Search results for "MATHEMATICAL MODELLING"
showing 10 items of 59 documents
Shallow flow stability analysis with applications in hydraulics
2016
Šķidruma plūsmas stabilitātes analīze ar pielietojumiem hidraulikā Promocijas darbā tiek veikta plūsmu l ineārā un vāji nelineārā stabilitātes analīze seklos sajaukšanās slāņos. Plūsma tiek pieņemta kā nedaudz izliekta garenvirzienā . Berzes koe ficients mainās šķērsvirzienā . Lineārā stabilitāte tiek analizēta no laika un telpas aspektiem. Turklāt problēma ir vispārināta divu komponenšu seklām plūsmām. Tiek izskatītas divas pieejas vāji nelineārās stabilitātes analīzei. Parādīts, ka amplitūdas vie nādojums ir kompleksais Ginzburga - Landau vienādojums (paralēlu plūsmu pieņēmums). Otra pieeja ņem vērā lēno garenvirziena bāzes plūsmas izmaiņ u . Tiek iegū ts pirmās kārtas amplitūdas attīstīb…
Mathematical Models and their Solutions for Domains of Compex Form
2014
Promocijas darbā tiek apskatīti dažādi oriģināli modeļi un to risinājumi sarežģītas formas apgabaliem. Intensīvās tērauda rūdīšanas procesi sistēmām ar ribām tiek aprakstīti ar 3D hiperbolisko, kā arī ar klasisko siltuma vadīšanas vienādojumu. Precīzā atrisinājuma iegūšanai izmantota Grīna funkciju metode un tās vispārinājums. Modernajos datoros sastopamajām sistēmām ar dubulsieniņu un dubultribu dota stacionārā un nestacionārā siltumvadīšanas problēma 2D gadījumā. Tās risinājums tiek iegūts ar konservatīvās viduvēšanas metodi, galīgo diferenču metodi un tās modifikāciju robežnosacījumiem. Piedāvāts jauns matemātiskais modelis vītola flautai, problēmas formulējumā izmantojot 1D lineāru viļņ…
Wastewater modification processes assessment in a stabilization reservoir.
2008
A semi-empirical mechanistic model able to simulate the dynamics of a stabilization reservoir was developed incorporating both settling of particulate components and chemical/biological processes. Several factors affecting the reservoir effluent quality were taken into account: hydraulics and hydrology, solar radiation, atmospheric reaeration, algae, zooplankton, organic matter, pathogen bacteria, and sediment-water interaction. The model quantifies the specific influence of each factor on effluent quality, evaluating the correlation between the different considered factors. State variables included in the model were: algae, dissolved oxygen, organic matter, zooplankton and indicator bacter…
A mathematical approach to predict the solids concentration in anaerobic membrane bioreactos (AnMBR): Evaluation of the volatile solids solubilization
2020
[EN] Anaerobic Membrane Bioreactors (AnMBR) are gaining attention as a suitable approach for sustainable low-strength wastewater treatment, as they bring together the advantages of both anaerobic treatments and membrane bioreactors. However, increasing the sludge retention time (SRT) necessary to favor hydrolysis increases the suspended solids concentration potentially leading to decreased permeate flux. Therefore, the availability of a mathematical approach to predict the solids concentration within an AnMBR can be very useful. In this work, a mathematical model describing the volatile solids concentration within the reactor as a function of the operating parameters and the influent charac…
Mathematical models and their solutions for different heat exchange processes in environment with layered structure
2012
Promocijas darbā tiek apskatīti 3D, 2D un 1D risinājumi stacionārām siltuma vadīšanas problēmām cilindriskā sistēmā ar ribu. Kā arī iztirzāti nestacionāru problēmu risinājumi hiperboliskām siltuma vadīšanas problēmām 1D cilindram un 2D cilindriskai sistēmai ar ribu. Iegūti kvazi-analītiski risinājumi cilindriskai sistēmai ar ribu, izmantojot konservatīvās viduvēšanas metodi. Izmantojot vispārinātu Grīna funkcijas metodi ir konstruēts precīzais analītiskais atrisinājums vairākām cilindriskām sistēmām ar ribu. Daži no stacionāriem modeļiem ir skaitliski konstruēti un sniegti aprēķinu piemēri. Darbā ir analizēti un salīdzināti iegūtie rezultāti. Atslēgas vārdi: konservatīvā viduvēšana, Grīna f…
Characteristics of participation - A mathematician and a mathematics educator collaborating on a developmental research project
2018
International audience; In this paper, a developmental research project involving offering mathematical modelling (MM) activities to university biology students is presented, and a particular aspect is studied, namely the project as a collaboration between mathematicians and mathematics educators. The aim of the paper is to investigate what characterizes their participation in the project, and how the characteristics of the project and its development might influence this participation. Interview data as well as observation data from the MM sessions are analysed, and findings show that the mathematics educator served as a broker influencing the practice of the mathematician. It is hoped tha…
Mathematical modelling and activation – a study on a large class, a project-based task and students' flow
2018
International audience; We studied how engineering students in a large class (n=346) can be activated by a project-based task, in which they have to model mathematically the motion of an object. The students had to throw an object, use (1) their smart phones for filming, and (2) tracker software for capturing the motion. Through a poster, they had to report their video analysis. We framed activation through the concept of flow, which is a state of being fully absorbed by an activity. We administered a web-based questionnaire (response rate 69%). The results show that such a project-based task is feasible with >300 students and activated them: three out of five experienced flow. Also, we val…
Minimizing membrane bioreactor environmental footprint by multiple objective optimization.
2020
This paper presents a modelling study aimed at minimizing the environmental foot print of a membrane bioreactor (MBR) for wastewater treatment. Specifically, an integrated model for MBR was employed in view of the management optimization of an MBR biological nutrient removal (BNR) pilot plant in terms of operational costs and direct greenhouse gases emissions. The influence of the operational parameters (OPs) on performance indicators (PIs) was investigated by adopting the Extended-FAST sensitivity analysis method. Further, a multi-objective analysis was performed by applying the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The results show-up that the sludge …
The development of the mathematical discourse of biology students working with mathematical modelling
2016
International audience; This poster reports from an ongoing developmental research project in which mathematical modelling tasks are introduced to biology students as a means of motivating them to engage more deeply in mathematical studies. In the present report the focus is on how the mathematical discourse of the students develops as they participate in the project. Data consisting of video recordings of four modelling sessions comprising both group work and whole-class discussion will be analysed using commognitive theory. Data collection is still ongoing, and no analyses have been conducted as yet, but preliminary observations indicate cases of commognitive conflict, as the students str…
Membrane Bioreactors for wastewater reuse: Respirometric assessment of biomass activity during a two year survey
2018
Abstract Stricter effluent limits, water shortage conditions, land availability requires today even more the needs of advanced wastewater treatments. Attractive solutions come from membrane bioreactors (MBR), Integrated Fixed Film Activated Sludge (IFAS) or combinations (i.e., IFAS-MBRs). One crucial aspect for the applicability of this overall new technology, compared to the conventional activated sludge systems, is the lack of knowledge for design and manage (e.g., kinetic constants, optimal operative conditions etc.). In view of the above frame, the aim of the present study was to assess the kinetic and stoichiometric parameters of bacterial species in MBRs by means of respirometric tech…