Abstract: The present paper expands details and confirms the transition mechanism between two subsequent polygonal patterns of the hollow-core vortex. Using power spectral analysis, we confirm in this work that the transition from any N-gon to (N+1)-gon pattern observed within a hollow-core vortex of shallow rotating flows occurs in two steps. The regime was quasi-periodic before the frequencies lock (synchronization). The ratios of locking frequencies were found to be equal to (N-1)/N.
Abstract: Water suspensions of in-organic (metals and oxides)
and organic nano-objects (chitozan and collagen) were subjected to
the treatment of direct and alternative electrical fields. In addition to
quasi-periodical spatial patterning resonance-like performance of
spatial distributions of these suspensions has been found at low
frequencies of alternating electrical field. These resonances are
explained as the result of creation of equilibrium states of groups of
charged nano-objects with opposite signs of charges at the interparticle
distances where the forces of Coulomb attraction are
compensated by the repulsion forces induced by relatively negative
polarization of hydrated regions surrounding the nanoparticles with
respect to pure water. The low frequencies of these resonances are
explained by comparatively big distances between the particles and
their big masses with t\respect to masses of atoms constituting
molecules with high resonance frequencies. These new resonances
open a new approach to detailed modeling and understanding of
mechanisms of the influence of electrical fields on the functioning of
internal organs of living organisms at the level of cells and neurons.
Abstract: We report the design and characterization of ultra high
quality factor filter based on one-dimensional photonic-crystal Thue-
Morse sequence structure. The behavior of aperiodic array of
photonic crystal structure is numerically investigated and we show
that by changing the angle of incident wave, desired wavelengths
could be tuned and a tunable filter is realized. Also it is shown that
high quality factor filter be achieved in the telecommunication
window around 1550 nm, with a device based on Thue-Morse
structure. Simulation results show that the proposed structure has a
quality factor more than 100000 and it is suitable for DWDM
communication applications.
Abstract: An Ivlev-type predator-prey system and stage-structured for predator concerning impulsive control strategy is considered. The conditions for the locally asymptotically stable prey-eradication periodic solution is obtained, by using Floquet theorem and small amplitude perturbation skills——when the impulsive period is less than the critical value. Otherwise, the system is permanence. Numerical examples show that the system considered has more complicated dynamics, including high-order quasi-periodic and periodic oscillating, period-doubling and period-halving bifurcation, chaos and attractor crisis, etc. Finally, the biological implications of the results and the impulsive control strategy are discussed.
Abstract: DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.
Abstract: We investigate properties of convective solutions of the
Boussinesq thermal convection in a moderately rotating spherical
shell allowing the inner and outer sphere rotation due to the viscous
torque of the fluid. The ratio of the inner and outer radii of the
spheres, the Prandtl number and the Taylor number are fixed to 0.4,
1 and 5002, respectively. The inertial moments of the inner and outer
spheres are fixed to about 0.22 and 100, respectively. The Rayleigh
number is varied from 2.6 × 104 to 3.4 × 104. In this parameter
range, convective solutions transit from equatorially symmetric quasiperiodic
ones to equatorially asymmetric chaotic ones as the Rayleigh
number is increased. The transition route in the system allowing
rotation of both the spheres is different from that in the co-rotating
system, which means the inner and outer spheres rotate with the
same constant angular velocity: the convective solutions transit as
equatorially symmetric quasi-periodic solution → equatorially symmetric
chaotic solution → equatorially asymmetric chaotic solution
in the system allowing both the spheres rotation, while equatorially
symmetric quasi-periodic solution → equatorially asymmetric quasiperiodic
solution → equatorially asymmetric chaotic solution in the
co-rotating system.
Abstract: This paper numerically investigates the effects of input
speed on the overall dynamic characteristics of a multi-body system
with differently located revolute clearance joints without friction. A
typical planar slider-crank mechanism is used as a demonstration case
in which the effects of the input speed on the dynamic performance
of the mechanism with a revolute clearance joint between the crank
and connecting rod, and between the connecting rod and slider are
separately investigated with comprehensive observations numerically
presented. It is observed that, changing the driving speed of a multibody
system makes the behavior of the system to change from
either periodic to chaotic, or chaotic to periodic depending on which
joint has clearance. The location of the clearance revolute joint and
the operating speed of a multi-body system play a crucial role in
predicting accurately the dynamic responses of the system. Therefore
the dynamic behavior of one clearance revolute joint cannot be used
as a general case for a mechanical system.