arXiv subjects

Farbod Alijani

Publications and source records attributed to Farbod Alijani.

At least 19 recordsLinked to original sources

arXiv2026

Dynamics of amorphous membranes in the two-dimensional limit

Atomically thin mechanical resonators have been realized predominantly in crystalline two-dimensional (2D) materials, such as graphene, where long-range crystalline order sets their elastic properties and defines their nonlinear resonant behavior. Extending these concepts to the amorphous 2D limit has remained largely unexplored. Here, we demonstrate that monolayer amorphous carbon (MAC) forms suspended membranes that support optothermal actuation and sensitive interferometric readout across both linear and nonlinear regimes of its resonant motion. We resolve thermomechanical motion, driven resonances, and multimode spectra in MAC nanodrums. The frequencies of fundamental vibration modes correspond to unusually low pretensions, placing monolayer MAC nanodrums in a regime where geometric nonlinearities, stress heterogeneity, and mode coupling emerge at comparatively low drive powers. Consistently, we observe pronounced nonlinear dynamics, including hardening, softening, and mixed Duffing responses, nonlinear damping, parametrically excited modes, and signatures of intermodal coupling. These results establish MAC as a robust nanoelectromechanical platform and open an experimental route to disorder-governed nanomechanics in the 2D amorphous limit.

cond-mat.mes-hall↗

arXiv2026

Optomechanical tuning of nonlinearity in graphene resonators

Graphene resonators exhibit unique mechanical and electrical properties, making them promising candidates for next-generation sensing applications. Here, we introduce an optomechanical approach that enables active, reversible, in situ tuning of the nonlinear nanomechanical response of graphene resonators. By exploiting photothermal heating and the resulting optomechanical interaction between the mechanical oscillations and the optical cavity formed by a graphene membrane suspended over a reflective substrate, we achieve dynamic control over both the linear restoring force and the nonlinear dynamic response of the resonator. We show that the strength and sign of the Duffing nonlinearity can be continuously tuned through the optical probe power and cavity depth, enabling transitions between hardening and softening behavior as well as near-complete suppression of geometric nonlinearities. Our results establish a versatile platform for on-demand engineering of nonlinear dynamics in graphene resonators and provide a general strategy for active control of the mechanical response of two-dimensional nanoelectromechanical systems.

cond-mat.mes-hall↗

arXiv2026

Experimental Quantification of Nonlinear Mode Coupling in Nanomechanical Resonators using Multi-tone Excitation

Nonlinear modal interactions in resonant systems govern a wide range of phenomena, with broad relevance across modern physics and engineering. Yet, experimentally determining the strength of nonlinear coupling in multimode resonators remains highly challenging. Here, we introduce a multi-tone spectroscopy method for identifying nonlinear coupling coefficients directly from experimental data. Our approach employs dual-tone excitation near selected resonances which, in combination with additional probing tones at higher-order modes, generates sideband responses associated with specific modal couplings. These spectral signatures are analyzed using an inverse reconstruction procedure to quantitatively determine the corresponding nonlinear coupling strengths in the frequency domain. Using this method, we determine ten pairwise nonlinear coupling parameters across five modes of highly tensioned nanostrings, enabling the reconstruction of fully experimental, device-specific nonlinear reduced-order models. Our experimentally derived models show excellent agreement with values obtained numerically using finite element based nonlinear reduced-order models. Our method is generic and can be used for the characterization of diverse modal and intermodal couplings in mechanical and hybrid resonant systems.

cond-mat.mes-hall↗

arXiv2026

A machine learning framework for uncovering stochastic nonlinear dynamics from noisy data

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of such systems can often be described by stochastic differential equations, a central challenge is understanding how noise influences the inference of system parameters and dynamics from data. Traditional symbolic regression methods can uncover governing equations but typically ignore uncertainty. Conversely, Gaussian processes provide principled uncertainty quantification but offer little insight into the underlying dynamics. In this work, we bridge this gap with a hybrid symbolic regression-probabilistic machine learning framework that recovers the symbolic form of the governing equations while simultaneously inferring uncertainty in the system parameters. The framework combines deep symbolic regression with Gaussian process-based maximum likelihood estimation to separately model the deterministic dynamics and the noise structure, without requiring prior assumptions about their functional forms. We verify the approach on numerical benchmarks, including harmonic, Duffing, and van der Pol oscillators, and validate it on an experimental system of coupled biological oscillators exhibiting synchronization, where the algorithm successfully identifies both the symbolic and stochastic components. The framework is data-efficient, requiring as few as 100-1000 data points, and robust to noise - demonstrating its broad potential in domains where uncertainty is intrinsic and both the structure and variability of dynamical systems must be understood.

cs.LG↗

arXiv2026

Cascade of Modal Interactions in Nanomechanical Resonators with Soft Clamping

We uncover a chain of nonlinear modal interactions in softly clamped nanostring resonators. The process involves the sequential coupling of five mechanical modes, during frequency sweeps, yielding a broad nonlinear response with nearly constant amplitude. We demonstrate that soft clamping enables this cascaded energy transfer and amplifies the effective geometric nonlinearity of the driven mode by an order of magnitude. Analytical and finite element-based reduced-order models capture the key features of the coupling cascade and clarify its underlying mechanism. The phenomenon is generic in nonlinear vibrational systems and can be tailored through soft-clamping design strategies.

cond-mat.mes-hall↗

arXiv2026

Frequency Stability of Graphene Nonlinear Parametric Oscillator

High-frequency stability is crucial for the performance of graphene resonators in sensing and timekeeping applications. However, the extreme miniaturization and high mechanical compliance that make graphene attractive also render it highly susceptible to nonlinearities, degrading frequency stability. Here, we demonstrate that graphene parametric oscillators provide an alternative nonlinear operating regime, where short-term frequency stability can be enhanced despite strong nonlinearity. By operating graphene resonators in a phase-locked loop (PLL), we experimentally demonstrate that parametric oscillations in the post-bifurcation regime achieve lower Allan deviation at fast integration times than Duffing oscillations at identical amplitudes. This improvement originates from strong nonlinear damping inherent to parametric oscillators, which suppresses amplitude-to-frequency noise conversion at large amplitudes. A minimal theoretical model captures observed phase diffusion and identifies nonlinear damping as the dominant mechanism governing phase noise reduction. These results highlight the role of nonlinear dissipation in enabling precision sensing beyond conventional limits of graphene oscillators.

cond-mat.mes-hall↗

arXiv2025

Mechanical Reinforcement of Graphene via Wrinkling

Mechanical cantilevers are central to nanotechnology, with ultimate sensitivity achieved at the atomic limit, where low bending rigidity makes stability the fundamental challenge. Here, we introduce a wrinkle-induced stiffening approach that enhances the bending rigidity of monolayer graphene by several orders of magnitude, enabling the fabrication of mechanically robust graphene cantilevers. When suspended over microcavities, these wrinkled membranes exhibit significant increases in both in-plane and out-of-plane stiffness, as confirmed by nanoindentation and resonance measurements, which also reveal that enhanced bending rigidity strongly influences their vibrational response. This behavior marks a transition from tension-dominated mechanics to a regime where bending effects become prominent, even in a single atomic layer. By sculpting these structures, we realize graphene cantilevers with measured bending rigidities between $10^6$ and $10^7$ eV, while maintaining femtogram-scale mass. These findings open new directions in nanomechanical sensing and cantilever-based technologies.

cond-mat.mes-hall↗

arXiv2024

Dissipation Dilution-Driven Topology Optimization for Maximizing the $Q$ Factor of Nanomechanical Resonators

The quality factor ($Q$ factor) of nanomechanical resonators is influenced by geometry and stress, a phenomenon called dissipation dilution. Studies have explored maximizing this effect, leading to softly-clamped resonator designs. This paper proposes a topology optimization methodology to design two-dimensional nanomechanical resonators with high $Q$ factors by maximizing dissipation dilution. A formulation based on the ratio of geometrically nonlinear to linear modal stiffnesses of a prestressed finite element model is used, with its corresponding adjoint sensitivity analysis formulation. Systematic design in square domains yields geometries with comparable $Q$ factors to literature. We analyze the trade-offs between resonance frequency and quality factor, and how these are reflected in the geometry of resonators. We further apply the methodology to optimize a resonator on a full hexagonal domain. By using the entire mesh -- i.e., without assuming any symmetries -- we find that the optimizer converges to a two-axis symmetric design comprised of four tethers.

cond-mat.mes-hall↗

arXiv2024

Finite Element-based Nonlinear Dynamic Optimization of Nanomechanical Resonators

Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si3N4 string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano)mechanical resonators with optimized performance for a wide variety of applications.

physics.app-ph↗

arXiv2024

Synchronization of E. coli bacteria moving in coupled wells

Synchronization plays a crucial role in the dynamics of living organisms, from fireflies flashing in unison to pacemaker cells that jointly generate heartbeats. Uncovering the mechanism behind these phenomena requires an understanding of individual biological oscillators and the coupling forces between them. Here, we develop a single-cell assay that studies rhythmic behavior in the motility of individual E.coli cells that can be mutually synchronized. Circular microcavities are used to isolate E.coli cells that swim along the cavity wall, resulting in self-sustained oscillations. Upon connecting these cavities by microchannels the bacterial motions can be coupled, yielding nonlinear dynamic synchronization patterns with phase slips. We demonstrate that the coordinated movement observed in coupled E. coli oscillators follows mathematical rules of synchronization which we use to quantify the coupling strength. These findings advance our understanding of motility in confinement, and lay the foundation for engineering desired dynamics in microbial active matter.

nlin.AO↗

arXiv2023

Quantifying stress distribution in ultra-large graphene drums through mode shape imaging

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here we introduce a new methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a unique manufacturing process to create ultra-large graphene drums with diameters of up to 1000 um. We solve the inverse problem of a Föppl--von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced metholodogy allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.

physics.app-ph↗

arXiv2023

Nonlinear dynamics and magneto-elasticity of nanodrums near the phase transition

Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensed-matter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin dynamics near a second-order phase transition on the nonlinear dynamics of 2D membranes has remained largely unexplored. Here, we investigate nonlinear magneto-mechanical coupling to antiferromagnetic order in suspended FePS$_3$-based heterostructure membranes. By monitoring the motion of these membranes as a function of temperature, we observe characteristic features in both nonlinear stiffness and damping close to the Néel temperature $T_{\rm{N}}$. We account for these experimental observations with an analytical magnetostriction model in which these nonlinearities emerge from a coupling between mechanical and magnetic oscillations, demonstrating that magneto-elasticity can lead to nonlinear damping. Our findings thus provide insights into the thermodynamics and magneto-mechanical energy dissipation mechanisms in nanomechanical resonators due to the material's phase change and magnetic order relaxation.

cond-mat.mes-hall↗

arXiv2023

Beating ringdowns of near-degenerate mechanical resonances

Mechanical resonators that possess coupled modes with harmonic frequency relations have recently sparked interest due to their suitability for controllable energy transfer and non-Hermitian dynamics. Here, we show coupling between high Q-factor ($>\!\!10^4$) resonances with a nearly 1:1 frequency relation in spatially-symmetric microresonators. We develop and demonstrate a method to analyze their dynamical behavior based on the simultaneous and resonant detection of both spectral peaks, and validate this with experimental results. The frequency difference between the peaks modulates their ringdown, and creates a beat pattern in the linear decay. This method applies both to the externally driven and the Brownian motion (thermal) regime, and allows characterization of both linear and nonlinear parameters. The mechanism behind this method renders it broadly applicable to both optical and electrical readout, as well as to different mechanical systems. This will aid studies using near-degenerate mechanical modes, for e.g., optomechanical energy transfer, synchronization and gyroscopic sensors.

physics.app-ph↗

arXiv2023

Characterizing multi-mode nonlinear dynamics of nanomechanical resonators

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear effects, it is shown that these models quickly deviate from experimental findings when multiple modes influence the nonlinear response. Here, we present a nonlinear reduced-order modelling methodology based on FEM simulations for capturing the global nonlinear dynamics of nanomechanical resonators. Our physics-based approach obtains the quadratic and cubic nonlinearities of resonators over a wide frequency range that spans 70 MHz. To qualitatively validate our approach, we perform experiments on a graphene nanodrum driven opto-thermally and show that the model can replicate diverse ranges of nonlinear phenomena, including multi-stability, parametric resonance, and different internal resonances without considering any empirical nonlinear fitting parameters. By providing a direct link between microscopic geometry, material parameters, and nonlinear dynamic response, we clarify the physical significance of nonlinear parameters that are obtained from fitting the dynamics of nanomechanical systems, and provide a route for designing devices with desired nonlinear behaviour.

cond-mat.mes-hall↗

arXiv2022

Dynamics of pressurized ultra-thin membranes

The resonance frequency of ultra-thin layered two-dimensional (2D) materials changes nonlinearly with the tension induced by the pressure from the surrounding gas. Although the dynamics of pressurized 2D material membranes have been extensively explored, recent experimental observations show significant deviations from analytical predictions. Here, we present a multi-mode continuum approach to capture the nonlinear pressure-frequency response of pre-tensioned membranes undergoing large deflections. We validate the model using experiments conducted on polysilicon drums excited opto-thermally and subjected to pressure changes in the surrounding medium. We demonstrate that considering the effect of pressure on the membrane tension is not sufficient for determining the resonance frequencies. In fact, it is essential to also account for the change in the membrane's shape in the pressurized configuration, the mid-plane stretching, and the contributions of higher modes to the mode shapes. Finally, we show how the presented high-frequency mechanical characterization method can be used to determine Young's modulus of ultra-thin membranes.

physics.app-ph↗

arXiv2022

Diamagnetic composites for high-Q levitating resonators

Levitation offers extreme isolation of mechanical systems from their environment, while enabling unconstrained high-precision translation and rotation of objects. Diamagnetic levitation is one of the most attractive levitation schemes, because it allows stable levitation at room temperature without the need for a continuous power supply. However, dissipation by eddy currents in conventional diamagnetic materials significantly limits the application potential of diamagnetically levitating systems. Here, we present a route towards high $Q$ macroscopic levitating resonators by substantially reducing eddy current damping using graphite particle based diamagnetic composites. We demonstrate resonators that feature quality factors $Q$ above 450,000 and vibration lifetimes beyond one hour, while levitating above permanent magnets in high vacuum at room temperature. The composite resonators have a $Q$ that is more than 400 times higher than that of diamagnetic graphite plates. By tuning the composite particle size and density, we investigate the dissipation reduction mechanism and enhance the $Q$ of the levitating resonators. Since their estimated acceleration noise is as low as some of the best superconducting levitating accelerometers at cryogenic temperatures, the high $Q$ and large mass of the presented composite resonators positions them as one of the most promising technologies for next generation ultra-sensitive room temperature accelerometers.

physics.app-ph↗

arXiv2022

Diamagnetically levitating resonant weighing scale

Diamagnetic levitation offers stable confinement of an object from its environment at zero power, and thus is a promising technique for developing next generation unclamped resonant sensors. In this work, we realize a resonant weighing scale using a graphite plate that is diamagnetically levitating over a checkerboard arrangement of permanent magnets. We characterize the bending vibrations of the levitating object using laser Doppler vibrometry and use microgram glass beads to calibrate the responsivity of the sensor's resonance frequency to mass changes. The sensor is used for real-time measurement of the evaporation rate of nano-litre droplets with high-accuracy. By analyzing the resonator's frequency stability, we show that the millimeter graphite sensor can reach mass resolutions down to 4.0ng, relevant to biological and chemical sensing concepts.

physics.ins-det↗

arXiv2022

Rigid body dynamics of diamagnetically levitating graphite resonators

Diamagnetic levitation is a promising technique for realizing resonant sensors and energy harvesters, since it offers thermal and mechanical isolation from the environment at zero power. To advance the application of diamagnetically levitating resonators, it is important to characterize their dynamics in the presence of both magnetic and gravitational fields. Here we experimentally actuate and measure rigid body modes of a diamagnetically levitating graphite plate. We numerically calculate the magnetic field and determine the influence of magnetic force on the resonance frequencies of the levitating plate. By analyzing damping mechanisms, we conclude that eddy current damping dominates dissipation in mm-sized plates. We use finite element simulations to model eddy current damping and find close agreement with experimental results. We also study the size-dependent Q-factors (Qs) of diamagnetically levitating plates and show that Qs above 100 million are theoretically attainable by reducing the size of the diamagnetic resonator down to microscale, making these systems of interest for next generation low-noise resonant sensors and oscillators.

physics.app-ph↗