Applying Dynamical Systems Theory to Improve Analysis of Time Series Transcriptional Data from Bioproduction Processes
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09 BIOMASS FUELS↗
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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.
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Simulated annealing of reduced magnetohydrodynamic systems
Theory of simulated annealing (SA), a method for equilibrium and stability analyses for Hamiltonian systems, is reviewed. The SA explained in this review is based on a double bracket formulation that derives from Hamiltonian structure. In addition to general theoretical aspects, the explicit formulation as well as numerical applications are presented. Both finite and infinite degree-of-freedom systems are treated, in particular, the heavy top, a toy model mimicking low-beta reduced magnetohydrodynamics (MHD) and low- and high-beta reduced MHD. Furthermore, the numerical results successfully demonstrate the usefulness of SA for equilibrium and stability analyses. At the same time, the results raise some future issues that are discussed in the paper.
Poisson Bracket↗
MULTILEVEL QUASI MONTE CARLO FOR SYSTEM RELIABILITY THEORY
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Eng, Ben [Sandia National Laboratories (SNL-CA), L↗
Hazard Analysis to Support Fusion Systems Safety Assessments
Reliability, safety, and performance are vital aspects of any nuclear operation. Fusion technology continues to grow in public, private, and research interest, and coupled with rapidly growing energy needs, fusion technology research is poised for fast progress. The development of a Fusion Nuclear Science Facility (FNSF) is seen as stepping stone for demonstrating long-cycle fusion. Naturally, such operation requires systems that are available, reliable, and safe. This work provides a novel demonstration of systems theory coupled with traditional hazard analysis to provide insights into the risk priority of components and systems found within the FNSF. The results of this work are a set of identified hazards that should be considered for the risk-informed design and development of the FNSF.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Understanding plasma turbulence through exact coherent structures
Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a generalized framework to analyze plasma turbulence that utilizes periodic orbit theory. In periodic orbit theory, doubly periodic solutions (coherent structures) of the governing equation(s) serve as building blocks of the considered turbulent dynamics. To illustrate the concept and method, the particularly simple Kuramoto–Sivashinsky (referred to here as LMRT for the original authors: LaQuey, Mahajan, Rutherford, and Tang) trapped-ion mode toy model is used. By applying numerical optimization techniques to the LMRT equation, we extract coherent spacetime patterns that represent the library of allowable fundamental structures of the equation. These structures provide a framework to systematically describe turbulence as a composition of recurrent solutions, revealing an underlying order within chaotic plasma motion. Although illustrated here using the simplified LMRT model for clarity, this framework provides a general strategy that can be extended to more complex and realistic models of plasma turbulence, including gyrokinetic systems. This offers a new method for predicting and potentially controlling transport processes in fusion plasmas by providing a bridge between nonlinear dynamical systems theory and plasma physics in the form of a generalized framework with which to analyze and understand spatially extended nonlinear partial differential equations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Predicting Critical Transitions in Multiscale Data
Predicting the dynamics of complex nonlinear systems remains a challenging problem both in dynamical systems theory as well as real world science and engineering applications. Data-driven methods utilizing the latest advances in machine learning (ML) provide a promising new paradigm for this task. Our work centered on Reservoir Computing (RC), which has shown itself to be capable of skillfully predicting chaotic dynamics in multiscale systems. In the first part of the work, the focus is on how to improve predictions of critical transitions in a class of slow-fast metastable systems in which the equations are known. An additional goal was to determine whether a relationship exists between RC and Koopman operator theory, to improve the efficiency and broaden the applicability of the approach. In the second part of this work, a variation on the RC model known as Reconstructive Reservoir Computing (RRC) is applied to real-world data to identify anomalies.
97 MATHEMATICS AND COMPUTING↗
Weighted Composition Operators for Learning Nonlinear Dynamics
Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.
97 MATHEMATICS AND COMPUTING↗
Predictive Complexity of Quantum Subsystems
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum. Predictive states of a subsystem are formed by equivalence classes of state vectors in the exterior Hilbert space that effectively predict the same future behavior of that subsystem for some time. As an illustrative example, we present calculations in the dynamics of an isotropic Heisenberg model spin chain and show that, in comparison to the entanglement entropy, the predictive complexity better signifies dynamically important events, such as magnon collisions. It can also serve as a local order parameter that can distinguish long and short range entanglement.
Asplund, Curtis T. (ORCID:0000000305575850)↗
QRCODE: Massively parallelized real-time time-dependent density functional theory for periodic systems
We present a new software module, QRCODE (Quantum Research for Calculating Optically Driven Excitations), for massively parallelized real-time time-dependent density functional theory (RT-TDDFT) calculations of periodic systems in the open-source Qbox software package. Our approach utilizes a custom implementation of a fast Fourier transformation scheme that significantly reduces inter-node message passing interface (MPI) communication of the major computational kernel and shows impressive scaling up to 16,344 CPU cores. In addition to improving computational performance, QRCODE contains a suite of various time propagators for accurate RT-TDDFT calculations. As benchmark applications of QRCODE, we calculate the current density and optical absorption spectra of hexagonal boron nitride (h-BN) and photo-driven reaction dynamics of the ozone-oxygen reaction. We also calculate the second and higher harmonic generation of monolayer and multi-layer boron nitride structures as examples of large material systems. Our optimized implementation of RT-TDDFT in QRCODE enables large-scale calculations of real-time electron dynamics of chemical and material systems with enhanced computational performance and impressive scaling across several thousand CPU cores.
97 MATHEMATICS AND COMPUTING↗
Expansion-driven Weibel instability in magnetohydrodynamics: Linear theory for static systems
The Weibel dispersion relation is obtained in the magnetohydrodynamic (MHD) approximation by including a tensor expression for temperature. MHD gives an upper cutoff wavenumber for Weibel growth identical to kinetic theory if the electron drift velocity is included in the evolution of the electron temperature. MHD overestimates growth rates compared to kinetic theory and gives maximum growth at larger wavenumbers, but it only leads to divergent results as temperature anisotropy tends to infinity. Thermal conduction in MHD lowers the growth rates and shifts maximum growth to smaller wavenumbers, but flux-limited or nonlocal thermal conduction is found to significantly limit these effects. The results are used as a first step in evaluating the potential of MHD to simulate expansion-driven Weibel instability, which occurs due to the temperature tensor only cooling in the direction of expansion. Finally, the small temperature anisotropy found in expansion-driven Weibel instability means that MHD could be an adequate model because growth rates are much less than the electron plasma frequency, and wavelengths are much greater than the Debye length.
Davies, J. R. [Univ. of Rochester, NY (United Stat↗
Coupled Lindblad Pseudomode Theory for Simulating Open Quantum Systems
Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that the number of coupled pseudomodes only needs to scale as polylog(𝑇/𝜖) in the simulation time 𝑇 and precision 𝜖. Inspired by the realization problem in control theory, we also develop a robust numerical algorithm for constructing the coupled modes that avoid the nonconvex optimization required by existing approaches. We demonstrate the effectiveness of our method by computing population dynamics and absorption spectra for the spin-boson model. Furthermore, this Letter provides a significant theoretical and computational improvement to the coupled Lindblad framework, which impacts a broad range of applications from classical simulations of quantum impurity problems to quantum simulations on near-term quantum platforms.
Anderson impurity model↗
Game Theory Approaches for System-level Incentive Design
This report presents a generalized Stackelberg game framework for designing and evaluating financial incentives that enhance power system resilience through strategic deployment of distributed energy resources(DERs) under various contingencies. The proposed approach addresses the challenge of coordinating individual community investment decisions to meet system-wide resilience objectives. The framework is demonstrated in a three-community test system subjected to two transmission contingency scenarios: inter-community line failure (Case 1) and complete main grid disconnection (Case 2). In both cases, three incentive levels are compared: a Base case with no financial incentives, and low and high incentive cases. In Case 1, the Base case (no incentives) results in a total installed DER capacity of 217.2 MW, with no load shedding due to alternative routing, but community costs remain high. Increasing incentives raises DER deployment to 286.9 MW, lowers aggregate community costs by $22M annually, and completely avoids the need for costly new transmission line construction. In Case 2, the Base case results in 24.3 MWh of unserved load; introducing incentives eliminates all load shedding and ensures up to 89 MWh of battery storage is available for emergency reserve. These results demonstrate that targeted incentives can dramatically improve grid resilience and cost-effectiveness. The framework thus offers policymakers and system planners a robust tool to quantify and compare the effectiveness of incentive programs for multi-community transmission networks behavior, system resilience, and economic efficiency.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Obstacles to Practical Digital Supply Chain Risk Management in the Energy Sector
Cyber supply chain risk management (C-SCRM) programs must consider operations that depend on the lifecycles of digital components such as hardware, firmware, software, and services. We integrate academic literature, historical incidents, and existing standards to identify obstacles faced by C-SCRM programs.
Business Process Management & Integration↗
Quasi-Lindblad pseudomode theory for open quantum systems
Here, we introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quarkonium Polarization Kinetic Equation from Open Quantum Systems and Effective Field Theories
Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of J/ψ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Theory of Two-Level Tunneling Systems in Superconductors
We develop a field theory formulation for the interaction of an ensemble of two-level tunneling systems (TLSs) with the electronic states of a superconductor. Predictions for the impact of two-level tunneling systems on superconductivity are presented, including T c and the spectrum of quasiparticle states for conventional BCS superconductors. We show that nonmagnetic TLS impurities in conventional s-wave superconductors can act as pair-breaking or pair-enhancing defects depending on the level population of the distribution of TLS impurities. We present calculations of the enhancement of superconductivity, both T c and the order parameter, for TLS defects in thermal equilibrium with the electrons and lattice. The scattering of quasiparticles by TLS impurities leads to subgap states below the bulk excitation gap, Δ, as well as resonances in the continuum above Δ. The energies and spectral weights of these states depend on the distribution of tunnel splittings, while the spectral weights are particularly sensitive to the level occupation of the TLS impurities. Under microwave excitation, or decoupling from the thermal bath, a nonequilibrium level population of the TLS distribution generates subgap quasiparticle states near the Fermi level that contribute to dissipation and thus degrade the performance of superconducting devices at low temperatures.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Two-dimensional non-equilibrium melting of charged colloids
Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.
critical phenomena↗
The mechanics of nucleation and growth and the surface tensions of active matter
Homogeneous nucleation, a textbook transition path for phase transitions, is typically understood on thermodynamic grounds through the prism of classical nucleation theory. However, recent studies have suggested the applicability of classical nucleation theory to systems far from equilibrium. Here, in this article, we formulate a purely mechanical perspective of homogeneous nucleation and growth, elucidating the criteria for the properties of a critical nucleus without appealing to equilibrium notions. Applying this theory to active fluids undergoing motility-induced phase separation, we find that nucleation proceeds in a qualitatively similar fashion to equilibrium systems, with concepts such as the Gibbs–Thomson effect and nucleation barriers remaining valid. We further demonstrate that the recovery of such concepts allows us to extend classical theories of nucleation rates and coarsening dynamics to active systems upon using the mechanically derived definitions of the nucleation barrier and surface tensions. Three distinct surface tensions—the mechanical, capillary, and Ostwald tensions—play a central role in our theory. While these three surface tensions are identical in equilibrium, our work highlights the distinctive role of each tension in the stability of active interfaces and the nucleation and growth of motility-induced phases.
Capillary waves↗