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A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to characterise some particular examples of…
In this paper, we propose a new mathematical optimization approach to make decisions on the optimal design of a logistic system to produce biogas from waste. We provide an integrated model that allows decision makers to optimally determine…
The Anaerobic Digestion Model No. 1 (ADM1) is a complex model which is widely accepted as a common platform for anaerobic process modeling and simulation. However, it has a large number of parameters and states that hinder its analytical…
A mathematical model for anaerobic digestion in plug-flow reactors is proposed on the basis of mass balance considerations. The model consists of a system of parabolic partial differential equations for the variables representing the…
These notes explore three amazing formulas proved by Abel in his 1826 Paris memoir on what we now call Abelian integrals. We discuss the first two formulas from the point of view of symbolic computation and explain their connection to…
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to…
A geometric approach is used to study a family of higher-order nonlinear Abel equations. The inverse problem of the Lagrangian dynamics is studied in the particular case of the second-order Abel equation and the existence of two alternative…
Digestion in the small intestine is the result of complex mechanical and biological phenomena which can be modelled at different scales. In a previous article, we introduced a system of ordinary differential equations for describing the…
We present an algebraic approach to evolutionary accumulation modelling (EvAM). EvAM is concerned with learning and predicting the order in which evolutionary features accumulate over time. Our approach is complementary to the more common…
A particular solution to the equations of motion of the Abelian Higgs model is given. The solution involves the Jacobi elliptic functions as well as the Heun functions.
Basing on the relation between the Coulomb Green function and the Green function of harmonic oscillator, the algebraic representation of the many-particle Coulomb Green function in the form of annihilation and creation operators is…
We develop a mathematical model for dynamic simulation of an alkaline electrolyzer plant. The plant includes the stack, a water recirculation system and hydrogen storage with compressor. We model each component of the system with mass and…
This paper is dedicated to present an exact solution for a nonlinear differential equation so-called Abel equation. This equation was known as one of the group of unsolvable differential equations. The present method is applicable for any…
We construct novel solutions in $d\ge 3$ space dimensions of a family of nonlinear evolutions equations that includes the critical hyperbolic Abelian Higgs model (AHM). For the AHM, these solutions exhibit an ensemble of $N\ge 1$…
Innovation in synthetic biology often still depends on large-scale experimental trial-and-error, domain expertise, and ingenuity. The application of rational design engineering methods promise to make this more efficient, faster, cheaper…
A novel mass generation procedure for an Abelian vector field is proposed. This procedure is based on the construction of a class of gauge theories whose free limit describes a free massless vector field and a set of massless real scalar…
Environmental management optimizing a long-run objective is an ergodic control problem whose resolution can be achieved by solving an associated non-local Hamilton-Jacobi-Bellman (HJB) equation having an effective Hamiltonian. Focusing on…
Many research projects are devoted to biomass production, selection of new crops and bio-refinery processes but in comparison, the biomass supply chain to satisfy the planned demands of refineries are relatively neglected, although it could…
A mathematical model of the process of carbon capture in a packed column by adsorption is developed and analysed. First a detailed study is made of the governing equations. Due to the complexity of the internal geometry it is standard…
We introduce new methods for the numerical solution of general Hamiltonian boundary value problems. The main feature of the new formulae is to produce numerical solutions along which the energy is precisely conserved, as is the case with…