Fractional vortices in the XY model with π\pi bonds

We define a new set of excitations in the XY model which we call ``fractional vortices''. In the frustrated XY model containing $\pi$ bonds, we make the ansatz that the ground state configurations can be characterized by pairs of oppositely charged fractional vortices. For a chain of $\pi$ bonds, the ground state energy and the phase configurations calculated on the basis of this ansatz agree well with the results from direct numerical simulations. Finally, we discuss the possible connection of these results to some recent experiments by Kirtley {\it et al} [Phys. Rev. B {\bf 51}, R12057 (1995)] on high-T$_c$ superconductors where fractional flux trapping was observed along certain grain boundaries.Comment: 13 pages, 14 figures included (.eps). No essential differences to previous version, however more compact forma

Emergence of weight-topology correlations in complex scale-free networks

Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can emerge from the same simple growth dynamics of the node connectivities and of the link weights. A weighted fitness network is introduced in which both nodes and links are assigned intrinsic fitness. This model can show a local dependence of the weight-topology correlations and can undergo a phase transition to a state in which the network is dominated by few links which acquire a finite fraction of the total weight of the network.Comment: (4 pages,3 figures

Theory of Two-Dimensional Josephson Arrays in a Resonant Cavity

We consider the dynamics of a two-dimensional array of underdamped Josephson junctions placed in a single-mode resonant cavity. Starting from a well-defined model Hamiltonian, which includes the effects of driving current and dissipative coupling to a heat bath, we write down the Heisenberg equations of motion for the variables of the Josephson junction and the cavity mode, extending our previous one-dimensional model. In the limit of large numbers of photons, these equations can be expressed as coupled differential equations and can be solved numerically. The numerical results show many features similar to experiment. These include (i) self-induced resonant steps (SIRS's) at voltages V = (n hbar Omega)/(2e), where Omega is the cavity frequency, and n is generally an integer; (ii) a threshold number N_c of active rows of junctions above which the array is coherent; and (iii) a time-averaged cavity energy which is quadratic in the number of active junctions, when the array is above threshold. Some differences between the observed and calculated threshold behavior are also observed in the simulations and discussed. In two dimensions, we find a conspicuous polarization effect: if the cavity mode is polarized perpendicular to the direction of current injection in a square array, it does not couple to the array and there is no power radiated into the cavity. We speculate that the perpendicular polarization would couple to the array, in the presence of magnetic-field-induced frustration. Finally, when the array is biased on a SIRS, then, for given junction parameters, the power radiated into the array is found to vary as the square of the number of active junctions, consistent with expectations for a coherent radiation.Comment: 11 pages, 8 eps figures, submitted to Phys. Rev

Several small Josephson junctions in a Resonant Cavity: Deviation from the Dicke Model

We have studied quantum-mechanically a system of several small identical Josephson junctions in a lossless single-mode cavity for different initial states, under conditions such that the system is at resonance. This system is analogous to a collection of identical atoms in a cavity, which is described under appropriate conditions by the Dicke model. We find that our system can be well approximated by a reduced Hamiltonian consisting of two levels per junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but contains an additional term resembling a dipole-dipole interaction between the junctions. This extra term arises when states outside the degenerate group are included via degenerate second-order (L\"{o}wdin) perturbation theory. As in the Dicke model, we find that, when N junctions are present in the cavity, the oscillation frequency due to the junction-cavity interaction is enhanced by $\sqrt{N}$. The corresponding decrease in the Rabi oscillation period may cause it to be smaller than the decoherence time due to dissipation, making these oscillations observable. Finally, we find that the frequency enhancement survives even if the junctions differ slightly from one another, as expected in a realistic system.Comment: 11 pages. To be published in Phys. Rev.

Scaling Properties of Random Walks on Small-World Networks

Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These properties include the average number of distinct sites visited by the random walker, the mean-square displacement of the walker, and the distribution of first-return times. The scaling form has three characteristic time regimes. At short times, the walker does not see the small-world shortcuts and effectively probes an ordinary Euclidean network in $d$-dimensions. At intermediate times, the properties of the walker shows scaling behavior characteristic of an infinite small-world network. Finally, at long times, the finite size of the network becomes important, and many of the properties of the walker saturate. We propose general analytical forms for the scaling properties in all three regimes, and show that these analytical forms are consistent with our numerical simulations.Comment: 7 pages, 8 figures, two-column format. Submitted to PR

An investigation into the efficacy of avatar-based systems for student advice

Student support is an important function in all universities. Most students expect access to support 24/7, but support staff cannot be available at all times of day. This paper addresses this problem, describing the development of an avatar-based system to guide students through the materials provided by a university student employability service. Firstly, students and staff were surveyed to establish the demand for such a system. The system was then constructed. Finally, the system was evaluated by students and staff, which led to a clearer understanding of the optimal role for avatar-based systems and consequent improvements to the system’s functionality

Exact results and scaling properties of small-world networks

We study the distribution function for minimal paths in small-world networks. Using properties of this distribution function, we derive analytic results which greatly simplify the numerical calculation of the average minimal distance, $\bar{\ell}$, and its variance, $\sigma^2$. We also discuss the scaling properties of the distribution function. Finally, we study the limit of large system sizes and obtain some analytic results.Comment: RevTeX, 4 pages, 5 figures included. Minor corrections and addition

The solution space of metabolic networks: producibility, robustness and fluctuations

Flux analysis is a class of constraint-based approaches to the study of biochemical reaction networks: they are based on determining the reaction flux configurations compatible with given stoichiometric and thermodynamic constraints. One of its main areas of application is the study of cellular metabolic networks. We briefly and selectively review the main approaches to this problem and then, building on recent work, we provide a characterization of the productive capabilities of the metabolic network of the bacterium E.coli in a specified growth medium in terms of the producible biochemical species. While a robust and physiologically meaningful production profile clearly emerges (including biomass components, biomass products, waste etc.), the underlying constraints still allow for significant fluctuations even in key metabolites like ATP and, as a consequence, apparently lay the ground for very different growth scenarios.Comment: 10 pages, prepared for the Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japa

Dynamics of a Josephson Array in a Resonant Cavity

We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B {\bf 63}, 144522 (2001); Phys. Rev. B {\bf 64}, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman {\it et al} [Phys. Rev. Lett. {\bf 79}, 2371 (1997)] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when $N_a$ active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in $N_a$, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.Comment: 15 pages, 10 eps figures, submitted to Phys. Rev.