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At least 145 records · Page 8

Cloud microphysical response to entrainment and mixing is locally inhomogeneous and globally homogeneous: Evidence from the lab

Entrainment of dry air into clouds strongly influences cloud optical and precipitation properties and the response of clouds to aerosol perturbations. The response of cloud droplet size distributions to entrainment–mixing is examined in the Pi convection-cloud chamber that creates a turbulent, steady-state cloud. The experiments are conducted by injecting dry air with temperature (T e ) and flow rate (Q e ) through a flange in the top boundary, into the otherwise well-mixed cloud, to mimic the entrainment–mixing process. Due to the large-scale circulation, the downwind region is directly affected by entrained dry air, whereas the upwind region is representative of the background conditions. Droplet concentration (Cn) and liquid water content (L) decrease in the downwind region, but the difference in the mean diameter of droplets (D m ) is small. The shape of cloud droplet size distributions relative to the injection point is unchanged, to within statistical uncertainty, resulting in a signature of inhomogeneous mixing, as expected for droplet evaporation times small compared to mixing time scales. As T e and Q e of entrained air increase, however, Cn, L, and D m of the whole cloud system decrease, resulting in a signature of homogeneous mixing. The apparent contradiction is understood as the cloud microphysical responses to entrainment and mixing differing on local and global scales: locally inhomogeneous and globally homogeneous. This implies that global versus local sampling of clouds can lead to seemingly contradictory results for mixing, which informs the long-standing debate about the microphysical response to entrainment and the parameterization of this process for coarse-resolution models.

54 ENVIRONMENTAL SCIENCES↗

Mixing Cell Model: A One-Dimensional Numerical Model for Assessment of Water Flow and Contaminant Transport in the Unsaturated Zone

This report describes the Mixing Cell Model code, a one dimensional model for water flow and solute transport in the unsaturated zone under steady state or transient flow conditions. The model is based on the principles and assumptions underlying mixing-cell model formulations. The unsaturated zone is discretized into a series of independent mixing cells. Each cell may have unique hydrologic, lithologic, and sorptive properties. Ordinary differential equations describe the material (water and solute) balance within each cell. Water-flow equations are derived from the continuity equation, assuming that unit gradient conditions exist at all times in each cell. Pressure gradients are considered implicitly through model discretization. Unsaturated hydraulic conductivity and moisture contents are determined by the material specific moisture-characteristic curves. Solute-transport processes include explicit treatment of advective processes, first order chain decay, and linear sorption reactions. Dispersion is addressed through implicit and explicit dispersion. Implicit dispersion is an inherent feature of all mixing-cell models and originates from the formulation of the problem in terms of mass balance around fully mixed volume elements. Expressions are provided that relate implicit dispersion to the physical dispersion of the system. Two FORTRAN codes were developed to solve the water flow and solute-transport equations: (1) the Mixing Cell Model for Flow (MCMF) solves transient water-flow problems and (2) the Mixing Cell Model for Transport (MCMT) solves the solute-transport problem. The transient water-flow problem is typically solved first by estimating the water flux through each cell in the model domain as a function of time using the MCMF code. These data are stored in either ASCII or binary files that are later read by the solute transport code (MCMT). Code output includes solute pore water concentrations, water and solute inventories in each cell and at each specified output time, and water and solute fluxes through each cell and specified output time. Computer run times for coupled transient water flow and solute transport were typically several seconds on a 2 GHz Intel Pentium IV desktop computer. The model was benchmarked against analytical solutions and finite element approximations to the partial differential equations (PDE) describing unsaturated flow and transport. Differences between the maximum solute flux estimated by the mixing cell model and the PDE models were typically less than two percent. This revision includes an option for a fixed concentration lower boundary condition for diffusive fluxes for versions 020321 and later.

54 ENVIRONMENTAL SCIENCES↗

Quantifying the Turbulent Entrainment‐Mixing Processes Based on Z ‐LWC Relationships of Cloud Droplets

Abstract Turbulent entrainment‐mixing processes profoundly influence the relationship between radar reflectivity factor and liquid water content ( Z ‐LWC) of cloud droplets. However, quantification of the entrainment‐mixing mechanisms based on the Z ‐LWC relationship is still lacking. To address this gap, 12,218 entrainment‐mixing cases are simulated using the Explicit Mixing Parcel Model. We examine the variations of the parameters in the power‐law relationship Z = a LWC b , and the relationship between parameter b and homogeneous mixing degree ( ψ ), a measure quantifying entrainment‐mixing processes. The results indicate that parameter b distributes within the range of 1–2, with a positive correlation between parameter b and ψ . The b ‐ ψ relationship is fitted, which connects the Z ‐LWC relationship for various entrainment‐mixing types. The results suggest the potential for employing a remote sensing approach to investigate the entrainment‐mixing mechanisms of non‐precipitating small cumulus/stratocumulus clouds, thereby overcoming the limitations of traditional observational studies that rely solely on aircraft observations.

54 ENVIRONMENTAL SCIENCES↗

Modeling gas–shell mixing in ICF with separated reactants

Mixing between fuel and shell materials in ICF implosions can affect implosion dynamics and even prevent ignition. We use data from a series of separated reactant experiments on the National Ignition Facility to calibrate and test the predictive power of gas–shell mix models. Two models are used to estimate fuel–shell mix: a Reynolds-averaged turbulence model and molecular diffusion. Minor uncertainties in capsule manufacture, experimental conditions, and values for mix model parameters produce significant variation in simulation results. Using input/output pairs from 1D simulations, we train Gaussian process surrogate models to predict experimental quantities of interest. The surrogates are used to construct posteriors for mix model parameters by marginalizing over uncertainties in capsule manufacture and experimental conditions. Mix models are calibrated with a subset of experimental data (neutron yields, ion temperature, and bang time) and tested using the remaining data. In general, both the diffusion and turbulence model correctly predict experimental DT and TT neutron yields. Despite having more free parameters, the turbulence model underpredicts ion temperature at high convergence ratio. Furthermore, the simpler diffusion model correctly predicts these temperatures, suggesting nonhydrodynamic gas–shell mix. The computational model consistently overpredicts DD neutron yield, indicating possible shortcomings outside of the mix model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Inertia-induced mixing and reaction maximization in laminar porous media flows

Solute transport and biogeochemical reactions in porous and fractured media flows are controlled by mixing, as are subsurface engineering operations such as contaminant remediation, geothermal energy production, and carbon sequestration. Porous media flows are generally regarded as slow, so the effects of fluid inertia on mixing and reaction are typically ignored. Here, we demonstrate through microfluidic experiments and numerical simulations of mixing-induced reaction that inertial recirculating flows readily emerge in laminar porous media flows and dramatically alter mixing and reaction dynamics. An optimal Reynolds number that maximizes the reaction rate is observed for individual pore throats of different sizes. This reaction maximization is attributed to the effects of recirculation flows on reactant availability, mixing, and reaction completion, which depend on the topology of recirculation relative to the boundary of the reactants or mixing interface. Recirculation enhances mixing and reactant availability, but a further increase in flow velocity reduces the residence time in recirculation, leading to a decrease in reaction rate. The reaction maximization is also confirmed in a flow channel with grain inclusions and randomized porous media. Interestingly, the domain-wide reaction rate shows a dramatic increase with increasing Re in the randomized porous media case. This is because fluid inertia induces complex three-dimensional flows in randomized porous media, which significantly increases transverse spreading and mixing. This study shows how inertial flows control reaction dynamics at the pore scale and beyond, thus having major implications for a wide range of environmental systems.

Chen, Michael A. (ORCID:0000000294614710)↗

Advances in Mixed Precision Algorithms: 2021 Edition

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are: Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; results and strategies for mixed precision IR using a sparse LU factorization; a mixed precision eigenvalue solver; Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; preparing hypre for mixed precision execution; mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; and detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.

97 MATHEMATICS AND COMPUTING↗

Advances in Mixed Precision Algorithms: 2021 Edition

Over the last year, the ECP xSDK-multiprecision effort has made tremendous progress in developing and deploying new mixed precision technology and customizing the algorithms for the hardware deployed in the ECP flagship supercomputers. The effort also has succeeded in creating a cross-laboratory community of scientists interested in mixed precision technology and now working together in deploying this technology for ECP applications. In this report, we highlight some of the most promising and impactful achievements of the last year. Among the highlights we present are • Mixed precision IR using a dense LU factorization and achieving a 1.8× speedup on Spock; • Results and strategies for mixed precision IR using a sparse LU factorization; • A mixed precision eigenvalue solver; • Mixed Precision GMRES-IR being deployed in Trilinos, and achieving a speedup of 1.4× over standard GMRES; • Compressed Basis (CB) GMRES being deployed in Ginkgo and achieving an average 1.4× speedup over standard GMRES; • Preparing hypre for mixed precision execution; • Mixed precision sparse approximate inverse preconditioners achieving an average speedup of 1.2×; • Detailed description of the memory accessor separating the arithmetic precision from the memory precision, and enabling memory-bound low precision BLAS 1/2 operations to increase the accuracy by using high precision in the computations without degrading the performance. We emphasize that many of the highlights presented here have also been submitted to peer-reviewed journals or established conferences, and are under peer-review or have already been published.

97 MATHEMATICS AND COMPUTING↗

Advancing the Understanding of Cloud Microphysical Processes and Aerosol Indirect Effects in High-Latitude Mixed-Phase Clouds by Linking ARM Measurements with Climate Model Simulations (Final Report)

The key objectives of this project were to advance our understanding of cloud microphysical characteristics and aerosol indirect effects on mixed-phase clouds in high latitudes. To improve the representation of ice and mixed-phase clouds in Earth System Models (ESMs), we propose an integrated observation and modeling study of cloud macro- and microphysical properties, including spatial heterogeneities, mass partitioning between ice crystals and supercooled liquid water, effects of ice nucleating particles (INPs), and efficiency of secondary ice production (SIP), etc. Specifically, we took four main approaches in this project: (1) examining macro- and microphysical properties of ice and mixed-phase clouds based on in-situ and ground-based observations from multiple field campaigns funded by the U.S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program, including the Mixed-Phase Arctic Cloud Experiment (M-PACE), Indirect and Semi-Direct Aerosol Campaign (ISDAC), Ice Nucleating Particle Sources at Oliktok Point (INPOP), ARM West Antarctic Radiation Experiment (AWARE), Measurements of Aerosols, Radiation, and Clouds over the Southern Ocean (MARCUS), and Macquarie Island Cloud and Radiation Experiment (MICRE); (2) evaluating the DOE Energy Exascale Earth System Model (E3SM) simulations based on observations, particularly for ice and mixed-phase cloud microphysical properties; (3) examining the impacts of INPs on ice and mixed-phase clouds. Specifically, a series of comparisons were conducted using observations over the Arctic, Southern Ocean, and Antarctica, including comparisons between the lower and higher southern latitudes as well as comparisons between the northern and southern hemispheres. In addition, aerosol indirect effects from distinct sources of dust particles were examined; and (4) investigating the impacts of SIP. Ultimately, these results helped to improve cloud microphysics and aerosol-cloud interaction parameterizations in the E3SM model. Overall, the project provided improved understanding regarding various factors, including thermodynamic, dynamic, and aerosol conditions, on the micro- and macrophysical properties of ice and mixed-phase clouds in the high latitudes. Resulting analysis helped to provide an improved physical basis for refining the current cloud microphysics parameterizations related to ice and mixed-phase clouds in E3SM.

54 ENVIRONMENTAL SCIENCES↗

Decontamination of Mixed Paper and Plastic Municipal Solid Waste Increases Low and High Temperature Conversion Yields

With the implementation of China’s Green Fence Policy and the following National Sword Policy, there is a need to divert previously accepted waste materials away from the landfill. Mixed plastic and paper wastes that are too contaminated to be economically recycled can be used for conversion into fuels and products. The effect of common contaminants present in waste streams must be determined to make municipal solid waste (MSW) a viable alternative to agricultural feedstocks for conversion. In this study, MSW was sourced from a dual stream materials recovery facility (MRF) in Emmet County, Michigan and characterized via mass balance. The most common contaminants in mixed paper and plastic were quantified and targeted for decontamination when mixed paper was explored for low temperature conversion pathways and plastics for high temperature conversion pathways. Ink, stickies, and plastic contamination were sorted out of the mixed paper stream and did not have an impact on sugar yields during enzymatic hydrolysis (EH). Although no improvement in yield was found, it was noted that copy paper within the mixed paper stream had an elevated pH and higher concentration of fermentation inhibitors, suggesting that intrinsic properties of some paper types may not be ideal for EH and fermentation conversion. Dilute alkaline pretreatment and mechanical refining of mixed paper increased the EH yield of mixed paper, suggesting this previously established process could be used as a decontamination method. “Dirt” and particulates were washed from mixed plastic using either an aqueous detergent or a non-aqueous chemical washing method. Liquid oil yields were increased during microwave assisted fast pyrolysis. All decontamination techniques met the cost target of less than $30/dry ton with plastic decontamination ranging from $18.16 to $24.81/dry ton. Because dilute alkaline pre-treatment and mechanical refining is considered part of the conversion process, the decontamination cost during feedstock preprocessing was considered $0/dry ton.

09 BIOMASS FUELS↗

Comprehensive quantification of height dependence of entrainment mixing between stratiform cloud top and environment

Different entrainment-mixing processes of turbulence are crucial to processes related to clouds; however, only a few qualitative studies have been concentrated on the vertical distributions of entrainment-mixing mechanisms with low vertical resolutions. To quantitatively study vertical profiles of entrainment-mixing mechanisms with a high resolution, the stratiform clouds observed in the Physics of Stratocumulus Top (POST) project are examined. The unique sawtooth flight pattern allows for an examination of the vertical distributions of entrainment-mixing mechanisms with a 5 m vertical resolution. Relative standard deviation of volume mean radius divided by relative standard deviation of liquid water content is introduced to be a new estimation of microphysical homogeneous mixing degree, to overcome difficulties of determining the adiabatic microphysical properties required in existing measures. The vertical profile of this new measure indicates that entrainment-mixing mechanisms become more homogeneous with decreasing altitudes and are consistent with the dynamical measures of Damköhler number and transition scale number. Further analysis shows that the vertical variation of entrainment-mixing mechanisms with decreasing altitudes is due to the increases of turbulent dissipation rate in cloud and relative humidity in droplet-free air and the decrease of size of droplet-free air. The results offer insights into the theoretical understanding and parameterizations of vertical variation of entrainment-mixing mechanisms.

54 ENVIRONMENTAL SCIENCES↗

The impact of aerosol mixing state on immersion freezing: insights from classical nucleation theory and particle-resolved simulations

Immersion freezing, initiated by ice-nucleating particles (INPs) in supercooled aqueous droplets, plays an important role in the formation of ice crystals within clouds. The efficiency of immersion freezing depends strongly on INP composition and, crucially, on the mixing state – how chemical species are distributed across the particle population. Here, we quantify the impact of aerosol mixing state on immersion freezing using a combined theoretical and particle-resolved modeling approach. We derive analytical expressions for the frozen fraction of internally and externally mixed INP populations based on classical nucleation theory, showing that the frozen fraction is sensitive to whether ice-active species are present in all particles or only in a subset of the population. We introduce a multi-species immersion freezing scheme into the particle-resolved model PartMC, using the water activity-based immersion freezing model (ABIFM) to compute freezing probabilities for mixed-composition particles. To improve computational efficiency, we implement a Binned Tau-Leaping algorithm and demonstrate an order-of-magnitude speedup with minimal accuracy loss. Simulations reproduce the analytical trends in limiting cases and extend the analysis to more general aerosol populations, where mixing state continues to exert a substantial control on frozen fraction. Sensitivity analyses across particle size, species type, and cooling condition reveal that the mixing state effect is most pronounced when small amounts of highly efficient INPs are mixed with less efficient materials. These findings underscore the need to represent aerosol mixing state explicitly in models of heterogeneous ice nucleation to reduce uncertainty in cloud-phase partitioning.

54 ENVIRONMENTAL SCIENCES↗

Fluid mixing apparatus using high- and low-pressure fluid streams

A fluid mixing apparatus includes mixing conduits that extend through a fluid plenum and that define injection holes therethrough. The fluid plenum, which surrounds a first wall defining a main passage fluidly coupled to a low-pressure fluid source, is surrounded itself by a second wall defining a high-pressure plenum fluidly coupled to a high-pressure fluid source. The mixing conduits fluidly couple the high-pressure plenum to the main passage, and the fluid from the fluid plenum is delivered with the high-pressure fluid to the main passage, where the fluids mix before being discharged from an outlet of the main passage. The fluid mixing apparatus may be used to mix one or more fuels with high- and low-pressure air in a gas turbine combustor. Alternately, the fluid mixing apparatus may mix a fluid with high- and low-pressure water streams.

Berry, Jonathan Dwight↗

Machine learning assisted modeling of mixing timescale for LES/PDF of high-Karlovitz turbulent premixed combustion

Accurate modeling of mixing in the transported probability density function (PDF) method remains a great challenge, especially for turbulent premixed combustion under extreme conditions such as high Karlovitz number Ka. Recently, a power-law based mixing timescale model was developed for the large-eddy simulations (LES)/PDF modeling of high-Ka number turbulent premixed flames. It is found in this work that the power-law mixing timescale model is highly sensitive to the model parameters. It is thus critically needed to develop accurate calibration of these model parameters. The empirical specification of the model parameters developed in Zhang et. al. is found to be inadequate for accurate modeling of the mixing timescale. Here, machine learning is introduced as an attractive alternative in this work for the specification of the model parameters. A high-Ka number DNS jet flame is used as the training and validation of the machine learning models. The choices of the input parameters are discussed and compared for the machine learning models. The effect of differential molecular diffusion on mixing is examined by including the effect of the Lewis number in the training of the machine learning models. The performance of different machine learning algorithms is compared for the specification of the mixing model parameters. Overall, excellent performance of the machine learning models is observed for assisting the mixing modeling. The feasibility, interpretability, applicability, generality, and portability of using machine learning are discussed in general to provide a perspective on applying data-driven machine learning for turbulent combustion modeling studies.

42 ENGINEERING↗

Numerical Mixing Suppresses Submesoscale Baroclinic Instabilities Over Sloping Bathymetry

Abstract The impacts of spurious numerical salinity mixing on the larger‐scale flow and tracer fields are characterized using idealized simulations. The idealized model is motivated by realistic simulations of the Texas‐Louisiana shelf and features oscillatory near‐inertial wind forcing. can exceed the physical mixing from the turbulence closure in frontal zones and within the mixed layer. This suggests that simulated mixing processes in frontal zones are driven largely by . Near‐inertial alongshore wind stress amplitude is varied to identify a base case that maximizes the ratio of to in simulations with no prescribed horizontal mixing. We then test the sensitivity of the base case with three tracer advection schemes (MPDATA, U3HC4, and HSIMT) and conduct ensemble runs with perturbed bathymetry. Instability growth is evaluated using the volume‐integrated eddy kinetic energy and available potential energy . While all schemes have similar total mixing, the HSIMT simulations have over double the volume‐integrated and 20% less relative to other schemes, which suppresses the release of and reduces the by roughly 25%. This results in reduced isohaline variability and steeper isopycnals, evidence that enhanced suppresses instability growth. Differences in and between the MPDATA and U3HC4 simulations are marginal. However, the U3HC4 simulations have 25% more . Experiments with variable horizontal viscosity and diffusivity coefficients show that small amounts of prescribed horizontal mixing improve the representation of the ocean state for all advection schemes by reducing the and increasing the .

54 ENVIRONMENTAL SCIENCES↗

Transient mixing behavior of a supercritical fluid injected into supercritical and subcritical environments

Transient, near-field mixing of a supercritical fluid injected into supercritical and subcritical environments is investigated experimentally. Fuel (propane) from a 100 μm diameter Bosch diesel injector is injected into a high-pressure test rig with a steady flow of heated, low-velocity nitrogen to control the ambient pressure and temperature. The fuel supply pressure is approximately 190 bar, allowing short injections lasting 3–4 ms to be performed in quick succession to acquire statistically significant datasets to represent the unsteady fuel–air mixing. Two test cases with the same ambient density and injector inlet pressure and temperature were chosen in an attempt to isolate effects of mixture phase behavior. Microscopic rainbow Schlieren deflectometry (RSD) is used for visualization and quantitative data acquisition. In the case of the supercritical ambient, the injector inlet and exit and ambient conditions are all supercritical. The RSD analysis reveals a mixing process similar to the single phase fluid mixing, though condensation is also observed locally, and can be explained by the adiabatic mixing theory presented in the paper. For the subcritical ambient case, the injector inlet is supercritical, but the injector exit and ambient conditions are both subcritical. The results show a rapid expansion in the near-field promoting mixing between propane and nitrogen. At downstream locations, significant condensation is also observed as predicted by the adiabatic mixing theory. As a result, the supercritical ambient case exhibited longer and narrower jet penetration compared to the subcritical ambient case.

02 PETROLEUM↗

Mixed-valence halide perovskites

Mixed-valence compounds—which feature an element in at least two different oxidation states—can display emergent optical and transport phenomena stemming from electron transfer between the different valences (intervalence charge-transfer; IVCT). As halide perovskites show promise as active materials in numerous optoelectronic devices, it is an opportune moment to incorporate and study the effects of mixed-valence in this versatile materials family, to access tunable electronic structures ranging from insulators to semiconductors to metals. Herein, we introduce the basic concepts of mixed-valence in molecules and discuss how these concepts may be extended to mixed-valence in extended solids. We then review the few studies of mixed valence in 3D and 2D halide perovskites and halide perovskites with mixed-valence impurities, ranging from studies in the early 1900s to the present day. In conclusion, through judicious choice of metal ion, its coordinating ligands and their geometry, and overall structural dimensionality, chemists can exert powerful synthetic control over electronic delocalization in mixed-valence perovskites, and we hope to see this intriguing materials class expand to encompass new compositions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Numerical study of multi-component flow and mixing in a scaled fission product venting system

Numerical simulation of isothermal multi-component gas flow was conducted to study fluid flow and mixing in a scaled low-pressure, low-temperature test facility for the fission product venting system (FPVS) of a gas cooled fast reactor (GFR). The geometry of FPVS test facility was an open loop including gradual expansion coupling and two 90°pipe elbows. First, the validation of large eddy simulation (LES) wall-adapting local eddy-viscosity (WALE) turbulent model was performed for transitional flow in a circular pipe with gradual expansion. The reactingFOAM solver in OpenFOAM v8 was employed. By introducing appropriate turbulence disturbance at the flow inlet, such as turbulence intensity, the numerical results showed good agreement in (1) the velocity profile downstream of the pipe expansion measured by particle image velocimetry (PIV) in this study, and (2) the reattachment length reported in the literature. Using this validated model, the numerical simulation of flow and component mixing was performed for the FPVS with an inlet flowrate corresponding to a Reynolds number of 2,400 to investigate the flow behavior and component mixing. Standard deviation of the mass fraction of component, referred to as absolute mixing index (AMI), was calculated to quantify the mixing of components, showing that the component mixing length determined by AMI is related to the reattachment length downstream of the expansion. Additionally, this study was able to identify the best location in the FPVS test facility to measure the velocity and concentration profies where multicomponent flow is well mixed.

15 GEOTHERMAL ENERGY↗

Models and Algorithms for Equilibrium Analysis of Mixed-Material Nucleic Acid Systems

Dynamic programming algorithms within the NUPACK software suite enable analysis of equilibrium base-pairing properties for complex and test tube ensembles containing arbitrary numbers of interacting nucleic acid strands. Currently, calculations are limited to single-material systems that are either all-RNA or all-DNA. Here, to enable analysis of mixed-material systems that are critical for modern applications in vitro, in situ, and in vivo, we develop physical models and dynamic programming algorithms that allow the material of the system to be specified at nucleotide resolution. Free energy parameter sets are constructed for both RNA/DNA and RNA/2'OMe-RNA mixed-material systems by combining available empirical mixed-material parameters with single-material parameter sets to enable treatment of the full complex and test tube ensembles. New dynamic programming recursions account for the material of each nucleotide throughout the recursive process. For a complex with N nucleotides, the mixed-material dynamic programming algorithms maintain the O(N 3 ) time complexity of the single-material algorithms, enabling efficient calculation of diverse physical quantities over complex and test tube ensembles (e.g., complex partition function, equilibrium complex concentrations, equilibrium base-pairing probabilities, minimum free energy secondary structure(s), and Boltzmann-sampled secondary structures) at a cost increase of roughly 2.0-3.5×. The results of existing single-material algorithms are exactly reproduced when applying the new mixed-material algorithms to single-material systems. Accuracy is significantly enhanced using mixed-material models and algorithms to predict RNA/DNA and RNA/2'OMe-RNA duplex melting temperatures from the experimental literature as well as RNA/DNA melt profiles from new experiments. In conclusion, mixed-material analyses can be performed online using the NUPACK web app (www.nupack.org) or locally using the NUPACK Python module.

2′OMe-RNA↗