Search NASA⌕ Search

SEARCH · Search NASA

Results for “Coupled oscillators”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Design of Hopfield Networks Based on Superconducting Coupled Oscillators

The global energy shortage has driven the development of many energy-efficient computational platforms beyond Moore's law, among which brain-inspired neuromorphic computing is one of the promising solutions. Associative memory and pattern recognition are important computations solved by brain-inspired Hopfield networks. Classical Hopfield networks store memories via fixed point attractors of their dynamics. In oscillatory Hopfield networks, these attractors are replaced by periodic orbits. Here, we design an oscillatory Hopfield network based on coupled superconducting oscillators. We first employ a mathematical phase reduction approach to map networks of coupled superconducting rapid single flux quantum (RSFQ) ring oscillators to coupled Kuramoto phase-oscillator networks. We use this theory to numerically optimize the hardware's mutual inductances in order to directly match the phase-reduced superconducting oscillators to a model of phase-oscillator-based Hopfield networks. The resulting network can store multiple oscillatory phase-locked memory patterns and recover the patterns based on the initial phase conditions. As different pattern recognition tasks, or learning, require tunable connectivity strengths between the oscillatory nodes, we further employ a coupler circuit that enables tuning the coupling strength between two oscillators by applying an external flux. We demonstrate the functionality of our design through numerical simulations of a small example network with oscillators operating at 86 GHz and recognizing patterns within 10 ns. Our approach enables the learning and retrieval of dynamical memory patterns with a wide range of applications where rhythmic dynamic output is beneficial.

Cheng, Ran↗
DOE OSTI2024

Quantum Drude oscillators coupled with Coulomb potential as an efficient model for bonded and non-covalent interactions in atomic dimers

The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.

Chemistry↗
DOE OSTI2023

Assessing the impact of Byzantine attacks on coupled phase oscillators

Abstract For many coupled dynamical systems, the interaction is the outcome of the measurement that each unit has of the others as e.g. in modern inverter-based power grids, autonomous vehicular platoons or swarms of drones, or it is the result of physical flows. Synchronization among all the components of these systems is of primal importance to avoid failures. The overall operational state of these systems therefore crucially depends on the correct and reliable functioning of the individual elements as well as the information they transmit through the network. Here, we investigate the effect of Byzantine attacks where one unit does not behave as expected, but is controlled by an external attacker. For such attacks, we assess the impact on the global collective behavior of nonlinearly coupled phase oscillators. We relate the synchronization error induced by the input signal to the properties of the attacked node. This allows to anticipate the potential of an attacker and identify which network components to secure.

Tyloo, Melvyn (ORCID:0000000317614095)↗
DOE OSTI2023

Quantum reservoir computing implementation on coherently coupled quantum oscillators

Quantum reservoir computing is a promising approach for quantum neural networks, capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits suffer from limited connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyze a specific hardware implementation based on superconducting circuits: with just two coupled quantum oscillators, we create a quantum reservoir comprising up to 81 neurons. We obtain state-of-the-art accuracy of 99% on benchmark tasks that otherwise require at least 24 classical oscillators to be solved. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computing, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures, with billions of neurons implemented with only 10 coupled quantum oscillators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Coherently coupled quantum oscillators for quantum reservoir computing

Here, we analyze the properties of a quantum system composed of two coherently coupled quantum oscillators and show through simulations that it fulfills the two properties required for reservoir computing: non-linearity and fading memory. We first show that the basis states of this system apply a set of nonlinear transformations on the input signals and thus can implement neurons. We then show that the system exhibits a fading memory that can be controlled by its dissipation rates. Finally we show that a strong coupling between the oscillators is important in order to ensure complex dynamics and to populate a number of basis state neurons that is exponential in the number of physical devices.

Dudas, Julien↗
DOE OSTI2026

Coexistence of Synchronization and Stochasticity in Thermally Coupled Mott Oscillators

Synchronization is conventionally regarded as a mechanism for suppressing variability and enforcing order in coupled systems, from pendula and lasers to neurons and electronic oscillators. Here, we show that synchronization can also embed stochasticity at finer scales. We observe this phenomenon in thermally coupled VO 2 neuristors, where robust in-phase synchronization at the microsecond scale coexists with spike onset fluctuations at the nanosecond scale, with no fixed leader. The coexistence of order and disorder originates from stochastic domain-level physics of the insulator–metal and metal–insulator transitions, where local variations in transition temperature drive cycle-to-cycle randomness in nucleation, percolation, and relaxation. A stochastic domain model reproduces this effect by generating synchronized spike trains with random lead–lag jitter, and experimental interspike interval statistics confirm the persistence of fine-scale variability despite macroscopic phase locking. These findings establish that synchronization and stochasticity can coexist within the same physical platform, revealing hidden disorder within collective order. Furthermore, this insight reframes synchronization as not purely deterministic, but as a universal context where microscopic variability can persist, with implications for electronics, cryptography, and the fundamental physics of order–disorder coexistence.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Exact solution of the relativistic Dunkl oscillator in (2+1) dimensions

In this paper we study the (2+1)-dimensional Dirac–Dunkl oscillator coupled to an external magnetic field. Our Hamiltonian is obtained from the standard Dirac oscillator coupled to an external magnetic field by changing the partial derivatives by the Dunkl derivatives. We solve the Dunkl–Klein–Gordon-type equations in polar coordinates in a closed form. The angular part eigenfunctions are given in terms of the Jacobi–Dunkl polynomials and the radial functions in terms of the Laguerre functions. Also, we compute the energy spectrum of this problem and show that, in the non-relativistic limit, it properly reduces to the Hamiltonian of the two dimensional harmonic oscillator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution

The synchronization of self-oscillating systems is vital to various biological functions, from the coordinated contraction of heart muscle to the self-organization of slime molds. Through modeling, we design bioinspired materials systems that spontaneously form shape-changing self-oscillators, which communicate to synchronize both their temporal and spatial behavior. Here, catalytic reactions at the bottom of a fluid-filled chamber and on mobile, flexible sheets generate the energy to “pump” the surrounding fluid, which also transports the immersed sheets. The sheets exert a force on the fluid that modifies the flow, which in turn affects the shape and movement of the flexible sheets. This feedback enables a single coated (active) and even an uncoated (passive) sheet to undergo self-oscillation, displaying different oscillatory modes with increases in the catalytic reaction rate. Two sheets (active or passive) introduce excluded volume, steric interactions. This distinctive combination of the hydrodynamic, fluid–structure, and steric interactions causes the sheets to form coupled oscillators, whose motion is synchronized in time and space. We develop a heuristic model that rationalizes this behavior. These coupled self-oscillators exhibit rich and tunable phase dynamics, which depends on the sheets’ initial placement, coverage by catalyst and relative size. Moreover, through variations in the reactant concentration, the system can switch between the different oscillatory modes. This breadth of dynamic behavior expands the functionality of the coupled oscillators, enabling soft robots to display a variety of self-sustained, self-regulating moves.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Active oscillatory associative memory

Traditionally, physical models of associative memory assume conditions of equilibrium. Here, we consider a prototypical oscillator model of associative memory and study how active noise sources that drive the system out of equilibrium, as well as nonlinearities in the interactions between the oscillators, affect the associative memory properties of the system. Our simulations show that pattern retrieval under active noise is more robust to the number of learned patterns and noise intensity than under passive noise. To understand this phenomenon, we analytically derive an effective energy correction due to the temporal correlations of active noise in the limit of short correlation decay time. We find that active noise deepens the energy wells corresponding to the patterns by strengthening the oscillator couplings, where the more nonlinear interactions are preferentially enhanced. Using replica theory, we demonstrate qualitative agreement between this effective picture and the retrieval simulations. Our work suggests that the nonlinearity in the oscillator couplings can improve memory under nonequilibrium conditions.

Chemistry↗
DOE OSTI2020

Nonequilibrium steady state and heat transport in nonlinear open quantum systems: Stochastic influence action and functional perturbative analysis

In this paper, we show that a nonequilibrium steady state (NESS) exists at late times in open quantum systems with weak nonlinearity by following its nonequilibrium dynamics with a perturbative analysis. We consider an oscillator chain containing three-types of anharmonicity: cubic α- and quartic β-type Fermi–Pasta–Ulam–Tsingou (FPUT) nearest-oscillator interactions and the on-site (pinned) Klein–Gordon (KG) quartic self-interaction. Assuming weak nonlinearity, we introduce a stochastic influence action approach to the problem and obtain the energy flows in different junctures across the chain. The formal results obtained here can be used for quantum transport problems in weakly nonlinear quantum systems. For α-type anharmonicity, we observe that the first-order corrections do not play any role in the thermal transport in the NESS of the configuration we considered. For KG and β-types anharmonicity, we work out explicitly the case of two weakly nonlinearly coupled oscillators, with results scalable to any number of oscillators. We examine the late-time energy flows from one thermal bath to the other via the coupled oscillators, and show that both the zeroth- and the first-order contributions of the energy flows become constant in time at late times, signaling the existence of a late-time NESS to first order in nonlinearity. Our perturbative calculations provide a measure of the strength of nonlinearity for nonlinear open quantum systems, which may help control the mesoscopic heat transport distinct from or close to linear transport. Furthermore, our results also give a benchmark for the numerical challenge of simulating heat transport. Our setup and predictions can be implemented and verified by investigating heat flow in an array of Josephson junctions in the limit of large Josephson energy with the platform of circuit QED.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

On the number of stable solutions in the Kuramoto model

We consider a system of n coupled oscillators described by the Kuramoto model with the dynamics given by θ˙=ω+Kf(θ). In this system, an equilibrium solution θ∗ is considered stable when ω+Kf(θ∗)=0, and the Jacobian matrix Df(θ∗) has a simple eigenvalue of zero, indicating the presence of a direction in which the oscillators can adjust their phases. Additionally, the remaining eigenvalues of Df(θ∗) are negative, indicating stability in orthogonal directions. A crucial constraint imposed on the equilibrium solution is that |Γ(θ∗)|≤π, where |Γ(θ∗)| represents the length of the shortest arc on the unit circle that contains the equilibrium solution θ∗. We provide a proof that there exists a unique solution satisfying the aforementioned stability criteria. This analysis enhances our understanding of the stability and uniqueness of these solutions, offering valuable insights into the dynamics of coupled oscillators in this system.

Arenas, Alex (ORCID:0000000309370334)↗
DOE OSTI2020

Coupling neutrino oscillations and simulations of core-collapse supernovae

At the present time even the most sophisticated, multidimensional simulations of core-collapse supernovae do not (self-consistently) include neutrino flavor transformation. This physics is missing despite the importance of neutrinos in the core-collapse explosion paradigm. Because of this dependence, any flavor transformation that occurs in the region between the protoneutron star and the shock could result in major effects upon the dynamics of the explosion. Here, we present the first hydrodynamic core-collapse supernova simulation which simultaneously includes flavor transformation of the free-streaming neutrinos in the neutrino transport. These oscillation calculations are dynamically updated and evolve self-consistently alongside the hydrodynamics. Using a M = 20 M ⊙ progenitor, we find that while the oscillations have an effect on the neutrino emission and the heating rates, flavor transformation alone does not lead to a successful explosion of this progenitor in spherical symmetry.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Structural inference of networked dynamical systems with universal differential equations

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). Here, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods are shown with their application to canonical networked nonlinear coupled oscillators.

97 MATHEMATICS AND COMPUTING↗