Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system

We study the problem of initiation of excitation waves in the FitzHugh-Nagumo model. Our approach follows earlier works and is based on the idea of approximating the boundary between basins of attraction of propagating waves and of the resting state as the stable manifold of a critical solution. Here, we obtain analytical expressions for the essential ingredients of the theory by singular perturbation using two small parameters, the separation of time scales of the activator and inhibitor, and the threshold in the activator's kinetics. This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2

Stokes phenomenon and matched asymptotic expansions

This paper describes the use of matched asymptotic expansions to illuminate the description of functions exhibiting Stokes phenomenon. In particular the approach highlights the way in which the local structure and the possibility of finding Stokes multipliers explicitly depend on the behaviour of the coefficients of the relevant asymptotic expansions

Scavenging by threatened turtles regulates freshwater ecosystem health during fish kills

Humans are increasing the frequency of fish kills by degrading freshwater ecosystems. Simultaneously, scavengers like freshwater turtles are declining globally, including in the Australian Murray–Darling Basin. Reduced scavenging may cause water quality problems impacting both ecosystems and humans. We used field and mesocosm experiments to test whether scavenging by turtles regulates water quality during simulated fish kills. In the field, we found that turtles were important scavengers of fish carrion. In mesocosms, turtles rapidly consumed carrion, and water quality in mesocosms with turtles returned to pre-fish kill levels faster than in turtle-free controls. Our experiments have important ecological implications, as they suggest that turtles are critical scavengers that regulate water quality in freshwater ecosystems. Recovery of turtle populations may be necessary to avoid the worsening of ecosystem health, particularly after fish kills, which would have devastating consequences for many freshwater species

A complex ray-tracing tool for high-frequency mean-field flow interaction effects in jets

This paper presents a complex ray-tracing tool for the calculation of high-frequency Green’s functions in 3D mean field jet flows. For a generic problem, the ray solution suffers from three main deficiencies: multiplicity of solutions, singularities at caustics, and the determining of complex solutions. The purpose of this paper is to generalize, combine and apply existing stationary media methods to moving media scenarios. Multiplicities are dealt with using an equivalent two-point boundary-value problem, whilst non-uniformities at caustics are corrected using diffraction catastrophes. Complex rays are found using a combination of imaginary perturbations, an assumption of caustic stability, and analytic continuation of the receiver curve. To demonstrate this method, the ray tool is compared against a high-frequency modal solution of Lilley’s equation for an off-axis point source. This solution is representative of high-frequency source positions in real jets and is rich in caustic structures. A full utilization of the ray tool is shown to provide excellent results<br/

A new method for the solution of the Schrodinger equation

We present a new method for the solution of the Schrodinger equation applicable to problems of non-perturbative nature. The method works by identifying three different scales in the problem, which then are treated independently: An asymptotic scale, which depends uniquely on the form of the potential at large distances; an intermediate scale, still characterized by an exponential decay of the wave function and, finally, a short distance scale, in which the wave function is sizable. The key feature of our method is the introduction of an arbitrary parameter in the last two scales, which is then used to optimize a perturbative expansion in a suitable parameter. We apply the method to the quantum anharmonic oscillator and find excellent results.Comment: 4 pages, 4 figures, RevTex

Private trade and monopoly structures : the East India Companies and the commodity trade to Europe in the eighteenth century

Our research is about the trade in material goods from Asia to Europe over this period, and its impact on Europe’s consumer and industrial cultures. It entails a comparative study of Europe’s East India Companies and the private trade from Asia over the period. The commodities trade was heavily dependent on private trade. The historiography to date has left a blind spot in this area, concentrating instead on corruption and malfeasance. Taking a global history approach we investigate the trade in specific consumer goods in many qualities and varieties that linked merchant communities and stimulated information flows. We set out how private trade functioned alongside and in connection with the various European East India companies; we investigate how this changed over time, how it drew on the Company infrastructure, and how it took the risks and developed new and niche markets for specific Asian commodities that the Companies could not sustain

Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions

We have extended, from order 12 through order 25, the high-temperature series expansions (in zero magnetic field) for the spin-spin correlations of the spin-S Ising models on the square, simple-cubic and body-centered-cubic lattices. On the basis of this large set of data, we confirm accurately the validity of the scaling and universality hypotheses by resuming several tests which involve the correlation function, its moments and the exponential or the second-moment correlation-lengths.Comment: 21 pages, 8 figure