The stochastic fluid–fluid model: A stochastic fluid model driven by an uncountable-state process,which is a stochastic fluid model itself

We introduce the Stochastic Fluid–Fluid Model, which offers powerful modeling ability for a wide range of real-life systems of significance. We first derive the infinitesimal generator, with respect to time, of the driving stochastic fluid model. We then use this to derive the infinitesimal generator of a particular Laplace–Stieltjes transform of the model, which is the foundation of our analysis. We develop expressions for the Laplace–Stieltjes transforms of various performance measures for the transient and limiting analysis of the model. This work is the first direct analysis of a stochastic fluid model that is Markovian on a continuous state space.     

Non-linear model parameter estimation–estimating a feasible parameter set with respect to model use

This article deals with non-linear model parameter estimation from experimental data. As for non-linear models a rigorous identifiability analysis is difficult to perform, parameter estimation is performed in such a way that uncertainty in the estimated parameter values is represented by the range of model use results when the model is used for a certain purpose. Using this approach, the article presents a simulation study where the objective is to discover whether the estimation of model parameters can be improved, so that a small enough range of model use results is obtained. The results of the study indicate that from plant measurements available for the estimation of model parameters, it is possible to extract data that are important for the estimation of model parameters relative to a certain model use. If these data are improved by a proper measurement campaign (e.g. proper choice of measured variables, better accuracy, higher measurement frequency) it is to be expected that a valid model for a certain model use will be obtained. The simulation study is performed for an activated sludge model from wastewater treatment, while the estimation of model parameters is done by Monte Carlo simulation.     

Change-point estimation for censored regression model

In this paper, we consider the change-point estimation in the censored regression model assuming that there exists one change point. A nonparametric estimate of the change-point is proposed and is shown to be strongly consistent. Furthermore, its convergence rate is also obtained.     

Burridge–Knopoff model and self-similarity

Seismic processes are well known to be self-similar in both spatial and temporal behavior. At the same time, the Burridge–Knopoff (BK) model of earthquake fault dynamics, one of the basic models of theoretical seismicity, does not possess self-similarity. We present an extension of the BK model, based on the introduction of nonlinear terms for the inter-block springs of the BK model, which results in the self-similarity of earth crust elastic properties being accounted for directly. Phase space analysis of the model reveals the behavior of a system of randomly kicked coupled oscillators. The nonlinear stiffness terms cause synchronization of the collective motion and produce stronger seismic events.     

A Dynamical model of the atmospheric turbulencefromtheunstablestratificationtothestablestratification

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A kinetic model for coagulation–fragmentation

The aim of this paper is to show an existence theorem for a kinetic model of coagulation–fragmentation with initial data satisfying the natural physical bounds, and assumptions of finite number of particles and finite Lp$L^p$-norm. We use the notion of renormalized solutions introduced by DiPerna and Lions (1989) [3], because of the lack of a priori   estimates. The proof is based on weak-compactness methods in L¹$L^1$, allowed by Lp$L^p$-norms propagation.     

A new coupled model for alloy solidification

A new coupled model in the binary alloy solidification has been developed. The model is based on the cellular automaton (CA) technique to calculate the evolution of the interface governed by temperature, solute diffusion and Gibbs-Thomson effect. The diffusion equation of temperature with the release of latent heat on the solid/liquid (S/L) interface is valid in the entire domain. The temperature diffusion without the release of latent heat and solute diffusion are solved in the entire domain. In the interface cells, the     

On pattern formation in the Gray-Scott model

In the paper, we investigate an elliptic system well-known as the Gray-Scott model and present some further results for positive solutions of this model. More precisely, we give the refined a priori estimates of positive solutions, and improve some previous results for the non-existence and existence of positive non-constant solutions as the parameters are varied, which imply some certain conditions where the pattern formation occurs or not.     

Harvesting of a phytoplankton–zooplankton model

Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.     

A discrete prey–predator model preserving the dynamics of a structurally unstable Lotka–Volterra model

Leslie's method to construct a discrete two dimensional dynamical system dynamically consistent with the Lotka–Volterra type of competing two species ordinary differential equations is applied in a newly extended manner for the Lotka–Volterra prey–predator system which is structurally unstable. We show that, independently of the time step size, the derived discrete prey–predator system is dynamically consistent with the continuous counterpart, keeping the nature of neutrally stable periodic orbit. Further, we show that the extended method to construct the discrete prey–predator system can provide a dynamically consistent model also for the logistic Lotka–Volterra one.     

An improvement on the Tracy and Chen model ‘A generalized model for weight restrictions in DEA’

Recently Tracy and Chen presented a parametric DEA model (PDEA) to assess relative efficiency in the presence of a generalized form of linear weight restrictions. This paper proposes a modification to the PDEA model that avoids the need to resort to searching algorithms to estimate efficiency, and assures that the correct efficiency scores are obtained in a single stage using mathematical programming solvers. The results of this model and the results of Tracy and Chen's PDEA model are compared using the examples reported in their paper. The results confirm the superiority of the model proposed in this paper.     

Complex behaviour in a production–distribution model

The purpose of this paper is to show how the cascaded structure of a production–distribution chain can produce a wide variety of dynamic behaviours. Despite the apparent simplicity of the chain, the bounded rationality of human decision making interferes with the information feedbacks, nonlinearities and time delays of the system to produce exceedingly complex behaviour. When simulated with realistic parameter values, the model can exhibit stationary periodic, quasiperiodic as well as chaotic and hyperchaotic motions. Lyapunov exponents are used to characterize the different types of behaviour. Repeated simulation reveals how the profile of operating cost is related to the modes of behaviour and to the conditions that generate chaos. Detailed maps of parameter space graphically show the influence of inventory control policies upon dynamics and costs. The analyses illustrate why it is so difficult for decision makers to “navigate” in low-cost policy parameter regions. Suggestions are made for decision heuristics that avoid high-cost, unstable solutions.     

A string model of “exotic” particles

The bosonic string is investigated using the approach to 4D string dynamics previously proposed by the author. The physical states and the mass spectrum are constructed. The scale invariance of the theory results in the linear dependence of the squared mass μ² on the “spin” . Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 115, No. 2, pp. 223–244 May. 1998.     

The empirical likelihood goodness-of-fit test for regression model

Goodness-of-fit test for regression modes has received much attention in literature. In this paper, empirical likelihood (EL) goodness-of-fit tests for regression models including classical parametric and autoregressive (AR) time series models are proposed. Unlike the existing locally smoothing and globally smoothing methodologies, the new method has the advantage that the tests are self-scale invariant and that the asymptotic null distribution is chi-squared. Simulations are carried out to illustrate the methodology.     

A ratio-dependent predator–prey model with diffusion

This paper deals with the existence and nonexistence of nonconstant positive steady-state solutions to a ratio-dependent predator–prey model with diffusion and with the homogeneous Neumann boundary condition. We demonstrate that there exists $a_0(b)$ satisfying $0<a_0(b)<m_1$ for $0<b<m_1$, such that if $0<b<m_1$ and $a_0(b)<a<m_1$, then the diffusion can create nonconstant positive steady-state solutions; whereas the diffusion cannot do provided $a>m_1$.