A Numerical Model with Finite Difference Schemes for Multi-Species Solute Transport in Porous Media

A precise forecast of contaminant and solute transport has an inevitable role in the management of water resources. In accordance with this purpose, in this paper, a novel one-dimensional numerical model for the transport of a decay chain through homogeneous porous media is proposed. To develop the suggested model, two different schemes of the finite difference method, namely the Lax-Wendroff scheme and Fourth-Order scheme, are used. The verification and validation of the established model are examined by the analytical results of three multi-species solute dispersion problems with three- and four-chain members. The total mean square error, L2- and L∞-norms are applied to assess the results. Although analyses show that both schemes provided reliable results, the numerical results of the Lax-Wendroff scheme are more accurate.

Effects of Inclination angle and Free Convection on Velocity Profile for a Steady 2-Dimensional Magnetohydrodynamic Fluid Flow in an Inclined Cylindrical Pipe

Effects of inclination and free convection on velocity profile for magnetohydrodynamic (MHD) fluid flow in an inclined cylindrical pipe has been investigated. The governing partial differential equations are the equations of continuity, momentum and energy which are converted into ordinary differential equation by employing similarity transformation and solved numerically by the Runge- Kutta fourth order scheme with shooting method. The findings, which are presented in the form of tables and graphs reveal that; when Hartmann number, Grashoff number and Gamma are decreased, the velocity of the fluid increases. The results of the study may be useful for the different model investigations, especially, in various areas of science and technology in which optimal inclination and free convection are utilized.

Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource

The dynamics of a specific consumer-resource model for Daphnia magna is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the model are compared as different parameters involved in the model change. In the case of Gompertz growth law, a new complex dynamic is found as the carrying capacity for the resource population increases. The numerical study is carried out with a second-order scheme that approximates the size-dependent density function for individuals in the consumer population. The numerical method is well adapted to the situation in which the growth rate for the consumer individuals is allowed to change the sign and, therefore, individuals in the consumer population can shrink in size as time evolves. The numerical simulations confirm that the shortage of the resource has, as a biological consequence, the effective shrink in size of individuals of the consumer population. Moreover, the choice of the growth law for the resource population can be selected by how the dynamics of the populations match with the qualitative behaviour of the data.

A Reverse Non-Stationary Generalized B-Splines Subdivision Scheme

In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons.

Fractional-order Approach to Modeling and Characterizing the Complex and Frequency-dependent Apparent Arterial Compliance: In Human and Animal Validation

Recently, experimental and theoretical studies have revealed the potential of fractional calculus to represent viscoelastic blood vessel and arterial biomechanical properties. This paper presents five fractional-order models to describe the dynamic relationship between aortic blood pressure and volume, representing the apparent vascular compliance. The proposed model employs fractional-order capacitor element (FOC) to lump the complex and frequency dependence characteristics of arterial compliance. FOC combines both resistive and capacitive properties, which the fractional differentiation order, alpha, can control. The proposed representations have been compared with generalized integer-order models of arterial compliance. All structures have been validated using different aortic pressure and flow rate waveforms collected from various human and animal species such as pigs and dogs. The results demonstrate that the fractional-order scheme can reconstruct the overall dynamic of the complex and frequency-dependent apparent compliance dynamic and reduce the complexity. The physiological relevance of the proposed models' parameters was assessed by evaluating the variance-based global sensitivity analysis. Moreover, the simplest fractional-order representation has been embed in a global arterial lumped parameter representation to develop a novel fractional-order modified arterial Windkessel. The introduced arterial model has been validated by applying real human and animal hemodynamic data and shows an accurate reconstruction of the proximal blood pressure. The novel proposed paradigm confers a potential to be adopted in clinical practice and basic cardiovascular mechanics research.

THE USE OF BODY METAPHOR IN DESCRIBING THE SOCIAL IN CHRISTINE DE PIZAN’S “THE BOOK OF THE BODY POLITIC”

The article analyzes «The Book of the Body Politic» (1404–1407) by Christine de Pizan to show how she updated the metaphor of body politic traditional for the Middle Ages, and what were the reasons for the creation of this treatise. In it, Christine excluded the clergy from the tripartite social order scheme: in the political body the sovereign replaced the pope and the clergy. Instead of the Church playing the leading role as the ‘soul’ of society, the author introduced humanistic concepts of "good arising from the virtue" and "morals". Christine also included the third estate in the political life of a kingdom, providing its stratification and hierarchization, and giving a profound description of its role in the body politic. The metaphorical concept of " body politic" broke away from the ecclesiastical and mystical connotations and took root in the secular, political-philosophical tradition.