Repository of Department of Physics in Osijek
Not a member yet
172 research outputs found
Sort by
Spheriak Harmonics and their Applications im Physics
Get PDFUvod u sferne harmonike započinjemo Laplaceovom diferencijalnom jednadžbom u sfernim
koordinatama. Sferne harmonike predstavljamo kao rješenje kutnog dijela Laplaceove
jednadžbe. Nakon upoznavanja sa svojstvima sfernih harmonika iskoristit ćemo Laplaceov
razvoj kako bi pronašli električni potencijal na površini sfere s danim rubnim uvjetom. U
daljnjem izlaganju upoznat ćemo se s operatorom kutne količine gibanja i pomoću njega
definirati Clebsch-Gordanove koeficijente te sfernim tenzorima pomoću kojih ćemo definirati
Wignerove matrice, ali i neke druge bitne identitete koji koriste sferne harmonike. Na kraju rada
ćemo ukratko reći nešto o vektorskim sfernim harmonicima.We begin our thesis with Laplace`s equation in a spherical coordinate system. Spherical
harmonics are represented as a solution to the angular part of Laplace`s equation. After
familiarising ourselves with the properties of spherical harmonics, we will use Laplace
expansion to find electric potential on the surface of a sphere with a given boundary condition.
Furthermore, we are going to use angular momentum operator to define Clebsch-Gordan
coefficients. In addition, we would familiarise ourselves with the concept of spherical tensors,
and using them we would define Wigner matrices and some other important spherical harmonics
identities. Finally, we would mention vector spherical harmonics and some of their properties
Distribution of Ambient Dose Equivalent in the City of Slavonski Brod
Get PDFU prvih nekoliko poglavlja ovog diplomskog rada dana je kratka teorijska podloga, u kojoj
su opisani osnovni pojmovi iz radioekologije, počevši od same definicije zračenja, do definicija
osnovnih dozimetrijskih veličina. U nastavku rada dana je metodologija mjerenja brzine
ambijentalnog doznog ekvivalenta na području grada Slavonskog Broda, koja su provedena
tijekom srpnja i kolovoza 2016. godine, u cilju ispitivanja potencijalnog utjecaja rafinerije nafte
Brod, koja je smještena uz obalu rijeke Save, na ozračenje stanovništva Slavonskog Broda. Uz ove
rezultate, također su izloženi i rezultati dobiveni uzorkovanjem rijeke Save i tla na području grada.
Grafički prikaz dobivenih rezultata predstavljen je unutar web GIS aplikacije, koja u ovisnosti o
korisničkom upitu selektira i izdvaja tražene položajne i atributne podatke o mjernim točkama.In the first few chapters of this master thesis a short theoretical background was given, in
which the basic concepts from radioecology were described, begining from the definition of the
radiation itself, to the definitions of a basic dosimetric quantities. In the following chapters, a
methodology of measuring ambient dose rate equivalent in the city of Slavonski Brod during the
period of July, 2016. to August, 2016., was given. The primary goal of this research was to examine
the potential influence of oil refinery Brod, situated along the Sava River, on ionizing radiation
exposure of the population of Slavonski Brod. Apart from this results, the results of Sava River
and soil sampling on locations in the city area were also presented. Cartographic view of the
recorded data is displayed within the web GIS application, which selects and extracts requested
spacial and attribute information about meaurement points, depending on the user made queries
The Difference Between Mathematical and Physical View on the Falling Ladder Problem
Get PDFPadajuće ljestve su dobar primjer kojim se može pokazati ključna razlika između
matematike i fizike.Jednostavan i naizgled prihvatljiv matematički model daje predviđanje koje
se očito ne slaže s iskustvom: brzina vrha padajućih ljestvi teži u beskonačno kad kut koji ljestve
zatvaraju s podom teži u nulu. U matematičkom je svijetu takvo ponašanje sasvim legitimno.
No takav model očito ne opisuje dobro fizički svjet - svijet u kojem živimo. Za opis fizičkog
svijeta model treba nadograditi. Drugim riječima, treba u obzir uzeti neka ograničenja koja
nameće fizika. Zbog tih ograničenja jednadžbe obično postaju zamršenije pa ih je teže riješiti,
no predviđanja modela bolje se slažu s opažanjima.
U ovom radu jednostavan matematički model padajućih ljestvi nadograđen je u dvije
etape. U jednostavnijem slučaju uzeta je u obzir činjenica da ljestve imaju masu (zbog koje u
gravitacijskom polju padaju), ali je ta masa stavljena u središte ljestvi. Korštena je, dakle,
dinamika točkatog tijela. U realističnijem slučaju masa je jednoliko raspoređena po ljestvama.
Tu je korištena dinamika krutog tijela. U oba je slučaja, radi jednostavnosti, trenje bilo
zanemareno. Oba fizička modela, očekivano, daju konačnu brzinu vrha padajućih ljestvi kad
ljestve dođu u vodoravni položaj.Falling ladders is a good example which can show the key difference between
mathematics and physics. A simple and seemingly acceptable mathematical model gives
prediction which obviously does not agree with experience: the speed at the top of the ladder
tends to infinity when the angle between the ladder and the floor tends to zero. In the
mathematical world such behavior is quite legitimately. But such model obviously does not
describe good physical world – the world we live in. To describe the physical world, the model
needs to be upgraded. In other words, it is necessary to take some restrictions imposed by
physics. Because of that restrictions, equations usually become more complicated and it's more
difficult to solve them. But that model predictions better get along with observations.
In this work, a simple mathematical model of falling ladders has been upgraded into
two stages. In the easier case we took a fact that ladders have a mass (because they fall in the
gravity field), but that mass is placed in the center of the ladder. So, the dynamics of the dot
body has been used. In a more realistic case, the mass is uniformly deployed by ladders. Solid
body dynamics has been used here. In both cases, for simplicity, friction was neglected. As
expected, both physical models give the ultimate speed of the top of the ladder when the ladder
comes to the horizontal position
Development of Educational Software for Teaching Electromagnetisam
Get PDFU radu se detaljno pojašnjava postupak izrade softvera uz prethodni naglasak o mogućnostima
njegove uporabe u nastavi. U prvom dijelu rada je rasprava o ulozi rčunala u nastavi kao i
učeničkim pretkoncepcijama u području elektromagnetizma s ciljem prepoznavanja potrebe za
izradom softvera za nastavu kako bi se one uspješnije otklonile. Nakon toga slijedi kratko
upoznavanje alata za izradu softvera i konceptualna razrada algoritma za simuliranje strujnog
kruga. Glavni dio rada čini detaljna uputa za izradu softvera uz dodatke izvornog programskog
koda u svrhu reprodukcije softvera za korištenje ili proširenje osnovnog programa. U završnom
dijelu rada priložena je priprema za nastavni sat održan uz pomoć izrađenog softvera, uz primjer
prilagodbe softvera specifičnoj jedinici gradiva.The thesis discusses the process of development of the software for teaching electromagnetism
and its application in physics education. A brief discussion on the most common students
misconceptions on electromagnetism is followed after the explanation of the purpose of
computer implementation in education. Furthermore, a short introduction on the use of software
tools in development of the educational software along with an elaboration of the algorithm used
to simulate an electric circuit is given. The software development instructions of the educational
software are the main part of the thesis with the further insight into the possible changes and
adaptions of the software to fulfil requirements and needs of the teachers and students in class.
The final part consists of a teachers preparation document as an example of the educational
software being used in class
Theory of Distributions
Get PDFRad na temu teorije raspodjela.
Zamjenjujemo klasične matematičke funkcije s drugačijim
načinom opisivanja prirodnih pojava.
Rad na temu teorije raspodjela. Zamjenjujemo klasične matematičke funkcije s drugačijim
načinom opisivanja prirodnih pojava
Torsion Balance-Coulombo's Law
Get PDFU diplomskom radu predstavljen je Coulombov zakon te eksperiment za potvrdu tog zakona
pomoću torzijske vage. Cilj rada bio je prikazati povijesni prikaz otkrića Coulombova zakona,
definirati i matematički zapisati taj zakon te ga eksperimentalno potvrditi izvedbom pokusa
pomoću torzijske vage. Kao uvod u problematiku rada opisana je Coulombova metoda potvrde
zakona, a ujedno je prikazana i matematička teorijska podloga. Glavni dio rada isključivo
je eksperimentalne prirode i temelji se na pripremi postava torzijske vage u laboratoriju Odjela
za fiziku te izvedbi eksperimenta u svrhu dokazivanja Coulombova zakona. Eksperiment je
podijeljen na dva dijela kako bi ispitali različite ovisnosti kuta otklona (sile). U posljednjem
dijelu rada, podaci dobiveni iz oba dijela eksperimenta, se tablično i grafički analiziraju te se
provjerava potvrda Coulombova zakona elektrostatike.This master thesis presents Coulomb's law and experiment with torsion balance as
confirmation of this law. The purpose of this paper is to present historic discovery of Coulomb's
law, to determine mathematically this law and to experimentally analyze and confirm this law
with torsion balance as main device. As an introduction to this paper we gave the explanation of
Coulomb's method of finding the law and after that we analyzed in detail theoretical
mathematical background of this law. The main part of the paper is of experimental nature and is
based on preparation of torsion balance in possession of our Department of Physics and
performing the actual experiment for confirming the law. Experiment is divided into two parts
with purpose of testing different dependences of torsion displacement angle (force). In the last
part, there are shown graphic and tabular analysis of data collected from both parts of experiment
with purpose of confirming the Coulomb's law of electrostatics
The Three Body Problem
Get PDFTema ovog rada je generalni problem triju tijela. Općenito, taj problem nije analitički rješiv
stoga se stavlja naglasak na reducirani problem triju tijela. Reducirani problem riješio je Lagrange,
koji je rekao da treće tijelo zanemarive mase može nesmetano opstati u sustavu na položaju pet
točaka koje su po njemu dobile naziv Lagrangeove točke .
U radu ću detaljno opisati stabilnost tih točaka te se uvjeriti da su tri točke nestabilne ,
a preostale dvije stabilne . Te točke od velike su praktične važnosti, a potvrda njihova
postojanja su grupa asteroida poznati pod nazivom „Trojanci“.The theme of this thesis is the general problem of three bodies. Generally, this problem is
not analytically solved, therefore we emphasize the reduced problem of the three bodies. Reduced
problem was solved Lagrange, who said that a third body of negligible mass can freely exist in the
system at the position of five points that are named after him, Lagrange point .
I will describe the stability of these points in detail and indicate that the three points are unstable
, and the remaining two are stable . These points are of great practical
significance, and proof of their existence is a group of asteroids known as "Trojans"
Detector of ionizing radiation - Geiger - Muller
Get PDFDiplomski rad s temom Detektor ionizirajućeg zračenja – Geiger – Müllerov brojač sastoji se od
dva dijela. U prvom, teorijskom, dijelu rada opisano je otkriće radioaktivnosti te najznačajnije
činjenice vezane za radioaktivnost. Nakon toga su opisani različiti detektori zračenja i njihove
karakteristike. Detaljno se opisuje Geiger – Müllerov brojač, njegova povijest, područje rada,
princip rada te druge bitne karakteristike. U drugom, eksperimentalnom, dijelu rada predstavljeni
su rezultati dobiveni eksperimentima pomoću Geiger – Müllerova brojača.Master thesis with the topic Detector of ionizing radiation – Geiger – Müller counter is divided
into two parts. In the first, theoretical, part of this work the discovery of radioactivity and the most
important facts of radioactivity are described. Later on, different radiation detectors and their
characteristics are described. Geiger – Müller counter is described in detail; its history, scope, work
principles and some other important properties. In the second, experimental, part of this work, the
results of the radiation measurements of different materials using Geiger – Müller counter are
presented
Metoda najmanjih kvadrata i njezina primjena u fizici
Get PDFU diplomskom radu predstavljena je metoda najmanjih kvadrata i njezina primjena u fizici.
Cilj rada je bio upoznati se s razvojem metode kroz povijest, postavljanje problema te prikazati
postupak njihova rješavanja kao i upoznavanje s primjenom same metode u području fizike. Kao
uvod u problematiku kojom se bavi ovaj diplomski rad, ukratko su objašnjeni osnovni pojmovi
regresijske analize. Središnji dio diplomskog rada sastoji se od dva poglavlja, koji su isključivo
vezani za metodu najmanjih kvadrata. U poglavlju Povijest metode najmanjih kvadrata opisan je
slijed kojim se metoda razvijala, dok je u poglavlju Metoda najmanjih kvadrata predstavljeno na
koji se način procjenjuje model regresije te je opisan postupak procjene nepoznatih parametara
regresije. Na kraju diplomskog rada dani su primjeri vezani uz područje fizikeThis master thesis presents the least squares method and its usage in physics. The purpose of
this paper was to describe the development of this method through history, problem setup and the
procedure of problem solving as well as its usage in physics. As an introduction to the thesis of this
paper, we gave a brief introduction to the main terms of regression analysis. The central part of the
paper is formed out of two chapters which entirely deal with least squares method. The chapter The
history of the least squares method describes the sequence in which the method had developed,
while the chapter Least squares method describes the assessment of regression model and the
assessment of unknown regression parameters. At the end of the paper we have presented examples
in field of physic
Evoluation of Galaxies
Get PDFU ovom završnom radu govorit ćemo o razvoju galaksija. Prvi dio rada odnosi se na
povijest svemira neposredno nakon velikog praska. Bit će opisani bitni fizikalni procesi koji su
vodili do formiranja prvih zvijezda i galaksija. Drugi dio rada obuhvaća razvoj i formiranje
pojedinih vrsta galaksije. U završnom dijelu rada bit će opisana morfološka klasifikacija galaksija
te pojedine vrste galaksija.This final thesis deals with galaxy evolution. First part of the thesis is about the universe
right after the big bang. Major physical processes, which lead to the formation of the first stars and
galaxies, will be described. Second part of the thesis includes evolution and formation of certain
galaxy species. In the final part, morphological classification of the galaxies and tevery galaxy
species will be described