Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations

We study the microscopic time fluctuations of traffic load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates R the traffic is stationary and the load time series exhibits antipersistence due to the regulatory role of the superstructure associated with two hub nodes in the network. We discuss how the superstructure affects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density Rc. Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free flow

Disorder-induced critical behavior in driven diffusive systems

Using dynamic renormalization group we study the transport in driven diffusive systems in the presence of quenched random drift velocity with long-range correlations along the transport direction. In dimensions $d\mathopen< 4$ we find fixed points representing novel universality classes of disorder-dominated self-organized criticality, and a continuous phase transition at a critical variance of disorder. Numerical values of the scaling exponents characterizing the distributions of relaxation clusters are in good agreement with the exponents measured in natural river networks

Graphene membrane as a pressure gauge

Straining graphene results in the appearance of a pseudo-magnetic field which alters its local electronic properties. Applying a pressure difference between the two sides of the membrane causes it to bend/bulge resulting in a resistance change. We find that the resistance changes linearly with pressure for bubbles of small radius while the response becomes non-linear for bubbles that stretch almost to the edges of the sample. This is explained as due to the strong interference of propagating electronic modes inside the bubble. Our calculations show that high gauge factors can be obtained in this way which makes graphene a good candidate for pressure sensing.Comment: 5 pages, 4 figure

Scaling of avalanche queues in directed dissipative sandpiles

We simulate queues of activity in a directed sandpile automaton in 1+1 dimensions by adding grains at the top row with driving rate $0 < r \leq 1$. The duration of elementary avalanches is exactly described by the distribution $P_1(t) \sim t^{-3/2}\exp{(-1/L_c)}$, limited either by the system size or by dissipation at defects $L_c= \min (L,\xi)$. Recognizing the probability $P_1$ as a distribution of service time of jobs arriving at a server with frequency $r$, the model represents a new example of the $$ server queue in the queue theory. We study numerically and analytically the tail behavior of the distributions of busy periods and energy dissipated in the queue and the probability of an infinite queue as a function of driving rate.Comment: 11 pages, 9 figures; To appear in Phys. Rev.

Finite driving rates in interface models of Barkhausen noise

We consider a single-interface model for the description of Barkhausen noise in soft ferromagnetic materials. Previously, the model had been used only in the adiabatic regime of infinitely slow field ramping. We introduce finite driving rates and analyze the scaling of event sizes and durations for different regimes of the driving rate. Coexistence of intermittency, with non-trivial scaling laws, and finite-velocity interface motion is observed for high enough driving rates. Power spectra show a decay $\sim \omega^{-t}$, with $t<2$ for finite driving rates, revealing the influence of the internal structure of avalanches.Comment: 7 pages, 6 figures, RevTeX, final version to be published in Phys. Rev.

Scale-free energy dissipation and dynamic phase transition in stochastic sandpiles

We study numerically scaling properties of the distribution of cumulative energy dissipated in an avalanche and the dynamic phase transition in a stochastic directed cellular automaton [B. Tadi\'c and D. Dhar, Phys. Rev. Lett. {\bf 79}, 1519 (1997)] in d=1+1 dimensions. In the critical steady state occurring for the probability of toppling $p\ge p^\star$= 0.70548, the dissipated energy distribution exhibits scaling behavior with new scaling exponents $\tau_E$ and D_E for slope and cut-off energy, respectively, indicating that the sandpile surface is a fractal. In contrast to avalanche exponents, the energy exponents appear to be p- dependent in the region $p^\star \le p <1$, however the product $(\tau_E-1)D_E$ remains universal. We estimate the roughness exponent of the transverse section of the pile as $\chi =0.44\pm 0.04$. Critical exponents characterizing the dynamic phase transition at $p^\star$ are obtained by direct simulation and scaling analysis of the survival probability distribution and the average outflow current. The transition belongs to a new universality class with the critical exponents $\nu_\| =\gamma =1.22 \pm 0.02$, $\beta =0.56\pm 0.02$ and $\nu_\bot = 0.761 \pm 0.029$, with apparent violation of hyperscaling. Generalized hyperscaling relation leads to $\beta + \beta ^\prime = (d-1)\nu_\bot$, where $\beta ^\prime = 0.195 \pm 0.012$ is the exponent governed by the ultimate survival probability

Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba

Mathematical-geographical analysis of the orientation of St John's church of the Studenica monastery

Considering the fact that ecclesiastical rules do not precisely say that a church must be directed 'to the East' or 'to sunrise', it should always be checked if there is a connection between the orientation of a church and geometry of the Sun. In this paper, such examination is performed on the example of the church of St. John (the 13th century), one of four churches of the Studenica monastery, in the following way: 1) using gnomon method, the azimuth of the main longitudinal axis of the church is measured; 2) the altitude above the horizon of the point in which the extended axis of the church touches the true horizon is determined by cartometry; 3) the most probable dates when the Sun rises at that point are determined: May 7th according to Gregorian calendar, or April 30th according to Julian calendar, in the 13th century. The applied method is described in details and it can be applied for the analysis of the orientation of any other medieval church. This method can determine the time when the church was founded, as well as the fact if the church is original, or possibly erected on the foundations of some older sacral object

Network theory approach for data evaluation in the dynamic force spectroscopy of biomolecular interactions

Investigations of molecular bonds between single molecules and molecular complexes by the dynamic force spectroscopy are subject to large fluctuations at nanoscale and possible other aspecific binding, which mask the experimental output. Big efforts are devoted to develop methods for effective selection of the relevant experimental data, before taking the quantitative analysis of bond parameters. Here we present a methodology which is based on the application of graph theory. The force-distance curves corresponding to repeated pulling events are mapped onto their correlation network (mathematical graph). On these graphs the groups of similar curves appear as topological modules, which are identified using the spectral analysis of graphs. We demonstrate the approach by analyzing a large ensemble of the force-distance curves measured on: ssDNA-ssDNA, peptide-RNA (system from HIV1), and peptide-Au surface. Within our data sets the methodology systematically separates subgroups of curves which are related to different intermolecular interactions and to spatial arrangements in which the molecules are brought together and/or pulling speeds. This demonstrates the sensitivity of the method to the spatial degrees of freedom, suggesting potential applications in the case of large molecular complexes and situations with multiple binding sites

Relativistički model kvarkova

A general Lorentz-covariant quark model of mesons, whose nonrelativistic limit corresponds to Isgur-Scora-Grinstein-Wise model, is constructed. It possesses the heavy quark symmetry and can be easily applied to calculation of form factors. Besides it can be engaged in novel tasks, such a the investigation of the two photon decay of scalar mesons. Its behaviour in the infinite momentum frame and the light cone is discussed.Izveli smo poopćeni Lorentz-kovarijantni model mezona čiji nerelativistički limes odgovara Isgur-Scora-Grinstein-Wiseovom modelu. Model ima teško-kvarkovsku simetriju i može se primijeniti za računanje faktora oblika. Osim toga u ovom se modelu mogu rješavati nove zadaće kao što je dvofotonski raspad skalarnih mezona. Raspravljamo svojstva modela u sustavu beskonačnog impulsa i na svjetlosnom stošcu