Modelling

Model is any formal expression about a natural phenomenon. If put into mathematical language, then we speak of a mathematical model.

Why do we need mathematical model at all?

First, "when you can measure what you are speaking about, and express it in numbers, you know something about it" (lord Kelvin). Second, mathematical models and computers today allow for detailed understanding of the most complicated environmental phenomena (e.g. typhoons), prediction of the evolution of the environmental processes (e.g. global warming), quantitative assessment of intrusions in the environment as well as control of the environmental processes (e.g. wastewater treatment plants). The course will get students acquainted with elementary modelling approaches based on first principles, initial skills in computer simulation of dynamic systems as well as ability to identify (simple) models from data.

Since the topic is multi-disciplinary, it assumes the students are familiar with fundamentals obtained in the courses of Mathematics and Physics as well as Statistics and Computer Science. Knowledge that the student gets in this course is generic and usable in almost every area of environmental sciences.

• Functions and their representation
• Preliminaries in differential and integral calculus and ordinary differential equations
• Theoretical (analytical) models
• Basics of numerical solutions of ordinary and partial differential equations
• Introduction to simulation
• Modelling the transport phenomena
• Physical, chemical and biological transformation of matter

Students will acquire:
• the ability to set up the mathematical model from process description and inventory of physical phenomena,
• the capacity to implement a model in simulation tool,
• students will become familiar with model assessment in the context of application,
• capacity to callibrate simple static models from data.

• W.H. Press et al. (1992). Numerical Recipes in C. The Art of Scientific Computing. Cambridge University Press.Catalogue E-version
• Paul’s Online Notes (Paul Dawkins, Lamar University)
• Calculus I http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
• Differential Equations http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

Written exam (50%), oral exam (50%)

Dr. Artem Badasyan is associate professor of physics at the University of Nova Gorica.

Last 5 publications:

• KARAPETYAN, Nelli H., BADASYAN, Artem, ANANYAN, Gayane V. Stronger affinity of water-soluble cationic porphyrins to cancer DNA under acidic conditions as a basis for selectivity. ACS omega. Jul. 2026, vol 11, issue 27, str. 40072-40078.
• SKOK, Janja, TIWARI, Pooja, VODOPIVEC SERAVALLI, Tina, LEBAR, Sergeja, FERJANČIČ BUDIHNA, Ana, MARTINČIČ CELJAR, Anže, MEGUŠAR, Polona, POVH, Matija, MENCIN, Nina, BAWAGE, Swapnil, SINGH, Shree Ram, BADASYAN, Artem, SEKIRNIK, Rok. Controlling in vitro mRNA polyadenylation by monitoring poly(A) polymerase consumption of ATP. International journal of molecular sciences. 2026, vol. 27, issue 7, [article no.] 2928, 20 str., ilustr. ISSN 1422-0067.
• YERITSYAN, Knarik, BADASYAN, Artem. FitFoldData : a web-based toolkit for circular dichroism and differential scanning calorimetry data analysis of protein thermal denaturation. ACS omega. 2025, vol 10, issue 39, str. 45524-45532.
• MACHREKI, Manel, BADASYAN, Artem, ŽIGON, Dušan, TYULIEV, Georgi, EMIN, Saim. Photoelectrochemical conversion of biomass alcohols using in-situ Sn-doped α−Fe2O3 thin films. Journal of environmental chemical engineering. [Online ed.]. Feb. 2025, vol. 13, issue 1, [article no.] 115363, str. 1-9.
• SIMONYAN, Karen, TSOKOLAKYAN, Astghik, BUNIATYAN, Vahe, BADASYAN, Artem, YERANOSYAN, Mkrtich. Urea detection in phosphate buffer and artificial urine : a simplified kinetic model of a pH-Sensitive EISCAP urea biosensor. Sensors. 2025, vol. 25, issue 21, [article no.] 6596, 17 str.