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Statistical Properties of Time-dependent Systems
Diego Fregolente Mendes De Oliveira, 2012, doktorska disertacija

Opis: In the dissertation I have dealt with time-dependent (nonautonomous) systems, the conservative (Hamiltonian) as well as dissipative, and investigated their dynamical and statistical properties. In conservative (Hamiltonian) time-dependent systems the energy is not conserved, whilst the Liouville theorem about the conservation of the phase space volume still applies. We are interested to know, whether the system can gain energy, and whether this energy can grow unbounded, up to infinity, and we are interested in the system's behaviour in the mean, as well as its statistical properties. An example of such a system goes back to the 1940s, when Fermi proposed the acceleration of cosmic rays (in the first place protons) upon the collisions with moving magnetic domains in the interstellar medium of our Galaxy, and in other galaxies. He then proposed a simple mechanical one-dimensional model, the so-called Fermi-Ulam Model (FUM), where a point particle is moving between two rigid walls, one being at rest and the other one oscillating. If the oscillation is periodic and smooth, it turned out in a nontrivial way, which is, in the modern era of understanding the chaotic dynamical systems, well understood, namely that the unbounded increasing of the energy (the so-called Fermi acceleration) is not possible, due to the barriers in form of invariant tori, which partition the phase space into regions, between which the transitions are not possible. The research has then been extended to other simple dyanamical systems, which have complex dynamics. The first was so-called bouncer model, in which a point particle bounces off the oscillating platform in a gravitational field. In this simple system the Fermi acceleration is possible. Later the research was directed towards two-dimensional billiard systems. It turned out that the Fermi acceleration is possible in all such systems, which are at least partially chaotic (of the mixed type), or even in a system that is integrable as static, namely in case of the elliptic billiard. (The circle billiard is an exception, because it is always integrable, as the angular momentum is conserved even in time-dependent case.) The study of time-dependent systems has developed strongly worldwide around the 1990s, in particular in 2000s, and became one of the central topics in nonlinear dynamics. It turned out, quite generally, but formal and implicit, in the sense of mathematical existence theorems, that in nonautonomous Hamilton systems the energy can grow unbounded, meaning that the system ``pumps" the energy from the environment with which it interacts. There are many open questions: how does the energy increase with time, in particular in the mean of some representative ensemble of initial conditions (typically the phase space of two-dimensional time-dependent billiards is four-dimensional.) It turned out that almost everywhere the power laws apply, empirically, based on the numerical calculations, but with various acceleration exponents. If the Fermi acceleration is not posssible, like e.g. in the FUM, due to the invariant tori, then after a certain time of acceleration stage the crossover into the regime of saturation takes place, whose characteristics also follow the power laws. One of the central themes in the dissertation is the study of these power laws, their critical exponents, analytical relationships among them, using the scaling analysis (Leonel, McClintock and Silva, Phys. Rev. Lett. 2004). Furthermore, the central theme is the question, what happens, if, in a nonautonomous Hamilton system which exhibits Fermi acceleration, we introduce dissipation, either at the collisions with the walls (collisional dissipation) or during the free motion (in-flight dissipation, due to the viscosity of the fluid or the drag force etc.). Dissipation typically transforms the periodic points into point attractors and chaotic components into chaotic attractors. The Fermi acceleration is always suppressed. We are interested in the phase portraits of
Ključne besede: nonlinear dynamics, dynamical systems, conservative and dissipative systems, time-dependent systems, Fermi acceleration, billiards, kicked systems, chaos, chaotic and periodic attractors, bifurcations, boundary crisis
Objavljeno: 19.09.2012; Ogledov: 1894; Prenosov: 72
.pdf Celotno besedilo (16,09 MB)

Times New Roman CE; Vpeljava interakcij posredovanih preko molekul topila v Poisson-Boltzmannovo teorijo
Klemen Bohinc, 2012, doktorska disertacija

Opis: Electrostatic interactions are omnipresent in colloidal and biological systems; for example they take place in aqueous solutions that contain mobile salt ions. Water plays a crucial role for the energetics of such systems. The ordering of water molecules changes the polarization and thus contributes to the electrostatic properties of the system. In particular, structural correlations between solvent molecules give rise to an inhomogeneous and non-local dielectric response that contributes to the energetics and the stability of biomacromolecules. This work is concerned with including solvent structures into mean-field electrostatics. It consists of three related subjects. In the first part we introduce a solvent model of interacting Langevin dipoles and incorporate that model into the Poisson-Boltzmann (PB) theory for an aqueous solution of monovalent ions in contact with a charged surface. The interplay between the electric double layer and the orientational ordering of solvent molecules determines the spatial decay of the solvent polarization. We showed that our model can result in a sign inversion of the electrostatic potential at a charged surface. The second part applies the PB model for a solvent of interacting Langevin dipoles to a mixed anionic/zwitterionic lipid layer. In the model the headgroups have ability to polarize the water in the headgroup region. The result is a positive electrostatic potential everywhere in the system. In the last part we introduce the Poisson-Helmholtz-Boltzmann theory, which adds to the electrostatic interaction potential between two ions an additional Yukawa potential. The latter accounts for solute-mediated ion-ion interactions. We demonstrate that these interactions can give rise to ion specific effects. One of the possible applications of the theory is related to the Hofmeister series. The presented analysis focuses on two systems. The first is the system of two charged surfaces embedded in a solution of only counterions, whereas the second system is one single charged surface in contact with a symmetric 1:1 electrolyte solution.
Ključne besede: Biomacromolecules, Solvent structure, Langevin dipoles, Electrostatics, Poisson and Helmholtz equations, Boundary-value problems, Yukawa potential
Objavljeno: 19.09.2012; Ogledov: 1577; Prenosov: 66
.pdf Celotno besedilo (1,71 MB)

Blaž Goričar, 2014, magistrsko delo

Opis: This Master's thesis research is about the localized coercivity enhancement of Nd-Fe-B magnets, which are used in electric motors. Computer simulations show, that when magnets operate at high temperatures, they experience large demagnetizing fields. However, this happens only on specific parts of the body of the magnet. The demagnetization can be prevented by locally enhancing the coercivity only on these specific parts. The goal of this Master’s thesis was to research the localized coercivity enhancement by creating a magnet, where one half would have different magnetic properties compared to the other half. Commercially available Nd-Fe-B magnets were bought from Shin-Etsu, Japan. The magnetic properties of the magnets were measured on two very different devices – the permeameter and the vibrating sample magnetometer. The demagnetization curves were compared. The coercivity of the magnet was improved with the electrophoretic deposition of dysprosium on the surface. The dysprosium then diffused, at high temperature, from the surface to the inside of the magnet along the grain boundaries. The microstructure of the magnet was analysed on the scanning electron microscope, while the content of the elements was quantitatively analysed with the EDS method. The demagnetization curves of both devices were comparable. The grain-boundary diffusion process of dysprosium with the electrophoretic deposition increased the coercivity of the magnet by 25 %, without any significant loss in remanence. The research on the localized grain-boundary diffusion was first done with measurements on the vibrating sample magnetometer and then confirmed with the Hall probe. We discovered that one part of the magnet could have different magnetic properties compared to the other half. There was a clear border between the two.
Ključne besede: Nd-Fe-B magnet, coercivity, magnetic properties, electrophoretic deposition, grain-boundary diffusion process.
Objavljeno: 09.09.2014; Ogledov: 1244; Prenosov: 65
.pdf Celotno besedilo (4,38 MB)

Heat diffusion in fractal geometry cooling surface
Matjaž Ramšak, Leopold Škerget, 2012, izvirni znanstveni članek

Opis: In the paper the numerical simulation of heat diffusion in the fractal geometry of och snowflake is presented using multidomain mixed Boundary Element Method. he idea and motivation of work is to improve the cooling of small electronic devices sing fractal geometry of surface similar to cooling ribs. The heat diffusion is ssumed as the only principle of heat transfer. The results are compared to the heat lux of a flat surface. The limiting case of infinite small fractal element is computed sing Richardson extrapolation.
Ključne besede: heat transfer, cooling of electronic devices, boundary element method, fractals
Objavljeno: 10.07.2015; Ogledov: 536; Prenosov: 135
.pdf Celotno besedilo (313,63 KB)
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Geodetic sets in graphs
Boštjan Brešar, Matjaž Kovše, Aleksandra Tepeh, 2011, samostojni znanstveni sestavek ali poglavje v monografski publikaciji

Opis: Na kratko so povzeti rezultati o geodetskih množicah v grafih. Po pregledu rezultatov iz prejšnjih raziskav se posvetimo geodetskemu številu in sorodnim invariantam v grafih. Podrobno so obravnavane geodetske množice kartezičnih produktov grafov in geodetske množice v medianskih grafih. Predstavljen je tudi algoritmični vidik in povezava z nekaterimi ostalimi koncepti iz teorije konveksnih in intervalskih struktur v grafih.
Ključne besede: matematika, teorija grafov, geodetsko število, geodetska množica, kartezični produkt, medianski graf, mejna množica, mathematics, graph theory, geodetic number, geodetic set, Cartesian product, median graph, boundary set
Objavljeno: 10.07.2015; Ogledov: 185; Prenosov: 13
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