37,242 research outputs found
Dispersal and noise: Various modes of synchrony in\ud ecological oscillators
We use the theory of noise-induced phase synchronization to analyze the effects of dispersal on the synchronization of a pair of predator-prey systems within a fluctuating environment (Moran effect). Assuming that each isolated local population acts as a limit cycle oscillator in the deterministic limit, we use phase reduction and averaging methods to derive a FokkerâPlanck equation describing the evolution of the probability density for pairwise phase differences between the oscillators. In the case of common environmental noise, the oscillators ultimately synchronize. However the approach to synchrony depends on whether or not dispersal in the absence of noise supports any stable asynchronous states. We also show how the combination of correlated (shared) and uncorrelated (unshared) noise with dispersal can lead to a multistable\ud
steady-state probability density
Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems
We consider an exit-time minimum problem with a running cost, and
unbounded controls. The occurrence of points where can be regarded as a
transversality loss. Furthermore, since controls range over unbounded sets, the
family of admissible trajectories may lack important compactness properties. In
the first part of the paper we show that the existence of a -minimum
restraint function provides not only global asymptotic controllability (despite
non-transversality) but also a state-dependent upper bound for the value
function (provided ). This extends to unbounded dynamics a former result
which heavily relied on the compactness of the control set.
In the second part of the paper we apply the general result to the case when
the system is polynomial in the control variable. Some elementary, algebraic,
properties of the convex hull of vector-valued polynomials' ranges allow some
simplifications of the main result, in terms of either near-affine-control
systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344
Cusp-scaling behavior in fractal dimension of chaotic scattering
A topological bifurcation in chaotic scattering is characterized by a sudden
change in the topology of the infinite set of unstable periodic orbits embedded
in the underlying chaotic invariant set. We uncover a scaling law for the
fractal dimension of the chaotic set for such a bifurcation. Our analysis and
numerical computations in both two- and three-degrees-of-freedom systems
suggest a striking feature associated with these subtle bifurcations: the
dimension typically exhibits a sharp, cusplike local minimum at the
bifurcation.Comment: 4 pages, 4 figures, Revte
Dissipative chaotic scattering
We show that weak dissipation, typical in realistic situations, can have a
metamorphic consequence on nonhyperbolic chaotic scattering in the sense that
the physically important particle-decay law is altered, no matter how small the
amount of dissipation. As a result, the previous conclusion about the unity of
the fractal dimension of the set of singularities in scattering functions, a
major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte
CFD analysis of jet mixing in low NOx flametube combustors
The Rich-burn/Quick-mix/Lean-burn (RQL) combustor was identified as a potential gas turbine combustor concept to reduce NO(x) emissions in High Speed Civil Transport (HSCT) aircraft. To demonstrate reduced NO(x) levels, cylindrical flametube versions of RQL combustors are being tested at NASA Lewis Research Center. A critical technology needed for the RQL combustor is a method of quickly mixing by-pass combustion air with rich-burn gases. Jet mixing in a cylindrical quick-mix section was numerically analyzed. The quick-mix configuration was five inches in diameter and employed twelve radial-inflow slots. The numerical analyses were performed with an advanced, validated 3-D Computational Fluid Dynamics (CFD) code named REFLEQS. Parametric variation of jet-to-mainstream momentum flux ratio (J) and slot aspect ratio was investigated. Both non-reacting and reacting analyses were performed. Results showed mixing and NO(x) emissions to be highly sensitive to J and slot aspect ratio. Lowest NO(x) emissions occurred when the dilution jet penetrated to approximately mid-radius. The viability of using 3-D CFD analyses for optimizing jet mixing was demonstrated
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