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The study of damage and failure in fractured rock masses is crucial. This study employs the representative volume element (RVE) method to develop a microscale rock model. The model simulates the propagation and rupture of fractures by integrating factors including actual mineralogical composition, the Weibull distribution function, the Mohr–Coulomb damage criterion, and strain softening. Results indicate that fractures reduce the uniaxial compressive strength of the rock and that peak strength is significantly correlated with crack geometries. Plastic damage in rocks was categorized into three stages: elastic, rapid growth, and postpeak softening. A logistic growth model describes the plastic volume change curves for rocks with various fracture geometries, establishing the relationship between plastic damage volume and damage variables. Constitutive models for rocks with varying fracture geometries under uniaxial compression were formulated. The accuracy and applicability of these models were validated, providing a theoretical basis for rock engineering applications. Highlights: A heterogeneous plastic damage model based on representative volume elements is developed.A logistic growth model was used to describe the plastic volume change curves for rocks containing different fracture geometries.The relationship between rock plastic damage volume and damage variables was established.Plastic damage constitutive models of rocks containing different fracture geometries under uniaxial compression were obtained and validated. [ABSTRACT FROM AUTHOR]

It is urgent to identify the development of the Corona Virus Disease 2019 (COVID‐19) in countries around the world. Therefore, visualization is particularly important for monitoring the COVID‐19. In this paper, we visually analyze the real‐time data of COVID‐19, to monitor the trend of COVID‐19 in the form of charts. At present, the COVID‐19 is still spreading. However, in the existing works, the visualization of COVID‐19 data has not established a certain connection between the forecast of the epidemic data and the forecast of the epidemic. To better predict the development trend of the COVID‐19, we establish a logistic growth model to predict the development of the epidemic by using the same data source in the visualization. However, the logistic growth model only has a single feature. To predict the epidemic situation in an all‐round way, we also predict the development trend of the COVID‐19 based on the Susceptible Exposed Infected Removed epidemic model with multiple features. We fit the data predicted by the model to the real COVID‐19 epidemic data. The simulation results show that the predicted epidemic development trend is consistent with the actual epidemic development trend, and our model performs well in predicting the trend of COVID‐19. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to deal with the randomness associated to ecological modelling. Data variability makes it necessary to analyse the impact of random perturbations on the fitted model parameters. We conduct such analysis for the logistic growth model with a certain sigmoid functional form of the carrying capacity, which was proposed in the literature for the study of parasite growth during infection. We show how the probability distributions of the parameters are set via the maximum entropy principle. Then the random variable transformation method allows for computing the density function of the population. [ABSTRACT FROM AUTHOR]

In this study, in addition to classical Logistic and Gompertz models with three parameters, their growth models with four parameters were given. After that it is searched the effect of these growth models on the choice of appropriate growth model by using two separate data sets. For this purpose, classical Logistic and Gompertz growth models and their growth models with four parameters are compared with some model selection criteria such as such as error sum of squares, coefficient of determination, adjusted coefficient of determination and akaike information criteria. For the data set used in this study, it is found that the results of these growth models with four parameters are better than the results of these growth models. Thus, it is considered that these growth models with four parameters can be used in addition to these classical growth models. In addition, some other growth models with four parameters can be investigated for getting the best model choice. Even Logistic and Gompertz models with five and more parameters can be investigated for getting the best model choice. [ABSTRACT FROM AUTHOR]

Growth models are often used when modelling various processes in life sciences, ecology, demography, social sciences, etc. Dynamical growth models are usually formulated in terms of an ODE (system of ODS's) or by an explicit solution to an ODE, such as the logistic, Gompertz, and Richardson growth models. To choose a suitable growth model it is useful to know the physics‐chemical meaning of the model. In many situations this meaning is best expressed by means of a reaction network that possibly induces the dynamical growth model via mass action kinetics. Such reaction networks are well known for a number of growth models, such as the saturation‐decay and the logistic Verhulst models. However, no such reaction networks exist for the Gompertz growth model. In this work we propose some reaction networks using mass action kinetics that induce growth models that are (in certain sense) close to the Gompertz model. The discussion of these reaction networks aims to a better understanding of the chemical properties of the Gompertz model and "Gompertzian‐type" growth models. Our method can be considered as an extension of the work of previous authors who "recasted" the Gompertz differential equation into a dynamical system of two differential equations that, apart of the basic species variable, involve an additional variable that can be interpreted as a "resource." Two new growth models based on mass action kinetics are introduced and studied in comparison with the Gompertz model. Numerical computations are presented using some specialized software tools. [ABSTRACT FROM AUTHOR]

Virtual plant modelling is becoming a hot issue both in computer graphics and agricultural researches. However, high‐realistic plant modelling and plant animation is still a problem both in theory and applications. In this study, an interactive animation method for virtual maize dynamic simulation is presented, and an experimental system is developed by using C + + program language and OpenGL library. Firstly, true three‐dimensional data and structural parameters of maize plant are collected as the foundation of modelling and animation. Secondly, an accurate virtual maize model is constructed based on interactive parameterised modelling. Constrained by logistic growth model, a group of key parameters is generated and precise maize animation with high‐realistic visualisation is created according to the factual plant growth. Furthermore, an applied system is developed based on the proposed algorithm, and a set of simulation results are generated by use of the system. The results show that the proposed method is feasible for realistic dynamic simulation and animation of maize. Finally, main contributions and limitations of the authors work are discussed, and some problems are addressed as the future works. [ABSTRACT FROM AUTHOR]