Multistability for nonlinear acoustic-gravity waves in a rotating atmosphere.

The multistable states of low-frequency, short-wavelength nonlinear acoustic-gravity waves propagating in a small slope with respect to the vertical ones are explored in a rotating atmosphere. The bifurcation patterns en route to irregular behaviors and the long-term dynamics of the low-order nonlinear model system are studied for varying air Prandtl number σ between 0.5 and 1. In contrast to non-rotation, the transition to the unsteady motion occurs both catastrophically and non-catastrophically due to the Earth's rotation. The connections between the Prandtl number and the slope parameter on the stabilities of the system are highlighted. The model system exhibits hysteresis-induced multistability with coexisting finite multi-periodic, periodic-chaotic attractors in certain parameter spaces depending on the initial conditions. Studies revealed that the rotation parameter instigates these heterogeneous coexisting attractors, resulting in the unpredictable dynamics. However, the relevance of this study is strongly restricted to a very small vertical wavelength, a small slope, and a weakly stratified atmosphere.

Organized structures of two bidirectionally coupled logistic maps.

We report some organized structures of two linearly coupled logistic maps with different harvesting. The coupled system exhibits chaos via period-bubbling and quasiperiodic routes for identical and weak coupling strength, in contrast to conventional period-doubling route for a simple logistic map. Studies reveal the existence of infinite families of periodic Arnold tongues and self-similar shrimp-shaped structures with period-adding sequences for periodic windows embedded in quasiperiodic and chaotic regions, respectively. Different Fibonacci-like sequences are formed leading to the Golden Mean. The shrimp-shaped structures maintain period 3-times self-similarity scaling. The quasiperiodicity route is the necessary condition for the occurrence of periodic Arnold tongues in this coupled system resulting in the appearance of shrimps in the chaotic region near the tongues. It is also revealed that the existence of shrimp implies the period-bubbling cascade but the reverse is not true. The bifurcation-induced hysteresis is born in a certain parameter range resulting in the birth of coexisting multiple attractors of different kinds. Basin sets of the coexisting attractors have either self-similar or intertwining fractal basin boundaries.

Numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses.

An updated numerical simulation of unsteady generalized Newtonian blood flow through differently shaped distensible arterial stenoses is developed. A shear-thinning fluid modelling the deformation dependent viscosity of blood is considered for the characterization of generalized Newtonian behaviour of blood. The arterial model is treated as two-dimensional and axisymmetric with an outline of the stenosis obtained from a three-dimensional casting of a mildly stenosed artery. The full Navier-Stokes equations governing blood flow are written in the dimensionless form and the solution is accomplished by finite time-step advancement through their finite difference staggered grid representations. The marker and cell (MAC) method comprising the use of a set of marker particles moving with the fluid is used for the purpose. Results are obtained for three differently shaped stenoses - irregular, smooth and cosine curve representations. The present results do agree well with those of existing investigations in the steady state, but contrary to their conclusions the present findings demonstrate that the excess pressure drop across the cosine and the smooth stenoses is caused by neither their smoothness nor their higher degree of symmetry relative to the irregular stenosis, but is rather an effect of area cover with respect to the irregular stenosis. This effect clearly prevails throughout the entire physiological range of Reynolds numbers. Further the in-depth study in flow patterns reveals the development of flow separation zones in the diverging part of the stenosis towards the arterial wall, and they are influenced by non-Newtonian blood rheology, distensibility of the wall and flow unsteadiness in order to validate the applicability of the present model.