiltration rate, wetting front distance, and infiltration time) and the VGM model parameters were obtained. We developed a simple approximate analytical method for estimating the VGM model parameters by testing 1DHA. Numerical data simulated by HYDRUS‐1D were compared with the analytical results and used to verify our method's feasibility. The results indicated that the FES could accurately predict the infiltration characteristics, with relative errors between the approximate analytical and numerical solutions of 0.8 to 8.5% for the distribution of soil water content, 0.1 to 0.8% for cumulative infiltration, 1.1 to 6.4% for infiltration rate, and 0.1 to 6.9% for wetting front distance. Estimates of the parameters indicated that errors ranged from 3.2 to 28.3% for α (inverse of the mean pore diameter) and 0.4 to 8.0% for n (pore size distribution index). The proposed methods can be used to predict 1DHA and to estimate α and n in the VGM model.

Design of Saturated Boundary Control for Hyperbolic Systems

This paper deals with the stabilization of 1-D linear hyperbolic systems with saturated feedback boundary control. By following a Lyapunov approach, sufficient conditions for global exponential stability in the L2 norm are given in the form of matrix inequalities. Numerical examples are presented to illustrate the theoretical results.

On L∞ stabilization of diagonal semilinear hyperbolic systems by saturated boundary control

This paper considers a diagonal semilinear system of hyperbolic partial differential equations with positive and constant velocities. The boundary condition is composed of an unstable linear term and a saturated feedback control. Weak solutions with initial data in L2([0, 1]) are considered and well-posedness of the system is proven using nonlinear semigroup techniques. Local L∞ exponential stability is tackled by a Lyapunov analysis and convergence of semigroups. Moreover, an explicit estimation of the region of attraction is given.

Experimental studies of gasoline petroleum fractions

The results of experimental studies of gasoline and petroleum fractions are discussed in the article, as well as their main physical and chemical properties, density and pressure of saturated vapors, liquid phase, two-phase region, critical region, and boundary curves. The article is recommended for agricultural specialists, researchers, teachers, graduate students, undergraduates, and students of agricultural universities in the field of “Agricultural Engineering”.

Options for low-global-warming-potential and natural refrigerants part I: Constrains of the shape of the P–T and T–S saturation phase boundaries

Current research focus is migrating toward low-global-warming-potential (GWP) and natural refrigerants to address the human impact on climate change. In this paper, we examine 13 refrigerants from the perspective of the characteristic shape of their respective temperature–entropy (T–S) and the logarithm of the pressure versus inverse absolute temperature (log P vs. T–1) saturated phase boundary. Such analyses explain why certain refrigerants possess a re-entrant characteristic while others do not. The re-entrant region is due to skewness of the saturation boundary. The cause of skewness is investigated for its importance in heat pump performance, design, and configuration. Re-entrant behavior contributes to premature mechanical wear of compressor components. Knowledge of the properties of the phase boundary on either side of the critical point, is useful for a better perspective on discriminating refrigerants, as hydrochlorofluorocarbons are phased out and replacement refrigerants must be found. We conclude by identifying a candidate low-GWP refrigerant for heat pumps. In Part II, we evaluate all 13 refrigerants in thermodynamic cycles based on exergy analysis to identify sources of irreversibility, the root cause of systemic inefficiency.

A simple system for moist convection: the Rainy–Bénard model

Rayleigh–Bénard convection is one of the most well-studied models in fluid mechanics. Atmospheric convection, one of the most important components of the climate system, is by comparison complicated and poorly understood. A key attribute of atmospheric convection is the buoyancy source provided by the condensation of water vapour, but the presence of radiation, compressibility, liquid water and ice further complicate the system and our understanding of it. In this paper we present an idealized model of moist convection by taking the Boussinesq limit of the ideal-gas equations and adding a condensate that obeys a simplified Clausius–Clapeyron relation. The system allows moist convection to be explored at a fundamental level and reduces to the classical Rayleigh–Bénard model if the latent heat of condensation is taken to be zero. The model has an exact, Rayleigh-number-independent ‘drizzle’ solution in which the diffusion of water vapour from a saturated lower surface is balanced by condensation, with the temperature field (and so the saturation value of the moisture) determined self-consistently by the heat released in the condensation. This state is the moist analogue of the conductive solution in the classical problem. We numerically determine the linear stability properties of this solution as a function of Rayleigh number and a non-dimensional latent-heat parameter. We also present some two-dimensional, time-dependent, nonlinear solutions at various values of Rayleigh number and the non-dimensional condensational parameters. At sufficiently low Rayleigh number the system converges to the drizzle solution, and we find no evidence that two-dimensional self-sustained convection can occur when that solution is stable. The flow transitions from steady to turbulent as the Rayleigh number or the effects of condensation are increased, with plumes triggered by gravity waves emanating from other plumes. The interior dries as the level of turbulence increases, because the plumes entrain more dry air and because the saturated boundary layer at the top becomes thinner. The flow develops a broad relative humidity minimum in the domain interior, only weakly dependent on Rayleigh number when that is high.

Numerical solution of the Richards equation based catchment runoff model with dd-adaptivity algorithm and Boussinesq equation estimator

This paper presents a pseudo-deterministic catchment runoff model based on the Richards equation model - the governing equation for subsurface flow. The subsurface flow in a catchment is described here by two-dimensional variably saturated flow (unsaturated and saturated). The governing equation is the Richards equation with a slight modification of the time derivative term, as considered e.g. by Neuman. The nonlinear nature of this problem appears in the unsaturated zone only, so it was possible to make use of adaptive domain decomposition algorithm. However delineating of the saturated zone boundary is a nonlinear computationally expensive issue. The simple one-dimensional Boussinesq equation was used here as a rough estimator of the saturated zone boundary. With this estimate the adaptive domain decomposition could always start with an optimal subdomain split, and thus it is now possible to avoid solving huge systems of linear equations in the initial iteration level. With this measure it is possible to construct an efficient two-dimensional pseudodeterministic catchment runoff model. Finally, the model is tested against real data originating from the Modrava 2 experimental catchment, Czech Republic.

Aqueous and Surface Chemistries of Photocatalytic Fe-Doped CeO2 Nanoparticles

The present work describes the effects of water on Fe-doped nanoparticulate CeO2, produced by flame spray pyrolysis, which is a critical environmental issue because CeO2 is not stable in typical atmospheric conditions. It is hygroscopic and absorbs ~29 wt % water in the bulk when exposed to water vapor but, more importantly, it forms a hydrated and passivating surface layer when immersed in liquid water. In the latter case, CeO2 initially undergoes direct and/or reductive dissolution, followed by the establishment of a passivating layer calculated to consist of ~69 mol % solid CeO2·2H2O and ~30 mol % gelled Ce(OH)4. Under static flow conditions, a saturated boundary layer also forms but, under turbulent flow conditions, this is removed. While the passivating hydrated surface layer, which is coherent probably owing to the continuous Ce(OH)4 gel, would be expected to eliminate the photoactivity, this does not occur. This apparent anomaly is explained by the calculation of (a) the thermodynamic stability diagrams for Ce and Fe; (b) the speciation diagrams for the Ce4+-H2O, Ce3+-H2O, Fe3+-H2O, and Fe2+-H2O systems; and (c) the Pourbaix diagrams for the Ce-H2O and Fe-H2O systems. Furthermore, consideration of the probable effects of the localized chemical and redox equilibria owing to the establishment of a very low pH (<0) at the liquid-solid interface also is important to the interpretation of the phenomena. These factors highlight the critical importance of the establishment of the passivating surface layer and its role in photocatalysis. A model for the mechanism of photocatalysis by the CeO2 component of the hydrated phase CeO2·2H2O is proposed, explaining the observation of the retention of photocatalysis following the apparent alteration of the surface of CeO2 upon hydration. The model involves the generation of charge carriers at the outer surface of the hydrated surface layer, followed by the formation of radicals, which decompose organic species that have diffused through the boundary layer, if present.

Investigation into the effectiveness of feed spacer configurations for reverse osmosis membrane modules using Computational Fluid Dynamics

Reverse osmosis operations for water treatment are usually energy intensive and responsible for most of the product price. Several studies used flow characteristics to compare different geometries of feed spacers, but these cannot completely explain the effectiveness of feed spacers for promoting mass transfer near membranes. A few recent studies introduced a concept (Spacer Configuration Efficacy, SCE) combining mass transfer and energy consumption, but SCE has been applied only to a limited extent.The present study uses 3-dimensional steady state Computational Fluid Dynamics with mass transfer to compare four channels with feed spacer configurations (Ladder-type, Triple, Wavy and Submerged) and an empty plain channel using SCE and other performance measures. In contrast to previous studies, a saturated concentration boundary condition is employed at the membrane surface and optimised meshing of the domain is discussed. Power law correlations for SCE and other performance measures developed from the simulation results enable quick evaluation of the spacers.Results indicated that the assumed saturated solute concentration at the membrane strongly affects the mass transfer coefficient. Based on SCE, the Wavy spacer configuration showed the highest performance for Re>120 among the obstructed geometries considered, while Ladder-type was better for Re<120.

Ultra-High-Strength Interstitial-Free Steel Processed by Equal-Channel Angular Pressing at Large Equivalent Strain

The billets of interstitial-free (IF) steel are deformed by equal-channel angular pressing (ECAP) at 298 K (25 °C) adopting the route BC up to an equivalent strain (e vm) of 24. The evolution of microstructures and their effects on the mechanical properties are examined. The microstructural refinement involves the elongation of grains, the subdivision of grains to the bands with high dislocation density, and the splitting of bands into the cell blocks and then cell blocks into the cells. The widths of the bands and the size of cells decrease with strain. The degree of reduction in the grain size is highest at the low strain level. However, most of the boundaries at this stage are of low-angle boundaries (at e vm = 3). Thereafter, the misorientation angle increases by progressive lattice rotation with strain. The coarse bands transform step by step from the lamellar structure to the ribbon-shaped grains and finally to the near-equiaxed grain structures with the subgrains of a saturated low-angle grain boundary fraction of 0.34 at very large strain >15. The as-received coarse-grained microstructure (grain size of 57.6 ± 21 µm) has been refined to 257 ± 48 nm at an equivalent strain of 24. The strength increases considerably up to e vm = 3 due to grain refinement and high dislocation density. However, the strengthening at later stages is mainly due to the increase in misorientation angle and refinement. Initial yield strength of 227 MPa is increased to a record value of 895 MPa on straining up to e vm = 24 at 298 K (25 °C). Uniform elongation decreases drastically at low equivalent strain but it regains marginally later. The ECAPed sample fails by a ductile fracture at e vm = 0.6 to 6 but by a mixed mode of ductile–brittle fracture at larger strain of 9 to 24.

Saturated boundary [formula omitted]-alliances in graphs

In this paper, we introduce a new concept of saturated vertices for the alliances. For a given graph G=(V,E) and S⊂V, a vertex v∈V is said to be S-saturated, if the number of its defenders is equal to the number of its attackers for S. We define new parameters |λ(S)| and |λ̄(S)| as the number of S-saturated vertices and not S-saturated vertices of S, respectively. We study mathematical properties of (global) saturated boundary defensive, offensive and powerful k-alliances and theoretical results are obtained by giving in particular some tight bounds and exact values on the cardinality of such alliances. As a main result, we give tight bounds for the cardinality of every minimal global boundary powerful (−1)-alliance (MGBPA) in terms only of the order and the size of graph. Furthermore, we establish two algorithms which generate graphs containing (connected) MGBPA from a given complete graph K2n.

Influence of cavity on scattering of wave field in half space saturated soil using boundary element method

(1) School of Civil and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China; (2) School of Civil Engineering and Architecture, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China

Asymptotic approach for nonlinear vibrating beams with saturation type boundary condition

This article attempts to analyze the complicated vibrational behavior of the Euler–Bernoulli beam exposed to saturated nonlinear boundary condition through proposing an innovative precise equivalent function. In this direction, the beam vibrational response is attained by way of a new effective analytical method namely Hamiltonian approach. Despite all the procedures based on perturbation methods that deadzone or saturation dead-band parameter is omitted during integration, this study indicates that how using Hamiltonian approach, the impact of dead-band parameter is taken into account leading to higher accuracy of the approximated solution. Finally, the precision of the proposed equivalent function is evaluated in comparison with the numerical solutions, giving excellent results.