Multidigraph Autocatalytic Set for Modelling Complex Systems

The motion of solid objects or even fluids can be described using mathematics. Wind movements, turbulence in the oceans, migration of birds, pandemic of diseases and all other phenomena or systems can be understood using mathematics, i.e., mathematical modelling. Some of the most common techniques used for mathematical modelling are Ordinary Differential Equation (ODE), Partial Differential Equation (PDE), Statistical Methods and Neural Network (NN). However, most of them require substantial amounts of data or an initial governing equation. Furthermore, if a system increases its complexity, namely, if the number and relation between its components increase, then the amount of data required and governing equations increase too. A graph is another well-established concept that is widely used in numerous applications in modelling some phenomena. It seldom requires data and closed form of relations. The advancement in the theory has led to the development of a new concept called autocatalytic set (ACS). In this paper, a new form of ACS, namely, multidigraph autocatalytic set (MACS) is introduced. It offers the freedom to model multi relations between components of a system once needed. The concept has produced some results in the form of theorems and in particular, its relation to the Perron–Frobenius theorem. The MACS Graph Algorithm (MACSGA) is then coded for dynamic modelling purposes. Finally, the MACSGA is implemented on the vector borne disease network system to exhibit MACS’s effectiveness and reliability. It successfully identified the two districts that were the main sources of the outbreak based on their reproduction number, R0

Some numerical methods for ice sheet behaviour and its visualization

The thermomechanical ice sheet modeling is used to simulate the behavior of ice sheets in the Antarctic region. This research investigates some parameters such as ice thickness, ice temperature and ice velocity. The numerical discretization to obtain a large sparse system of unconditionally stable is based on explicit and Crank Nicolson implicit methods. The numerical solver for solving the large sparse systems is Jacobi and Gauss Seidel methods. Matlab version 2011a has been chosen as the platform to support the numerical computations. The numerical results prove that the thermomechanical ice sheet modelling is well suited to simulate the ice sheet behavior in terms of thickness, temperature and velocity. The contribution of this paper is to successfully discretize the ice thickness model based on Finite Difference Method. The ice sheet model is considered a good prediction model based on its visualization using Comsol Multiphysics software

Multidigraph Autocatalytic Set for Modelling Complex Systems

The motion of solid objects or even fluids can be described using mathematics. Wind movements, turbulence in the oceans, migration of birds, pandemic of diseases and all other phenomena or systems can be understood using mathematics, i.e., mathematical modelling. Some of the most common techniques used for mathematical modelling are Ordinary Differential Equation (ODE), Partial Differential Equation (PDE), Statistical Methods and Neural Network (NN). However, most of them require substantial amounts of data or an initial governing equation. Furthermore, if a system increases its complexity, namely, if the number and relation between its components increase, then the amount of data required and governing equations increase too. A graph is another well-established concept that is widely used in numerous applications in modelling some phenomena. It seldom requires data and closed form of relations. The advancement in the theory has led to the development of a new concept called autocatalytic set (ACS). In this paper, a new form of ACS, namely, multidigraph autocatalytic set (MACS) is introduced. It offers the freedom to model multi relations between components of a system once needed. The concept has produced some results in the form of theorems and in particular, its relation to the Perron–Frobenius theorem. The MACS Graph Algorithm (MACSGA) is then coded for dynamic modelling purposes. Finally, the MACSGA is implemented on the vector borne disease network system to exhibit MACS’s effectiveness and reliability. It successfully identified the two districts that were the main sources of the outbreak based on their reproduction number, R0