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Challenges in teaching mathematics in Serbia
Get PDFThe purpose of this paper is to address the critical issue of the shortage of mathematics teachers and professors in Serbia. The old teaching staff is drying up, and there is a lack of new teaching potential. The demoralization of current math teachers is an ongoing concern and as a result, hardly any student want to become math teacher. Soon we will only be able to realize that no one wants to teach mathematics anymore. We will focus on the causes and consequences of the perceived problem
On the application of the double-averaging methodology in modelling vegetated open-channel flows
Get PDFThe double-averaging methodology (DAM) arose to respond to a need to provide
a mathematically rigorous tool for describing spatially heterogeneous turbulent
flows. Initial developments originate from micrometeorologists who revealed
notable discrepancies between measured and simulated temperature and
moisture fields above trees when using only Reynolds-averaged Navier-Stokes
(RANS) equations with various turbulence model closures. The discrepancies were
attributed to the spatial inhomogeneity of the flow field caused by vegetation.
Thus, additional spatial averaging of RANS equations over horizontal planes
sufficiently large to provide statistical averaging of all differences caused by an
arbitrary distribution of plants and the influence of the biggest vortices responsible
for the transfer of momentum was suggested. The advantages of using the DAM
in open-channel hydraulics of gravel-bed rivers were recognised in the early 2000s
when DAM was first applied and consequently improved. Open-channel vegetated
flows are another example of spatially heterogene¬ous turbulent flows to which
the DAM can be applied. The paper presents the results of the DoubleVeg project
led by the author, in which a new set of equations was derived. After introducing
the basic DAM concepts, the procedure of deriving Depth-Integrated Double
Averaged Navier-Stokes equations is presented. Consequently, the main
challenges in solving these equations are discussed, and the results of initial testing
of systems of homogeneous and non-homogeneous equations are shown.Ово је предавање по позиву на 9. међународној конференцији "Савремена достигнућа у грађевинарству 2024" одржаној 25-26. априла 2024. године у Суботици
Experimental analysis of cross-laminated timber floors
Get PDFCross-laminated timber (CLT) floors have gained in popularity due to their outstanding strength, aesthetic appeal, good fire resistance, and high level of prefabrication. However, due to their high stiffness-to-weight ratio, CLT floors are highly susceptible to pedestrian-induced vibrations. In design practice, vibration serviceability is usually assessed by assuming a floor as a set of CLT panels with no inter-panel connections, which leads to overestimation of the vibration response. In this paper, an experimental dynamic testing was carried out to identify modal properties and pedestrian-induced response of two CLT floors with different number of panels in a floor assembly. Influence of the inter-panel connections on the floor modal properties and pedestrian-induced vibration response is particularly studied and discussed
Неке класе Теплицових матрица одређене Лежандровим полиномима
No full textТеплицове матрице, са својом јединственом структуром и разноврсним карактеристикама, предстаљају значајан аспект савремене математичке истраживачке сфере, отварајући врата бројним применама, попут решаваnjа линеарних система, анализе нумеричких метода, моделовња у теорији графова, обраде сигнала и слика, моделовња секвенци у временским серијама. Ове матрице постају посебно интересантне када су њихови елементи Лежандрови полиноми, који имају xироку примену, од теорије бројева, до комбинаторике, анализе података и извесних нумериqких метода. У оквиру овог излагаnjа биће представљени резултати који се односе на еуклидску и нуклеарну норму неких класа Теплицових матрица, истражујући њихове карактеристике и разноврсне примене у различитим математичким областима
Simplified methodology for fatigue analysis of reinforced asphalt systems
Get PDFFatigue analysis has an important role in evaluating the durability and performance of asphalt pavements, especially when novel or alternative materials are used. Numerous laboratory studies have investigated fatigue performance with the aim of estimating field behavior as accurately as feasible. Therefore, there are currently many different test methods and data analysis approaches that can be used. One of the most common laboratory test methods is the four-point bending beam (4PBB) test, which results are usually analyzed using the so-called traditional (where 50% reduction in initial stiffness is considered as failure criterion) or the energy ratio (ER) approach. However, outcomes from previous studies have shown that these approaches may not be appropriate and reliable if geogrids are used as a reinforcement. As a possible solution, this study proposes a new simplified flex point (SFP) approach that considers the flex point of the strain amplitude curve, measured during 4PBB fatigue tests, to calculate the number of cycles to failure. These three approaches were applied to four double-layered asphalt sets: one unreinforced and three reinforced with geogrids of different strength (50 x 50, 100 x 100 and 100 x 200 kN/m). The impact of reinforcement on the fatigue life was evaluated by comparing the critical strain values (ε6) of reinforced and unreinforced sets through the fatigue resistance improvement factor. The research findings showed that the use of geogrids improves fatigue life when the SFP and ER approaches are applied and that the traditional approach might not always be appropriate for assessing the fatigue resistance of reinforced asphalt mixtures
Experimental and analytical assessment of modal properties of CLT panels
No full textCross laminated timber (CLT) panels provide an efficient, economic and eco-friendly solution
for floors in both single- and multi-storey buildings. Due to their light-weight and often longspans,
design of these floors is generally governed by serviceability limit state criteria, such as
deflection and vibration limits. However, design guidelines which address vibration behaviour
of CLT floors is limited, mainly due to lack of reliable experimental data. This paper presents an
experimental modal testing of CLT panels performed with the aim of extracting modal properties
(natural frequency, damping and mode shape) for the first three modes of vibration. Analytical
models from the relevant design standards and available literature were used to predict
fundamental frequency of the panels which were compared with the experimental results
Preparing for Revitalization of the Turbines of the Đerdap 2 HPP: Measurement of Velocity Distribution at Turbine Inlets
No full textKontinualno merenje protoka na brojnim turbinama hidroelektrana se standardno radi nekom od relativnih metoda (na primer Winter-Kennedy). Umesto da se meri složeno polje brzina u jednoj proticajnoj ravni i da se njenom integracijom dobije protok, meri se samo jedna karakteristična veličina a na fizičkom modelu se odrede parametri preslikavanja vrednosti te veličine u trenutni protok. Najčešće se koristi Winter-Kennedy metoda gde se merenjem razlike pritisaka dobija relativna (indeksna) vrednost protoka. Merna nesigurnost tako određenog protoka je znatno veća od nesigurnosti merenja ostalih relevantnih veličina za određivanje optimalnih radnih uslova turbine. Da bi se smanjila merna nesigurnost, potrebno je „apsolutnim merenjima“ celog polja brzina odrediti trenutni protok i preračunati, u realnim uslovima, korekcije indeksne metode. To se posebno odnosi na hidroelektrane čija dispozicija nije „idealna“ kao što je bila na fizičkom modelu, kao što je HE „Đerdap 2“ sa poznatim problemom „kosog dostrujavanja“. Sa ciljem bolje procene hidrauličke efikasnosti turbina i prikupljanja podataka o realnim uslovima rada turbina i ulazne rešetke, a zbog planiranih radova na revitalizaciji, projektovan je i primenjen inovativni sistem za apsolutno merenje protoka koji je prikazan u ovom radu. Na pokretni ram, pozicioniran na ulazu u turbinu uzvodno od grube rešetke, postavljeno je 15 elektromagnetnih (EM) senzora u jednoj horizontalnoj ravni, zajedno sa dva redudantna akustična Doppler senzora. Svaki od senzora meri sve tri komponente brzina. Ram se podiže duž cele visine proticajnog preseka snimajući celo polje brzina. Položaj rama se prati pomoću dva enkodera, dok se dva senzora pritiska koriste za merenje dubine vode. Merenja su sinhronizovana sa lokalnim SCADA sistemom odakle se preuzimaju podaci o radu turbine. Uvažavajući specifičnosti mernog sistema, novorazvijenih EM sondi i postojećih hidrauličkih uslova, razvijena je adekvatna procedura za procenu nesigurnosti izmerenog protoka. U ovom radu je prikazana merna metoda i dati su neki rezultati merenja na agregatima HE „Đerdap 2“.The continuous flow measurement on hydroelectric turbine units is conventionally carried out using the relative methods (mostly Winter-Kennedy), where the complex velocity field in flow cross section is replaced by a single measured quantity. On a physical model, mapping parameters are determined. The Winter-Kennedy method is most used, where this relative (index) flow quantity is obtained by measuring differential pressure. The measurement uncertainty of the determined flow using this method is usually significantly higher than the uncertainty of other relevant quantities for determining the optimal turbine operating conditions. To reduce the flow uncertainty, it is necessary to perform "absolute measurements" of the entire velocity field and determine the necessary corrections to the index method under real operating conditions. This is especially true for plants where disposition is different from one used on physical model, which is the case of “Đerdap 2” and recognized problem of skewed inflow. With the aim of better assessing the hydraulic efficiency of turbines and to collect data on the actual operating velocity distribution in the inlet section in front of trash-rack needed for planned revitalization works, an innovative system for absolute flow measurement has been designed and implemented. The moving frame was designed and installed at the turbine inlet, upstream from the trash-rack. The 15 electromagnetic (EM) sensors and two redundant acoustic Doppler sensors were installed on horizontal bar. Each sensor measures all three velocity components. The frame moves by lifting along the entire height of the flow section, allowing the entire velocity field to be scanned. The position of the frame is tracked by two encoders, while two pressure sensors are used to measure the water depth. Measurements are synchronized with the local SCADA system, so appropriate turbine operation data are also used. Considering the specificities of the measurement system itself with newly developed EM sensors, as well as hydraulic conditions, an adequate procedure has been developed to assess the uncertainty of the measured flow. This paper presents the measurement method and provides some measurement results on the units of the “Đerdap 2” hydroelectric power plant
Practical applicability of mathematical optimization for reservoir operation and river basin management: a state-of-the-art review
No full textThe sheer number of publications that deal with the topic of optimizing the management of river basins has grown exponentially since the early 1980s, and this growth is still on the rise. Despite this, the practical actions of most reservoir operators are still based on their gut feelings, or at best on straightforward rules that did not originate from rigorous scientific studies but are rather the result of the operator’s experience or simple spreadsheet calculations. Many publications have already pointed out the gap between theory and practice over the past few decades; however, none have so far offered clear guidelines on how to overcome this gap. This paper presents an extensive literature review to examine potential reasons for this gap. In addition to this, a numerical test problem demonstrates a novel way of using linear programming for constructing Pareto-optimal solutions for a large class of multi-objective optimization problems
A Comparative Study of Fatigue Analysis Methods Applied to Reinforced Asphalt Systems
No full textThis study presents findings obtained by applying three distinct methods to
assess the fatigue resistance of double-layered asphalt systems: traditional (50%
reduction in initial stiffness), energy ratio, and recently developed simplified
flex point (SFP). Asphalt specimens with plain and polymer-modified bitumen
were investigated using four-point bending beam test in both reinforced and
unreinforced forms. Two different kinds of bitumen emulsion were used as the
tack coat, plain and polymer-modified, whereas a polymer-coated fiberglass
geogrid was used as reinforcement. The results revealed that the choice of
fatigue analysis method may significantly affect the assessment of fatigue
resistance. It was further discovered that the SFP method was found to provide
an accurate representation of grid efficiency, particularly for specimens with
plain bitumen. Results also demonstrated that grid reinforcement improves
fatigue resistance for approximately 15–20 μm/m, regardless of the mixture
type, highlighting its potential to increase pavement durability. However,
the study emphasizes the necessity for additional investigations into various
geogrid materials and the establishment of relationships between different
analytical methods for more efficient pavement design
Determination of local ionospheric models for precise positioning by global navigation satellite systems
No full textDoktorska disertacija je posvećena određivanju lokalnih modela jonosfere za potrebe preciznog pozicioniranja globalnim navigacionim satelitskim sistemima. Takođe, disertacija je posvećena i adekvatnom kombinovanju kreiranih lokalnih modela u regionalne modele za područje teritorije Republike Srbije.
Numerička istraživanja su sprovedena na osnovu velikog broja podataka opažanja GNSS prijemnika raspoređenih tako da ravnomerno pokrivaju relevantnu teritoriju od interesa u okviru odabranog vremenskog opsega koji je obuhvatio period od 28 dana. Lokalni i regionalni modeli jonosfere kreirani su na osnovu ocenjenih vrednosti totalnog sadržaja elektrona modeliranjem determinističke i stohastičke komponente.
U okviru modeliranja determinističke komponente, nepoznati TEC parametri su razmatrani kao harmonijske funkcije, pa je za ocenu nepoznatih parametara jonosfere korišćena globalna sferno-harmonijska reprezentacija prilagođena lokalnoj, odnosno regionalnoj primeni. Stohastička komponenta modelirana je na osnovu ocene stohastičkih parametara jonosfere. Prilikom kreiranja modela, razmatrani su i članovi viših redova jonosferske korekcije, odnosno članovi drugog i trećeg reda, kao i član koji se odnosi na efekte savijanja signala.
Validacija dobijenih rezultata izvršena je na osnovu javno dostupnih podataka u vidu globalnih jonosferskih mapa. Na osnovu rezultata validacije može se zaključiti da je saglasnost dobijenih rezultata do nivoa 5 TECU jedinica za teritoriju Republike Srbije.
Na osnovu kreiranih lokalnih i regionalnih modela jonosfere izvršena je analiza modeliranog stohastičkog dela kreiranih modela u cilju predloga metodologije detekcije naglih promena na Suncu. Analizirano je ukupno 9 specifičnih događaja nastalih kao posledica aktivnosti Sunca u okviru izabranog vremenskog opsega - četiri geomagnetne oluje klasifikovanog intenziteta većeg od G0, kao i pet Sunčevih X flerova klasifikovanih u okviru raspona klasa od C5 do M5.
Finalno, u okviru istraživanja su analizirane i promene u okviru D sloja jonosfere usled periodičnih sezonskih promena i promena tokom Sunčevog ciklusa kako bi se analizirao njihov uticaj na vrednosti totalnog sadržaja elektrona. Takođe, analiziran je i relevantan uticaj u periodima maksimalnih perturbacija izazvanih Sunčevim X flerovima.
Osnovni rezultati koji proizilaze iz opisanih istraživanja su:
• Na osnovu podataka prikupljenih primenom GNSS tehnologije moguće je kreirati lokalne modele jonosfere koji reprezentuju stanje jonosfere na nivou lokalnog područja od interesa;
• Na osnovu kreiranih lokalnih modela je moguće adekvatnim kombinovanjem kreirati regionalne modele visoke rezolucije i tačnosti koji u određenoj meri bolje oslikavaju stanje jonosfere od javno dostupnih globalnih modela;
• Regionalni modeli kreirani na prikazani način sadrže informacije o determinističkoj i stohastičkoj komponenti i kao takvi bolje oslikavaju stanje jonosfere za definisani period na koji se odnose;
• Na osnovu kreiranih modela jonosfere moguće je dodatno poboljšati tačnost dobijenih koordinata tačaka dodatno oslobođenih uticaja naglih promena na Suncu;
• Na osnovu podataka kreiranih lokalnih modela nije moguće detektovati nagle promene na Suncu u vidu Sunčevih X flerova;
• Na osnovu stohastičkih podataka kreiranih lokalnih modela moguće je prikazati prostorno-vremenski varijabilitet jonosfere iznad relevantnog područja, ali nije moguće sa sigurnošću utvrditi poreklo uticaja uočenih varijacija imajući u vidu kompleksnost i veliki stepen zavisnosti pojava aktivnosti na Suncu i onih u okviru geomagnetnog polja;
• Prilikom modelovanja ukupnog TEC-a, u periodu mirnih uslova moguće je zanemariti uticaj elektronske koncentracije D sloja. Međutim, pri mirnim uslovima oko letnjeg solsticija u periodu oko maksimuma Sunčevog ciklusa, uticaj D sloja ne mora biti zanemarljiv. U periodu maksimalnih perturbacija elektronske koncentracije u D sloju usled uticaja Sunčevih X flerova klase C5 i jačih, neophodno je uvrstiti uticaj ovog sloja prilikom modelovanja ukupnog TEC-a.The doctoral dissertation is dedicated to the determination of local ionospheric models for precise positioning by global navigation satellite systems. Also, the dissertation is dedicated to adequately combining the created local models into regional models for the territory of the Republic of Serbia.
Numerical investigations were carried out using a large number of GNSS receiver observation data distributed evenly to cover the relevant territory of interest within a selected time range of 28 days. Based on the estimated values of the total electron content, local and regional ionospheric models were created by modeling the deterministic and stochastic components.
Within the modeling of the deterministic component, the TEC were treated as harmonic function, and in order to estimate unknown ionospheric parameters, the global spherical-harmonic representation was used and adapted to local and regional applications. The stochastic component was modeled based on the estimation of stochastic ionospheric parameters. During the modeling, higher-order terms of the ionospheric correction, that is, second- and third-order terms and terms related to the signal bending effect, were also considered.
The validation of the obtained results was performed based on publicly available data in the form of global ionospheric maps. Based on the validation results, it can be concluded that the compliance of the obtained results is up to the level of 5 TECU units for the territory of the Republic of Serbia.
Based on the created local and regional ionospheric models, an analysis of the modeled stochastic part of the created models was performed to propose a methodology for detecting sudden changes in the Sun. A total of 9 specific events resulting from the activity of the Sun within the selected time range were analyzed - four geomagnetic storms with a classified intensity greater than G0, as well as five Solar X flares classified within the range of classes from C5 to M5.
Finally, as part of the research, changes in the ionospheric D region caused by periodic seasonal and solar cycle changes were also analyzed in order to examine their influence on the values of the total electron content. Also, the relevant influence in periods of maximum perturbations caused by the Sun’s X flares was analyzed.
The following are the main results of the described research:
• Based on the GNSS data, it is possible to create local ionospheric models that represent the state of the ionosphere at the level of the local area of interest;
• Based on the created local models, it is possible to create regional models of high resolution and accuracy, which, to a certain extent, better reflect the state of the ionosphere than publicly available global models;
• Regional models created in the shown manner contain information about the deterministic and stochastic components and, as such, better reflect the state of the ionosphere for the related period;
• Based on the created ionospheric models, it is possible to additionally improve the accuracy of the estimated coordinates of points additionally freed from the influence of sudden changes in the Sun;
• Based on the created local models data, it is not possible to detect sudden changes in the Sun in the form of Solar X flares;
• Based on the stochastic component of created local models, it is possible to show the spatio-temporal variability of the ionosphere above the relevant area, but it is not possible to determine with certainty the origin of the influence of the observed variations, bearing in mind the complexity and high degree of dependence of the occurrences of activity on the Sun and those within the geomagnetic field;
• When modeling the TEC in a period of quiet conditions, it is possible to ignore the influence of the D region electron density. However, under quiet conditions around the summer solstice in the period around the maximum of the solar cycle, the influence of the D region may not be negligible. In the period of maximum perturbations of the electron density in the D region due to the influence of the Sun’s X flares of class C5 and stronger, it is necessary to include the D region influence when modeling the TEC