2,034 research outputs found
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
The Invisible Thin Red Line
The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)âs non-standard tense realism, according to which reality is divided up into maximally coherent collections of tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world
The bearable lightness of being
How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories-such as object, property, and relation-are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical form: for example, the question whether there are numbers is the question whether there are true atomic statements in which expressions function as singular terms which, if they have reference at all, stand for numbers, and the question whether there are properties of a given type is a question about whether there are meaningful predicates of an appropriate degree and level. This approach is defended against the objection that it must be wrong because makes what there depend on us or our language. Some problems confronting the Fregean approach-including Frege's notorious paradox of the concept horse-are addressed. It is argued that the approach results in a modest and sober deflationary understanding of ontological commitments
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 Greenâs 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 Lilleyâs 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/
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 MurrayâDarling 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 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
Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation
We introduce an alternative to the method of matched asymptotic expansions.
In the "traditional" implementation, approximate solutions, valid in different
(but overlapping) regions are matched by using "intermediate" variables. Here
we propose to match at the level of the equations involved, via a "uniform
expansion" whose equations enfold those of the approximations to be matched.
This has the advantage that one does not need to explicitly solve the
asymptotic equations to do the matching, which can be quite impossible for some
problems. In addition, it allows matching to proceed in certain wave situations
where the traditional approach fails because the time behaviors differ (e.g.,
one of the expansions does not include dissipation). On the other hand, this
approach does not provide the fairly explicit approximations resulting from
standard matching. In fact, this is not even its aim, which to produce the
"simplest" set of equations that capture the behavior
Criteria for 2D kinematics in an interacting Fermi gas
Ultracold Fermi gases subject to tight transverse confinement offer a highly
controllable setting to study the two-dimensional (2D) BCS to
Berezinskii-Kosterlitz-Thouless superfluid crossover. Achieving the 2D regime
requires confining particles to their transverse ground state which presents
challenges in interacting systems. Here, we establish the conditions for an
interacting Fermi gas to behave kinematically 2D. Transverse excitations are
detected by measuring the transverse expansion rate which displays a sudden
increase when the atom number exceeds a critical value signifying a
density driven departure from 2D kinematics. For weak interactions is
set by the aspect ratio of the trap. Close to a Feshbach resonance, however,
the stronger interactions reduce and excitations appear at lower
density.Comment: Replaced with published version, includes supplementary informatio
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