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This paper aims to investigate the stability of hydro-turbine governing system (HTGS) with sloping ceiling tailrace tunnel (SCTT) and upstream surge tank (UST) considering nonlinear hydro-turbine characteristics (NHTCs). Firstly, the mathematical model of HTGS is presented based on nonlinear seventh-order state equation, which is verified by example analysis so as to study the stability of HTGS. Subsequently, the effect of HTGS parameters on the stability of the system is investigated with numerical simulation. Finally, the coupling effect mechanism of SCTT and UST on stability under the effect of NHTCs is revealed by using contrastive analysis. The results are summarized as follows: (1) T a , K d and T wt perform larger effect on the stability of HTGS, while the influence of F and T wy is mild; (2) the NHTCs are beneficial under negative load disturbance and unfavorable under positive load disturbance for the stability and dynamic performance of HTGS; (3) the coupling effect of SCTT and UST outperforms the results of SCTT or UST alone under all load disturbances; (4) the incorporation of UST to the established model plays a certain role in stability compensation, while the introduction of SCTT not only improves the stability but also achieves smaller amplitude and lower frequency. [ABSTRACT FROM AUTHOR]

In high-power laser systems, the large-aperture continuous phase plates (CPPs) are designed and fabricated with continuous varying structured topography to serve as the class of phase-modulating beam-conditioning optics. To achieve better optical performance, its fabrication highly depends on the reiterative figuring to eliminate the form error relative to the designed CPP surface. However, the characteristics of large aperture and complex structured topography make the quality inspection of CPPs still challenging. A typical inspection process includes measuring the CPPs with the sub-aperture stitching technique, followed by the characterization procedure with respect to the CPP design description. This paper proposes an innovative stitching-embedded characterization method for imprinting the large-aperture CPPs, which combines the sub-aperture stitching and characterization procedure together. First, the concept and mathematical model of the stitching-embedded characterization method is presented. Then, both numerical simulations and experiments were undertaken to verify the proposed method, and the results demonstrate its feasibility and reasonability to provide the more reliable form error evaluation while simplify the analysis procedure compared with the conventional inspection process. • The stitching-embedded characterization method is presented for imprinting the large-aperture CPPs. • The mathematical model is established to integrate the sub-aperture stitching into the characterization procedure. • Numerical simulations were undertaken to verify the proposed method, which can achieve sub-nanometer accuracy in simulation. • In application, the proposed method can achieve more reliable form error evaluation with lower time cost. [ABSTRACT FROM AUTHOR]

A nonlinear energy-based controller and a Lyapunov-based model predictive control (MPC) technology are constructed in sequence for shipboard boom cranes, while taking full state constraints into account. The mathematical model is firstly transformed to ease the explicit influences of ship rollings on the desired positions and payload swings. Barrier Lyapunov functions (BLFs) are then involved in the energy-based controller to deal with different types of state constraints, in which constraints with positive bounds are also effectively tackled with a modified BLF. By adding a contractive constraint with the energy-based controller in traditional MPC framework, Lyapunov-based MPC is then established, in which the recursive feasibility and stability is ensured effectively and easily. Asymptotical stability of two controllers is analyzed and guaranteed in theory, respectively. Compared with the energy-based controller, control performance is improved and enhanced by the Lyapunov-based MPC through solving the optimal control problem. Simulations are finally implemented, and comparisons are also carried out to demonstrate the effectiveness and features of the established controllers in this paper. • An energy-based controller is independently developed for shipboard boom cranes. The asymmetrical constraints on all states are strictly respected and asymptotic stability is guaranteed by embedding BLFs in the Lyapunov function and controller. • To the best of our knowledge, Lyapunov-based MPC is firstly applied to shipboard boom cranes while tackling full state constraints. The recursive feasibility and asymptotic stability are ensured by taking energy-based controller as initial guesses and contractive constraints. • Two groups of numerical simulations are implemented to demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

• The mathematical model on the grounding resistance of the vertical electrode is proposed. • Accuracy of the mathematical model is proved by computer simulation analysis and the field measurement examination in this paper. • The mathematical model can be used in the design of vertical grounding electrode effectively. In this paper, a mathematical model on the grounding resistance of vertical electrode is proposed. The proposed mathematical model is modeled with consideration of the effects of parameters such as the length and diameter of vertical electrode, the soil resistivity and the embedding depth. This mathematical model can be applied effectively to the design of grounding system using vertical electrode in harmonious soil with the resistivity values less than 900Ω∙m. The accuracy of proposed model is proved by the simulation analysis and measurement examination of the electric field in this paper. [ABSTRACT FROM AUTHOR]

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to tackle a variety of computing tasks, among them the computation of shortest paths and the design of efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we generalize the dynamics to the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterizations of the optimum solution. [ABSTRACT FROM AUTHOR]

• The article proposes a new mathematical model of the inductive displacement sensor. • The model uses composite functions and a multi-objective optimization algorithm to design the coil structure parameters of the sensor. • The model aims to improve the sensor's linearity and sensitivity. • The new design method is verified by numerical simulation and physical experiments. This paper proposes a novel mathematical model that has high accuracy based on a multi-objective optimization algorithm for the inductive displacement sensors, which is popular in industrial production due to their simple design and reliable performance. The proposed model uses composite functions to establish the structural parameters of the coil winding. The non-dominated sorting genetic algorithm II (NSGA-II) is used to solve a series of non-dominated problems related to the coil structure parameters with the goal of achieving superior sensor performance. Density clustering sorting is used to select the desired non-dominated solutions. The designed sensor has a nonlinearity of 0.16%, and numerical simulations and physical experiments confirm the effectiveness of the new design method. [ABSTRACT FROM AUTHOR]

This paper proposes a new method to achieve the resonant behavior of a point absorber floating buoy type of Wave Energy Converter using direct drive power take-off system. The system has four main components: a frame; a buoy with a guiding shaft; a supplementary mass coupled with a linear generator and a variable stiffness structure. Firstly, the motion in the vertical direction of the buoy in the sea is converted to an oscillating motion of the supplementary mass. Next, the mass is coupled with a copper coil. The coil motion inside a magnetic wall induces an electrical current in the coil as a linear generator. Besides, a pair of pre-tension springs creates a negative stiffness phenomenon that acts on the motion of the mass and increases the performance of the system. Finally, a variable stiffness structure is installed to control the trajectory of the mass, it can increase the velocity of the mass motion thus the performance of the system is improved. Configuration and working principles of WEC were introduced, studied and analyzed. The mathematical model was presented to explain system behavior. The numerical simulation had been carried out to evaluate the operation of the system. The experimental test rig had been set up and implemented to verify the effectiveness of the proposed structure. • This paper proposes a new method of Wave Energy Converter using a direct drive power take-off system. • The novel variable stiffness mechanism (VSM) has been proposed and investigated. • The mathematical model and experimental test rig are built to validate the system performance. • The mass travels a distance that is longer than that of the excitation motion up to 6 times. • The ball screw and motor are controlled to increase the tension force of the springs and boost the motion of the sup-mass. [ABSTRACT FROM AUTHOR]

• Normal mode stability analysis performed on counjugate heat transfer (CHT) 1D problem. • Stability analysis reveals existence of lower stability bound for coupling coefficient in Robin-Dirichlet interface boundary conditions. • Validity of stability analysis results is verified empirically. • Stability analysis is extended to more general CHT problems. This paper aims to evaluate and validate a mathematical coupling model, based on a normal mode stability analysis, for steady conjugate heat transfer problems. In order to achieve this goal, an aerothermal computational code was designed specifically ex novo to meet the needs of the current study. A large number of numerical simulations were carried out within the framework of the Dirichlet-Robin fluid-solid interface procedure and with conditions strictly identical to those adopted in the mathematical model. These coupled computations have been synthesized in five representative cases. The computed results show that the stability limit and the numerical Biot number derived from the coupling model are very reliable parameters. Many other physical and numerical aspects, such as the splitting of the coupling period are also considered in this work from which some interesting and promising results are obtained. At the end of this paper, we assess the general potential, limits and constraints of the mathematical model and its extension to multidimensional cases is discussed. [ABSTRACT FROM AUTHOR]

We considered in the paper a mathematical model used to replicate the conversion from confined to unconfined flow due to groundwater abstraction. We argued that the existing model, while very useful, however, does not capture the effect of the aquitard with fractures, as in such media there is a crossover behavior from stretched exponential to power law. We modified the model by replacing the exponential decay component with the generalized Mittag-Leffler function, which yields a model with nonlocal properties. To solve the system, we consider two different approaches, the first consists of discretizing the model directly using the forward Euler method, and the second consists of converting the model to an integral equation and deriving the solution by employing a polynomial interpolation approach. We presented using the Von Neumann stability approach for the confined part and both yield stability unconditionally. Some numerical simulations are performed. • Generalized-Mittag-Leffler function and distribution. • Conversion from confined to unconfined flow. • Numerical schemes. • Laplace transform and related diagrams. [ABSTRACT FROM AUTHOR]

• The mathematical model is useful for analyzing the heat exchanger performance. • The most probable variant of heat exchanger operation is established. • There is a risk of frost accumulation within the fixed-bed regenerator. The paper describes an original mathematical model of heat and mass transfer for a fixed bed regenerator used to determine the effect of internal airflow leakage on heat exchanger efficiency. First, the build and operating principles of a fixed-bed heat exchanger were discussed. The presence of internal leakage was shown along with a proposed solution for its elimination. Then, a mathematical model based on a modified ε-NTU method for numerical simulation and analysis of coupled heat and mass transfer in a fixed-bed heat exchanger was presented. The model was supplemented with an additional detailed submodel designed to determine frost surface temperature and frost growth analysis. Initial numerical simulations of the operation of the model were performed for low outdoor air temperature conditions. Different zones of heat and mass transfer within the regenerator matrix were distinguished. The presence of accumulated frost area and its influence on the course of heat and mass transfer processes was revealed. In addition, the presence of a relative humidity limit curve associated with a mass balance deficiency conditioning the occurrence of frost accumulation was established. [ABSTRACT FROM AUTHOR]

This paper aims at developing a nonlinear mathematical model for the unsteady wake galloping forces (UWGF) acting on a circular cylinder in the wake of a fixed identical circular cylinder, which is always neglected in quasi-steady analysis. Numerical simulations are conducted to obtain the synchronous unsteady aerodynamic lift forces and displacements of wake galloping at Reynolds numbers (Re) of 1640–8420. The downstream cylinder is free to vibrate in the cross-flow direction with a mass-damping m*ζ = 0.267. The spacing ratio is fixed at L/D = 4 (where L is the center-to-center distance between the cylinders and D is the cylinder diameter). The UWGF model is built by combining the self-excited force and the vortex-induced force based on the spectra of the aerodynamic lift forces. Using an energy equivalent principle, the self-excited force can be divided into three parts: aerodynamic damping terms, aerodynamic stiffness terms and pure force terms. The identified aerodynamic parameters show that the aerodynamic damping terms are key factors determining the stable amplitude of wake galloping. The vortex-induced forces trigger an initial displacement to excite vibration in the early stage and have no influence on the stable amplitude. The proposed UWGF model is verified by experimental results and can calculate wake galloping responses better than the quasi-steady theory. • The UWGF model is built by combining the self-excited force and the vortex-induced force based on the spectra of lift forces. • The aerodynamic damping terms are key parameters determining the amplitude of wake galloping. • The proposed UWGF model can be easily applied and the impact of each model term on the responses of wake galloping can be figured out clearly. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel 1D singularly perturbed reaction–convection–diffusion mathematical model, with non-linear coefficients (SP-RCD model), for the physical modeling of a fuel cell. The model is a generalization of the macro-homogeneous model, revisited from the point of view of singularly perturbed differential equations. To solve the system of coupled second-order differential equations, we propose a numerical scheme based on vanishing the artificial diffusion of the finite element method within an iterative fixed-point algorithm. We also propose an adaptive Shishkin mesh, as a function of the derivative of the current density in the subdomain with a fast-growing slope. Results of the proposed SP-RCD model are comparable to those of the macro-homogeneous model. In addition, it describes the oxygen concentration profiles in the thickness of the cathode catalytic layer under different operating currents and represents, with enough precision, the experimental polarization curve reported in the literature. • We introduce a novel RCD mathematical model for the numerical simulation of PEM fuel cells. • We introduce a method for stabilizing the numerical solution, it introduces artificial diffusion (AD), until stabilization, then AD is removed. • We introduce a numerical strategy for adapting a Shishkin mesh, avoiding user-made tuning. • Mathematical arguments about convergence are provided. • We validate the algorithm with reported cases and other model. [ABSTRACT FROM AUTHOR]

This study focuses on the flow characteristics of the irregular MCPR (multi-chamber perforated resonator), mainly including the velocity field distribution and the pressure loss. The differences of the velocity field distribution between the straight-through irregular MCPR and the bent irregular MCPR are compared, the influence of the bent pipe on the velocity field distribution inside the irregular MCPR has been summarized. In addition, the influence of different influencing factors on the pressure loss of the irregular MCPR has been revealed. The influencing factors in this paper are the shape of resonator cross section, the perforation rate inside the resonator, the angle of the bent pipe and the inlet flow rate. The mathematical model of pressure loss is fitted according to the numerical simulation. In order to verify the accuracy of the model, a full experimental investigation has been conducted. The results indicate that the experimental results are in good agreement with the predicted values of the model. This study is helpful for design of irregular MCPR with better acoustic performance, lower pressure loss and flexible installation space. [ABSTRACT FROM AUTHOR]

In this paper a simplified mathematical model related to human phonation process is presented. Main attention is paid to the treatment of vocal fold vibrations excited by viscous incompressible airflow, which is stopped (chopped) by their periodical contacts. The Hertz impact model is used in the structural part and two new strategies are suggested to treat the contact phenomena in the fluid model. The numerical discretization by finite element (FE) method is described and the model problem is numerically approximated using a penalty approach in the inlet boundary condition for airflow and a thin porous layer in the glottis during the glottal closure. The numerical results are presented and discussed. [ABSTRACT FROM AUTHOR]