Matematička analiza nestacionarnog toka mikropolarnog fluida u tankoj domeni

The main subject of this dissertation consists of studying the micropolar fluid model, which represents a generalization of the well--known classical Navier--Stokes model, mainly in the sense that it takes into account the microstructure of the fluid and effects such as shrinking and rotation of the particles of the fluid. Our first goal is to prove the existence and uniqueness of a generalized nonsteady micropolar Poiseuille solution in an infinite cylinder. This is achieved by decomposing the problem into two parts: the classical two--dimensional micropolar problem with known existence and uniqueness results and the micropolar inverse problem, where we prove the corresponding results using semidiscretization in time. Next, we derive an asymptotic model for the nonsteady micropolar fluid flow in a thin pipe assuming the solution has the uni--directional nonsteady micropolar Poiseuille form. The problem is separated by linearity and we treat two problems by constructing two--scale asymptotic approximations in powers of $\epsilon$, representing the pipe's thickness. The model is justified via error estimates in the appropriate norms. In the case of circular cross--section and external force functions depending only on time, naturally appearing in many applications, the asymptotic expansion is explicitly computed up to the second order and numerical illustrations are provided to indicate the effect of the correctors. Finally, a more complex model is proposed describing the nonsteady micropolar fluid flow in a thin curved pipe, and the effects of flexion, torsion, micropolarity and time derivative are studied. The asymptotic expansions are explicitly computed up to the second--order and the model is justified by means of the error estimate in general as well as for special cases.Glavna tema ove disertacije je proučavanje modela mikropolarnog fluida, koji predstavlja generalizaciju dobro poznatog klasičnog Navier--Stokesovog modela, prvenstveno u smislu da uzima u obzir mikrostrukturu fluida i efekte kao što su smanjivanje i rotacija čestica fluida. Naš prvi cilj je dokazati egzistenciju i jedinstvenost generaliziranog nestacionarnog mikropolarnog Poiseuille rješenja u beskonačnom cilindru. Ovo postižemo rastavljanjem problema na dva dijela: klasični dvodimenzionalni mikropolarni problem s poznatim rezultatima egzistencije i jedinstvenosti te mikropolarni inverzni problem, gdje dokazujemo odgovarajuće rezultate semidiskretizacijom u vremenu. Nadalje, izvodimo asimptotički model za nestacionarni tok mikropolarnog fluida u tankoj cijevi pod pretpostavkom da rješenje ima Poiseuilleov jednosmjerni nestacionarni mikropolarni oblik. Problem razdvajamo po linearnosti i tretiramo dva problema konstruirajući dvoskalnu asimptotičku aproksimaciju u potencijama parametra $\epsilon$, koji predstavlja debljinu cijevi. Model je opravdan koristeći ocjenu pogreške u odgovarajućim normama. U slučaju kružnog poprečnog presjeka i funkcija vanjskih sila koje ovise samo o vremenu, koji se prirodno pojavljuju u raznim primjenama, asimptotički razvoj je izračunat eksplicitno do drugog reda i numeričke ilustracije su prezentirane kako bi se jasnije naznačio utjecaj korektora. Napokon, na kraju predlažemo i složeniji model koji opisuje nestacionarni tok mikropolarnog fluida u tankoj zakrivljenoj cijevi te se proučavaju efekti fleksije, torzije, mikropolarnosti kao i utjecaja vremenske derivacije. Asimptotički razvoji su izračunati eksplicitno do drugog reda i model je opravdan ocjenom pogreške u općenitom kao i u specijalnim slučajevima

Matematička analiza nestacionarnog toka mikropolarnog fluida u tankoj domeni

The main subject of this dissertation consists of studying the micropolar fluid model, which represents a generalization of the well--known classical Navier--Stokes model, mainly in the sense that it takes into account the microstructure of the fluid and effects such as shrinking and rotation of the particles of the fluid. Our first goal is to prove the existence and uniqueness of a generalized nonsteady micropolar Poiseuille solution in an infinite cylinder. This is achieved by decomposing the problem into two parts: the classical two--dimensional micropolar problem with known existence and uniqueness results and the micropolar inverse problem, where we prove the corresponding results using semidiscretization in time. Next, we derive an asymptotic model for the nonsteady micropolar fluid flow in a thin pipe assuming the solution has the uni--directional nonsteady micropolar Poiseuille form. The problem is separated by linearity and we treat two problems by constructing two--scale asymptotic approximations in powers of $\epsilon$, representing the pipe's thickness. The model is justified via error estimates in the appropriate norms. In the case of circular cross--section and external force functions depending only on time, naturally appearing in many applications, the asymptotic expansion is explicitly computed up to the second order and numerical illustrations are provided to indicate the effect of the correctors. Finally, a more complex model is proposed describing the nonsteady micropolar fluid flow in a thin curved pipe, and the effects of flexion, torsion, micropolarity and time derivative are studied. The asymptotic expansions are explicitly computed up to the second--order and the model is justified by means of the error estimate in general as well as for special cases.Glavna tema ove disertacije je proučavanje modela mikropolarnog fluida, koji predstavlja generalizaciju dobro poznatog klasičnog Navier--Stokesovog modela, prvenstveno u smislu da uzima u obzir mikrostrukturu fluida i efekte kao što su smanjivanje i rotacija čestica fluida. Naš prvi cilj je dokazati egzistenciju i jedinstvenost generaliziranog nestacionarnog mikropolarnog Poiseuille rješenja u beskonačnom cilindru. Ovo postižemo rastavljanjem problema na dva dijela: klasični dvodimenzionalni mikropolarni problem s poznatim rezultatima egzistencije i jedinstvenosti te mikropolarni inverzni problem, gdje dokazujemo odgovarajuće rezultate semidiskretizacijom u vremenu. Nadalje, izvodimo asimptotički model za nestacionarni tok mikropolarnog fluida u tankoj cijevi pod pretpostavkom da rješenje ima Poiseuilleov jednosmjerni nestacionarni mikropolarni oblik. Problem razdvajamo po linearnosti i tretiramo dva problema konstruirajući dvoskalnu asimptotičku aproksimaciju u potencijama parametra $\epsilon$, koji predstavlja debljinu cijevi. Model je opravdan koristeći ocjenu pogreške u odgovarajućim normama. U slučaju kružnog poprečnog presjeka i funkcija vanjskih sila koje ovise samo o vremenu, koji se prirodno pojavljuju u raznim primjenama, asimptotički razvoj je izračunat eksplicitno do drugog reda i numeričke ilustracije su prezentirane kako bi se jasnije naznačio utjecaj korektora. Napokon, na kraju predlažemo i složeniji model koji opisuje nestacionarni tok mikropolarnog fluida u tankoj zakrivljenoj cijevi te se proučavaju efekti fleksije, torzije, mikropolarnosti kao i utjecaja vremenske derivacije. Asimptotički razvoji su izračunati eksplicitno do drugog reda i model je opravdan ocjenom pogreške u općenitom kao i u specijalnim slučajevima

СРПСКОВИЗАНТИЈСКО НАСЛЕЂЕ И ОДНОС ПРЕМА ТРАДИЦИЈИ У ПОСЛЕРАТНОМ МОДЕРНИЗМУ

This paper examines the attitude towards tradition, especially medieval heritage in the poetry of Serbian postwar modernism, particularly in the poetry of Vasko Popa, Miodrag Pavlović, Ivan V. Lalić and Ljubomir Simović. We establish a definition of the term “Serbian-Byzantine heritage” and discuss its position in the history of Serbian literature. Since a reactivation of medieval lyrical patterns takes place within a creative tradition renewal in postwar poetry, the paper defines the inner impulses and forms of this renewal. Subsequently, it examines the nature of the lyrical return to medieval literature. We discuss the extent that the activation of poetic, aesthetic and ideological particularities of old Serbian literature owes to the tradition of European modernism and how much it actually represents an autochthone process determined by the internal logic of Serbian literature. Finally, we determine the distinctive medieval poetic views – lyrical totality, a desire for completeness, the idea of history – that were reactivated in the poetry of postwar modernism as an answer to contemporary poets’ questions.У раду се истражује однос према традицији, посебно према средњовековном наслеђу у поезији српског послератног модернизма, пре свега у песништву Васка Попе, Миодрага Павловића, Ивана В. Лалића и Љубомира Симовића. Одређује се значење термина српсковизантијско наслеђе и разматра његов положај у историји српске књижевности. Реактивирање средњовековних поетичких образаца одиграва се у склопу стваралачке обнове традиције у послератном песништву, па се у раду посебно одређују унутрашњи импулси и видови под којима се ова обнова одвија. Затим се испитује природа песничког повратка средњовековној књижевности. Разматра се колико активирање поетичких, естетичких и идеолошких особености старе српске књижевности дугује традицији европског модернизма, а колико заправо представља унутрашњом логиком српске књижевности условљен и аутохтон процес. Напокон, одређују се особени средњовековни поетички ставови – поетски тоталитет, жудња за целином, идеја историје – који су реактивирани у поезији послератног модернизма као одговор на савремена песничка питања

СРПСКОВИЗАНТИЈСКО НАСЛЕЂЕ И ОДНОС ПРЕМА ТРАДИЦИЈИ У ПОСЛЕРАТНОМ МОДЕРНИЗМУ

У раду се истражује однос према традицији, посебно према средњовековном наслеђу у поезији српског послератног модернизма, пре свега у песништву Васка Попе, Миодрага Павловића, Ивана В. Лалића и Љубомира Симовића. Одређује се значење термина српсковизантијско наслеђе и разматра његов положај у историји српске књижевности. Реактивирање средњовековних поетичких образаца одиграва се у склопу стваралачке обнове традиције у послератном песништву, па се у раду посебно одређују унутрашњи импулси и видови под којима се ова обнова одвија. Затим се испитује природа песничког повратка средњовековној књижевности. Разматра се колико активирање поетичких, естетичких и идеолошких особености старе српске књижевности дугује традицији европског модернизма, а колико заправо представља унутрашњом логиком српске књижевности условљен и аутохтон процес. Напокон, одређују се особени средњовековни поетички ставови – поетски тоталитет, жудња за целином, идеја историје – који су реактивирани у поезији послератног модернизма као одговор на савремена песничка питања

PHENETHYL ANGELATE – A NEW ESTER FROM IMMORTELLE ESSENTIAL OIL?

Esters of angelic, senecioic and tiglic acids with various saturated/unsaturated/aromatic alcohols contribute to the aroma of many essential oils. However, mass spectrometry with electron-impact ionization sometimes fails to distinguish these regio-/geometric isomers and this was the case with the minor constituent of Helichrysum italicum (immortelle) essential oil that was tentatively identified as the ester of 2-phenyl-1-ethanol with one of the mentioned acids. Our efforts to identify this phenethyl ester were also hampered by the inconsistency or by the lack of appropriate RI data in the literature. Therefore, we prepared and fully spectrally characterized (1D- and 2D-NMR, IR, MS) synthetic samples of all three isomeric esters. Subsequent GC analyses of immortelle oil samples with spiked synthetic phenethyl esters unambiguously confirmed that the compound in question was phenethyl angelate. This rare plant secondary metabolite has been previously reported only twice as a constituent of samples of natural origin. However, the outcomes of our study strongly imply that this molecule was misidentified in these earlier studies with the corresponding senecioate/tiglate. Thus, the existing libraries of RI/MS data for tiglates and angelates have to be upgraded with appropriate data for senecioates to avoid these kinds of errors in the future

Effects of small boundary perturbation on the MHD duct flow

In this paper, we investigate the effects of small boundary perturbation on the laminar motion of a conducting fluid in a rectangular duct under applied transverse magnetic field. A small boundary perturbation of magnitude ∈ is applied on cross-section of the duct. Using the asymptotic analysis with respect to ∈, we derive the effective model given by the explicit formulae for the velocity and induced magnetic field. Numerical results are provided confirming that the considered perturbation has nonlocal impact on the asymptotic solution.Croatian Science FoundationMinisterio de Economía y Competitivida

The impact of zno nanoparticles application on yield components of different wheat genotypes

The properties of zinc oxide nanoparticles (ZnO NPs) and their use have been shown as prominent for application in agriculture since it can bring certain benefits in agricultural production. The objective of this study was to estimate the impact of seed priming with ZnO NPs on yield components, plant height and spike length on wheat. In order to estimate the effects of ZnO nanoparticles on yield component, four winter wheat genotypes namely, NS Pobeda, NS Futura, NS 40S and NK Ingenio were selected. Seeds of each wheat genotypes were primed with different concentrations of ZnO NPs (0, 10, 100 and 1000 mg l-1) for 48 h in dark box by continuous aeration. Primed seeds were after sown in soil pots with 60-70% moisture contents during the till maturity. Considerable improvement was observed in plant height and spike length which increased with rates of ZnO NPs compared to the control. At rates of 10 mg l-1 ZnO NPs, the greatest increases in plant height and spike length were observed for genotypes NS Pobeda and NS Futura. At 100 mg l-1 ZnO NPs, the greatest increase for both traits was observed for genotypes NS 40S and NK Ingenio. Maximum rates of ZnO nanoparticles reduced both observed traits of wheat. The result indicated that ZnO nanoparticles can significantly increase plant height and spike length of wheat, but also plant response to ZnO nanoparticles significantly depends on concentration of application, as well as from wheat genotype

Facile synthesis of hydrophilic polymer-capped upconverting NaYF4:Yb,Er particles

Over the last decade, solvothermal decomposition of organometallic compounds has been indicated as one of the most convenient method for the synthesis of monodisperse lanthanide doped upconverting fluorides. Due to their hydrophobic nature such particles could not be used for a conjugation of the molecular targeting agents which is necessary for optical imaging of biological tissues. In this work, hydrophilic NaYF4:Yb,Er (17 mol% Yb; 3mol% Er) nanoparticles were synthesized by facile one-pot hydrothermal synthesis performed with a help of chitosan (CS) and poly(acrylic acid) (PAA). Obtained powders were analyzed by X-ray powder diffraction (XRPD), field emission scanning electron microscopy (FESEM), Fourier transform infrared (FTIR) and photoluminescence (PL) spectroscopy. The obtained results implied that particle size, shape and surface characteristics are dependent on the polymer choice. Although both powders crystallize in the same crystal arrangement (cubic, Fm-3m) more intense red emission, assigned to the Er3+ 4F9/2 → 4I15/2 electronic transitions, characterize spherical NaYF4:Yb,Er@CS particles. To asses a biological safety of their use, viability of the human gingival fibroblasts (HFG) was additionally tested by a colorimetric MTT assay

Developing thermal insulation cement-based mortars with recycled aggregate in accordance with net zero principles

The performance of thermo-insulation rendering mortars with alternations in ratios of powdered cordierite and talc was examined. The goal was to confirm that recycled kilnware cordierite can be reapplied in the mortar design without significant deterioration in performance in comparison with OPC mortar. Differential thermal analysis was employed for examining thermally induced reactions. The cavitation erosion, in testing sequences ranging from 30 to 120 minutes, was used to assess the compactness of the mortar structure. The physico-mechanical properties of experimental mortars were investigated. The morphologies of the mortar tablets upon cavitation were studied using a scanning electron microscope. It was established that cordierite and talc filler in amounts up to 20% enhance microstructural packing and mechanical strengths due to improved cementation and therefore contribute to cavitation erosion resistance. Higher amounts of talc cause structural degradation and mass loss during cavitation tests. Reducing manufacturing costs, energy consumption, and greenhouse gas emissions are the main objectives of the production of this waste-based construction composite, as the reuse of waste materials can help achieve a number of Sustainable Development Goals

Određivanje otpornosti na dejstvo kavitacije uzoraka pirofilita

U radu je ispitivana otpornost pod dejstvom kavitacije uzoraka sinterovanog pirofilita. Polazni uzorak pirofilita iz ležišta Parsović- BiH mleven je u vibracionom mlinu na granulaciju 20μm, presovan je i sinterovan na temperaturama (ºC): 1000; 1100; 1200. Za procenu kavitacione otpornosti praćena je promena mase uzorka u funkciji vremena delovanja kavitacije. Primenjena je ultrazvučna vibraciona metoda sa stacionarnim uzorkom prema standardu ASTM G32. Izračunate su kavitacione brzine za sve uzorke, kao osnovni pokazatelj otpornosti materijala pod dejstvom kavitacije. Promena morfologije površine uzorka sa vremenom ispitivanja praćena je primenom skenirajuće elektronske mikroskopije. Na osnovu vrednosti kavitacione brzine i analize morfologije oštećenja površine određena je kavitaciona otpornost ispitivanih uzoraka na bazi pirofilita. Dobijeni rezultati ukazuju da uzorci sinterovanog pirofilita imaju zadovoljavajuću otpornost na dejstvo kavitacije i mogu se primeniti u uslovima manjih kavitacionih opterećenja