Alexander C. Kalloniatis

Bio: Alexander C. Kalloniatis is an academic researcher from University of Adelaide. The author has contributed to research in topics: Kuramoto model & Quantum chromodynamics. The author has an hindex of 15, co-authored 66 publications receiving 611 citations. Previous affiliations of Alexander C. Kalloniatis include Australian Department of Defence & University of Tasmania.

From incoherence to synchronicity in the network Kuramoto model.

Abstract: We study the synchronization properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronize from the stability of this behavior. While self-synchronization is a consequence of genuine nonperturbative dynamics, the stability in dynamical systems is usually accessible by fluctuations about a fixed point, here taken to be the phase synchronized solution. We examine this problem in terms of modes of the graph Laplacian, by which the absolute Lyapunov stability of the phase synchronized fixed point is readily demonstrated. Departures from stability are seen to arise at the next order in fluctuations where, depending on a truncation in the number of time-dependent Laplacian modes, the dynamical equations can be reduced to forms resembling those for species population models, the logistic and the Lotka-Volterra equations. Methods from these systems are exploited to analytically derive new critical couplings signaling deviation from classical stability. We thereby analytically explain the existence of an intermediate regime of behavior between incoherence and synchronization, where system wide periodic behaviors are exhibited and stable, unstable, and hyperbolic fixed points can be identified. We discuss these results in light of numerical solutions of the equations of motion for various networks.

Lattice Hadron Physics

Abstract: Quenching Effects in Lattice Hadron Physics.- Quark Propagator From LQCD and its Physical Implications.- Generalised Spin Projection for Fermion Actions.- Baryon Spectroscopy in Lattice QCD.- Hadron Structure an QCD: Effective Field Theory for Lattice Simulations.- Lattice Chiral Fermions From Continuum Defects.- Strong and Weak Interactions in a Finite Volume.- Hadron Properties With FLIC Fermions.

Dimensional renormalization: Ladders and rainbows

Abstract: Renormalization factors are most easily extracted by going to the massless limit of the quantum field theory and retaining only a single momentum scale. We derive the factors and renormalized Green{close_quote}s functions to {ital all} orders in perturbation theory for rainbow graphs and vertex (or scattering) diagrams at zero momentum transfer, in the context of dimensional regularization, and we prove that the correct anomalous dimensions for those processes emerge in the limit {ital D}{r_arrow}4. {copyright} {ital 1996 The American Physical Society.}

Discretized light-cone quantization of electrodynamics.

Abstract: Discretized light-cone quantization of (3+1)-dimensional electrodynamics is discussed, with careful attention paid to the interplay between gauge choice and boundary conditions. In the zero longitudinal momentum sector of the theory a general gauge fixing is performed, and the corresponding relations that determine the zero modes of the gauge field are obtained. One particularly natural gauge choice in the zero mode sector is identified, for which the constraint relations are simplest and the fields may be taken to satisfy the usual canonical commutation relations. The constraints are solved in perturbation theory, and the Poincare generators [ital P][sup [mu]] are constructed. The effect of the zero mode contributions on the one-loop fermion self-energy is studied.

Lévy processes and infinitely divisible distributions

Abstract: Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Synchronization in complex oscillator networks and smart grids

Abstract: The emergence of synchronization in a network of coupled oscillators is a fascinating topic in various scientific disciplines. A widely adopted model of a coupled oscillator network is characterized by a population of heterogeneous phase oscillators, a graph describing the interaction among them, and diffusive and sinusoidal coupling. It is known that a strongly coupled and sufficiently homogeneous network synchronizes, but the exact threshold from incoherence to synchrony is unknown. Here, we present a unique, concise, and closed-form condition for synchronization of the fully nonlinear, nonequilibrium, and dynamic network. Our synchronization condition can be stated elegantly in terms of the network topology and parameters or equivalently in terms of an intuitive, linear, and static auxiliary system. Our results significantly improve upon the existing conditions advocated thus far, they are provably exact for various interesting network topologies and parameters; they are statistically correct for almost all networks; and they can be applied equally to synchronization phenomena arising in physics and biology as well as in engineered oscillator networks, such as electrical power networks. We illustrate the validity, the accuracy, and the practical applicability of our results in complex network scenarios and in smart grid applications.