About

Mina Paul is a Clinical Associate Professor of General Dentistry at the Henry M. Goldman School of Dental Medicine. She holds an MPH from Boston University, earned in 1996, and a DMD from the University of Pennsylvania, obtained in 1987. Her role involves teaching and practicing general dentistry, with a focus on providing state-of-the-art dental care through the school's teaching clinic and faculty practice. Her work emphasizes preventive and restorative dentistry, contributing to the education of students and the delivery of comprehensive patient services at the institution.

Research topics

• Physics
• Mechanics
• Materials science
• Thermodynamics
• Classical mechanics
• Mathematics
• Acoustics
• Optics
• Quantum mechanics
• Meteorology

Selected publications

• Theoretical modeling of the dynamic range of an elastic nanobeam under tension with a geometric nonlinearity

  Journal of Applied Physics · 2025-08-01 · 1 citations

  articleOpen accessSenior author

  A theoretical description of the weakly nonlinear and mode-dependent dynamics of a nanoscale beam that is under intrinsic tension is developed. A full analysis of the dynamic range of the beam over a wide range of conditions is presented. The dynamic range is bounded from below by the amplitude of vibration due to thermal motion, and it is bounded from above by large amplitude oscillations where the geometric nonlinearity plays a significant role due to stretching induced tension. The dynamics are analyzed using a beam with clamped boundaries, a string model, and a beam with hinged boundaries. The range of validity for the different models is quantified in detail. A hinged-beam model is found to provide an accurate description, with insightful closed-form analytical expressions, over a wide range of conditions. The relative importance of bending and tension in the mode-dependent dynamics of the beam is determined. Bending is shown to be important for the higher modes of oscillation with the onset of its importance dependent upon the amount of intrinsic tension that is present. The theoretical predictions are directly compared with experimental measurements for the first ten modes of two nanoscale beams. We discuss the accuracy of these approaches and their use for the development of emerging micro and nanoscale technologies that exploit the multimodal dynamics of small elastic beams operating in the linear regime.

  PublisherOA PDFDOI

• Computing the multimodal stochastic dynamics of a nanobeam in a viscous fluid

  Journal of Applied Physics · 2024-12-16

  articleOpen accessSenior author

  The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone. Although theoretical descriptions exist for idealized conditions, computing the stochastic multimodal dynamics for the complex conditions of an experiment is very challenging. We show that this is possible using deterministic finite-element calculations with the fluctuation dissipation theorem by exploring the multimodal stochastic dynamics of a doubly clamped nanobeam. We use a very general, and flexible, finite-element computational approach to quantify the stochastic dynamics of multiple modes simultaneously using only a single deterministic simulation. We include the experimentally relevant features of an intrinsic tension in the beam and the influence of a nearby rigid boundary on the dynamics through viscous fluid interactions. We quantify the stochastic dynamics of the first 11 flexural modes of the beam when immersed in air or water. We compare the numerical results with theory, where possible, and find excellent agreement. We quantify the limitations of the computational approach and describe its range of applicability. These results pave the way for computational studies of the stochastic dynamics of complex 3D elastic structures in a viscous fluid where theoretical descriptions are not available.

  PublisherOA PDFDOI

• Exploring the role of diffusive coupling in spatiotemporal chaos

  Chaos An Interdisciplinary Journal of Nonlinear Science · 2024-10-01

  articleOpen accessSenior author

  We explore the chaotic dynamics of a large one-dimensional lattice of coupled maps with diffusive coupling of varying strength using the covariant Lyapunov vectors (CLVs). Using a lattice of diffusively coupled quadratic maps, we quantify the growth of spatial structures in the chaotic dynamics as the strength of diffusion is increased. When the diffusion strength is increased from zero, we find that the leading Lyapunov exponent decreases rapidly from a positive value to zero to yield a small window of periodic dynamics which is then followed by chaotic dynamics. For values of the diffusion strength beyond the window of periodic dynamics, the leading Lyapunov exponent does not vary significantly with the strength of diffusion with the exception of a small variation for the largest diffusion strengths we explore. The Lyapunov spectrum and fractal dimension are described analytically as a function of the diffusion strength using the eigenvalues of the coupling operator. The spatial features of the CLVs are quantified and compared with the eigenvectors of the coupling operator. The chaotic dynamics are composed entirely of physical modes for all of the conditions we explore. The leading CLV is highly localized and localization decreases with increasing strength of the spatial coupling. The violation of the dominance of Oseledets splitting indicates that the entanglement of pairs of CLVs becomes more significant between neighboring CLVs as the strength of diffusion is increased.

  PublisherOA PDFDOI

• Mode-dependent scaling of nonlinearity and linear dynamic range in a NEMS resonator

  Applied Physics Letters · 2024-08-19 · 4 citations

  articleOpen access

  Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of nanoelectromechanical systems' (NEMSs) resonators. A thorough understanding of the nonlinear dynamics of higher eigenmodes of NEMS resonators would be beneficial for progress, given their use in applications and fundamental studies. Here, we characterize the nonlinearity and the linear dynamic range (LDR) of each eigenmode of two nanomechanical beam resonators with different intrinsic tension values up to eigenmode n = 11. We find that the modal Duffing constant increases as n4, while the critical amplitude for the onset of nonlinearity decreases as 1/n. The LDR, determined from the ratio of the critical amplitude to the thermal noise amplitude, increases weakly with n. Our findings are consistent with our theory treating the beam as a string, with the nonlinearity emerging from stretching at high amplitudes. These scaling laws, observed in experiments and validated theoretically, can be leveraged for pushing the limits of NEMS-based sensing even further.

  PublisherOA PDFDOI

• Computing the multimodal stochastic dynamics of a nanobeam in a viscous fluid

  arXiv (Cornell University) · 2024-11-29

  preprintOpen accessSenior author

  The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone. Although theoretical descriptions exist for idealized conditions, computing the stochastic multimodal dynamics for the complex conditions of experiment is very challenging. We show that this is possible using deterministic finite element calculations with the fluctuation dissipation theorem by exploring the multimodal stochastic dynamics of a doubly-clamped nanobeam. We use a very general, and flexible, finite-element computational approach to quantify the stochastic dynamics of multiple modes simultaneously using only a single deterministic simulation. We include the experimentally relevant features of an intrinsic tension in the beam and the influence of a nearby rigid boundary on the dynamics through viscous fluid interactions. We quantify the stochastic dynamics of the first eleven flexural modes of the beam when immersed in air or water. We compare the numerical results with theory, where possible, and find excellent agreement. We quantify the limitations of the computational approach and describe its range of applicability. These results pave the way for computational studies of the stochastic dynamics of complex 3D elastic structures in a viscous fluid where theoretical descriptions are not available.

  PublisherOA PDFDOI

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

  PubMed · 2023-03-24

  preprintOpen accessSenior author

  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 less localized 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.

  PublisherOA PDFDOI

• Multimode Brownian dynamics of a nanomechanical resonator in a viscous fluid

  Physical Review Applied · 2023-10-24 · 5 citations

  articleOpen access

  The ultimate precision attainable in a mechanical measurement can be determined from the random Brownian motion of the mechanical structure, if the nature of the fluctuations is well understood. To this end, the authors study the Brownian fluctuations of a nanomechanical beam in a viscous fluid. Their predictions based on elasticity theory, fluid dynamics, and statistical mechanics agree well with their experiments, indicating that the observed fluctuations come with ``viscous memory'', but no spatial correlations. The insights from this work are expected to impact the design of nanoelectromechanical systems, cantilevers for atomic force microscopy, and other mechanical sensors.

  PublisherOA PDFDOI

• Using covariant Lyapunov vectors to quantify high-dimensional chaos with a conservation law

  Physical review. E · 2023-11-02 · 2 citations

  articleOpen accessSenior author

  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 less localized 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.

  PublisherOA PDFDOI

• The fluid dynamics of propagating fronts with solutal and thermal coupling

  Journal of Fluid Mechanics · 2022 · 13 citations

  Senior authorCorresponding
  • Mechanics
  • Physics
  • Materials science

  We numerically explore the propagation of reacting fronts in a shallow and horizontal layer of fluid. We focus on fronts that couple with the fluid due to density differences between the products and reactants and also due to heat release from the reaction. We explore fronts where this solutal and thermal coupling is cooperative or antagonistic. We quantify the fluid motion induced by the front and investigate the interactions of the front with the fluid as it propagates through quiescent, cellular and chaotic flow fields. The solutal coupling induces an extended convection roll that travels with the front, the thermal coupling due to heat release from the reaction generates a pair of convection rolls that travels with the front, and when both couplings are present there is a complex signature of these contributions. The details of the front dynamics depend significantly upon the interactions of the front-induced flow field with the fluid ahead of the front.

  PublisherOA PDFDOI

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

  Journal of Applied Physics · 2022-07-15 · 6 citations

  articleOpen accessSenior authorCorresponding

  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 experiments, and the validity of a simplified string approximation is demonstrated.

  PublisherOA PDFDOI

Recent grants

• Collaborative Research: The Nonlinear Stochastic Dynamics of Micro and Nanomechanical Systems

  NSF · $322k · 2020–2024

• Collaborative Research: Revealing the Geometry of Spatio-temporal Chaos with Computational Topology: Theory, Numerics and Experiments

  NSF · $106k · 2016–2020

• CAREER: Spatiotemporal Chaos in Fluid Convection: New Physical Insights from Numerics

  NSF · $400k · 2008–2014

• CDI-TYPE II--COLLABORATIVE RESEARCH: Using Algebraic Topology to Connect Models with Measurements in Complex Nonequilibrium Systems

  NSF · $380k · 2011–2016

• The Complex Dynamics of Large Systems with Long-Range Interactions: New Insights from Covariant Lyapunov Vectors

  NSF · $326k · 2022–2026

Frequent coauthors

• Konstantin Mischaikow

  40 shared

• Michael F. Schatz

  Georgia Institute of Technology

  39 shared

• Rachel Levanger

  36 shared

• Jacek Cyranka

  University of Warsaw

  31 shared

• M. Xu

  Nanjing University of Aeronautics and Astronautics

  28 shared

• K. L. Ekinci

  Boston University

  21 shared

• Mu Xu

  18 shared

• Matthew B. Francom

  16 shared

Education

• M.D.

  University of Pennsylvania

  1987

• Other

  Boston University

  1996