Dinamika kemostata

undergraduate thesis

• Title (english): Dynamic of the chemostat
• Author: Margareta Poje
• Mentor: Ivica Gusić (mentor)
• Committee member: Ivica Gusić (predsjednik povjerenstva)
• Committee member: Miroslav Jerković (član povjerenstva)
• Committee member: Irena Škorić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Chemical Engineering and Technology; Zagreb
• Defense date and country: 2018-09-18, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics; Algebra

Abstract

Opisan je matematički model koji simulira procese u kemostatu, zasnovan na autonomnom sustavu od dvije diferencijalne jednadžbe. Sustav je rješavan pomoću programskog paketa MATLAB R2018a. Rezultati su prikazani grafički i numerički za zadane vrijednosti parametara i početnih uvjeta. U modelu se, bez obzira na početne uvjete, uz fiksne parametre (Kmaks, Km, D, α i Cspr) ravnotežne koncentracije mikroorganizama i hranjivih tvari ne mijenjaju. Nadalje, smanjenje koeficijenta iskorištenja α (uz ostale fiksirane parametre) rezultira obrnuto proporcionalnim povećanjem populacije bakterija pri ravnotežnom stanju, a nema utjecaja na ravnotežnu koncentraciju hranjiva. Pokazano je da, uz predloženi izbor parametara, sve trajektorije teže fiksnoj točki neovisno o početnim uvjetima.

Abstract (english)

A mathematical model, based on the autonomous system of two differential equations, for simulation of processes in the chemostat is described. The system is solved using the software package MATLAB R2018a. The results are presented graphically and numerically for given parameters and various initial conditions. Regardless of the initial conditions, with fixed parameters (Kmax, Km, D, α and Cr), concentrations of microorganisms and nutrient remain unchanged at equilibrium. Furthermore, decrease of the nutrient utilization coefficient α (with other parameters fixed) resulted in an inversely proportional increase of the bacterial population at equilibrium, but without influence on the concentration of nutrient. It has been shown that all trajectories converge to the fixed point, independently of the initial conditions.

• Keywords: kemostat; diferencijalna jednadžba; MATLAB; dinamika kemostata; Monodova kinetika
• Keywords (english): chemostat; differential equation; MATLAB; chemostat dynamics; Monod kinetics
• Language: croatian
• URN:NBN: urn:nbn:hr:149:993944
• Study programme: Title: Applied Chemistry - Undergraduate study; specializations in: Environmental chemistry and green technologies, Advanced materials and technologies, Applied organic chemistry; Course: Applied organic chemistry; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) primijenjene kemije (sveučilišni/a prvostupnik/prvostupnica (baccalaureus/baccalaurea) primijenjene kemije)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-05-20 11:27:59