2,208 research outputs found
On the nature of the torus in the complex Lorenz equations.
The complex Lorenz equations are a nonlinear fifth-order set of physically derived differential equations which exhibit an exact analytic limit cycle which subsequently bifurcates to a torus. In this paper we build upon previously derived results to examine a connection between this torus at high and low r1 bifurcation parameter) and between zero and nonzero r2(complexity parameter); in so doing, we are able to gain insight on the effect of the rotational invariance of the system, and on how extra weak dispersion (r2 ≠0) affects the chaotic behavior of the real Lorenz system (which describes a weakly dissipative, dispersive instability)
A delay recruitment model of the cardiovascular control system.
Copyright will be owned by Springer. We develop a nonlinear delay-differential equation for the human cardiovascular control system, and use it to explore blood pressure and heart rate variability under short-term baroreflex control. The model incorporates an intrinsically stable heart rate in the absence of nervous control, and features baroreflex influence on both heart rate and peripheral resistance. Analytical simplifications of the model allow a general investigation of the rôles played by gain and delay, and the effects of ageing.
A Dichotomy Theorem for Circular Colouring Reconfiguration
The "reconfiguration problem" for circular colourings asks, given two
-colourings and of a graph , is it possible to transform
into by changing the colour of one vertex at a time such that every
intermediate mapping is a -colouring? We show that this problem can be
solved in polynomial time for and is PSPACE-complete for
. This generalizes a known dichotomy theorem for reconfiguring
classical graph colourings.Comment: 22 pages, 5 figure
Theory of quantum frequency translation of light in optical fiber: application to interference of two photons of different color
We study quantum frequency translation and two-color photon interference
enabled by the Bragg scattering four-wave mixing process in optical fiber.
Using realistic model parameters, we computationally and analytically determine
the Green function and Schmidt modes for cases with various pump-pulse lengths.
These cases can be categorized as either "non-discriminatory" or
"discriminatory" in regards to their propensity to exhibit high-efficiency
translation or high-visibility two-photon interference for many different
shapes of input wave packets or for only a few input wave packets,
respectively. Also, for a particular case, the Schmidt mode set was found to be
nearly equal to a Hermite-Gaussian function set. The methods and results also
apply with little modification to frequency conversion by sum-frequency
conversion in optical crystals
- …