arXiv subjects

Ahmed A. Barakat

Publications and source records attributed to Ahmed A. Barakat.

3 recordsLinked to original sources

arXiv2026

Bifurcation Structure of Double Hysteresis and Isolated Branches in a Parametric Duffing Nanoresonator

Direct and parametric driving together generate nonlinear response structures beyond conventional Duffing hysteresis, including multiple switching regions and isolated branches. Understanding how these structures are connected requires identifying the bifurcations that reorganize the response as the parametric excitation is varied. At a phase difference of 45 degrees between the direct and parametric excitations, we experimentally and analytically determine how the steady-state response changes as the parametric excitation is increased. A single resonance peak first splits into two while the response remains single valued. Two successive cusp bifurcations then create two saddle-node pairs and establish a double-hysteretic response. At the parametric-instability threshold, one saddle node of each pair is displaced towards unbounded amplitude and detuning, and an isolated-branch structure emerges above threshold. A parametric representation of the steady state distinguishes amplitude extrema from genuine saddle-node bifurcations and provides analytical conditions for these changes. Measurements on a dielectrically actuated pre-stressed SiN nanostring reproduce the predicted response and associated switching behavior. These results establish the bifurcation pathway connecting the different response structures at this phase configuration, providing a systematic basis for controlling multistability and switching in parametrically driven nonlinear resonators.

cond-mat.mes-hall↗

arXiv2026

Reconstructing the system coefficients for coupled harmonic oscillators

Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this research question within the framework of inverse problems. In this work, we consider optimization techniques to solve the inverse problem using Tikhonov regularization and data from laboratory experiments. We propose an iterative strategy that eliminates the need for further laboratory experiments. Our method is applied to identify the coupling and damping coefficients in a system of oscillators, ensuring an efficient and experiment-free approach. We present our results and compare them with those obtained from an alternative, purely experimental approach. By employing our proposed strategy, we demonstrate a significant reduction in the number of laboratory experiments required.

math.OC↗

arXiv2025

Fundamental and second-subharmonic Autler-Townes splitting in classical systems

The dynamic Stark effect and the Autler-Townes splitting (ATS) are hallmarks of driven two-level systems. We establish a direct correspondence between these quantum phenomena and the parametric normal mode splitting in coupled classical oscillators. This gives rise to a second-subharmonic ATS under a two-tone parametric drive. We find excellent agreement between the theory and the vibrations of a nanomechanical two-mode system, capturing both the fundamental and second-subharmonic ATS, and allowing quantitative extraction of the modal coupling irrespective of the degree of modal hybridization.

cond-mat.mes-hall↗