Robustness of planar random graphs to targeted attacks

In this paper, robustness of planar trivalent random graphs to targeted attacks of highest connected nodes is investigated using numerical simulations. It is shown that these graphs are relatively robust. The nonrandom node removal process of targeted attacks is also investigated as a special case of non-uniform site percolation. Critical exponents are calculated by measuring various properties of the distribution of percolation clusters. They are found to be roughly compatible with critical exponents of uniform percolation on these graphs.Comment: 9 pages, 11 figures. Added references.Corrected typos. Paragraph added in section II and in the conclusion. Published versio

Разработка и использование виртуальных лабораторных работ для преподавания дисциплин цикла «Автоматика»

The report describes the cycle of virtual laboratory works on modeling the automatic regulation system parameters of different objects in metallurgy industry, developed at the Department of Thermal Physics and Computer Science in Metallurgy UFU as the part of the development program of the university.В докладе дано описание цикла виртуальных лабораторных работ по моделированию автоматических систем регулирования параметров различных объектов в металлургии, разработанных на кафедре теплофизики и информатики в металлургии УрФУ в рамках программы развития университета

Transition from small to large world in growing networks

We examine the global organization of growing networks in which a new vertex is attached to already existing ones with a probability depending on their age. We find that the network is infinite- or finite-dimensional depending on whether the attachment probability decays slower or faster than $(age)^{-1}$. The network becomes one-dimensional when the attachment probability decays faster than $(age)^{-2}$. We describe structural characteristics of these phases and transitions between them.Comment: 5 page

ИЗУЧЕНИЕ ОПТИЧЕСКИХ СВОЙСТВ КОМПЛЕКСОВ ЦИКЛОДЕКСТРИН-ФОТОСЕНСИБИЛИЗАТОР mTHPC

The photostability of complexes of the mTHPC photosensitizer with different types of cyclodextrins was studied. The photostability is a characteristic of the bond strength of the photosensitizer-carrier complex. The conclusions about the most appropriate type of cyclodextrin for photodynamic therapy were made. The optimal ratio of photosensitizer and carrier concentrations was determined.Исследована фотоустойчивость комплексов фотосенсибилизатора mTHPC с различными типами циклодекстринов, как характеристика прочности связывания фотосенсибилизатора с носителем. Сделаны выводы о наиболее подходящем типе циклодекстрина, для которого определено оптимальное соотношении концентраций фотосенсибилизатор-носитель

Fluctuation-driven capacity distribution in complex networks

Maximizing robustness and minimizing cost are common objectives in the design of infrastructure networks. However, most infrastructure networks evolve and operate in a highly decentralized fashion, which may significantly impact the allocation of resources across the system. Here, we investigate this question by focusing on the relation between capacity and load in different types of real-world communication and transportation networks. We find strong empirical evidence that the actual capacity of the network elements tends to be similar to the maximum available capacity, if the cost is not strongly constraining. As more weight is given to the cost, however, the capacity approaches the load nonlinearly. In particular, all systems analyzed show larger unoccupied portions of the capacities on network elements subjected to smaller loads, which is in sharp contrast with the assumptions involved in (linear) models proposed in previous theoretical studies. We describe the observed behavior of the capacity-load relation as a function of the relative importance of the cost by using a model that optimizes capacities to cope with network traffic fluctuations. These results suggest that infrastructure systems have evolved under pressure to minimize local failures, but not necessarily global failures that can be caused by the spread of local damage through cascading processes

Pseudofractal Scale-free Web

We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent $\gamma=1+\ln3/\ln2$. Properties of this simple structure are surprisingly close to those of growing random scale-free networks with $\gamma$ in the most interesting region, between 2 and 3. We succeed to find exactly and numerically with high precision all main characteristics of the graph. In particular, we obtain the exact shortest-path-length distribution. For the large network ($\ln N \gg 1$) the distribution tends to a Gaussian of width $\sim \sqrt{\ln N}$ centered at $\bar{\ell} \sim \ln N$. We show that the eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail with exponent $2+\gamma$.Comment: 5 pages, 3 figure

Diluted antiferromagnet in a ferromagnetic enviroment

The question of robustness of a network under random ``attacks'' is treated in the framework of critical phenomena. The persistence of spontaneous magnetization of a ferromagnetic system to the random inclusion of antiferromagnetic interactions is investigated. After examing the static properties of the quenched version (in respect to the random antiferromagnetic interactions) of the model, the persistence of the magnetization is analysed also in the annealed approximation, and the difference in the results are discussed

Replica Field Theory for Deterministic Models (II): A Non-Random Spin Glass with Glassy Behavior

We introduce and study a model which admits a complex landscape without containing quenched disorder. Continuing our previous investigation we introduce a disordered model which allows us to reconstruct all the main features of the original phase diagram, including a low $T$ spin glass phase and a complex dynamical behavior.Comment: 35 pages with uu figures, Roma 102

Theory of the first-order isostructural valence phase transitions in mixed valence compounds YbIn_{x}Ag_{1-x}Cu_{4}

For describing the first-order isostructural valence phase transition in mixed valence compounds we develop a new approach based on the lattice Anderson model. We take into account the Coulomb interaction between localized f and conduction band electrons and two mechanisms of electron-lattice coupling. One is related to the volume dependence of the hybridization. The other is related to local deformations produced by f- shell size fluctuations accompanying valence fluctuations. The large f -state degeneracy allows us to use the 1/N expansion method. Within the model we develop a mean-field theory for the first-order valence phase transition in YbInCu_{4}. It is shown that the Coulomb interaction enhances the exchange interaction between f and conduction band electron spins and is the driving force of the phase transition. A comparison between the theoretical calculations and experimental measurements of the valence change, susceptibility, specific heat, entropy, elastic constants and volume change in YbInCu_{4} and YbAgCu_{4} are presented, and a good quantitative agreement is found. On the basis of the model we describe the evolution from the first-order valence phase transition to the continuous transition into the heavy-fermion ground state in the series of compounds YbIn_{1-x}Ag_{x}Cu_{4}. The effect of pressure on physical properties of YbInCu_{4} is studied and the H-T phase diagram is found.Comment: 17 pages RevTeX, 9 Postscript figures, to be submitted to Phys.Rev.