arXiv subjects

Adarsh Ganesan

Publications and source records attributed to Adarsh Ganesan.

At least 19 recordsLinked to original sources

arXiv2026

Multi-Tongue Frequency Fractal Dynamics in Hodgkin-Huxley Neurons Induced by Temporal Interference Stimulation

We investigate neuronal excitability in the Hodgkin--Huxley model under temporal interference (TI) stimulation in a previously unexplored Hertz-resonant regime and uncover a striking nonlinear response that we term ``multitongue frequency fractals''. Unlike single-frequency driving, which yields a smooth resonant valley, dual-frequency excitation fragments this response into a hierarchy of sharply modulated tongues whose number and structure grow with observation time, revealing clear self-similar architecture. These features emerge from transitions between non-cascaded and cascaded high-harmonic and subharmonic generation as detuning varies, and are maximised near the intrinsic ionic timescale at $ω\approx 0.2~\mathrm{rad/ms}$. The proliferation of tongues with observation time follows a Farey-mediant hierarchy and is quantitatively consistent with a box-counting-style scaling exponent $D \approx 1.36$. These results demonstrate that TI stimulation can elicit rich, hierarchically organised frequency responses even in classical excitable membranes, revealing fractal organisation in Hodgkin--Huxley dynamics.

nlin.PS↗

arXiv2026

On the Time-Domain Waveforms Leading to Frequency Comb Spectra

Frequency-comb spectra can arise from distinct time-domain waveforms. We develop a Fourier-based framework that relates waveform symmetry, regularity, and modulation to the structure of overtone- and sideband frequency combs. Analytical derivations show that symmetry determines the allowed harmonic orders, while waveform regularity governs spectral decay: discontinuities produce $n^{-1}$ scaling, derivative discontinuities yield $n^{-2}$ scaling, and smooth nonlinear mappings can produce rapidly decaying harmonics. For modulated carriers, we distinguish consecutive sidebands, symmetry-induced missing orders, and nonuniformly spaced frequency components. In particular, spectral sparsity does not necessarily imply a nonuniform frequency lattice. Comparisons of analytical coefficients with calculated time-domain signals and Fourier spectra establish the correspondence between waveform properties and spectral signatures. The results provide a mathematical basis for interpreting frequency-comb structures while identifying the limitations of magnitude-only spectra in determining their underlying physical mechanisms.

nlin.PS↗

arXiv2026

Neuromorphic Computing Based on Parametrically-Driven Oscillators and Frequency Combs

Parametrically driven oscillators exhibit distinct dynamical regimes that strongly influence their computational capability as physical reservoirs. Here, we demonstrate reservoir computing in a two-mode system exhibiting 2:1 parametric resonance using Mackey--Glass, Rössler, and Lorenz chaotic time-series prediction tasks. Mapping the normalized mean squared error over parameter space reveals that the lowest prediction errors consistently occur within the parametric resonance regime, where nonlinear interactions are activated while temporal coherence is preserved. In contrast, although frequency-comb states increase spectral dimensionality, prediction performance degrades in the chaotic comb regime due to loss of phase coherence. We further show that the modulation depth $Δ\text{F}$, detuning $κ$, damping ratio $γ_{21}$, and input data rate systematically reshape the accessible dynamical regimes and thereby control the reservoir performance. These results identify parametric resonance as a robust operating regime for oscillator-based neuromorphic computing and establish dynamical regime engineering as a route toward physical reservoir optimization.

cs.NE↗

arXiv2026

Phononic Frequency Combs in Twisted Bilayer Transition Metal Dichalcogenide Heterostructures from First Principles

Phononic frequency combs are equidistant spectral ladders generated when a driven vibrational mode transfers energy to an autoparametrically excited subharmonic mode through anharmonic intermode coupling. In previous studies, the coupling strength governing this energy transfer has typically been treated as a free parameter, extracted from a fabricated device, or adopted from an earlier calculation for a specific mode pair. As a result, whether a given crystal can support a phononic frequency comb, and the drive strength required to generate it, has not been predictable a priori. Here we obtain the complete parameter set from density functional theory. Twisted bilayers of \MoSSe{} and \MoSMoSe{} at the commensurate angle $21.787^{\circ}$ adopt space group $P3$ in a 42-atom \rootseven{} moiré supercell. The second-order force constants provide the mode frequencies; the third-order constants provide the linewidths through the Boltzmann transport equation and hence the quality factors; and the same third-order tensor projected onto the phonon eigenvectors of a chosen mode pair provides the anharmonic couplings $\kt$ and $\kss$. Both bilayers constitute a mode pair within $0.8\%$ of the $2\!:\!1$ resonance with $ω_1/ω_2 = 1.9923$ in \MoSSe{} and $1.9943$ in \MoSMoSe{}. By integrating the resulting two-mode equations, both modes generate combs through a discontinuous transition: at $701\,\fth$ in \MoSSe{} the envelope variance rises from $2.1\times10^{3}$ to $1.37\times10^{4}$ and the tooth count of mode 1 from 7 to 16 within a single $5\,\fth$ increment, identifying the onset as subcritical. The spectral entropy peaks \emph{before} this jump, at $341\,\fth$. The two compounds carry comparable coupling, differing by a factor of $1.2$. However, the comb excitation threshold is set by the quality-factors of signal modes: $Q_2 = 672$ for \MoSSe{} and $Q_2 = 3844$ for \MoSMoSe{}.

cond-mat.mtrl-sci↗

arXiv2026

Frequency comb generation in active optomechanical cavities

We numerically investigate frequency-comb generation in an electrically pumped vertical-cavity surface-emitting laser coupled to two mechanical modes of a suspended mirror. Displacement-dependent cavity loss and radiation-pressure feedback couple the mechanical motion to the carrier and photon densities, producing harmonics and combination-frequency components in the photon-density spectrum. Mechanical quality factors primarily control the intensity of comb lines, whereas resonance frequencies determine their spectral distribution. The initial mechanical amplitudes influence the threshold current and relative spectral intensities, with the simultaneous excitation of both modes yielding a broader set of observable components. These results establish the dependence of the calculated comb structure on mechanical dissipation, resonance frequencies, and initial conditions in an active optomechanical cavity.

physics.optics↗

arXiv2026

The Evolution of IBM's Quantum Information Software Kit (Qiskit): A Review of its Applications

Quantum computing is being increasingly adopted for solving classically intractable problems across various domains. However, the availability of accessible and scalable software frameworks remains essential for practical experimentation and adoption. IBM's open-source quantum computing toolkit 'Qiskit' has become a key player in this space by offering tools for circuit design, simulation, hardware execution, and domain-specific applications. This survey provides a systematic review of how Qiskit has evolved and what it has contributed to several critical fields including cryptography and cybersecurity, image and signal processing, climate science and energy applications, and finance. We show how Qiskit facilitates hybrid classical-quantum workflows and enables the deployment of algorithms on physical quantum hardware through error mitigation and modular integration approaches. Our exploration covers several key applications, including quantum key distribution, climate simulation, and quantum-enhanced portfolio optimization, while providing practical insights into their implementation. This work also covers the framework's technical structure and current limitations associated with scalability and reproducibility. By bringing together developments that have been scattered across different areas, this work serves as a reference point for researchers and practitioners who want to understand or contribute to Qiskit-enabled quantum computing.

quant-ph↗

arXiv2026

Game, Set, Quantum: Parameterized Quantum Circuit for Correlated Equilibrium in Bayesian Games

Strategic decision-making among many agents under incomplete information is central to economics, security, and multi-agent artificial intelligence (AI). Computing equilibria in such settings is challenging because the joint type-action space grows exponentially with the number of players. In binary-type, binary-action Bayesian games with $n$ players, an explicit representation over type-action profiles requires $O(2^{2n})$ entries, making direct linear-programming (LP) formulations increasingly costly as $n$ grows. We propose a hybrid quantum-classical framework for approximating Bayes correlated equilibrium (BCE) using a parameterized quantum circuit (PQC). The PQC represents the conditional distribution over joint actions using $O(nL)$ trainable parameters, where $L$ denotes the circuit depth; for the largest trained setting, $n=8$ and $L=2$, this corresponds to $48$ trainable angles. Each player count is trained independently by maximizing expected social welfare with a penalty on positive aggregated BCE obedience violations. On a strategically coupled Bayesian congestion game with $n=2,4,6,8$ players, feasible PQC solutions attain higher welfare than MCCFR and DCFR product-strategy baselines while satisfying $ε_{\max}\leq10^{-3}$, where $ε_{\max}$ denotes the maximum positive aggregated BCE obedience violation. Across five independent runs per setting, all runs are feasible for $n=2,4,6$, while four of five are feasible for $n=8$. PQC welfare remains below the exact LP optimum, with the absolute gap increasing with $n$, while classical state-vector simulation prevents PQC training beyond eight players. These results demonstrate the use of a compact PQC parameterization for approximate equilibrium computation and quantify its welfare, feasibility, and classical simulation scaling on the studied benchmark.

quant-ph↗

arXiv2026

Chemical Frequency Combs in Reaction-Diffusion Oscillators

Frequency combs, evenly spaced spectral lines locked to one fundamental frequency, are well known in optics and have also been found in phononic, magnonic, ferroelectric, and cosmological systems, but have not yet been studied in oscillating chemical reactions. In this work, we show that reaction-diffusion oscillators can also produce frequency combs. We use the Brusselator model and derive its Hopf bifurcation condition directly from the rate equations. We find that the trimolecular autocatalytic term is the only source of nonlinear harmonic content. Above the Hopf threshold, our simulations of target-wave patterns show a clear fundamental frequency followed by a long, evenly spaced ladder of harmonics, with each harmonic weaker than the one before it. We then vary the reactant concentrations and kinetic parameters one at a time and find that this comb structure holds across a wide range of values. We also test this idea experimentally using the Belousov-Zhabotinsky reaction. Intensity signals recorded at different points in a target pattern show a shared fundamental frequency with several weakening harmonics, matching the simulated pattern closely. Together, these results show that reaction-diffusion chemistry is a new platform for generating frequency combs.

nlin.PS↗

arXiv2026

On the Nonlinear Sensitivity of Phononic Frequency Combs to Physical Perturbations

Phononic frequency combs offer a rich platform for nonlinear sensing, yet how their observable properties respond to changes in physical parameters remains poorly understood. Using a reduced two-mode autoparametric resonance model, we investigate how primary and secondary detuning, drive amplitude, and relative damping jointly shape amplitude and frequency sensitivity across the nonlinear parameter space. We find that sensitivity is far from uniform: primary detuning shifts the comb response smoothly, secondary detuning produces sharply localized transitions near resonance manifolds, and drive amplitude concentrates peak sensitivity close to the activation threshold rather than deep within the comb state. The relative damping redistributes energy continuously between modes without introducing discontinuities. The nonlinear sensitivity of amplitude and frequency observables across all parameters points to a common physical origin in autoparametric resonance, nonlinear saturation, and coupling-induced synchronization, offering a coherent basis for designing nonlinear sensing platforms with deliberate, parameter-aware sensitivity engineering.

nlin.PS↗

arXiv2026

Financial Frequency Combs

Frequency combs are discrete, equally spaced, phase-coherent spectral lines that emerge from nonlinear mode coupling in physical systems. We show that the incommensurate fractional-order financial model of Huang, Li, Ma, and Chen, whose Caputo derivatives encode macroeconomic long-range memory, generates an analogous structure in its steady-state spectrum. The comb appears only over specific values and ranges of the saving amount $a$, the investment cost $b$, and the demand elasticity $c$, outside which the spectral lines lose their equal spacing. It persists across extended parameter regimes and stays invariant to perturbations in the initial interest rate $x_0$ and investment demand $y_0$, while distinct spectral regimes appear at different initial price levels $z_0$. The comb is generated only when the fractional-order exponents $q_1$, $q_2$, and $q_3$ associated with interest rate, investment demand, and price index are above the critical threshold values. At even higher values of these exponents, the frequency comb transitions into chaos. These findings show that the long-run cyclic structure of a memory-bearing financial economy organises into a discrete, deterministic spectral fingerprint rather than a stochastic continuum.

nlin.PS↗

arXiv2026

Nonlinear Dynamical Regimes of Cosmological Frequency Combs

We study the emergence of Cosmological Frequency Combs (CFCs) in a quintessence cosmology with an exponential potential using a dynamical systems formulation. Expressing the evolution equations in expansion-normalized variables yields an autonomous nonlinear system that supports time-periodic attractors corresponding to limit cycles, producing comb like spectral structures in cosmological observables without external periodic forcing. Numerical simulations reveal transitions between single frequency, comb like and chaotic regimes controlled by the fundamental frequency, background equation of state parameter, and initial conditions. Coherent comb structures arise only within well defined dynamical windows, while very low frequencies and unfavorable initial conditions suppress phase locking. These results show that CFCs naturally emerge from nonlinear cosmological dynamics and motivate further study of their possible observational implications.

astro-ph.CO↗

arXiv2026

Observation of Compressional Acoustic Wave Responses in Cell Culture Media Using a Quartz Crystal Microbalance

Quartz Crystal Microbalance (QCM) sensors are widely used to study biological and soft-matter interfaces due to their exceptional sensitivity to mass loading and interfacial mechanical properties. While classical QCM theory assumes predominantly shear-wave coupling into a semi-infinite Newtonian liquid, finite liquid thickness and acoustic reflections give rise to pronounced compressional (longitudinal) wave effects that strongly modulate both resonance frequency and motional resistance. Such compressional acoustic-wave responses should be properly accounted for when sensing in the liquid phase, for instance when working with cell suspensions. In this work, we systematically investigate compressional-wave responses in cell culture media including DMEM and RPMI-1640 across varying droplet volumes using a 5 MHz AT-cut QCM. Time-resolved measurements are analyzed using four parameters: the time period of compressional acoustic waves (Tca), the time associated with a phase shift between resonance frequency and resistance oscillations (Tp), the peak-to-peak shifts in frequency (Δfpp) and resistance (ΔRpp). DMEM and RPMI-1640 both exhibit strong volume-dependent periodic oscillations. At lower volumes, they exhibit low-frequency oscillations with a time period of approximately 40 minutes. However, as volume increases, the oscillations gradually evolve into high-frequency oscillations with a time period Tca of approximately 5 minutes. The peak-to-peak shifts (Δfpp) and (ΔRpp) are approximately 100-150 Hz and 40-60 Ω, respectively. The resonance frequency and resistance oscillations also exhibit a phase shift Tp of approximately 10 minutes. These results highlight that compressional-wave artifacts occur even in simple cell culture media, necessitating their explicit consideration when interpreting QCM data in the presence of cells.

cond-mat.soft↗

arXiv2026

Spontaneous Symmetry Breaking and Collective Higgs-Goldstone Dynamics in Solid-State Phononic Frequency Combs

We investigate the generation of phononic frequency combs arising from nonlinear coupling between Higgs-like and Goldstone-like phonon modes in hexagonal InMnO3. The Higgs-like mode, an infrared-active optical phonon, is resonantly driven by a short, high-electric field terahertz pulse, while the optically inactive Goldstone-like mode is indirectly excited through intrinsic nonlinear mode coupling. Using a nonlinear phononics model, we numerically solve the coupled equations of motion governing the lattice dynamics and analyze the resulting time- and frequency-domain responses. By systematically varying key drive and material parameters-including electric field amplitude, pulse width, driving frequency, and mode damping-we identify the conditions under which stable phononic frequency combs emerge. Our results reveal clear threshold behaviors for comb formation, tunability of comb spacing and spectral bandwidth through external control parameters, and a breakdown of coherent comb structure at high drive strengths or weak damping. These findings demonstrate how nonlinear Higgs-Goldstone interactions enable controllable phononic frequency comb generation and provide insight into ultrafast lattice dynamics in symmetry-broken materials.

cond-mat.mtrl-sci↗

arXiv2025

Simultaneous photonic and phononic bandgaps in a hexagonal lattice geometry with gradually transforming circular-to-triangular air gap holes

The integration of photonic and phononic bandgaps within a single scalable architecture promises transformative advances in optomechanical and acousto-optic devices. Here, we design and simulate a two-dimensional hexagonal lattice in silicon with air-gap holes that transition smoothly from circular to triangular via tuneable geometrical parameters including air-gap hole radius (R) and tether length (l). By independently varying these two parameters, we systematically explore diverse honeycomb lattice geometries and their bandgap properties. This transformation from circular to triangular air-gap holes enables suppression of both electromagnetic and elastic wave modes through Bragg scattering and symmetry modulation. We demonstrate that systematic variation of R and l allows tuning of photonic and phononic bandgaps upto 49.7% and 24.8% respectively. This possibility of geometrically tuning bandgaps provide a strong foundation for applications in Bragg filters, sensors etc. without the need for complex defects or exotic materials.

physics.optics↗

arXiv2025

On the Generation of Phononic Frequency Combs Using Defect Modes of Phononic Crystals

This paper proposes a method for generating phononic frequency combs (PFCs) using defect-localized modes in a two-dimensional hexagonal phononic crystal. Localized vibration modes from a singular point defect produce evenly spaced spectral lines corresponding to PFCs. Numerical modelling reveals robust energy transfer under a single-tone drive, generating spectral sidebands. These results demonstrate defect engineering in phononic crystals as a tunable platform for PFC generation with significant applications in high-resolution sensing, timing, and quantum-acoustic technologies.

physics.app-ph↗

arXiv2025

Design and Analysis of Curved Electrode Configurations for Enhanced Sensitivity in 1-Axis MEMS Accelerometers

This paper presents a comprehensive analytical and simulation-based study of curved electrode geometries for enhancing the sensitivity of MEMS capacitive accelerometers. Expressions for the capacitance between a planar movable electrode and six distinct fixed electrode profiles (biconvex, biconcave, concavo-convex, convexo-concave, plano-convex, and plano-concave) are derived, enabling direct calculation of differential gain and sensitivity as functions of electrode curvature and gap displacement. These analytical models are then rigorously validated using finite element simulations performed using COMSOL Multiphysics under identical bias and boundary conditions. The simulation results demonstrate agreement with the analytical results with a deviation of less than 7% in all configurations. The results also reveal that biconvex curved electrodes yield the greatest sensitivity improvement over the planar electrodes, with sensitivity monotonically increasing with arc length, while concave and plano-concave designs exhibit reduced performance. The concavo-convex and convexo-concave configurations furthermore introduce polarity inversion in the output voltage, offering additional design flexibility. Importantly, these sensitivity enhancements are achieved without any change in the overall volumetric dimensions of the device or the proofmass dimensions of the module for achieving higher-resolution inertial sensing.

eess.SY↗

arXiv2025

Inertial Imaging of Dual Mass Distributions on a Graphene Nanodrum: A Computational Study

This paper presents the possibility for inertial imaging of spatially patterned annular mass distributions of a circular graphene nanodrum resonator. By placing two distinct analytes in concentric annular regions, we harness the vibrational mode-specific sensitivities of the nanodrum to estimate their respective mass densities. An analytical formulation based on the Rayleigh-Ritz principle is developed to relate radial mass loading to modal frequency shifts. Finite element simulations are performed in COMSOL Multiphysics to obtain the shifts in the resonance frequency of vibrational modes under varying geometrical configurations of annular rings. By processing these frequency shifts through a transformation matrix, we estimate the concomitant mass distributions of annular rings. The results indicate that the estimation errors are lower for analytes placed near the antinodal regions of the dominant vibration mode, with the lowest error being 1.82 % for analyte A and 2.03 % for analyte B. Furthermore, thinner annular rings demonstrate enhanced detection accuracy due to reduced modal overlap. This study demonstrates an analytical strategy for mass detection using a graphene nanodrum by providing insights into optimal analyte placement and structural design for high-precision multi-target mass sensing applications.

cond-mat.mes-hall↗

arXiv2025

Experimental Observation of Temporally-Evolving Stochastic Vibration Patterns in a Vibrating Motor

This paper presents the observations of temporally evolving stochastic vibration patterns of a coin vibrating motor. Various voltages are applied to the coin vibrating motor, and the resulting vibrations are recorded using an accelerometer. Although an overall upward trend in mean vibration amplitude is observed with increasing drive voltage, instantaneous waveforms displayed pronounced nonlinear and quasiperiodic amplitude modulations, frequency shifts, and stochastic deviations that intensified at higher voltages. Additional experiments involving periodic pressing of the motor and the propagating medium revealed the dependence of nonlinear electromechanical responses on the initial conditions. These results demonstrate that the dynamic behaviour of the coin-type motor is governed by a complex nonlinear dependence on current and displacement, with significant implications for precision control in miniature actuator applications.

nlin.PS↗