arXiv subjects

Aminur Rahman

Publications and source records attributed to Aminur Rahman.

23 records · Page 2Linked to original sources

arXiv2015

RS Flip-Flop Circuit Dynamics Revisited

Logical RS flip-flop circuits are investigated once again in the context of discrete planar dynamical systems, but this time starting with simple bilinear (minimal) component models based on fundamental principles. The dynamics of the minimal model is described in detail, and shown to exhibit some of the expected properties, but not the chaotic regimes typically found in simulations of physical realizations of chaotic RS flip-flop circuits. Any physical realization of a chaotic logical circuit must necessarily involve small perturbations - usually with quite large or even nonexisting derivatives - and possibly some symmetry-breaking. Therefore, perturbed forms of the minimal model are also analyzed in considerable detail. It is proved that perturbed minimal models can exhibit chaotic regimes, sometimes associated with chaotic strange attractors, as well as some of the bifurcation features present in several more elaborate and less fundamentally grounded dynamical models that have been investigated in the recent literature. Validation of the approach developed is provided by some comparisons with (mainly simulated) dynamical results obtained from more traditional investigations.

nlin.CD↗

arXiv2015

A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment

We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of solitary wave collisions, that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the solitary wave problem, stressing the fundamental role collective-coordinate models played in understanding this phenomenon. We derive the equations governing the motion of a point particle confined to such a surface and then design a surface on which to roll the ball, such that its motion will evolve under the same equations that approximately govern solitary wave collisions. We report on physical experiments, carried out in an undergraduate applied mathematics course, that seem to verify one aspect of chaotic scattering, the so-called two-bounce resonance.

nlin.CD↗

arXiv2014

GPU Accelerated Fractal Image Compression for Medical Imaging in Parallel Computing Platform

In this paper, we implemented both sequential and parallel version of fractal image compression algorithms using CUDA (Compute Unified Device Architecture) programming model for parallelizing the program in Graphics Processing Unit for medical images, as they are highly similar within the image itself. There are several improvement in the implementation of the algorithm as well. Fractal image compression is based on the self similarity of an image, meaning an image having similarity in majority of the regions. We take this opportunity to implement the compression algorithm and monitor the effect of it using both parallel and sequential implementation. Fractal compression has the property of high compression rate and the dimensionless scheme. Compression scheme for fractal image is of two kind, one is encoding and another is decoding. Encoding is very much computational expensive. On the other hand decoding is less computational. The application of fractal compression to medical images would allow obtaining much higher compression ratios. While the fractal magnification an inseparable feature of the fractal compression would be very useful in presenting the reconstructed image in a highly readable form. However, like all irreversible methods, the fractal compression is connected with the problem of information loss, which is especially troublesome in the medical imaging. A very time consuming encoding pro- cess, which can last even several hours, is another bothersome drawback of the fractal compression.

cs.DC↗

arXiv2013

Peixoto's Structural Stability Theorem: The One-dimensional Version

Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in upper level undergraduate courses on dynamical systems or differential equations. This is mainly because of the depth and length of the proofs. In this note/module, we formulate and prove the one-dimensional analogs of Peixoto's theorems in an intuitive and fairly simple way using only concepts and results that for the most part should be familiar to upper level undergraduate students in the mathematical sciences or related fields. The intention is to provide students who may be interested in further study in dynamical systems with an accessible one-dimensional treatment of structural stability theory that should help make Peixoto's theorems and their more recent generalizations easier to appreciate and understand.

math.DS↗

arXiv2013

Discrete Dynamical Modeling and Analysis of the R-S Flip-Flop Circuit

A simple discrete planar dynamical model for the ideal (logical) R-S flip-flop circuit is developed with an eye toward mimicking the dynamical behavior observed for actual physical realizations of this circuit. It is shown that the model exhibits most of the qualitative features ascribed to the R-S flip-flop circuit, such as an intrinsic instability associated with unit set and reset inputs, manifested in a chaotic sequence of output states that tend to oscillate among all possible output states, and the existence of periodic orbits of arbitrarily high period that depend on the various intrinsic system parameters. The investigation involves a combination of analytical methods from the modern theory of discrete dynamical systems, and numerical simulations that illustrate the dazzling array of dynamics that can be generated by the model. Validation of the discrete model is accomplished by comparison with certain Poincaré map like representations of the dynamics corresponding to three-dimensional differential equation models of electrical circuits that produce R-S flip-flop behavior.

math.DS↗