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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Designing open quantum systems with known steady states: Davies generators and beyond

We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.

Guo, Jinkang [Department of Physics and Center for↗
DOE OSTI2021

Real-Time Alignment and Reorientation of Polymer Chains in Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) exhibit soft elasticity due to the alignment and reorientation of mesogens upon mechanical loading, which provides additional mechanisms to absorb and dissipate energy. This enhanced response makes LCEs potentially transformative materials for biomedical devices, tissue replacements, and protective equipment. However, there is a critical knowledge gap in understanding the highly rate-dependent dissipative behaviors of LCEs due to the lack of real-time characterization techniques that probe the microscale network structure and link it to the mechanical deformation of LCEs. In this work, we employ in situ optical measurements to evaluate the alignment and reorientation degree of mesogens in LCEs. The data are correlated to the quantitative physical analysis using polarized Fourier-transform infrared spectroscopy. The time scale of mesogen alignment is determined at different strain levels and loading rates. The mesogen reorientation kinetics is characterized to establish its relationship with the macroscale tensile strain, and compared to theoretical predictions. Overall, this work provides the first detailed study on the time-dependent evolution of mesogen alignment and reorientation in deformed LCEs. It also provides an effective and more accessible approach for other researchers to investigate the structural-property relationships of different types of polymers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Turbulent properties from Doppler lidar

Permanent and mobile facilities deployed by the ARM program cover a wide range of climatic regions, with a suite of active remote-sensing of cloud and aerosol profiles complemented by comprehensive in-situ measurements of the chemical, physical and optical properties of aerosol measured at the surface. To be able to fully exploit these datasets requires an understanding of the transport from the surface and within the atmosphere, especially within the planetary boundary layer. This requires a method of identifying when the surface and atmosphere are dynamically-linked. Determining the state of the boundary layer, and defining a well-mixed boundary-layer, is therefore suitably described in terms of mixing; here, we will assume that mixing essentially means turbulent mixing. This necessitates accurate measurements of the winds and turbulent mixing in the atmosphere. Doppler lidar is an excellent tool for observing turbulent properties, and ARM has deployed commercially available Doppler lidars at many of the fixed and mobile facilities. Doppler lidars have been shown to provide accurate retrievals of wind and turbulent properties within the boundary layer , however, robust characterization and calculation of the Doppler lidar measurement uncertainties is required before deriving higher level data products.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Equipping Neural Network Surrogates with Uncertainty for Propagation in Physical Systems

Coarse-grained or filtered models typically rely on closure models to account for unresolved scales. For instance, large eddy simulation for modeling turbulent fluid flows explicitly resolves the largest scales, but requires modeling closure terms to account for the sub-filter scales. With the vast amount of data available from high-fidelity simulations, there are unique opportunities to leverage data-driven modeling techniques to formulate expressive and flexible closure models. Despite their flexibility, data-driven models struggle in domain shift settings, i.e. when deployed in configurations not captured in the training dataset. In particular, the efficacy of neural network surrogates is difficult to assess a priori due to the deterministic, point-estimate nature of predictions. In high-consequence applications, such models require reliable uncertainty estimates in the data-informed and out-of-distribution regimes. To quantify uncertainties in both regimes, we employ Bayesian neural networks which are able to capture both epistemic and aleatoric uncertainties. We will discuss challenges associated with the training and evaluation of these networks. Furthermore, we will discuss uncertainty embedding strategies to enable efficient sampling and propagation of uncertainty through high-fidelity simulations.

Bayesian neural networks↗
DOE OSTI2024

Probabilistic and maximum entropy modeling of chemical reaction systems: Characteristics and comparisons to mass action kinetic models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy model is characterized by a high probability of free energy dissipation rate and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy model predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Derivation of A Representative Elementary Volume (REV) for Upscaled Two-Phase Flow in Porous Media

Relative permeability plays an important role in the upscaling of multiphase flow in porous media from the pore scale to the Darcy scale. The entire concept of relative permeability is contingent on the existence of a representative elementary volume (REV). As we move to smaller samples to measure relative permeability, such as with digital core analysis, the concept of a classical REV has become increasingly unlikely when using the conventional approach to defining a representative volume. The “‘conventional”’ understanding of an REV is that a large enough volume must be considered such that spatial variability averages out. In digital rock methods, such as pore-scale simulations based on micro-computed tomography (CT) images, the domain size is typically 2 to 4 mm. This is approximately the length scale of a single-phase flow REV using the classic REV approach. However, the single-phase perspective does not consider the complex dynamics and fluctuations often observed in multiphase flow systems, even at centimeter-scale experiments and/or simulations. A fundamental question is, therefore, whether the domain size commonly used in digital rock simulations can provide a consistent energy budget such that the concept of relative permeability exists. Based on first principles, relative permeability accounts for the rate of energy dissipated in a stationary process. If the dynamics are fluctuating, the energy dissipated can vary but will average out over a long enough timescale. The key to determining the validity of the relative permeability is the timescale of the measurement, not the spatial scale. The conventional REV theory assumes that spatial, temporal, and ensemble averages are equivalent in an ergodic system, but it does not provide a way to test this assumption. We provide a formal way to identify the timescale where the relative permeability accurately captures energy dissipation as a way to validate relative permeability measurements and quantitatively assess their accuracy. This result will be tested for a practical SCAL test, determining how long a flow experiment needs to be run to accurately characterize the rate of energy dissipation by the flow. The outcome will be a best practice guide for the determination of relative permeability from core-scale experiments and/or digital core simulations that ensure the energy budget is fully accounted for in the relative permeability coefficient.

Mcclure, James [Virginia Tech, Blacksburg]↗
DOE OSTI2026

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Autonomous quantum error correction and fault-tolerant quantum computation with squeezed cat qubits

We propose an autonomous quantum error correction scheme using squeezed cat (SC) code against excitation loss in continuous-variable systems. Through reservoir engineering, we show that a structured dissipation can stabilize a two-component SC while autonomously correcting the errors. The implementation of such dissipation only requires low-order nonlinear couplings among three bosonic modes or between a bosonic mode and a qutrit. While our proposed scheme is device independent, it is readily implementable with current experimental platforms such as superconducting circuits and trapped-ion systems. Compared to the stabilized cat, the stabilized SC has a much lower dominant error rate and a significantly enhanced noise bias. Furthermore, the bias-preserving operations for the SC have much lower error rates. In combination, the stabilized SC leads to substantially better logical performance when concatenating with an outer discrete-variable code. The surface-SC scheme achieves more than one order of magnitude increase in the threshold ratio between the loss rate κ 1 and the engineered dissipation rate κ 2 . Under a practical noise ratio κ 1 /κ 2 = 10 -3 , the repetition-SC scheme can reach a 10 -15 logical error rate even with a small mean excitation number of 4, which already suffices for practically useful quantum algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Do Arctic mixed-phase clouds sometimes dissipate due to insufficient aerosol? Evidence from comparisons between observations and idealized simulations

Abstract. Mixed-phase clouds are ubiquitous in the Arctic. These clouds can persist for days and dissipate in a matter of hours. It is sometimes unknown what causes this sudden dissipation, but aerosol–cloud interactions may be involved. Arctic aerosol concentrations can be low enough to affect cloud formation and structure, and it has been hypothesized that, in some instances, concentrations can drop below some critical value needed to maintain a cloud. We use observations from a Department of Energy ARM site on the northern slope of Alaska at Oliktok Point (OLI), the Arctic Summer Cloud Ocean Study (ASCOS) field campaign in the high Arctic Ocean, and the Integrated Characterisation of Energy, Clouds, Atmospheric state, and Precipitation at Summit – Aerosol Cloud Experiment (ICECAPS-ACE) project at the NSF (National Science Foundation) Summit Station in Greenland (SMT) to identify one case per site where Arctic boundary layer clouds dissipated coincidentally with a decrease in surface aerosol concentrations. These cases are used to initialize idealized large eddy simulations (LESs) in which aerosol concentrations are held constant until, at a specified time, all aerosols are removed instantaneously – effectively creating an extreme case of aerosol-limited dissipation which represents the fastest a cloud could possibly dissipate via this process. These LESs are compared against the observed data to determine whether cases could, potentially, be dissipating due to insufficient aerosol. The OLI case's observed liquid water path (LWP) dissipated faster than its simulation, indicating that other processes are likely the primary drivers of the dissipation. The ASCOS and SMT observed LWP dissipated at similar rates to their respective simulations, suggesting that aerosol-limited dissipation may be occurring in these instances. We also find that the microphysical response to this extreme aerosol forcing depends greatly on the specific case being simulated. Cases with drizzling liquid layers are simulated to dissipate by accelerating precipitation when aerosol is removed while the case with a non-drizzling liquid layer dissipates quickly, possibly glaciating via the Wegener–Bergeron–Findeisen (WBF) process. The non-drizzling case is also more sensitive to ice-nucleating particle (INP) concentrations than the drizzling cases. Overall, the simulations suggest that aerosol-limited cloud dissipation in the Arctic is plausible and that there are at least two microphysical pathways by which aerosol-limited dissipation can occur.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Profiling the molecular destruction rates of temperature and humidity as well as the turbulent kinetic energy dissipation in the convective boundary layer

A simultaneous deployment of Doppler, temperature, and water-vapor lidars is able to provide profiles of molecular destruction rates and turbulent kinetic energy (TKE) dissipation in the convective boundary layer (CBL). Horizontal wind profiles and profiles of vertical wind, temperature, and moisture fluctuations are combined, and transversal temporal autocovariance functions (ACFs) are determined for deriving the dissipation and molecular destruction rates. These are fundamental loss terms in the TKE as well as the potential temperature and mixing ratio variance equations. These ACFs are fitted to their theoretical shapes and coefficients in the inertial subrange. Error bars are estimated by a propagation of noise errors. Sophisticated analyses of the ACFs are performed in order to choose the correct range of lags of the fits for fitting their theoretical shapes in the inertial subrange as well as for minimizing systematic errors due to temporal and spatial averaging and micro- and mesoscale circulations. We demonstrate that we achieve very consistent results of the derived profiles of turbulent variables regardless of whether 1 or 10 s time resolutions are used. We also show that the temporal and spatial length scales of the fluctuations in vertical wind, moisture, and potential temperature are similar with a spatial integral scale of ≈160 m at least in the mixed layer (ML). The profiles of the molecular destruction rates show a maximum in the interfacial layer (IL) and reach values of ϵ m ≃ 7 x 10 -4 g 2 kg −2 s −1 for mixing ratio and ϵ θ ≃ 1.6 x 10 -3 K 2 s −1 for potential temperature. In contrast, the maximum of the TKE dissipation is reached in the ML and amounts to ≃ 10 -2 m 2 s −3 . We also demonstrate that the vertical wind ACF coefficient k w ∝ $\overline{w'^{2}}$ and the TKE dissipation ϵ ∝ ($\overline{w'^{2}}$) 3/2 . For the molecular destruction rates, we show that ϵ m ∝ $\overline{m'^{2}}$ ($\overline{w'^{2}}$) 1/2 and ϵ θ ∝ $\overline{θ'^{2}}$ ($\overline{w'^{2}}$) 1/2 . These equations can be used for parameterizations of ϵ, ϵ m , and ϵ θ . All noise error bars are derived by error propagation and are small enough to compare the results with previous observations and large-eddy simulations. The results agree well with previous observations but show more detailed structures in the IL. Consequently, the synergy resulting from this new combination of active remote sensors enables the profiling of turbulent variables such as integral scales, variances, TKE dissipation, and the molecular destruction rates as well as deriving relationships between them. The results can be used for the parameterization of turbulent variables, TKE budget analyses, and the verification of large-eddy simulations.

dissipation rate↗
DOE OSTI2024

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence

We consider a nearly collisionless plasma consisting of a species of “test particles” in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field—a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space—known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C 2 ∝ ∫ ∫ d x d v 〈 f 2 〉 —a quantity that here plays the role of (negative) entropy of the distribution function. We find that C 2 is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C 2 in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equation for the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C 2 to high s (towards the collisional dissipation range) at every k , the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C 2 is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k -space ( s -space) flux of C 2 is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the ( k , s ) plane, with power-law asymptotics at large k and s . Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a “critical balance” in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Safety First: Stability and Dissipation of Line-tied Force-free Flux Tubes in Magnetized Coronae

Abstract Magnetized plasma columns and extended magnetic structures with both footpoints anchored to a surface layer are an important building block of astrophysical dissipation models. Current loops shining in X-rays during the growth of plasma instabilities are observed in the corona of the Sun and are expected to exist in highly magnetized neutron star magnetospheres and accretion disk coronae. For varying twist and system sizes, we investigate the stability of line-tied force-free flux tubes and the dissipation of twist energy during instabilities using linear analysis and time-dependent force-free electrodynamics simulations. Kink modes ( m = 1) and efficient magnetic energy dissipation develop for plasma safety factors q ≲ 1, where q is the inverse of the number of magnetic field line windings per column length. Higher-order fluting modes ( m > 1) can distort equilibrium flux tubes for q > 1 but induce significantly less dissipation. In our analysis, the characteristic pitch μ ˜ 0 of flux-tube field lines determines the growth rate ( ∝ μ ˜ 0 3 ) and minimum wavelength of the kink instability ( ∝ μ ˜ 0 − 1 ). We use these scalings to determine a minimum flux tube length for the growth of the kink instability for any given μ ˜ 0 . By drawing analogies to idealized magnetar magnetospheres with varying regimes of boundary shearing rates, we discuss the expected impact of the pitch-dependent growth rates for magnetospheric dissipation in magnetar conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Region-based convolutional neural network for wind turbine wake characterization from scanning lidars

A convolutional neural network is applied to lidar scan images from three experimental campaigns to identify and characterize wind turbine wakes. Initially developed as a proof-of-concept model and applied to a single data set in complex terrain, the model is now improved and generalized and applied to two other unique lidar data sets, one located near an escarpment and one located offshore. The model, initially developed using lidar scans collected in predominantly westerly flow, exhibits sensitivity to wind flow direction. The model is thus successfully generalized through implementing a standard rotation process to scan images before input into the convolutional neural network to ensure the flow is westerly. The sample size of lidar scans used to train the model is increased, and along with the generalization process, these changes to the model are shown to enhance accuracy and robustness when characterizing dissipating and asymmetric wakes. Applied to the offshore data set in which nearly 20 wind turbine wakes are included per scan, the improved model exhibits a 95% success rate in characterizing wakes and a 74% success rate in characterizing dissipating wake fragments. The improved model is shown to generalize well to the two new data sets, although an increase in wake characterization accuracy is offset by an increase in model sensitivity and false positive wake identifications.

17 WIND ENERGY↗
DOE OSTI2024

Monodomain Liquid‐Crystal Elastomer Lattices for Broad Strain‐Rate Mechanical Damping

Designing structures that effectively dissipate energy across a broad range of mechanical loading rates, including those from compression, shock, and vibration, poses a significant engineering challenge. In this study, liquid‐crystal elastomers (LCEs), which possess anisotropic properties due to the alignment of their polymer backbone, are explored. As a result, LCEs exhibit a soft elastic response under mechanical loading, making them ideal for energy dissipation. Advances in additive manufacturing (AM) enable simple fabrication of foamlike dissipative structures with complex lattice geometries. Herein, direct ink write 3D printing, an extrusion AM method, is used to fabricate aligned, monodomain LCE lattice structures for broad strain‐rate mechanical damping. In this work, it is shown that these structures can dissipate strain energy in quasi‐static environments, comparable to traditional elastomeric lattices, and provide improved damping under high strain‐rate drop testing due to LCE soft elasticity. Additionally, under dynamic mechanical vibration, monodomain LCE lattices enhance damping at structural natural frequencies and provide high‐frequency attenuation. Finally, in these findings, a promising method is presented for fabricating mechanical damping devices that effectively dissipate energy across a broad range of loading rates.

3D printings↗
DOE OSTI2024

DRDMannTurb: A Python package for scalable, data-driven synthetic turbulence

Synthetic turbulence models (STMs) are used in wind engineering to generate realistic flow fields and are employed as inputs to industrial wind simulations. Examples include prescribing inlet conditions in large eddy simulations that model loads on wind turbines and tall buildings. We are interested in STMs capable of generating fluctuations based on prescribed second-moment statistics since such models can simulate environmental conditions that closely resemble on-site observations. To this end, the widely used Mann model (see Mann, 1994, 1998) is the inspiration for DRDMannTurb. The Mann model is described by three physical parameters: a magnitude parameter influencing the global variance of the wind field and corresponding to the Kolmogorov constant multiplied by the rate of viscous dissipation of the turbulent kinetic energy to the two-thirds, αϵ 2/3 , a turbulence length scale parameter L, and a nondimensional parameter Γ related to the lifetime of the eddies. A number of studies, as well as international standards (e.g., those by the International Electrotechnical Commission (IEC)), include recommended values for these three parameters with the goal of standardizing wind simulations according to observed energy spectra. Yet, having only three parameters, the Mann model faces limitations in accurately representing the diversity of observable spectra. This Python package enables users to extend the Mann model and more accurately fit field measurements through flexible neural network models of the eddy lifetime function. Following Keith et al. (2021), we refer to this class of models as Deep Rapid Distortion (DRD) models. DRDMannTurb also includes a general module implementing an efficient method for synthetic turbulence generation based on a domain decomposition technique. This technique is also described in Keith et al. (2021).

17 WIND ENERGY↗
DOE OSTI2023

Functionally graded thermal vias for inductor winding heat flow control

Embodiments of the disclosure relate to apparatuses for enhanced thermal management of an inductor assembly using functionally-graded thermal vias for heat flow control in the windings of the inductor. In one embodiment, a PCB for an inductor assembly includes a top surface and a bottom surface. Two or more electrically-conductive layers are embedded within the PCB and stacked vertically between the top surface and the bottom surface. The two or more electrically-conductive layers are electrically connected to form an inductor winding. A plurality of thermal vias thermally connects each of the two or more electrically-conductive layers to a cold plate thermally connected to the bottom surface. A number of thermal vias thermally connecting each electrically-conductive layer to the cold plate is directly proportional to a predetermined rate of heat dissipation from the electrically-conductive layer.

Dede, Ercan↗
DOE OSTI2025

On the Stability Analysis of Astrophysical Cooling Functions

To model the temperature evolution of optically thin astrophysical environments at MHD scales, radiative and collisional cooling rates are typically either pretabulated or fit into a functional form and then input into MHD codes as a radiative loss function. Thermal balance requires estimates of the analogous heating rates, which are harder to calculate, and due to uncertainties in the underlying dissipative heating processes these rates are often simply parameterized. The resulting net cooling function defines an equilibrium curve that varies with density and temperature. Such cooling functions can make the gas prone to thermal instability (TI), which will cause departures from equilibrium. There has been no systematic study of thermally unstable parameter space for nonequilibrium states. Motivated by our recent finding that there is a related linear instability, catastrophic cooling instability, that can dominate over TI, here we carry out such a study. We show that Balbus instability criteria for TI can be used to define a critical cooling rate, Λ c , that permits a nonequilibrium analysis of cooling functions through the mapping of TI zones. We furthermore illustrate how thermal conduction modifies the shape of TI zones. Upon applying a Λ c -based stability analysis to coronal loop simulations, we find that loops undergoing periodic episodes of coronal rain formation are linearly unstable to catastrophic cooling instability, while TI is stabilized by thermal conduction.

79 ASTRONOMY AND ASTROPHYSICS↗