1. Optimization methods for solving transportation problems on networksKatja Prnaver, 2011, doktorska disertacija Opis: In this thesis we study problems from real situations, which can be applied to network
graphs and solved using mathematical graph theory.
We start with the problem of oriented network design. The problem originates from
networks, where the flow over the arcs is important and many times limited with the capacity
of the networks. There are several techniques and results on the problem of assigning the
flow through the network channels. In our problem, we try to find the optimal network
structure, which could be used in the design phase of the network. With metaheuristics,
we search for optimal network structures for a given number of nodes. We define triangle
neighborhood and compare the results of the algorithm with the conjecture by Choplin et
al. [8].
Further, we study the problem of order picking and order batching in block structured
warehouses. For order picking problem, we present the extension of a dynamic programming
algorithm by Ratliff and Rosenthal [42], which enables the development of an algorithm for
an unlimited number of blocks. In order to achieve this, a new presentation of states and
transitions of dynamic programming algorithm is given. We prove that the resulting path is
optimal for the given structure. We compare the optimal path lengths to the results found in
literature and also investigate the impact of warehouse layout parameters onto the routing.
Closely related to the problem of order picking, we investigate the order batching problem.
We discuss the variation of the order batching problem with time windows and present
the algorithmic approach to solving the problem. The previously presented optimal path
algorithm is applied in the algorithm to ensure even better quality of results. We introduce
the evaluation function of a batch and compare the results of the algorithm with the test
data from the literature as well as with data from the real warehouse.
We conclude by summarizing the results and stating some possible extensions and further
work. Ključne besede: graph theory, networks, optimization, shortest path problem, traveling salesman problem, algorithms, metaheuristics, order batching Objavljeno: 03.06.2011; Ogledov: 3765; Prenosov: 147 Celotno besedilo (925,86 KB) 
2. Symmetry preserving algorithm for large displacement frictionless contact by the prediscretization penalty methodDušan Gabriel, Jiři Plešek, Miran Ulbin, 2004, izvirni znanstveni članek Opis: A threedimensional contact algorithm based on the prediscretization penalty method is presented. Using the prediscretization formulation gives rise to contact searching performed at the surface Gaussian integration points. It is shown that the proposed method is consistent with the continuum formulation ofthe problem and allows an easy incorporation of higherorder elements with midside nodes to the analysis. Moreover, a symmetric treatment of mutually contacting surfaces is preserved even under large displacement increments. Theproposed algorithm utilizes the BFGS method modified for constrained nonlinear systems. The effectiveness of quadratic isoparametric elements in contact analysis is tested in terms of numerical examples verified by analytical solutions and experimental measurements. The symmetry of the algorithm is clearly manifested in the problem of impact of two elastic cylinders. Ključne besede: mechanics, numerical methods, contacting surfaces, contact problems, 3D contact algorithm, discretization, higher order elements, finite element method, Gauss point search, prediscretization penalty method Objavljeno: 01.06.2012; Ogledov: 1456; Prenosov: 37 Povezava na celotno besedilo 
3. Competition between local disordering and global ordering fields in nematic liquid crystalsMatej Cvetko, Milan Ambrožič, Samo Kralj, 2010, izvirni znanstveni članek Opis: We study the influence of external electric or magnetic field B on orientational ordering of nematic liquid crystals or of other rodlike objects (e.g. nanotubes immersed in a liquid) in the presence of random anisotropy field type of disorder. The LebwohlLasher lattice type of semimicroscopic approach is used at zero temperature. Therefore, results are valid well below the transition into the isotropic phase. We calculate the correlation function of systems as a function of B, concentration p of impurities imposing random anisotropy field disorder, the disorder strength W and system dimensionality (2D and 3D systems). In order to probe memory effects we calculate correlation length ▫$xi$▫ for random and homogeneous initial configurations. We determine the crossover fields Bc(p) separating roughly the ordered and disordered regime. Memory effects are apparent only in the latter case, i.e. for B < Bc. Ključne besede: disorder, ImryMa theorem, liquid crystals, memory effect, orientational order Objavljeno: 07.06.2012; Ogledov: 740; Prenosov: 147 Celotno besedilo (747,18 KB) Gradivo ima več datotek! Več...

4. Memory effects in randomly perturbed systems exhibiting continuous symmetry breakingMatej Cvetko, Milan Ambrožič, Samo Kralj, 2009, izvirni znanstveni članek Opis: We studied pattern characteristics in randomly perturbed structures exhibitingcontinuous symmetry breaking. A LebwohlLashertype lattice model was used which described well the onset of orientational ordering of a system of rodlike objects. For example, such systems mimic the orientational ordering tendency in liquid crystals or in an ensemble of nanotubes. We set impurities to impose a random anisotropy type of disorder on the objects. Structural characteristics were studied as a function of concentration of impurities, interaction strength w between impurities and rodlike objects, external ordering strength and history of samples. We showed that the characteristic linear size of patterns and range of ordering strongly depend on the history of samples for weak enough strength w. The twodimensional and threedimensional simulations yielded qualitatively similar results. Ključne besede: liquid crystals, memory effect, nanotubes, structural order, percolation Objavljeno: 07.06.2012; Ogledov: 745; Prenosov: 67 Povezava na celotno besedilo 
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6. 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: 1025; Prenosov: 68 Celotno besedilo (2,86 MB) 
7. Sobol, Zeev; Vogt, Hendrik: On the L[sub]ptheory of C[sub]0semigroups associated with secondorder elliptic operators. I.  J. Funct. Anal. 193, no. 1, 2454 (2002). [ISSN 00221236]Miklavž Mastinšek, 2003, recenzija, prikaz knjige, kritika Ključne besede: matematika, teorija operatorjev, ▫$L_p$▫lastnosti eliptičnih diferencialih operatorjev drugega reda, pozitivne ▫$C_0$▫polgrupe, teorija perturbacij, mathematics, operator theory, ▫$L_p$▫properties of secondorder elliptical differential operators, positive ▫$C_0$▫semigroups, approximations by sectorial forms, perturbation theory of positive operators Objavljeno: 10.07.2015; Ogledov: 280; Prenosov: 6 Povezava na celotno besedilo 
8. Liskevich, Vitali; Sobol, Zeev; Vogt, Hendrik: On the L[sub]ptheory of C[sub]0semigroups associated with secondorder elliptic operators. II.  J. Funct. Anal. 193, no. 1, 5576 (2002). [ISSN 00221236]Miklavž Mastinšek, 2003, recenzija, prikaz knjige, kritika Ključne besede: matematika, teorija operatorjev, ▫$L_p$▫lastnosti eliptičnih diferencialih operatorjev drugega reda, ▫$C_0$▫polgrupe, eliptični operatorji, mathematics, operator theory, ▫$L_p$▫properties of secondorder elliptical differential operators, quasicontractve ▫$C_0$▫semigroups, uniformly elliptic operators Objavljeno: 10.07.2015; Ogledov: 238; Prenosov: 14 Povezava na celotno besedilo 
9. A note on precise tracking of suckling position by pigletsJanko Skok, Dejan Škorjanc, 2014, izvirni znanstveni članek Opis: Piglets establish a relatively stable teat order after the first week of lactation, when each piglet chooses a preferred teat or teat pair where they tend to suckle permanently. The mechanism underlying the choice that leads each piglet to the same suckling position is still not clarified. In the present case study, piglets with different preferred suckling positions (anterior, posterior) were transferred to a foster sow after completion of the regular 4 weeks of lactation by their biological mother. For both sows, which were identical based on parity, litter size and farrowing date, we examined the suckling positions of the experimental piglets. Piglets occupied exactly the same suckling positions on both sows. Thus, piglets precisely track positions on the mammary complex of a sows udder even when previously learned discriminable stimuli have been changed, such as odours, tastes, morphologies (of sows udder or the sow itself), vocalizations, and neighbouring littermates. Our observation indicates that the spatial configuration of the mammary complex, which is determined by two parallel rows of teats arranged in pairs, can hypothetically be proposed as an important cue for piglet suckling orientation. Therefore, additional attention should be given to the exact spatial position of piglets (and vacant positions) on the mammary complex of biological and foster mothers in order to reduce stress from crossfostering, which is standard practice in contemporary piglet production. Ključne besede: piglets, teat order, suckling orientation, mammary complex, spatial configuration Objavljeno: 20.07.2017; Ogledov: 291; Prenosov: 35 Celotno besedilo (1,78 MB) Gradivo ima več datotek! Več...

10. 