Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions

In real systems,the unpredictable jump changes of the random environment can induce the critical transitions(CTs)between two non-adjacent states,which are more catastrophic.Taking an asymmetric Lévy-noise-induced tri-stable model with desirable,sub-desirable,and undesirable states as a prototype class of real systems,a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out.We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability,which is named as the absorbed region.Then,a new concept of the parameter dependent basin of the unsafe regime(PDBUR)under the asymmetric Lévy noise is introduced.It is an efficient tool for approximately quantifying the ranges of the parameters,where the noise-induced CTs from the desirable state directly to the undesirable one may occur.More importantly,it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT.

Uniform modeling of parameter dependent nonlinear systems

This paper addresses the problem of approximating parameter dependent nonlinear systems in a unified framework. This modeling has been presented for the first time in the form of parameter dependent piecewise affine systems. In this model, the matrices and vectors defining piecewise affine systems are affine functions of parameters. Modeling of the system is done based on distinct spaces of state and parameter, and the operating regions are partitioned into the sections that we call 'multiplied simplices'. It is proven that this method of partitioning leads to less complexity of the approximated model compared with the few existing methods for modeling of parameter dependent nonlinear systems. It is also proven that the approximation is continuous for continuous functions and can be arbitrarily close to the original one. Next, the approximation error is calculated for a special class of parameter dependent nonlinear systems. For this class of systems, by solving an optimization problem, the operating regions can be partitioned into the minimum number of hyper-rectangles such that the modeling error does not exceed a specified value. This modeling method can be the first step towards analyzing the parameter dependent nonlinear systems with a uniform method.

Regional averaged controllability for hyperbolic parameter dependent systems

The purpose of this paper is to extend the notion of regional controllability for hyperbolic parameter dependent systems.The key idea is the characterization of the averaged regional control with minimal energy.This control steers the state average(with respect to such a parameter)towards the desired state only on a given part of the system evolution domain.In this paper,we give the precis definition and the properties of this new concept.Then,we use an approach based on an extension of the Hilbert uniqueness method devoted to the calculation of the control in two different cases:zone control and pointwise control.

Continuous Dependence of Bounded Φ-Variation Solutions on Parameters for Kurzweil Equations

The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ- variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations.

THE INTEGRAL AS A FUNCTlON OF THE UPPER LIMIT AND DEPENDING ON A PARAMETER TO SOLVE DRAWING THROUGH IDLING ROLLS

The relocity and sirain-rate .field which are different from Avilzur's have beenestablished in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler, an analylical upper-bound solution todrawing stress through idling rolls has been obtained in this paper.

Balanced Truncation Based on Generalized Multiscale Finite Element Method for the Parameter-Dependent Elliptic Problem

In this paper,we combine the generalized multiscale finite element method(GMsFEM)with the balanced truncation(BT)method to address a parameterdependent elliptic problem.Basically,in progress of a model reduction we try to obtain accurate solutions with less computational resources.It is realized via a spectral decomposition from the dominant eigenvalues,that is used for an enrichment of multiscale basis functions in the GMsFEM.The multiscale bases computations are localized to specified coarse neighborhoods,and follow an offline-online process in which eigenvalue problems are used to capture the underlying system behaviors.In the BT on reduced scales,we present a local-global strategy where it requires the observability and controllability of solutions to a set of Lyapunov equations.As the Lyapunov equations need expensive computations,the efficiency of our combined approach is shown to be readily flexible with respect to the online space and an reduced dimension.Numerical experiments are provided to validate the robustness of our approach for the parameter-dependent elliptic model.

EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS

This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green＇s function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories.

Effect of temperature on the efficiency of organometallic perovskite solar cells

In recent years perovskite solar cells have attracted an increasing scientific and technological interest in the scientific community. It is important to know that the temperature is one of the factors which have a strong effect on the efficiency of perovskite solar cell. This study communicates a temperature analysis on the pho- tovoltaic parameters of CH3NH3Pbl3-based perovskite solar cell in a broad interval from 80 to 360 K. Strong temperature-dependent photovoltaic effects have been observed in the type of solar cell, which could be mainly attributed to CH3NH3PbI3, showing a ferroelectric-paraelectric phase transition at low temperature （T 〈 160 K）. An increase in temperature over the room temperature decreased the perovskite solar cell performance and reduced its efficiency from 16Z to 9%. The investigation with electronic impedance spectroscopy reveals that at low temperature （T 〈 120 K） the charge transport layer limits the device performance, while at high temperature （T 〉 200 K）, the interfacial charge recombination becomes the dominant factor.

Conceptual Modelling and Data Based Techniques to Understand Urban Water Use and Wastewater Production

A systems approach is used to describe the generation and variation of wastewater in an urban area. This is a multivariable system and its combined response at the outlet of this system, which is usually the entrance ofa wastewater treatment plant, depends on a number of environmental （precipitation and temperature） as well as social （size of the urban area, population changes, water consumption per capita） variables. There is a large number of available models and tools for describing the urban water system, however, the interactions between the individual components are rarely considered within the same modelling framework. In this paper a parsimonious methodology is proposed in order to understand and estimate the wastewater generation and its characteristics in an urban area using any information provided by the available data. The model incorporates both the flows of stormwater discharge and wastewater production that arrive to the wastewater treatment plant. A state dependent variable is introduced to simulate the consumptive uses in the urban area. Data availability and system＇s complexity affect the ability to achieve enhanced model performance, however, in the presented case study, preliminary results from the application of the presented model in the Greater Athens Area illustrate the potential of the conceptual modelling approach.

On Holder Dependence of the Parameterized Hartman–Grobman Theorem

The well-known Hartman-Grobman Theorem says that a C~1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphismΦ.For parameterized systems F_(θ),known results show that the corresponding homeomorphismsΦ_(θ)exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameterθ.In this paper,we further extend the results to Holder dependence ofΦ_(θ)onθby Pugh's strategy,but introducing a kind of special Holder norm instead of the usual supremum norm in the proof to control the linear parts of F_(θ).This requires a new Holder linearization result for every F_(θ).

Impact parameter and beam energy dependence for azimuthal asymmetry of direct photons and free protons in intermediate energy heavy-ion collisions

Hard photon emitted from energetic heavy ion collisions is of very interesting since it does not experience the late-stage nuclear interaction, therefore it is useful to explore the early-stage information of matter phase. In this work, we have calculated the impact parameter and beam energy dependence for azimuthal asymmetry, characterized by directed transverse flow parameter F and elliptic asymmetry coeffcient v2, of direct photons and the corresponding free protons in intermediate energy heavy-ion collisions. It is further shown the anti-correlated azimuthal asymmetry between direct photons and free protons.

Min-max model predictive control for constrained nonlinear systems via multiple LPV embeddings

A min-max model predictive control strategy is proposed for a class of constrained nonlinear system whose trajectories can be embedded within those of a bank of linear parameter varying （LPV） models. The embedding LPV models can yield much better approximation of the nonlinear system dynamics than a single LTV model. For each LPV model, a parameter-dependent Lyapunov function is introduced to obtain poly-quadratically stable control law and to guarantee the feasibility and stability of the origi- nal nonlinear system. This approach can greatly reduce computational burden in traditional nonlinear predictive control strategy. Finally a simulation example illustrating the strategy is presented.

Model-based and Fuzzy Logic Approaches to Condition Monitoring of Operational Wind Turbines

It is common for wind turbines to be installed in remote locations on land or offshore, leading to difficulties in routine inspection and maintenance. Further, wind turbines in these locations are often subject to harsh operating conditions. These challenges mean there is a requirement for a high degree of maintenance. The data generated by monitoring systems can be used to obtain models of wind turbines operating under different conditions, and hence predict output signals based on known inputs. A model-based condition monitoring system can be implemented by comparing output data obtained from operational turbines with those predicted by the models, so as to detect changes that could be due to the presence of faults. This paper discusses several techniques for model-based condition monitoring systems: linear models, artificial neural networks, and state dependent parameter "pseudo" transfer functions.The models are identified using supervisory control and data acquisition(SCADA) data acquired from an operational wind firm. It is found that the multiple-input single-output state dependent parameter method outperforms both multivariate linear and artificial neural network-based approaches. Subsequently, state dependent parameter models are used to develop adaptive thresholds for critical output signals. In order to provide an early warning of a developing fault, it is necessary to interpret the amount by which the threshold is exceeded, together with the period of time over which this occurs. In this regard, a fuzzy logic-based inference system is proposed and demonstrated to be practically feasible.

On the Hochstadt–Lieberman Theorem for Discontinuous Boundary-valued Problems

In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.