21 citations · 110 across the 20 of their papers we have counts for
21 papers
Multi-bounce resonances in the interaction of walking droplets
George Zhang, Ivan C. Christov, Aminur Rahman
Discrete dynamical models of walking droplets ("walkers") have allowed swift numerical experiments revealing heretofore unobserved quantum statistics and related behaviors in a cla…
The One-dimensional Version of Peixoto's Structural Stability Theorem: A Calculus-based Proof
Aminur Rahman, Denis Blackmore
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,…
Stochastic discrete dynamical model for the hydrodynamic analog of a quantum mirage
Gonzalo Ferrandez Quinto, Aminur Rahman
Recently discrete dynamical models of walking droplet dynamics have allowed for fast numerical simulations of their horizontal chaotic motion and consequently the long-time statist…
Deep Learning Based Object Tracking in Walking Droplet and Granular Intruder Experiments
Erdi Kara, George Zhang, Joseph J. Williams +5
We present a deep-learning based tracking objects of interest in walking droplet and granular intruder experiments. In a typical walking droplet experiment, a liquid droplet, known…
Damped-driven system of bouncing droplets leading to deterministic diffusive behavior
Aminur Rahman
Damped-driven systems are ubiquitous in science, however the damping and driving mechanisms are often quite convoluted. This manuscript presents an experimental and theoretical inv…
Universal Dynamics of Damped-Driven Systems: The Logistic Map as a Normal Form for Energy Balance
J. Nathan Kutz, Aminur Rahman, Megan R. Ebers +2
Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities…
Spatio-temporal models of infectious disease with high rates of asymptomatic transmission
Aminur Rahman, Angela Peace, Ramesh Kesawan +1
The surprisingly mercurial Covid-19 pandemic has highlighted the need to not only accelerate research on infectious disease, but to also study them using novel techniques and persp…
Walking droplets as a damped-driven system
Aminur Rahman, J. Nathan Kutz
We consider the dynamics of a droplet on a vibrating fluid bath. This hydrodynamic quantum analog system is shown to elicit the canonical behavior of damped-driven systems, includi…
Walking Droplets Through the Lens of Dynamical Systems
Aminur Rahman, Denis Blackmore
Over the past decade the study of fluidic droplets bouncing and skipping (or ``walking'') on a vibrating fluid bath has gone from an interesting experiment to a vibrant research fi…
Tumor ablation due to inhomogeneous -- anisotropic diffusion in generic 3-dimensional topologies
Erdi Kara, Aminur Rahman, Eugenio Aulisa +1
We derive a full 3-dimensional (3-D) model of inhomogeneous -- anisotropic diffusion in a tumor region coupled to a binary population model. The diffusion tensors are acquired usin…
Generalized Attracting Horseshoe in the Rössler Attractor
Karthik Murthy, Parth Sojitra, Aminur Rahman +2
We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations - realizable by a rather simple electronic circuit - capable of producing a gen…
Modeling of drug diffusion in a solid tumor leading to tumor cell death
Aminur Rahman, Souparno Ghosh, Ranadip Pal
It has been shown recently that changing the fluidic properties of a drug can improve its efficacy in ablating solid tumors. We develop a modeling framework for tumor ablation, and…
Standard map-like models for single and multiple walkers in an annular cavity
Aminur Rahman
Recent experiments on walking droplets in an annular cavity showed the existence of complex dynamics including chaotically changing velocity. This article presents models, influenc…
Exotic Bifurcations Inspired by Walking Droplet Dynamics
Aminur Rahman, Denis Blackmore
We identify two rather novel types of (compound) dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifold…
Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops
Aminur Rahman, Ian Jordan, Denis Blackmore
It has been observed through experiments and SPICE simulations that logical circuits based upon Chua's circuit exhibit complex dynamical behavior. This behavior can be used to desi…
Neimark--Sacker bifurcation and evidence of chaos in a discrete dynamical model of walkers
Aminur Rahman, Denis Blackmore
Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across t…
RS Flip-Flop Circuit Dynamics Revisited
Aminur Rahman, Denis Blackmore
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 model…
A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment
Roy H. Goodman, Aminur Rahman, Michael Bellanich +1
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 solita…
GPU Accelerated Fractal Image Compression for Medical Imaging in Parallel Computing Platform
Md. Enamul Haque, Abdullah Al Kaisan, Mahmudur R Saniat +1
In this paper, we implemented both sequential and parallel version of fractal image compression algorithms using CUDA (Compute Unified Device Architecture) programming model for pa…
Peixoto's Structural Stability Theorem: The One-dimensional Version
Aminur Rahman
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,…
Discrete Dynamical Modeling and Analysis of the R-S Flip-Flop Circuit
Denis Blackmore, Aminur Rahman, Jigar Shah
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…