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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Effect of Silica and Mixing Time on Microstructures of Porous Polymer Composite by Emulsion Templating

Porous polymer composite with tailored porosity is applied in the myriads of areas such as energy storage, oil/water absorption, bioengineering, and advanced areas of material science. The emulsion templating technology is one of the most popular methods for synthesizing porous polymer composite. It involves solidifying a two-phase mixture of porogen and polymer, then removing porogen to create pores within the continuous emulsion phase by polymerization or curing. The surfactant plays a pivotal role in accomplishing a stable emulsion, a key factor in designing the internal porous structure. This study highlights the effect of silica filler and mixing time on pore morphology, i.e., shape, size, and distribution. on polydimethylsiloxane (PDMS) porous structure utilizing the water-in-oil emulsion templating method. Span® 80 is used as a surfactant to reduce the surface tension between water, silica, and PDMS and simultaneously create a strong foaming effect. Different weight concentrations of silica (1-10 wt%) were chosen while keeping the internal phase, i.e., water (50 wt%) constant. The designed porous structures were further characterized through scanning electron microscopy (SEM). Porous composite specimens fabricated with higher silica content and mixing time consistently exhibit smaller pore sizes than specimens fabricated with lower mixing time and silica content. A breakthrough of pore morphology is seen at silica content higher than 5wt% at 1 min mixing, however, pore morphology drastically changes when mixing time increases from 1 min to 6 min. Variation of finer mixing time beyond 1 min shows stepwise changes in pore morphology from a large single-phase porous structure to a bi-modal porous structure which eventually become a smaller single-mode porous structure. Thus, the emulsion templating technique, in combination with different filler content and mixing time, will effectively aid in designing engineered porous polymer composite with varying stiffness and pore morphology.

Porous polymer, Emulsion templating, Surfactant, P↗
DOE OSTI2026

Mixed-precision numerics in scientific applications: survey and perspectives

The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision capabilities, which can achieve performance improvements of up to 8x compared to double-precision in extreme compute-intensive workloads, remain largely untapped in most scientific applications. A growing number of efforts have shown that mixed-precision algorithmic innovations can deliver superior performance without sacrificing accuracy. These developments should prompt computational scientists to seriously consider whether their scientific modeling and simulation applications could benefit from the acceleration offered by new hardware and mixed-precision algorithms. In this survey, we (1) review progress across diverse scientific domains—fluid dynamics, weather and climate, quantum chemistry, and computational genomics—that have begun adopting mixed-precision strategies; (2) examine state-of-the-art algorithmic techniques such as iterative refinement, splitting and emulation schemes, and adaptive precision solvers; (3) assess their implications for accuracy, performance, and resource utilization; and (4) survey the emerging software ecosystem that enables mixed-precision methods at scale. We conclude with perspectives and recommendations on cross-cutting opportunities, domain-specific challenges, and the role of co-design between application scientists, numerical analysts, and computer scientists. Collectively, this survey underscores that mixed-precision numerics can reshape computational science by aligning algorithms with the evolving landscape of hardware capabilities.

Graphics processing units↗
DOE OSTI2023

Observational study of relationships between entrainment rate, homogeneity of mixing, and cloud droplet relative dispersion

The entrainment–mixing process is key to the cloud’s dynamical and microphysical processes. However, to the best of our knowledge, no study has quantitatively linked entrainment rate and homogeneity of mixing. Additionally, their combined effects on cloud droplet relative dispersion and physical mechanisms are even more unclear. This study analyzed the aircraft measurements of cumulus clouds collected in the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems field campaign to identify these relationships. The relationship between the entrainment rate and homogeneous mixing degree was found to be moderately positive, and the underlying mechanisms related to mixing and evaporation time scales and environmental relative humidity were explored. The relationship between relative dispersion and entrainment rate changes from positive to negative with increasing entrainment rate, depending on the dominance of evaporation of large or small droplets. The relative dispersion first increases and then decreases with increasing homogeneous mixing degree, validating the results of previous model simulations. Further, the results shed new light on understanding the interactions between cloud microphysics and cloud dynamics through turbulent entrainment and mixing processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Insights into mixing of non-isothermal multi-polymer melts for complex plastics recycling

Catalytic recycling or upcycling of plastics is often limited not by catalyst performance, but by transport, arising from highly viscous, non-Newtonian polymer melts. In this work, we develop a reactor-scale framework that integrates rheological measurements, constitutive modeling, computational fluid dynamics (CFD), and experiments to quantify mixing, heat transfer, and dispersion in surrogate hydrocarbon melts representing mixed plastics systems. Temperature- and shear rate-dependent viscosity of low-density polyethylene (LDPE) and high-density polyethylene (HDPE) is measured to create two surrogate polymers (PLD and PHD) that capture the dominant shear-thinning flow behavior while neglecting strong elastic effects, enabling tractable simulation of non-isothermal, polymer-melt mixing using a Carreau-Arrhenius generalized Newtonian framework. Three-dimensional CFD simulations are employed to evaluate impeller performance in PLD using mixing time, cavern volume, thermal uniformity, and interfacial area for regimes in which viscoelastic effects are not dominant. We show that magnetic stir bars commonly used in lab-scale studies produce large thermal gradients (~60 °C) and poor mixing, even under idealized power delivery and polymer flow conditions. In contrast, close-clearance anchor impellers achieve near-isothermal operation, reduce mixing times by up to 5×, and provide >90% active circulation volume. We further demonstrate that, at low pseudo-Deborah number (De*), motor power requirements can be predicted directly from shear rate-dependent rheology using the Carreau-Arrhenius framework, enabling rational selection of operating conditions. Extension to surrogate immiscible multi-polymer systems based on PLD and PHD shows that interfacial area is highly sensitive to operating conditions and impeller design, with coaxial anchor-turbine configurations enhancing dispersion by up to 4 × .

Close-clearance impellers↗
DOE OSTI2025

Influences of shock imprinting on mix in a 3D-printed porous media

Mixing of materials in porous media can cause a significant impact on fusion yield as previously demonstrated by the National Ignition Facility (NIF) MARBLE Campaign. Initially, the reactants are separated, with deuterium in the lattice struts and a tritium gas fill in the voids. Lattice parameters such as the strut thickness and relative pitch, provide a control for the mix parameters in the experiment. Los Alamos National Laboratory’s (LANL) BOSQUE project looks to better understand how the mix of the reactants and shell materials impact the fusion burn and resultant yield on various laser platforms. xRAGE’s Eulerian hydrodynamics and adaptive mesh refinement (AMR) provide the unique ability to study the impacts of multiscale features of complex lattice structures. This modeling provides the ability to measure shock front variations as the wave progress’ through a given media. Initial conditions of the lattice are essential to accurately model mix and burn measured by experiment. By varying the initial orientation and densities of these lattice regions the early time dynamics of how the shock is launched into the system is changed and advocates for the study of resulting effects. In this work, we will study the sensitivities of shock effects in varying 3D printed geometric systems and how these shocks alter the structure and mix in the lattice. We will discuss both preliminary experimental results and simulations to help plan and constrain future experiments where we will study the impact of different lattice geometries and lattice bulk densities. This work concludes with the relative impacts of lattice geometries on shock speeds at different bulk densities and the resultant mix widths due to those shock interactions. We see agreement with theory at the higher end of our bulk density study, however, as we approach lower bulk density systems the dynamics of these interactions begin to change.

2 Photon Polymerization↗
DOE OSTI2025

Numerical simulation of flow and mixing in fracture intersections

Fluid transport through fractured geological formations is strongly influenced by the redistribution of solutes at fracture intersections. In this study, we perform detailed numerical simulations of flow and scalar transport within the intersection of two smooth, planar fractures. The analysis focuses on the mixing ratio, the proportion of solute flux exiting along the outlet branch aligned with the primary inlet flow direction, relative to the total solute flux at the outlets. We systematically investigate how the mixing ratio varies with four key parameters: Peclet number, Reynolds number, flow rate ratio between outlet branches, and fracture intersection angle. Results show that the mixing ratio decreases with increasing Peclet number and outlet flow rate ratio, consistent with reduced diffusive spreading and enhanced streamline routing. While low Reynolds numbers have minimal impact, inertial effects at higher Reynolds numbers significantly increase the mixing ratio. Additionally, acute and obtuse intersection angles alter flow partitioning and modify the solute distribution at the outlets. These findings provide a quantitative basis for incorporating physically realistic mixing behavior—intermediate between complete mixing and streamline-following assumptions—into network-scale transport models. The results have direct relevance to subsurface energy systems, including geothermal energy production, carbon sequestration, and contaminant remediation.

58 GEOSCIENCES↗
DOE OSTI2023

Unraveling the impact of the degree of dry mixing on dry-processed lithium-ion battery electrodes

Dry processing of lithium-ion battery electrodes facilely realizes the powder-to-film manner, which is thus regarded as a highly promising strategy for lithium-ion battery manufacturing. However, a fundamental understanding of the impact of the involved dry mixing is still rarely reported. In this work, the degree of dry mixing is monitored by the dry mixing time, and a set of dry-processed electrodes with different degree of dry mixing is accordingly prepared and comprehensively studied. This work novelly reveals that the degree of dry mixing exhibits pronounced impact on the morphology, the homogeneity of electrode components and the degree of PTFE fiberization, which leads to difference in the mechanical strength and electrochemical performance of dry-processed electrodes. Accordingly, it is suggested that a moderate degree of dry mixing is preferred for high-performance dry-processed lithium-ion battery electrodes.

25 ENERGY STORAGE↗
DOE OSTI2025

Disentangling the gap between pure and mixed-gas performance of thin film composite membranes through improved cell design and testing methods

Testing thin film composite (TFC) membrane coupons at low stage-cuts (≤5%) in a sweep-gas permeation system is a common practice to obtain mixed-gas separation properties for benchmarking performance and making scale-up decisions. However, even under these idealized conditions, mixed-gas permeance and selectivity can be more than 30% lower than their pure-gas values, partially due to concentration polarization, an effect that typically intensifies with increased membrane permeance. This study investigates the effect of cell design on mixed-gas testing using PolyActive TM TFC membranes with pure-gas CO 2 permeance of 1700 – 3100 gas permeance unit (GPU), covering the permeance range of most state-of-the-art CO 2 /N 2 separation membranes. Here, we designed and 3D-printed a counter-current permeation cell with enhanced feed and sweep flow efficiency, resulting in a 33 – 41% increase in mixed-gas CO 2 permeance compared to traditional permeation cells. Furthermore, we compared sweep-gas and vacuum permeation methods using traditional permeation cells, revealing that the latter delivers 41% higher mixed-gas CO 2 permeance, because vacuuming effectively minimizes the downstream concentration polarization. These findings highlight the importance of cell design and permeation apparatus selection in lab-scale mixed-gas testing, with strong implications for module design and process optimization at the industrial scale.

mixed gas performance↗
DOE OSTI2023

The Chemical and Electronic Properties of Stability-Enhanced, Mixed Ir-TiO x Oxygen Evolution Reaction Catalysts

Iridium has emerged as the leading catalyst material for the anodic oxygen evolution reaction (OER) in acidic media. Often, iridium is mixed with more stable materials such as titanium. For these materials, the electronic structure of titanium plays a crucial role since with varying degrees of oxidation titanium transforms to semiconducting or even insulating phases. Yet, the electronic properties of mixed Ir-TiO x catalysts have never been systematically studied. In this study, we correlate the catalytic performance of mixed Ir-TiO x -based OER catalysts with the electronic structure of the surface layers. For this, a thin film material library with a 20-70 at. % Ir (Ir/[Ir + Ti]) compositional gradient was prepared. We used inductively coupled plasma mass spectrometry to test the OER activity and stability of the set of mixed Ir-TiO x catalyst candidate materials. Complementary, Ti L 2,3 - and O K-edge X-ray absorption spectroscopy and depth-dependent X-ray photoelectron spectroscopy measurements were performed to correlate the catalytic performance with the composition and electronic property profiles of these mixed Ir-TiO x OER anode catalysts. The spectroscopic analysis reveals that titanium is present as an intermixed matrix of semiconductive but stable TiO 2 , conductive but less stable titanium-suboxides (TiO x ), and highly conductive but highly unstable metallic Ti(0). The extent of the titanium oxidation strongly depends on the titanium content, with a lower degree of oxidation observed for lower titanium (and thus higher iridium) contents. For an iridium loading of 70 at. %, the respective mixed Ir-TiO x catalyst showed a similar OER activity to that of the pure metallic iridium (1.74 vs 1.59 VRHE, respectively) but with a 71% lower iridium dissolution rate relative to the pure metallic iridium. This demonstrates the stabilization effect of titanium addition while maintaining high OER activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Sensitivity of Global Ocean Deoxygenation to Vertical and Isopycnal Mixing in an Ocean Biogeochemistry Model

Large-scale loss of oxygen under global warming is termed “ocean deoxygenation” and is caused by the imbalance between physical supply and biological consumption of oxygen in the ocean interior. Significant progress has been made in the theoretical understanding of ocean deoxygenation; however, many questions remain unresolved. The oxygen change in the tropical thermocline is poorly understood, with diverging projections among different models. Physical oxygen supply is controlled by a suite of processes that transport oxygen-rich surface waters into the interior ocean, which is expected to weaken due to increasing stratification under global warming. Using a numerical model and a series of sensitivity experiments, the role of ocean mixing is examined in terms of effects on the mean state and the response to a transient warming. Both vertical and horizontal (isopycnal) mixing coefficients are systematically varied over a wide range, and the resulting oxygen distributions in equilibrated and transient simulations are examined. The spatial patterns of oxygen loss are sensitive to both vertical and isopycnal mixing, and the sign of tropical oxygen trend under climate warming can reverse depending on the choice of mixing parameters. An elevated level of isopycnal mixing disrupts the vertical advective-diffusive balance of the tropical thermocline, increasing the mean state oxygen as well as the magnitude of the transient oxygen decline. These results provide first-order explanations for the diverging behaviors of simulated tropical oxygen with respect to ocean mixing parameters.

58 GEOSCIENCES↗
DOE OSTI2025

Future grid mix impacts on whole-building life cycle assessment

Building construction and operation are a significant contribution to global greenhouse gas emissions, so understanding and mitigating emissions is crucial for reliable and realistic emissions accounting. Whole-building Life Cycle Assessment (WBLCA) is an emissions accounting method that considers lifetime environmental impacts of a building during its construction, operation, and eventual end-of-life. When performing WBLCAs, emission calculations from the building's operation over the entire building lifespan are typically based on today's energy grid mixes. This method does not consider changes or advancements in the clean energy proportion within the grid mix and can over or under-inflate results, skewing the ratio of embodied vs. operational environmental impacts. While a variety of prediction tools estimate what future grid emissions might be, predictions can vary widely. To predict the clean energy ratio within future grid mixes and the potential impact these changes might have on WBLCA, annual data from several existing U.S. grid models was averaged and probabilistic modeling was used to extend the usable projections of shorter forecasts. Results show that clean energy sources will likely continue to increase over time, although the rate of growth varies by model. On average, by 2085, the clean energy penetration of the grid is projected to reach ~81% and renewable energy is projected to reach ~71%, although no widespread consensus is reached. To understand how the future grid mix impacts lifetime building emissions within a WBLCA context, the team analyzed two 2021 IECC-compliant all-electric residential buildings: one built from traditional materials and construction processes and the other built with carbon sequestering materials and modular assembly, with a portion of energy generated on site. The results indicate that a moderate estimate of future electricity grid mixes shows a reduction of yearly operational emissions for traditional residential buildings of 55% between 2025 and 2085, and a corresponding reduction of 48% of total emissions over a 60 year building lifespan. This study offers a nuanced approach to account for the variability of future grid mix models and provides an average trend-line based on a robust collection of scenarios.

Life Cycle Assessment (LCA)↗
DOE OSTI2022

Freshwater Input and Vertical Mixing in the Canada Basin’s Seasonal Halocline: 1975 versus 2006–12

Abstract The Arctic seasonal halocline impacts the exchange of heat, energy, and nutrients between the surface and the deeper ocean, and it is changing in response to Arctic sea ice melt over the past several decades. Here, we assess seasonal halocline formation in 1975 and 2006–12 by comparing daily, May–September, salinity profiles collected in the Canada Basin under sea ice. We evaluate differences between the two time periods using a one-dimensional (1D) bulk model to quantify differences in freshwater input and vertical mixing. The 1D metrics indicate that two separate factors contribute similarly to stronger stratification in 2006–12 relative to 1975: 1) larger surface freshwater input and 2) less vertical mixing of that freshwater. The larger freshwater input is mainly important in August–September, consistent with a longer melt season in recent years. The reduced vertical mixing is mainly important from June until mid-August, when similar levels of freshwater input in 1975 and 2006–12 are mixed over a different depth range, resulting in different stratification. These results imply that decadal changes to ice–ocean dynamics, in addition to freshwater input, significantly contribute to the stronger seasonal stratification in 2006–12 relative to 1975. These findings highlight the need for near-surface process studies to elucidate the impact of lateral processes and ice–ocean momentum exchange on vertical mixing. Moreover, the results may provide insight for improving the representation of decadal changes to Arctic upper-ocean stratification in climate models that do not capture decadal changes to vertical mixing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Investigating the Effects of Mixing Dynamics on Twin-Screw Granule Quality Attributes via the Development of a Physics-Based Process Map

Twin-screw granulation (TSG) is an emerging continuous wet granulation technique that has not been widely applied in the industry due to a poor mechanistic understanding of the process. This study focuses on improving this mechanistic understanding by analyzing the effects of the mixing dynamics on the granule quality attributes (PSD, content uniformity, and microstructure). Mixing is an important dynamic process that simultaneously occurs along with the granulation rate mechanisms during the wet granulation process. An improved mechanistic understanding was achieved by identifying and quantifying the physically relevant intermediate parameters that affect the mixing dynamics in TSG, and then their effects on the granule attributes were analyzed by investigating their effects on the granulation rate mechanisms. The fill level, granule liquid saturation, extent of nucleation, and powder wettability were found to be the key physically relevant intermediate parameters that affect the mixing inside the twin-screw granulator. An improved geometrical model for the fill level was developed and validated against existing experimental data. Finally, a process map was developed to depict the effects of mixing on the temporal and spatial evolution of the materials inside the twin-screw granulator. This process map illustrates the mechanism of nucleation and the growth of the granules based on the fundamental material properties of the primary powders (solubility and wettability), liquid binders (viscosity), and mixing dynamics present in the system. Furthermore, it was shown that the process map can be used to predict the granule product quality based on the granule growth mechanism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2017

Vibrational Dependence of Line Coupling and Line Mixing in Self-Broadened Parallel Bands of NH3

Line coupling and line mixing effects have been calculated for several self-broadened NH3 lines in parallel bands involving an excited v2 mode. It is well known that once the v2 mode is excited, the inversion splitting quickly increases as this quantum number increases. In the present study, we have shown that the v2 dependence of the inversion splitting plays a dominant role in the calculated line-shape parameters. For the v2 band with a 36 cm-1 splitting, the intra-doublet couplings practically disappear and for the 2v2 and 2v2 - v2 bands with much higher splitting values, they are completely absent. With respect to the inter-doublet coupling, it becomes the most efficient coupling mechanism for the v2 band, but it is also completely absent for bands with higher v2 quantum numbers. Because line mixing is caused by line coupling, the above conclusions on line coupling are also applicable for line mixing. Concerning the check of our calculated line mixing effects, while the present formalism has well explained the line mixing signatures observed in the v1 band, there are large discrepancies between the measured Rosenkranz mixing parameters and our calculated results for the v2 and 2v2 bands. In order to clarify these discrepancies, we propose to make some new measurements. In addition, we have calculated self-broadened half-widths in the v2 and 2v2 bands and made comparisons with several measurements and with the values listed in HITRAN 2012. In general, the agreements with measurements are very good. In contrast, the agreement with HITRAN 2012 is poor, indicating that the empirical formula used to predict the HITRAN 2012 data has to be updated.

Parallel bands↗
NASA NTRSDate not supplied

Linear Mixed-Effects Models for Human-in-the-Loop Tracking Experiment Data

Linear mixed-effects models provide several benefits over more traditional statistical inference tests that are particularly useful for most human-in-the-loop tracking experiment data. However, surprisingly, mixed models are virtually not used for the analysis of tracking experiment data. This paper uses of linear mixed-effects models to analyze combined tracking data from two previous human-in-the-loop roll tracking experiments that compared control behavior metrics collected in both a research aircraft and a motion-base simulator. In the experiments, pilots' behavior under 10 different motion configurations with varying motion filter gains and break frequencies was evaluated and compared to that in the real aircraft. The linear mixed-effects model analysis on the combined dataset confirmed the main statistical outcomes of the individual experiments. The main benefits of mixed models for this type of data were demonstrated by successfully combining data from two experiments that used different experimental conditions and of which one had an additional apparatus and the other a missing participant. Finally, the mixed-model analysis was able to explicitly test for scientifically relevant statistical differences in the dependent measures between the aircraft and simulator, as well as both experiments.

manual control↗
NASA NTRS2022

Seasonal and Interannual Variability of Tidal Mixing Signatures in Indonesian Seas from High-Resolution Sea Surface Temperature

With their complex narrow passages and vigorous mixing, the Indonesian seas provide the only low-latitude pathway between the Pacific and Indian Oceans and thus play an essential role in regulating Pacific-Indian Ocean exchange, regional air-sea interaction, and ultimately, global climate phenomena. While previous investigations using remote sensing and numerical simulations strongly suggest that this mixing is tidally driven, the impacts of monsoon and El Niño Southern Oscillation (ENSO) on tidal mixing in the Indonesian seas must play an important role. Here we use high-resolution sea surface temperature from June 2002 to June 2021 to reveal monsoon and ENSO modulations of mixing. The largest spring-neap (fortnightly) signals are found to be localized in the narrow passages/straits and sills, with more vigorous tidal mixing during the southeast (boreal summer) monsoon and El Niño than that during the northwest (boreal winter monsoon) and La Niña. Therefore, tidal mixing, which necessarily responds to seasonal and interannual changes in stratification, must also play a feedback role in regulating seasonal and interannual variability of water mass transformations and Indonesian throughflow. The findings have implications for longer-term variations and changes of Pacific–Indian ocean water mass transformation, circulation, and climate.

Indonesian seas↗
DOE OSTI2023

The homogeneous mixing of MgO and H 2 O at extreme conditions

Investigating water worlds presents a unique opportunity to understand the fundamental processes of planetary formation and evolution. One key aspect is characterizing the interactions between water and rock under the pressures and temperatures present within these worlds. Investigating the conditions for the homogeneous mixing of these materials is imperative to characterizing bulk properties and evolution of water-rich exoplanets. Here, in this study, we use density functional molecular dynamics simulations to study MgO-H 2 O mixtures at high pressure–temperature conditions where H 2 O occurs in solid, superionic, or liquid form. MgO, the representative rocky material, can be either solid or liquid. We start from 500 K at 120 GPa, increasing the temperature step by step up to 8000 K. By inspection, we determine the temperature at which MgO-HO homogeneously mix in our simulations. At 6000 K and 174 GPa is when we find the system to homogeneously mix. This heat-until-it-mixes approach provides us with an upper bound on the temperature for the mixing of MgO and H 2 O. We find that homogeneous mixing occurs at sufficiently low temperatures to be relevant for the collisional growth of a water-rich planet.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Information loss, mixing and emergent type III 1 factors

A manifestation of the black hole information loss problem is that the two-point function of probe operators in a large Anti-de Sitter black hole decays in time, whereas, on the boundary CFT, it is expected to be an almost periodic function of time. We point out that the decay of the two-point function (clustering in time) holds important clues to the nature of observable algebras, states, and dynamics in quantum gravity. We call operators that cluster in time “mixing” and explore the necessary and sufficient conditions for mixing. The information loss problem is a special case of the statement that in type I algebras, there exists no mixing operators. We prove that, in a thermofield double state (KMS state), if mixing operators form an algebra (close under multiplication), the resulting algebra must be a von Neumann type III 1 factor. In other words, the physically intuitive requirement that all nonconserved operators should exponentially mix is so strong that it fixes the observable algebra to be an exotic algebra called a type III1 factor. More generally, for an arbitrary out-of-equilibrium state of a general quantum system (von Neumann algebra), we show that if the set of operators that mix under modular flow forms an algebra, it is a type III1 von Neumann factor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗