Preface to the special issue on “Mathematical modeling and analysis in health and natural sciences”

Ricerche di Matematica -     

Freud’s Identity of Differential Geometry, the Einstein-Hilbert Equations and the Vexatious Problem of the Energy-Momentum Conservation in GR

We reveal in a rigorous mathematical way using the theory of differential forms, here viewed as sections of a Clifford bundle over a Lorentzian manifold, the true meaning of Freud’s identity of differential geometry discovered in 1939 (as a generalization of results already obtained by Einstein in 1916) and rediscovered in disguised forms by several people. We show moreover that contrary to some claims in the literature there is not a single (mathematical) inconsistency between Freud’s identity (which is a decomposition of the Einstein indexed 3-forms in two gauge dependent objects) and the field equations of General Relativity. However, as we show there is an obvious inconsistency in the way that Freud’s identity is usually applied in the formulation of energy-momentum “conservation laws” in GR. In order for this paper to be useful for a large class of readers (even those ones making a first contact with the theory of differential forms) all calculations are done with all details (disclosing some of the “tricks of the trade” of the subject).      

Methods for the investigation of dynamical systems with impulse action and “mortal” dynamical systems

The notions of dynamical systems with impulse action and mortal dynamical systems are introduced. Their connection with the idealizations of ordinary dynamical systems is considered. General methods for the investigation of these systems are worked out.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1605–1613, November, 1991.     

Nonlinear stability and convergence of finite-difference methods for the “good” Boussinesq equation

Summary The good Boussinesq equationu _tt =–u _xxxx +u _xx +(u ²) _xx has recently been found to possess an interesting soliton-interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the good Boussinesq equation. Numerical experimentas are also reported.     

Holistic oil field value management: using system dynamics for ‘intermediate level’ and ‘value-based’ modelling in the oil industry

System dynamics has been seen primarily as a strategic tool, most effectively used at the highest level of strategy to identify robust policy interventions under a wide range of scenarios. However, an alternative, complementary and powerful role is emerging. This is at an ‘intermediate level’ in organisations to coordinate and integrate policies across the value chain. It is at this level where business value, as defined by the discounted value of future free cash flow, is both created and destroyed. This paper introduces the need for ‘intermediate-level’ and ‘value-based’ modelling and emphasises the natural role of system dynamics in supporting a methodology to fulfil the need. It describes the development of an approach and its application in the oil industry to coordinate the response of people and tools within operational, financial and commercial functions across the value chain to address a variety of problems and issues.