A microscopic ancient river channel identification method based on maximum entropy principle and Wigner-Ville Distribution and its application

In view of the problem of fine characterization of narrow and thin channels,the maximum entropy criterion is used to enhance the focusing characteristics of Wigner-Ville Distribution.On the basis of effectively improving the time-frequency resolution of seismic signal,a new method of microscopic ancient river channel identification is established.Based on the principle of the equivalence between the maximum entropy power spectrum and the AR model power spectrum,the prediction error and the autoregression coefficient of AR model are obtained using the Burg algorithm and Levinson-Durbin recurrence rule.Under the condition of the first derivative of autocorrelation function being 0,the Wigner-Ville Distribution of seismic signal is calculated,and the Wigner-Ville Distribution time-frequency power spectrum(MEWVD)is obtained under the maxi-mum entropy criterion of the microscopic ancient river channel.Through analysis of emulational seismic signal and forward numerical simulation signal of narrow thin model,it is found that MEWVD can effectively avoid the interference of cross term of Wigner-Ville Distribution,and obtain more accurate spectral characteristics than STFT and CWT signal analysis methods.It is also proved that the narrow and thin river channels of different scales can be identified effectively by MEWVD of different frequencies.The method is applied to the third member of Jurassic Shaximiao Formation(J2s33-2)gas reservoir of the Zhongji-ang gas field in Sichuan Basin.The spatial information of width and direction of narrow and thin river channels with width less than 500 m and sandstone thickness less than 35 m is accurately identified,providing bases for well deployment and horizontal well fracturing section selection.

Surface Elevation Distribution of Sea Waves Based on the Maximum Entropy Principle

A probability density function of surface elevation is obtained through improvement of the method introduced by Cieslikiewicz who employed the maximum entropy principle to investigate the surface elevation distribution. The density function can be easily extended to higher order according to demand and is non-negative everywhere, satisfying the basic behavior of the probability, Moreover because the distribution is derived without any assumption about sea waves, it is found from comparison with several accepted distributions that the new form of distribution can be applied in a wider range of wave conditions, In addition, the density function can be used to fit some observed distributions of surface vertical acceleration although something remains unsolved.

APPLICATION OF MAXIMUM ENTROPY PRINCIPLE METHOD TO THE STUDY OF WAVE CLIMATE STATISTICAL CHARACTERISTICS

The Maximum Entropy Principle (MEP) method is elaborated, and thecorresponding probability density evaluation method for the random fluctuation system is introduced,the goal of the article is to find the best fitting method for the wave climate statisticaldistribution. For the first time, a kind of new maximum entropy probability distribution (MEPdistribution) expression is deduced in accordance with the second order moment of a random process.Different from all the fitting methods in the past, the MEP distribution can describe theprobability distribution of any random fluctuation system conveniently and reasonably. If themoments of the random signal is limited to the second order, that is, the ratio of theroot-mean-square value to the mean value of the random variable is obtained from the random sample,the corresponding MEP distribution can be computed according to the deduced expression in thisessay. The concept of the wave climate is introduced here, and the MEP distribution is applied tofit the probability density distributions of the significant wave height and spectral peak period.Take the Mexico Gulf as an example, three stations at different locations, depths and wind wavestrengths are chosen in the half-closed gulf, the significant wave height and spectral peak perioddistributions at each station are fitted with the MEP distribution, the Weibull distribution and theLog-normal distribution respectively, the fitted results are compared with the field observations,the results show that the MEP distribution is the best fitting method, and the Weibull distributionis the worst one when applied to the significant wave height and spectral peak period distributionsat different locations, water depths and wind wave strengths in the Gulf. The conclusion shows thefeasibility and reasonability of fitting wave climate statistical distributions with the deduced MEPdistributions in this essay, and furthermore proves the great potential of MEP method to the studyof wave statistical properties.

Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory

Thermodynamics plays an important role in gravitational theories.It is a principle that is independent of gravitational dynamics,and there is still no rigorous proof to show that it is consistent with the dynamical principle.We consider a self-gravitating perfect fluid system with the general diffeomorphism-covariant purely gravitational theory.Based on the Noether charge method proposed by Iyer and Wald,considering static off/on-shell variational configurations,which satisfy the gravitational constraint equation,we rigorously prove that the extrema of the total entropy of a perfect fluid inside a compact region for a fixed total particle number demands that the static configuration is an on-shell solution after we introduce some appropriate boundary conditions,i.e.,it also satisfies the spatial gravitational equations.This means that the entropy principle of the fluid stores the same information as the gravitational equation in a static configuration.Our proof is universal and holds for any diffeomorphism-covariant purely gravitational theories,such as Einstein gravity,f(R)gravity,Lovelock gravity,f(Gauss-Bonnet)gravity and Einstein-Weyl gravity.Our result indicates the consistency between ordinary thermodynamics and gravitational dynamics.

A Maximum-Entropy Compound Distribution Model for Extreme Wave Heights of Typhoon-Affected Sea Areas

A new compound distribution model for extreme wave heights of typhoon-affected sea areas is proposed on the basis of the maximum-entropy principle. The new model is formed by nesting a discrete distribution in a continuous one, having eight parameters which can be determined in terms of observed data of typhoon occurrence-frequency and extreme wave heights by numerically solving two sets of equations derived in this paper. The model is examined by using it to predict the N-year return-period wave height at two hydrology stations in the Yellow Sea, and the predicted results are compared with those predicted by use of some other compound distribution models. Examinations and comparisons show that the model has some advantages for predicting the N-year return-period wave height in typhoon-affected sea areas.

Maximum Entropy and Bayesian Inference for the Monty Hall Problem

We devise an approach to Bayesian statistics and their applications in the analysis of the Monty Hall problem. We combine knowledge gained through applications of the Maximum Entropy Principle and Nash equilibrium strategies to provide results concerning the use of Bayesian approaches unique to the Monty Hall problem. We use a model to describe Monty’s decision process and clarify that Bayesian inference results in an “irrelevant, therefore invariant” hypothesis. We discuss the advantages of Bayesian inference over the frequentist inference in tackling the uneven prior probability Monty Hall variant. We demonstrate that the use of Bayesian statistics conforms to the Maximum Entropy Principle in information theory and Bayesian approach successfully resolves dilemmas in the uneven probability Monty Hall variant. Our findings have applications in the decision making, information theory, bioinformatics, quantum game theory and beyond.

Entropy of a rotating and charged black string to all orders in the Planck length

By using the entanglement entropy method, this paper calculates the statistical entropy of the Bose and Fermi fields in thin films, and derives the Bekenstein-Hawking entropy and its correction term on the background of a rotating and charged black string. Here, the quantum field is entangled with quantum states in the black string and thin film to the event horizon from outside the rotating and charged black string. Taking into account the effect of the generalized uncertainty principle on quantum state density, it removes the difficulty of the divergence of state density near the event horizon in the brick-wall model. These calculations and discussions imply that high density quantum states near the event horizon of a black string are strongly correlated with the quantum states in a black string and that black string entropy is a quantum effect. The ultraviolet cut-off in the brick-wall model is not reasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the viewpoint of quantum statistical mechanics, the correction value of Bekenstein-Hawking entropy is obtained. This allows the fundamental recognition of the correction value of black string entropy at nonspherical coordinates.

Fourth-Order Predictive Modelling: I. General-Purpose Closed-Form Fourth-Order Moments-Constrained MaxEnt Distribution

This work (in two parts) will present a novel predictive modeling methodology aimed at obtaining “best-estimate results with reduced uncertainties” for the first four moments (mean values, covariance, skewness and kurtosis) of the optimally predicted distribution of model results and calibrated model parameters, by combining fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses to model parameters. Underlying the construction of this fourth-order predictive modeling methodology is the “maximum entropy principle” which is initially used to obtain a novel closed-form expression of the (moments-constrained) fourth-order Maximum Entropy (MaxEnt) probability distribution constructed from the first four moments (means, covariances, skewness, kurtosis), which are assumed to be known, of an otherwise unknown distribution of a high-dimensional multivariate uncertain quantity of interest. This fourth-order MaxEnt distribution provides optimal compatibility of the available information while simultaneously ensuring minimal spurious information content, yielding an estimate of a probability density with the highest uncertainty among all densities satisfying the known moment constraints. Since this novel generic fourth-order MaxEnt distribution is of interest in its own right for applications in addition to predictive modeling, its construction is presented separately, in this first part of a two-part work. The fourth-order predictive modeling methodology that will be constructed by particularizing this generic fourth-order MaxEnt distribution will be presented in the accompanying work (Part-2).

Application of MEP Method to the Study of statistical Properties of Random Waves

The maximum entropy principle (MEP) method and the corresponding probability evaluation method are introduced, and the maximum entropy probability distribution expression is deduced in moment of the second order. Fully developed wave height distribution in deep water and wave height and period distribution for different depths in wind wave channel experiment are obtained from the MEP method, and the results are compared with the distribution and the experimental histogram. The wave height and period distribution for the Lianyungang port is also obtained by the MEP method, and the results are compared with the Weibull distribution and the field histogram.

SOME REGULARITIES OF HEAVY RAIN IN XINJIANG,CHINA

The paper studied the distribution law of Xinjiang's heavy rain in time-area-depth by theoretical expression deduced from the entropy maximum principle and found some regularities of heavy rainfall in Xinjiang based on analyzing 32-year observational data from about 400 hydrological and meteorological stations.It has practical significance for studying Xinjiang's heavy rainfall,designing water conservancy and reducing flood catastrophe caused by heavy rain.

Counting single cells and computing their heterogeneity:from phenotypic frequencies to mean value of a quantitative biomarker

This tutorial presents a mathematical theory that relates the probability of sample frequencies,of M phenotypes in an isogenic population of N cells,to the probability distribution of the sample mean of a quantitative biomarker,when the N is very large.An analogue to the statistical mechanics of canonical ensemble is discussed.

Constructal design progress for eight types of heat sinks

This review paper summarizes constructal design progress performed by the authors for eight types of heat sinks with ten performance indexes being taken as the optimization objectives,respectively,by combining the methods of theoretical analysis and numerical calculation.The eight types of heat sinks are uniform height rectangular fin heat sink,non-uniform height rectangular fin heat sink,inline cylindrical pin-fin heat sink(ICPHS),plate single-row pin fin heat sink(PSRPHS),plate inline pin fin heat sink(PIPHS),plate staggered pin fin heat sink(PSPHS),single-layered microchannel heat sink(SLMCHS)with rectangular cross sections and double-layered microchannel heat sink(DLMCHS)with rectangular cross sections,respectively.And the ten performance indexes are heat transfer rate maximization,maximum thermal resistance minimization,minimization of equivalent thermal resistance which is defined based on the entransy dissipation rate(equivalent thermal resistance for short),field synergy number maximization,entropy generation rate minimization,operation cost minimization,thermo-economic function value minimization,pressure drop minimization,enhanced heat transfer factor maximization and efficiency evaluation criterion number maximization,respectively.The optimal constructs of the eight types of heat sinks with different constraints and based on the different optimization objectives are compared with each other.The results indicated that the optimal constructs mostly are different based on different optimization objectives under the same boundary condition.The optimization objective should be suitable chosen based on the focus when the constructal design for one heat sink is performed.The results obtained herein have some important theoretical significances and application values,and can provide scientific bases and theoretical guidelines for the thermal design of real heat sinks and their applications.