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Probability interpretation is the cornerstone of standard quantum mechanics. To ensure the validity of the probability interpretation, wavefunctions have to satisfy the square-integrable (SI) condition, which gives rise to the well-known phenomenon of energy quantization in confined quantum systems. On the other hand, nonsquare-integrable (NSI) solutions to the Schrödinger equation are usually ruled out and have long been believed to be irrelevant to energy quantization. This paper proposes a quantum-trajectory approach to energy quantization by releasing the SI condition and considering both SI and NSI solutions to the Schrödinger equation. Contrary to our common belief, we find that both SI and NSI wavefunctions contribute to energy quantization. SI wavefunctions help to locate the bifurcation points at which energy has a step jump, while NSI wavefunctions form the flat parts of the stair-like distribution of the quantized energies. The consideration of NSI wavefunctions furthermore reveals a new quantum phenomenon regarding the synchronicity between the energy quantization process and the center-saddle bifurcation process. [ABSTRACT FROM AUTHOR]

This paper investigates the force transmission modes, mainly described by probability density distributions, in non-cohesive dry and cohesive wet granular materials by discrete element modeling. The critical state force transmission patterns are focused on with the contact model effect being analyzed. By shearing relatively dense and loose dry specimens to the critical state in the conventional triaxial loading path, it is observed that there is a unique critical state force transmission mode. There is a universe critical state force distribution pattern for both the normal contact forces and tangential contact forces. Furthermore, it is found that using either the linear Hooke or the non-linear Hertz model does not affect the universe force transmission mode, and it is only related to the grain size distribution. Wet granular materials are also simulated by incorporating a water bridge model. Dense and loose wet granular materials are tested, and the critical state behavior for the wet material is also observed. The critical state strength and void ratio of wet granular materials are higher than those of a non-cohesive material. The critical state inter-particle distribution is altered from that of a non-cohesive material with higher probability in relatively weak forces. Grains in non-cohesive materials are under compressive stresses, and their principal directions are mainly in the axial loading direction. However, for cohesive wet granular materials, some particles are in tension, and the tensile stresses are in the horizontal direction on which the confinement is applied. The additional confinement by the tensile stress explains the macro strength and dilatancy increase in wet samples. [ABSTRACT FROM AUTHOR]

Stochastic distribution control (SDC) systems are a group of systems where the outputs considered is the measured probability density function (PDF) of the system output whilst subjected to a normal crisp input. The purpose of the active fault tolerant control of such systems is to use the fault estimation information and other measured information to make the output PDF still track the given distribution when the objective PDF is known. However, if the target PDF is unavailable, the PDF tracking operation will be impossible. Minimum entropy control of the system output can be considered as an alternative strategy. The mean represents the center location of the stochastic variable, and it is reasonable that the minimum entropy fault tolerant controller can be designed subjected to mean constraint. In this paper, using the rational square-root B-spline model for the shape control of the system output probability density function (PDF), a nonlinear adaptive observer based fault diagnosis algorithm is proposed to diagnose the fault. Through the controller reconfiguration, the system entropy subjected to mean restriction can still be minimized when fault occurs. An illustrative example is utilized to demonstrate the use of the minimum entropy fault tolerant control algorithms. [ABSTRACT FROM AUTHOR]

With the increasing permeability of photovoltaic (PV) power production, the uncertainties and randomness of PV power have played a critical role in the operation and dispatch of the power grid and amplified the abandon rate of PV power. Consequently, the accuracy of PV power forecast urgently needs to be improved. Based on the amplitude and fluctuation characteristics of the PV power forecast error, a short-term PV output forecast method that considers the error calibration is proposed. Firstly, typical climate categories are defined to classify the historical PV power data. On the one hand, due to the non-negligible diversity of error amplitudes in different categories, the probability density distributions of relative error (RE) are generated for each category. Distribution fitting is performed to simulate probability density function (PDF) curves, and the RE samples are drawn from the fitted curves to obtain the sampling values of the RE. On the other hand, based on the fluctuation characteristic of RE, the recent RE data are utilized to analyze the error fluctuation conditions of the forecast points so as to obtain the compensation values of the RE. The compensation values are adopted to sequence the sampling values by choosing the sampling values closest to the compensation ones to be the fitted values of the RE. On this basis, the fitted values of the RE are employed to correct the forecast values of PV power and improve the forecast accuracy. [ABSTRACT FROM AUTHOR]

A standard result in quantum mechanics is this: if two observables are commuting then they have a classical joint distribution in every state. A converse is demonstrated here: If a classical joint distribution for the pair agrees with standard quantum facts, then the observables must commute. This has consequences for some historical and recent quantum nonlocal models: they are analytically disallowed without the need for experiment, as they imply that all local observables must commute among themselves. [ABSTRACT FROM AUTHOR]

This paper presents a techno-economic assessment of the wind power potential for eight locations distributed over the Northern part of Cyprus. The wind speed data were collected from the meteorological department located in Lefkoşa, Northern Cyprus.Ten distribution models were used to analyze the wind speed characteristics and wind energy potential at the selected locations. The maximum-likelihood method was used for calculating the parameters of the distribution functions.The power law model is utilized to determine the mean wind speed at various heights. In addition, the wind power density for each location was estimated. Furthermore, the performances of different small-scale vertical axis 3–10 kW wind turbines were evaluated to find those that were suitable and efficient for power generation in the studied locations.The results showed that the annual mean wind speed in the regions is greater than 2 m/s at a height of 10 m. Moreover, it is indicated that Generalized Extreme Value distribution provided the best fit to the actual data for the regions of Lefkoşa, Ercan, Girne, Güzelyurt, and Dipkarpaz. However, the Log-Logistic, Weibull, and Gamma distributions gave a better fit to the actual data of Gazimağusa, YeniBoğaziçi, and Salamis, respectively. The Rayleigh distribution does not fit the actual data from all regions. Furthermore, the values of wind power densityat the areas studied ranged from 38.76 W/m2 to 134.29 W/m2 at a height of 50 m, which indicated that wind energy sources in these selected locations are classified as poor. Meanwhile, based on the wind analysis, small-scale wind turbine use can be suitable for generating electricity in the studied locations. Consequently, an Aeolos-V2 with a rating of 5 kW was found to be capable of producing the annual energy needs of an average household in Northern Cyprus. [ABSTRACT FROM AUTHOR]