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2. STABILITY AND METASTABILITY OF NEMATIC GLASSESAmid Ranjkesh Siahkal, 2014, doktorska disertacija Opis: Structures exhibiting continuous symmetry breaking are extremely susceptible to various perturbations. The reason behind is the existence of Goldstone modes in the gauge
component of the order parameter describing broken symmetry. The socalled LarkinImry–Ma argument claims that even infinitesimally weak random fieldtype disorder destroys long range order (LRO) which would otherwise be present in the absence of random disorder. Furthermore, it claims that the system breaks into domain type configuration having short range order (SRO), where the characteristic domain size scales as ksi= W^2/(4d). Here W measures the strength of random field interaction and d is the dimensionality of space. However, some studies claim that structures with quasi long range order (QLRO) are established instead of SRO. The main focus of this doctor thesis is the character of nematic structures in the random field. I studied theoretically and numerically nematic structures that are obtained by continuous symmetry breaking in orientational degrees of freedom on
decreasing the temperature T, starting from the ordinary liquid, the so called isotropic phase. In particular, I investigated conditions for which the LarkinImryMa theorem holds true. So far statistical interpretations of such systems have typically used two different semi
microscopic type models: i) the Random Anisotropic Nematic (RAN) and ii) the Sprinkled Silica Spin (SSS) model. The RAN model is a LebwohlLasher (LL) model with nematic molecules locally coupled with uncorrelated random anisotropic field at each site, while the SSS model has a finite concentration of impurities frozen in random directions. I used a three dimensional (d = 3) model intermediate between SSS and RAN models, with finite
concentration p of frozen impurities, where p < pc (pc stands for the percolation threshold). The simulations were performed at different temperatures for temperaturequenched (TQH) and ﬁeldquenched histories (FQH), as well as for temperatureannealed histories (AH). The
ﬁrst two of these limits represent extreme histories encountered in typical experimental studies. Numerically, I studied the impact of control parameters (T, p, W) and history of samples (TQH, FQH, AH) on structural properties of the system. Within the model I was varying p, temperature T, interaction strength W and also sample histories. From final configurations, I calculated orientational order parameters and twopoint correlation
functions. Next, I estimated the size of the LarkinImryMa domains d. Finite sizescaling was also used to determine the range of the orientational ordering, as a function of W, p, T and sample history. The main results of my study are the following. In general, the system exhibited strong memory effects, indicating important role of history of samples. Furthermore, obtained results were relatively robust (from macroscopic point of view), indicating substantial energy barriers among competing states. On increasing the strength W, I typically obtained the following sequence of orders: LRO, QLRO, and SRO. For some concentrations p,however, SRO was absent. The crossover anchoring strength between QLRO and SRO strongly depends on history of samples, and it has the lowest values for TQH. From my simulations it follows that for the model used the LarkinImryMa argument holds only in limited range of model parameters. In most cases I obtain QLRO instead of SRO. However, in all structures there is imprint of LarkinImryMa domains, exhibiting scaling d 1/ (W2p) in the weak anchoring regime. This suggests that we do not have a “classical ” QLRO with algebraic decay with distance. Similar results were obtained in the studies of magnetic systems. Ključne besede: nematic liquid crystals, topological defect, order parameter, symmetry breaking, domains, Random field, larkinImry–Ma theorem, speroNematics Objavljeno: 15.07.2014; Ogledov: 988; Prenosov: 66 Celotno besedilo (2,86 MB) 
3. Graphʼs theory approach for searching the shortest routing path in RIP protocolSaša Klampfer, Jože Mohorko, Žarko Čučej, Amor Chowdhury, 2012, izvirni znanstveni članek Opis: Routing is a problem domain with an infinite number of finalsolutions. One of the possible approaches to solving such problems is using graph theory. This paper presents mathematical analysis methodologies based on circular graphs for solving a shortest path routing problem. The problem is focused on searching for the shortest path within a circular graph. Such a search coincides with the network routing problem domain. In this paper, we introduce in the detail all necessary parts needed to understand such an approach. This includes: definition of the routing problem domain, introduction to circular graphs and their usage, circular graphʼs properties, definition of walks through a circular graph, searching and determining the shortest path within a circular graph, etc. The state of the art routing methods, implemented in contemporary highly sophisticated routers, includes wellknown weightbased algorithms and distancevectorsbased algorithms. The proposed solution can be placed between the two abovementioned methods. Each of these known methods strives for optimal results, but each of them also has its own deficiencies, which should be rectified with the proposed new method. This theoretically presented method is argued by a practical example and compared with the RIP (Routing Information Protocol) technique, where we look for the shortest path and possible walks through a specified circular graph. Ključne besede: circular graphs, shortest path, graph diameter, walk through, CIGRP, connectivity matrix, network topology, symmetry, fully connected graph Objavljeno: 10.07.2015; Ogledov: 873; Prenosov: 37 Povezava na celotno besedilo 
4. General U(1) x U(1) Ftheory compactifications and beyond: geometry of unHiggsings and novel matter structureMirjam Cvetič, Denis Klevers, Hernan Piragua, Washington Taylor, 2015, izvirni znanstveni članek Opis: We construct the general form of an Ftheory compactification with two U(1) factors based on a general elliptically fibered CalabiYau manifold with MordellWeil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier Ftheory constructions with U(1) x U(1) gauge symmetry. Generic U(1) x U(1) models can be related to a Higgsed nonAbelian model with gauge group SU(2) x SU(2) x SU(3), SU(2)(3) x SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the MordellWeil group are replaced with local vertical divisors associated with the Cartan generators of nonAbelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed nonAbelian model. The nonAbelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1)(k) factors with k > 2, which can be studied by Higgsing theories with larger nonAbelian gauge groups. Ključne besede: Ftheory, differential geometry, algebraic geometry, gauge symmetry Objavljeno: 14.06.2017; Ogledov: 235; Prenosov: 105 Celotno besedilo (1,36 MB) Gradivo ima več datotek! Več...

5. Basin stability for chimera statesSarbendu Rakshit, Bidesh Bera, Matjaž Perc, Dibakar Ghosh, 2017, izvirni znanstveni članek Opis: Chimera states, namely complex spatiotemporal patterns that consist of coexisting domains of spatially coherent and incoherent dynamics, are investigated in a network of coupled identical oscillators. These intriguing spatiotemporal patterns were first reported in nonlocally coupled phase oscillators, and it was shown that such mixed type behavior occurs only for specific initial conditions in nonlocally and globally coupled networks. The influence of initial conditions on chimera states has remained a fundamental problem since their discovery. In this report, we investigate the robustness of chimera states together with incoherent and coherent states in dependence on the initial conditions. For this, we use the basin stability method which is related to the volume of the basin of attraction, and we consider nonlocally and globally coupled timedelayed MackeyGlass oscillators as example. Previously, it was shown that the existence of chimera states can be characterized by mean phase velocity and a statistical measure, such as the strength of incoherence, by using well prepared initial conditions. Here we show further how the coexistence of different dynamical states can be identified and quantified by means of the basin stability measure over a wide range of the parameter space. Ključne besede: synchronization, oscillations, symmetry breaking, network Objavljeno: 23.06.2017; Ogledov: 213; Prenosov: 83 Celotno besedilo (4,46 MB) Gradivo ima več datotek! Več...

6. Symmetry breaking and structure of a mixture of nematic liquid crystals and anisotropic nanoparticlesMarjan Krašna, Matej Cvetko, Milan Ambrožič, 2010, izvirni znanstveni članek Opis: Orientational ordering of a homogeneous mixture of uniaxial liquid crystalline(LC) molecules and magnetic nanoparticles (NPs) is studied using the LebwohlLasher lattice model. We consider cases where NPs tend to be oriented perpendicularly to LC molecules due to elastic forces. We study domaintype configurations of ensembles, which are quenched from the isotropic phase. We show that for large enough concentrations of NPs the long range uniaxial nematic ordering is replaced by short range order exhibiting strong biaxiality. This suggests that the impact of NPs on orientational ordering of LCs for appropriate concentrations of NPs is reminiscent to the influence of quenched random fields which locally enforce a biaxial ordering. Ključne besede: liquid crystals, nanoparticles, disorder, orientational order, quenched disorder, symmetry breaking Objavljeno: 03.08.2017; Ogledov: 185; Prenosov: 101 Celotno besedilo (447,84 KB) Gradivo ima več datotek! Več...

7. Mirror image properties in human languagesIreneusz Kida, 2009, izvirni znanstveni članek Opis: In this paper I discuss the phenomenon of mirror image properties in human languages. I give examples from English, Polish, Malay, Gothic, Latin and Classical Greek. Although I take into consideration only a few languages, my paper has further implications, namely, that mirror image properties exist in any language of the world. I start with a description of the natural phenomenon of mirror image and then extend my discussion to language. I talk about mirror image sentences, reduplication, and palindromes. Ključne besede: linguistics, grammar, symmetry, duplication, mirror images, palindromes, comparative studies Objavljeno: 31.01.2018; Ogledov: 106; Prenosov: 53 Celotno besedilo (242,33 KB) Gradivo ima več datotek! Več...

8. A new solution for shallow and deep tunnels by considering the gravitational loadsMohammad Reza Zareifard, Ahmad Fahimifar, 2012, izvirni znanstveni članek Opis: A new, elastoplastic, analyticalnumerical solution, considering the axialsymmetry condition, for a circular tunnel excavated in a strainsoftening and Hoek–Brown rock mass is proposed. To examine the effect of initial stress variations, and also the boundary conditions at the ground surface, the formulations are derived for different directions around the tunnel. Furthermore, the effect of the weight of the plastic zone is taken into account in this regard. As the derived differential equations have no explicit analytical solutions for the plastic zone, the finitedifference method (FDM) is used in this study. On the other hand, analytical expressions are derived for the elastic zone. Several illustrative examples are given to demonstrate the performance of the proposed solution, and to examine the effect of various boundary conditions. It is concluded that the classic solutions, based on the hydrostatic farfield stress, and neglecting the effect of the boundary conditions at the ground surface, give applicable results for a wide range of practical problems. However, ignoring the weight of the plastic zone in the analyses can lead to large errors in the calculations. Ključne besede: groundresponse curve, elastoplastic analysis, boundary condition, axial symmetry, gravitational loads Objavljeno: 13.06.2018; Ogledov: 237; Prenosov: 25 Celotno besedilo (406,96 KB) Gradivo ima več datotek! Več...
