arXiv subjects

Johnathon Barbish

Publications and source records attributed to Johnathon Barbish.

3 recordsLinked to original sources

arXiv2026

Statistical Properties of a Fluctuation-Driven Nanomechanical Duffing Resonator

We investigate the fluctuating nonlinear dynamics of multiple modes of a nanomechanical doubly clamped beam resonator. Each mode is driven by Gaussian force noise centered around the resonance; the mode response is monitored while the force magnitude is increased, inducing a transition from harmonic to the nonlinear Duffing regime. To characterize the dynamics, we introduce an effective temperature based on the mode fluctuation amplitude. As the nonlinearity becomes prominent at large amplitudes, we observe a reduction in the effective thermal energy and a crossover in response statistics from Gaussian to platykurtic, consistent with the dynamics expected in a Duffing potential.

cond-mat.mes-hall↗

arXiv2023

Using Covariant Lyapunov Vectors to Quantify High Dimensional Chaos with a Conservation Law

We explore the high dimensional chaos of a one-dimensional lattice of diffusively coupled tent maps using the covariant Lyapunov vectors (CLVs). We investigate the connection between the dynamics of the maps in the physical space and the dynamics of the covariant Lyapunov vectors and covariant Lyapunov exponents that describe the direction and growth (or decay) of small perturbations in the tangent space. We explore the tangent space splitting into physical and transient modes and find that the splitting persists for all of the conditions we explore. In general, the leading CLVs are highly localized in space and the CLVs become more delocalized with increasing Lyapunov index. We consider the dynamics with a conservation law whose strength is controlled by a parameter that can be continuously varied. Our results indicate that a conservation law delocalizes the spatial variation of the CLVs. We find that when a conservation law is present, the leading CLVs are entangled with fewer of their neighboring CLVs than in the absence of a conservation law.

nlin.CD↗

arXiv2022

The dynamics of an externally driven nanoscale beam that is under high tension and immersed in a viscous fluid

We explore the dynamics of a nanoscale doubly-clamped beam that is under high tension, immersed in a viscous fluid, and driven externally by a spatially varying drive force. We develop a theoretical description that is valid for all possible values of tension, includes the motion of the higher modes of the beam, and accounts for a harmonic force that is applied over a limited spatial region of the beam near its ends. We compare our theoretical predictions with experimental measurements for a nanoscale beam that is driven electrothermally and immersed in air and water. The theoretical predictions show good agreement with experiment and the validity of a simplified string approximation is demonstrated.

cond-mat.mes-hall↗