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

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

Finite Element Modeling of Extravehicular Mobility Units for Use With Human Body Models – Motivation, Major Challenges, Use Cases and Preliminary Work

Finite element modeling of pressurized spacesuits and implementation with human body models offers many advantages over physical experimentation, but also presents significant challenges. A model of pressurized spacesuit softgoods was developed, integrated with an existing hardgoods model, and fitted to a human body model. Two representative loading scenarios were simulated: dynamic external suit loading and internal occupant-driven loading, to serve as proof-of-concept for the modeling techniques employed. The modeled interactions behaved as intended and illustrate that finite element models of pressurized spacesuits can be used in conjunction with human body models to assess the biomechanical behavior. Further model development and experimental validation are needed.

Finite Element↗
DOE OSTI2013

WHEN MODEL MEETS REALITY – A REVIEW OF SPAR LEVEL 2 MODEL AGAINST FUKUSHIMA ACCIDENT

The Standardized Plant Analysis Risk (SPAR) models are a set of probabilistic risk assessment (PRA) models used by the Nuclear Regulatory Commission (NRC) to evaluate the risk of operations at U.S. nuclear power plants and provide inputs to risk informed regulatory process. A small number of SPAR Level 2 models have been developed mostly for feasibility study purpose. They extend the Level 1 models to include containment systems, group plant damage states, and model containment phenomenology and accident progression in containment event trees. A severe earthquake and tsunami hit the eastern coast of Japan in March 2011 and caused significant damages on the reactors in Fukushima Daiichi site. Station blackout (SBO), core damage, containment damage, hydrogen explosion, and intensive radioactivity release, which have been previous analyzed and assumed as postulated accident progression in PRA models, now occurred with various degrees in the multi-units Fukushima Daiichi site. This paper reviews and compares a typical BWR SPAR Level 2 model with the “real” accident progressions and sequences occurred in Fukushima Daiichi Units 1, 2, and 3. It shows that the SPAR Level 2 model is a robust PRA model that could very reasonably describe the accident progression for a real and complicated nuclear accident in the world. On the other hand, the comparison shows that the SPAR model could be enhanced by incorporating some accident characteristics for better representation of severe accident progression.

42 ENGINEERING↗
DOE OSTI2018

South Asian monsoon precipitation in CMIP5: a link between inter-model spread and the representations of tropical convection

CMIP5 models exhibit a mean dry bias and a large inter-model spread in simulating Indian monsoon precipitation but the origins of the bias and spread have not been well understood. Using moisture and energy budget analysis that exploits the weak temperature gradients in the tropics, we show that they are linked to the convection simulated over the equatorial Indian Ocean. About half of the 21 models analyzed operate at the steep gradient of the non-linear relationship between the normalized precipitable water and normalized precipitation, where small differences in the former are amplified as large differences in precipitation. These models preferentially produce higher precipitation over the equatorial Indian Ocean, and contribute disproportionately to the inter-model spread and multi-model mean dry bias in monsoon precipitation. Conversely, models on the flat side of the relationship are in better agreement with each other and with observations. Under the RCP8.5 forcing scenario, models on the steep part of the relationship project stronger response to warming and dominate the inter-model spread in the projection. This study identified the normalized precipitable water as a key metric for understanding the behavior of model simulated equatorial and Indian monsoon precipitation.

Hagos, Samson (ORCID:0000000175919933)↗
DOE OSTI2015

Impacts of rising air temperatures and emissions mitigation on electricity demand and supply in the United States: a multi-model comparison

The electric power sector both affects and is affected by climate change. Numerous studies highlight the potential of the power sector to reduce greenhouse gas emissions. Yet fewer studies have explored the physical impacts of climate change on the power sector. The present analysis examines how projected rising temperatures affect the demand for and supply of electricity. We apply a common set of temperature projections to three well-known electric sector models in the United States: the US version of the Global Change Assessment Model (GCAM-USA), the Regional Electricity Deployment System model (ReEDS), and the Integrated Planning Model (IPM®). Incorporating the effects of rising temperatures from a control scenario without emission mitigation into the models raises electricity demand by 1.6 to 6.5 % in 2050 with similar changes in emissions. The increase in system costs in the reference scenario to meet this additional demand is comparable to the change in system costs associated with decreasing power sector emissions by approximately 50 % in 2050. This result underscores the importance of adequately incorporating the effects of long-run temperature change in climate policy analysis.

McFarland, James↗
DOE OSTI2019

Model of temperature, evaporation, and productivity in elevated experimental algae raceways and comparison with commercial raceways

Elevated Experimental Raceways (EERs) have been used at many research sites in the United States to evaluate algal biomass productivity. This paper develops temperature and evaporation models for EERs and then evaluates whether the temperature profile and resultant productivity in an EER is representative of large-scale commercial raceways. Open water surface evaporation and temperature models with shading algorithms were programmed in Python and calibrated with temperature and evaporation data from the EERs in the Regional Algal Feedstock Testbed (RAFT) experiments at the University of Arizona. The final calibrated model for EERs was named the EERTEM (Elevated Experimental Raceway Temperature and Evaporation Model). The energy balance algorithms in the Biomass Assessment Tool (BAT model) were also added to the Python code and used to develop temperature simulations of standard commercial paddlewheel raceways. A comparison of BAT and EERTEM simulations indicated that EER temperature fluctuations are not representative of in ground commercial paddlewheel raceways, primarily due to the buffering effect of soil heat flux in commercial raceways. With the different temperature profiles, biomass productivities of three algae species in the EERs were compared to productivities in commercial raceways. Differences in productivity between EERTEM and BAT model temperature profiles were observed when the maximum daytime temperature of one raceway was in the optimal growth range but the temperature of the other raceway exceeded or was below the optimal growth range.

Khawam, George↗
DOE OSTI2016

Modeling fuels and fire effects in 3D: Model description and applications

Scientists and managers critically need ways to assess how fuel treatments alter fire behavior, yet few tools currently exist for this purpose. In this work, we present a spatially-explicit-fuel-modeling system, FuelManager, which models fuels, vegetation growth, fire behavior (using a physics-based model, FIRETEC), and fire effects. FuelManager's flexible approach facilitates modeling fuels across a wide range of detail. Large trees or shrubs with specific coordinates are modeled as individual “Plants”, while understory plants are modeled as collections of plants called “LayerSets”. Both Plants and LayerSets contain various fuel particles (leaves, needles, twigs) with various properties including shape, size and surface area to volume ratio. A wide range of vegetation and treatments can be modeled, analyzed quantitatively and visualized in a 3D viewer. We describe the modeling approach and demonstrate fuel modeling at different levels of detail, fuel treatment and fire effects capabilities. Lastly, detailed model equations are provided in the Appendices.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Modeling of fluid injection-induced fault reactivation using coupled fluid flow and mechanical interface model

The present study is aimed at developing a numerical model to reproduce coupled hydro-mechanical processes associated with fault reactivation by fluid injection in low permeability rock, as part of the DECOVALEX-2019 project Task B. We proposed a modeling approach for simulating the processes using the TOUGH-FLAC simulator, and modeled a fault reactivation experiment conducted at Mont Terri Rock Laboratory in Switzerland. The first step of the study involved benchmark calculations considering a simplified fault plane and geometry. Fluid flow along a fault was modeled using elements of aperture-sized thickness on the basis of Darcy's law and the cubic law in TOUGH2, whereas the mechanical behavior of a single fault was represented by zero-thickness interface elements in FLAC3D upon which a slip and/or separation is allowed. A methodology to connect a TOUGH2 volume element to a FLAC3D interface element was developed for handling the hydro-mechanical interactions on the fault during fluid injection. Two different fault models for describing the evolutions of hydraulic aperture by elastic fracture opening and failure-induced aperture increase were considered in the benchmark calculations. In the coupling process, the changes in geometrical features and hydrological properties induced by mechanical deformation were continuously updated. The transient responses of the fault and host rock to stepwise pressurization were examined during the simulation. The hydro-mechanical behavior, including the injection flow rate, pressure distribution around the borehole, stress conditions, and displacements in normal and shear directions were monitored in the surrounding rock and along the fault. The results of benchmark calculations suggest that the developed model reasonably represents the hydro-mechanical behavior of a fault and the surrounding rock. This modeling approach was applied to the fault reactivation experiment of the Mont Terri Rock Laboratory. In this interpretive modeling, a parametric study was conducted to examine the effects of input parameters regarding in situ stress and fault properties on the hydro-mechanical responses of the fault to water injection. Then, an optimal parameter set to reproduce the field experiment results was chosen by trial-and-error. The injection flow rate and pressure response during fault reactivation closely matched those obtained at the site, which indicates the capability of the model to appropriately capture the progressive pathway evolution during fault reactivation tests at the site. Finally, the anchor displacements were overestimated by the model, but a fair agreement was obtained in terms of the order of magnitude and the variation tendency.

58 GEOSCIENCES↗
DOE OSTI2023

Unraveling the 2021 Central Tennessee flood event using a hierarchical multi-model inundation modeling framework

Flood prediction systems need hierarchical atmospheric, hydrologic, and hydraulic models to predict rainfall, runoff, streamflow, and floodplain inundation. The accuracy of such systems depends on the error propagation through the modeling chain, sensitivity to input data, and choice of models. In this study, we used multiple precipitation forcings (hindcast and forecast) to drive hydrologic and hydrodynamic models to analyze the impacts of various drivers on the estimates of flood inundation depth and extent. We implement this framework to unravel the August 2021 extreme flooding event that occurred in Central Tennessee, USA. We used two radar-based quantitative precipitation estimates (STAGE4 and MRMS) as well as quantitative precipitation forecasts (QPF) from the National Weather Service Weather Prediction Center (WPC) to drive a series of models in the hierarchical framework, including the Variable Infiltration Capacity (VIC) land surface model, the Routing Application for Parallel Computation of Discharge (RAPID) river routing model, and the AutoRoute and TRITON inundation models. An evaluation with observed high-water marks demonstrates that the framework can reasonably simulate flood inundation. Despite the complex error propagation mechanism of the modeling chain, we show that inundation estimates are most sensitive to rainfall estimates. Most notably, QPF significantly underestimates flood magnitudes and inundations leading to unanticipated severe flooding for all stakeholders involved in the event. Finally, we discuss the implications of the hydrodynamic modeling framework for real-time flood forecasting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Improving the modeling of near-wall interphase heat transfer in porous media models of Pebble Bed Reactors

Here, this work aims to improve capabilities for modeling localized effects in porous media models of Pebble Bed Reactors. The wall-channeling effect is the primary local phenomenon of interest in a PBR, where the presence of the reflector wall disrupts the pebble packing, causing the pebbles near the wall to pack less efficiently and creating large void regions. Accurate modeling of the near-wall region is important as it will affect core bypass flow and temperature predictions. Porous media models are commonly used for design scoping and plant-level simulations of PBRs. Although these models have some capabilities to model the near-wall region, the correlations that are available in porous media codes are often inaccurate when a multi-region model is used to discretize the near-wall region. This work employs a high-to-low analysis to study the accuracy of available interphase heat transfer closures. NekRS, a spectral element computational fluid dynamics code, is used to perform Large Eddy Simulations. These LES simulation results are compared to porous media model results from the Pronghorn porous media code. The friction term of the KTA drag closure is first improved, reducing the error in the prediction of the near-wall velocity from over 50% to less than 5%. This is combined with improvements to the form term from previous works to produce a drag closure that is capable of accurately modeling the wall-channeling effect across a variety of flow conditions. The Nusselt number predictions of several heat transfer correlations are compared to the high-fidelity results where it is found that the KTA heat transfer correlation is capable of accurately predicting the local Nusselt numbers that were determined in the high-fidelity simulation. Comparison of the radial solid temperature profiles, however, reveal discrepancies between NekRS and Pronghorn. It is discovered that the implementation of the interphase heat transfer coefficient that exists in many current porous media codes is not valid when local porosities are modeled. Instead, it is suggested that the interphase heat transfer coefficient should be dependent on the local porosity, the Nusselt number, and the local solid surface-to-volume ratio. Implementation of this change produces improvement in the agreement between the results obtained by NekRS and Pronghorn while using the KTA heat transfer correlation.

interphase heat transfer↗
DOE OSTI2024

A comparison of model validation approaches for echo state networks using climate model replicates

As global temperatures continue to rise, climate mitigation strategies such as stratospheric aerosol injections (SAI) are increasingly discussed, but the downstream effects of these strategies are not well understood. As such, there is interest in developing statistical methods to quantify the evolution of climate variable relationships during the time period surrounding an SAI. Feature importance applied to echo state network (ESN) models has been proposed as a way to understand the effects of SAI using a data-driven model. This approach depends on the ESN fitting the data well. If not, the feature importance may place importance on features that are not representative of the underlying relationships. Typically, time series prediction models such as ESNs are assessed using out-of-sample performance metrics that divide the times series into separate training and testing sets. However, this model assessment approach is geared towards forecasting applications and not scenarios such as the motivating SAI example where the objective is using a data driven model to capture variable relationships. Here, in this paper, we demonstrate a novel use of climate model replicates to investigate the applicability of the commonly used repeated hold-out model assessment approach for the SAI application. Simulations of an SAI are generated using a simplified climate model, and different initialization conditions are used to provide independent training and testing sets containing the same SAI event. The climate model replicates enable out-of-sample measures of model performance, which are compared to the single time series hold-out validation approach. For our case study, it is found that the repeated hold-out sample performance is comparable, but conservative, to the replicate out-of-sample performance when the training set contains enough time after the aerosol injection.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

CHARMM-GUI Nanomaterial Modeler for Modeling and Simulation of Nanomaterial Systems

Molecular modeling and simulation are invaluable tools for nanoscience that predict mechanical, physicochemical, and thermodynamic properties of nanomaterials and provide molecular-level insight into underlying mechanisms. However, building nanomaterial-containing systems remains challenging due to the lack of reliable and integrated cyberinfrastructures. Here we present Nanomaterial Modeler in CHARMM-GUI, a web-based cyberinfrastructure that provides an automated process to generate various nanomaterial models, associated topologies, and configuration files to perform state-of- the-art molecular dynamics simulations using most simulation packages. The nanomaterial models are based on the interface force field, one of the most reliable force fields (FFs). The transferability of nanomaterial models among the simulation programs was assessed by single-point energy calculations, which yielded 0.01% relative absolute energy differences for various surface models and equilibrium nanoparticle shapes. Three widely used Lennard-Jones (LJ) cutoff methods are employed to evaluate the compatibility of nanomaterial models with respect to conventional biomolecular FFs: simple truncation at r = 12 Å (12 cutoff), force-based switching over 10 to 12 Å (10-12 fsw), and LJ particle mesh Ewald with no cutoff (LJPME). The FF parameters with these LJ cutoff methods are extensively validated by reproducing structural, interfacial, and mechanical properties. As a result, we find that the computed density and surface energies are in good agreement with reported experimental results, although the simulation results increase in the following order: 10-12 fsw <12 cutoff < LJPME. Nanomaterials in which LJ interactions are a major component show relatively higher deviations (up to 4% in density and 8% in surface energy differences) compared with the experiment. Nanomaterial Modeler's capability is also demonstrated by generating complex systems of nanomaterial-biomolecule and nanomaterial-polymer interfaces with a combination of existing CHARMM-GUI modules. We hope that Nanomaterial Modeler can be used to carry out innovative nanomaterial modeling and simulations to acquire insight into the structure, dynamics, and underlying mechanisms of complex nanomaterial-containing systems.

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

Evaluation of Ocean Biogeochemistry and Carbon Cycling in CMIP Earth System Models With the International Ocean Model Benchmarking (IOMB) Software System

Abstract The International Ocean Model Benchmarking (IOMB) software package is a new community resource that we use here to evaluate surface and upper ocean biogeochemical variables and integrated anthropogenic carbon uptake from earth system models (ESMs) contributing to the 5th and 6th phases of the Coupled Model Intercomparison Project (CMIP5 and CMIP6). IOMB generates graphics and tables for systematically comparing model predictions against multiple datasets. Our analysis reveals some improvement in the multi‐model mean from CMIP5 to CMIP6 for most of the variables we examined. Compared to data‐constrained estimates of ocean anthropogenic carbon uptake for the 1994–2007 period, negative biases exist for many models between 30 and 50°S. Global model estimates of anthropogenic carbon uptake for the same period do not change significantly from CMIP5 to CMIP6, with the combined ensemble mean estimate of 27.8 ± 0.5 Pg C lower than a data‐constrained estimate of 33.0 ± 4.0 Pg C. At the same time, the change in the natural carbon inventory from CMIP is estimated to be a source of 0.7 ± 0.3 Pg C, which is considerably smaller in magnitude than a data‐constrained estimate of 5.0 ± 3.0 Pg C. With chlorofluorocarbon (CFC) predictions available for several models, we demonstrate that negative anthropogenic dissolved inorganic carbon biases coincide with negative biases in CFC concentration, highlighting the importance of weak exchange between the surface and interior ocean in regulating rates of anthropogenic carbon uptake. To examine the robustness of this attribution across the CMIP models, we calculate the global vertical temperature gradient between 200 and 1,000 m as a metric for global stratification and exchange between the surface and deeper waters. We find a linear relationship between the bias of the vertical temperature gradients and the bias in global anthropogenic carbon uptake, consistent with the hypothesis that model biases in anthropogenic carbon uptake are related to biases in surface‐to‐interior exchange by physical processes.

58 GEOSCIENCES↗
DOE OSTI2023

Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes

Abstract In this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demonstrated in Part 1 where upscaled models are rigorously derived in moderately reactive physical regimes. After encoding the algorithm into Symbolica, an automated upscaling framework, we upscale two reactive mass transport problems and numerically validate the resulting nonlinear homogenized models by showing the absolute error estimates predicted by homogenization theory are satisfied. In both problems, nontrivial closure forms and closure problems are automatically formulated using the encoded strategy with no human interaction, nor prior knowledge regarding the closure required for the systems. We hope these demonstrations spark further interest in automated analytical frameworks for multiscale modeling, as such capabilities are invaluable for generating rigorous multiscale models of complex phenomena in porous media.

Pietrzyk, Kyle↗
DOE OSTI2023

Differentiable modelling to unify machine learning and physical models for geosciences

Process-based modelling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. Here, in this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs.

58 GEOSCIENCES↗
DOE OSTI2015

Model for transport and reaction of defects and carriers within displacement cascades in gallium arsenide

A model is presented for recombination of charge carriers at evolving displacement damage in gallium arsenide, which includes clustering of the defects in atomic displacement cascades produced by neutron or ion irradiation. The carrier recombination model is based on an atomistic description of capture and emission of carriers by the defects with time evolution resulting from the migration and reaction of the defects. The physics and equations on which the model is based are presented, along with the details of the numerical methods used for their solution. The model uses a continuum description of diffusion, field-drift and reaction of carriers, and defects within a representative spherically symmetric cluster of defects. The initial radial defect profiles within the cluster were determined through pair-correlation-function analysis of the spatial distribution of defects obtained from the binary-collision code MARLOWE, using recoil energies for fission neutrons. Properties of the defects are discussed and values for their parameters are given, many of which were obtained from density functional theory. The model provides a basis for predicting the transient response of III-V heterojunction bipolar transistors to displacement damage from energetic particle irradiation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Spicing up continuum solvation models with SaLSA: The spherically averaged liquid susceptibility ansatz

Continuum solvation models enable electronic structure calculations of systems in liquid environments, but because of the large number of empirical parameters, they are limited to the class of systems in their fit set (typically organic molecules). Here, we derive a solvation model with no empirical parameters for the dielectric response by taking the linear response limit of a classical density functional for molecular liquids. This model directly incorporates the nonlocal dielectric response of the liquid using an angular momentum expansion, and with a single fit parameter for dispersion contributions it predicts solvation energies of neutral molecules with a RMS error of 1.3 kcal/mol in water and 0.8 kcal/mol in chloroform and carbon tetrachloride. We show that this model is more accurate for strongly polar and charged systems than previous solvation models because of the parameter-free electric response, and demonstrate its suitability for ab initio solvation, including self-consistent solvation in quantum Monte Carlo calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Discontinuous non-equilibrium phase transition in a threshold Schloegl model for autocatalysis: Generic two-phase coexistence and metastability

Threshold versions of Schloegl’s model on a lattice, which involve autocatalytic creation and spontaneous annihilation of particles, can provide a simple prototype for discontinuous non-equilibrium phase transitions. These models are equivalent to so-called threshold contact processes. A discontinuous transition between populated and vacuum states can occur selecting a threshold of N ≥ 2 for the minimum number, N, of neighboring particles enabling autocatalytic creation at an empty site. Fundamental open questions remain given the lack of a thermodynamic framework for analysis. For a square lattice with N = 2, we show that phase coexistence occurs not at a unique value but for a finite range of particle annihilation rate (the natural control parameter). This generic two-phase coexistence also persists when perturbing the model to allow spontaneous particle creation. Such behavior contrasts both the Gibbs phase rule for thermodynamic systems and also previous analysis for this model. We find metastability near the transition corresponding to a non-zero effective line tension, also contrasting previously suggested critical behavior. Mean-field type analysis, extended to treat spatially heterogeneous states, further elucidates model behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Multi-shell model of ion-induced nucleic acid condensation

We present a semi-quantitative model of condensation of short nucleic acid (NA) duplexes induced by trivalent cobalt(III) hexammine (CoHex) ions. The model is based on partitioning of bound counterion distribution around single NA duplex into “external” and “internal” ion binding shells distinguished by the proximity to duplex helical axis. In the aggregated phase the shells overlap, which leads to significantly increased attraction of CoHex ions in these overlaps with the neighboring duplexes. The duplex aggregation free energy is decomposed into attractive and repulsive components in such a way that they can be represented by simple analytical expressions with parameters derived from molecular dynamic simulations and numerical solutions of Poisson equation. The attractive term depends on the fractions of bound ions in the overlapping shells and affinity of CoHex to the “external” shell of nearly neutralized duplex. The repulsive components of the free energy are duplex configurational entropy loss upon the aggregation and the electrostatic repulsion of the duplexes that remains after neutralization by bound CoHex ions. The estimates of the aggregation free energy are consistent with the experimental range of NA duplex condensation propensities, including the unusually poor condensation of RNA structures and subtle sequence effects upon DNA condensation. The model predicts that, in contrast to DNA, RNA duplexes may condense into tighter packed aggregates with a higher degree of duplex neutralization. An appreciable CoHex mediated RNA-RNA attraction requires closer inter-duplex separation to engage CoHex ions (bound mostly in the “internal” shell of RNA) into short-range attractive interactions. The model also predicts that longer NA fragments will condense more readily than shorter ones. The ability of this model to explain experimentally observed trends in NA condensation lends support to proposed NA condensation picture based on the multivalent “ion binding shells.”.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗