Narrow Results

The drift of rigidly rotating spiral waves in an excitable medium induced by synchronous and asynchronous mechanical deformation is investigated numerically and analytically. The resonant drift of spiral waves induced by a mechanical deformation with ω = ω₀ and ω = 3ω₀ is observed. At ω = ω₀, synchronous and greatest degree of asynchronous mechanical deformations are specially investigated. For the case ω = 3ω₀, synchronous mechanism deformation locks the spiral while decreasing of degree of synchronization increases the drift velocity. We derive an approximate but explicit formula of the spiral drift velocity and direction which is consistent with the numerical results.

We study the diffusion of chaotic orbits in an N-body model simulating a barred spiral galaxy. Chaotic orbits with initial conditions outside corotation support the spiral structure of the galaxy due to the phenomenon of stickiness close and along the unstable asymptotic manifolds of the unstable periodic orbits. These orbits are diffused outwards after about 13 rotations of the bar. During this time, the spiral structure is clearly visible and then it fades out gradually. The diffusion time for the majority of the chaotic orbits with initial conditions inside corotation is much longer than the age of the Universe. These orbits support mainly the outer parts of the bar. However, a part of the chaotic orbits inside corotation are diffused outwards fast and support the spiral structure.

Using geometric inversion with respect to the origin, we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann sphere. We study its basic properties, and apply it to the study of the Hopf–Takens bifurcation at infinity.

Spatio-temporal pattern formation has opened up a wide area of research to understand the dynamics between various interacting populations such as a prey and a predator, competing species etc. The governing equations are typically modeled by a reaction–diffusion system. The commonly known patterns, namely, traveling wave, periodic traveling wave, spot, labyrinthine, mixture of spot and stripe, spatio-temporal chaos and interacting spiral chaos can be observed in the spatio-temporal extension of various interacting population models. Apart from these, the other two types of patterns, namely, spiral and target patterns also evolve under suitable parametric conditions near the Turing–Hopf threshold though there is no systematic approach to determine the exact formalism of their emergence. In this paper, we have used a multiscale perturbation analysis to determine these patterns in the spatio-temporal extension of Bazykin’s prey–predator model. An important finding of this work is the use of approximated analytical solution as the initial condition to obtain spiral and target patterns with the help of numerical simulations. Analytical results are general in nature and hence can be used for any spatio-temporal model of interacting population as well as other pattern forming systems which are capable of producing spiral and target patterns.

Although the thermoacoustic refrigeration (TAR) system has been recognized as a potential alternative environmentally cooling system, the low coefficient of performance (COP) has yet to make it marketable. One major factor contributing towards the low COP is the fabrication method applied to the stack component which is the most important component in the TAR. In this paper, comparison of the performance of a (i) 3D printed stack, (ii) a hand fabricated Mylar stack and (iii) an off-the-shelf Celcor substrates stack has been done; these being based on optimized design parameters using Multi-Objective Genetic Algorithm (MOGA). The performance is determined from the temperature attained at the cold end of the stack and the temperature difference across the stack. Experimental results showed that the 3D printed stack has the best performance by achieving a temperature, $T_c=18.9^{\circ }$C at the cold end and a temperature difference of $\mathrm{\Delta }T=18.1^{\circ }$C across the stack, about 60% of the designed temperature difference even though the fabricated 3D printed stack deviated from the optimal design due to fabrication constraint as compared to that of the Mylar stack which was closer to the optimal design. This 3D printing of the stack promises a big potential in the improvement of the TAR performance because of the consistency achievable with the precise dimensions of the stack.