Related papers: Mathematics for energy systems: Methods, modeling …
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity,…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…
Mathematical ideas and approaches common in complexity-related fields have been fruitfully applied in experimental high energy physics also. We briefly review some of the cross-pollination that is occurring.
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
The operations of linear algebra, calculus, and statistics are routinely applied to measurement scales but certain mathematical conditions must be satisfied in order for these operations to be applicable. We call attention to the conditions…
As new technologies move to the fore, our understanding of the world may seem to have shrunk in comparison, for despite new developments in research, much of it is reduced or rather, abstracted for marketability. Thus, the purpose of this…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the…
Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
This document is both a synthesis of current notions about complex systems, and a practical approach description. A disambiguation is proposed and exposes possible reasons for controversies related to causation and emergence. Theoretical…
The main topic of this work concerns the formulation of the equations of motion and the consequent energy balance that they imply for this type of systems, In particular, the analytical development that we will carry out on the equations of…
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the…
The purpose of this report is to show that computer and allied technologies can be used to increase energy efficiency. The report is divided into transport, industrial, commercial and domestic sections, which correspond to the major energy…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
Many complex systems can be modeled as multiagent systems in which the constituent entities (agents) interact with each other. The global dynamics of such a system is determined by the nature of the local interactions among the agents.…
Energy system optimization models are becoming increasingly popular for analyzing energy markets, such as the impact of new policies or interactions between energy carriers. One key challenge of these models is the trade-off between…
A freely available educational application (a mobile website) is presented. This provides access to educational material and drilling on selected topics within mathematics and statistics with an emphasis on tablets and mobile phones. The…