Mapping Fusion and Synchronized Hyperedge Replacement into Logic Programming

In this paper we compare three different formalisms that can be used in the area of models for distributed, concurrent and mobile systems. In particular we analyze the relationships between a process calculus, the Fusion Calculus, graph transformations in the Synchronized Hyperedge Replacement with Hoare synchronization (HSHR) approach and logic programming. We present a translation from Fusion Calculus into HSHR (whereas Fusion Calculus uses Milner synchronization) and prove a correspondence between the reduction semantics of Fusion Calculus and HSHR transitions. We also present a mapping from HSHR into a transactional version of logic programming and prove that there is a full correspondence between the two formalisms. The resulting mapping from Fusion Calculus to logic programming is interesting since it shows the tight analogies between the two formalisms, in particular for handling name generation and mobility. The intermediate step in terms of HSHR is convenient since graph transformations allow for multiple, remote synchronizations, as required by Fusion Calculus semantics.Comment: 44 pages, 8 figures, to appear in a special issue of Theory and Practice of Logic Programming, minor revisio

Quantum Rabi model for N-state atoms

A tractable N-state Rabi Hamiltonian is introduced by extending the parity symmetry of the two-state model. The single-mode case provides a few-parameter description of a novel class of periodic systems, predicting that the ground state of certain four-state atom-cavity systems will undergo parity change at strong coupling. A group-theoretical treatment provides physical insight into dynamics and a modified rotating wave approximation obtains accurate analytical energies. The dissipative case can be applied to study excitation energy transfer in molecular rings or chains.Comment: 5 pages, 3 figures + supplement (2 pages); to appear in Phys. Rev. Let

The Ising model and planar N=4 Yang-Mills

The scattering-matrix for planar Yang-Mills with N=4 supersymmetry relies on the assumption that integrability holds to all orders in perturbation theory. In this note we define a map from the spectral variables x^{\pm}, parameterizing the long-range magnon momenta, to couplings in a two-dimensional Ising model. Under this map integrability of planar N=4 Yang-Mills becomes equivalent to the Yang-Baxter equation for the two-dimensional Ising model, and the long-range variables x^{\pm} translate into the entries of the Ising transfer matrices. We explore the Ising correlation length which equals the inverse magnon momentum in the small momentum limit. The critical regime is thus reached for vanishing magnon momentum. We also discuss the meaning of the Kramers-Wannier duality transformation on the gauge theory, together with that of the Ising model critical points.Comment: 24 pages. v2: References added and minor typos correcte

Interface growth in two dimensions: A Loewner-equation approach

The problem of Laplacian growth in two dimensions is considered within the Loewner-equation framework. Initially the problem of fingered growth recently discussed by Gubiec and Szymczak [T. Gubiec and P. Szymczak, Phys. Rev. E 77, 041602 (2008)] is revisited and a new exact solution for a three-finger configuration is reported. Then a general class of growth models for an interface growing in the upper-half plane is introduced and the corresponding Loewner equation for the problem is derived. Several examples are given including interfaces with one or more tips as well as multiple growing interfaces. A generalization of our interface growth model in terms of ``Loewner domains,'' where the growth rule is specified by a time evolving measure, is briefly discussed.Comment: To appear in Physical Review

Nonlinear mode coupling in rotating stars and the r-mode instability in neutron stars

We develop the formalism required to study the nonlinear interaction of modes in rotating Newtonian stars in the weakly nonlinear regime. The formalism simplifies and extends previous treatments. At linear order, we elucidate and extend slightly a formalism due to Schutz, show how to decompose a general motion of a rotating star into a sum over modes, and obtain uncoupled equations of motion for the mode amplitudes under the influence of an external force. Nonlinear effects are added perturbatively via three-mode couplings. We describe a new, efficient way to compute the coupling coefficients, to zeroth order in the stellar rotation rate, using spin-weighted spherical harmonics. We apply this formalism to derive some properties of the coupling coefficients relevant to the nonlinear interactions of unstable r-modes in neutron stars, postponing numerical integrations of the coupled equations of motion to a later paper. From an astrophysical viewpoint, the most interesting result of this paper is that many couplings of r-modes to other rotational modes (modes with zero frequencies in the non-rotating limit) are small: either they vanish altogether because of various selection rules, or they vanish to lowest order in the angular velocity. In zero-buoyancy stars, the coupling of three r-modes is forbidden entirely and the coupling of two r-modes to one hybrid rotational mode vanishes to zeroth order in rotation frequency. In incompressible stars, the coupling of any three rotational modes vanishes to zeroth order in rotation frequency.Comment: 62 pages, no figures. Corrected error in computation of coupling coefficients, added new selection rule and an appendix on energy and angular momentum of mode

Extended Connectors: Structuring Glue Operators in BIP

Based on a variation of the BIP operational semantics using the offer predicate introduced in our previous work, we extend the algebras used to model glue operators in BIP to encompass priorities. This extension uses the Algebra of Causal Interaction Trees, T(P), as a pivot: existing transformations automatically provide the extensions for the Algebra of Connectors. We then extend the axiomatisation of T(P), since the equivalence induced by the new operational semantics is weaker than that induced by the interaction semantics. This extension leads to canonical normal forms for all structures and to a simplification of the algorithm for the synthesis of connectors from Boolean coordination constraints.Comment: In Proceedings ICE 2013, arXiv:1310.401

Asymptotology of Chemical Reaction Networks

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed.Comment: 23 pages, 8 figures, 84 refs, Corrected Journal Versio

Among-site variability in the stochastic dynamics of East African coral reefs

Coral reefs are dynamic systems whose composition is highly influenced by unpredictable biotic and abiotic factors. Understanding the spatial scale at which long-term predictions of reef composition can be made will be crucial for guiding conservation efforts. Using a 22-year time series of benthic composition data from 20 reefs on the Kenyan and Tanzanian coast, we studied the long-term behaviour of Bayesian vector autoregressive state-space models for reef dynamics, incorporating among-site variability. We estimate that if there were no among-site variability, the total long-term variability would be approximately one third of its current value. Thus among-site variability contributes more to long-term variability in reef composition than does temporal variability. Individual sites are more predictable than previously thought, and predictions based on current snapshots are informative about long-term properties. Our approach allowed us to identify a subset of possible climate refugia sites with high conservation value, where the long-term probability of coral cover <= 0.1 was very low. Analytical results show that this probability is most strongly influenced by among-site variability and by interactions among benthic components within sites. These findings suggest that conservation initiatives might be successful at the site scale as well as the regional scale.Comment: 97 pages, 49 figure