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MaestroWF is a Python tool and software package for loading YAML study specifications that represents a simulation campaign. The package is capable of parameterizing a study, pulling dependencies automatically, formatting output directories, and managing the flow and execution of the campaign. MaestroWF also provides a set of abstracted objects that can also be used to develop user specific scripts for launching simulation campaigns.
A tool kit was developed to simulate and analyze passive radiation measurements of molten salt reactor (MSR) operations to support development of nuclear safeguards approaches for this emerging reactor technology. A Transient Simulation Framework of Reconfigurable Modules (TRANSFORM) multiphysics simulation of an MSR produces time-dependent isotopic inventories at user-selected locations within the model. The tool kit implements the Gamma Detector Response and Analysis Software (GADRAS) application programming interface to inject the TRANSFORM isotopic inventories extracted/processed by a Python pipeline into GADRAS models of user-defined geometries. The TRANSFORM inventories are the source terms used to obtain synthetic measurements from GADRAS-defined detectors. The speed of TRANSFORM and GADRAS simulations enables surveying the large design space of MSRs (e.g., fuel type, fuel salt composition, number of loops) and the plethora of measurements (e.g., location, detector type, and collimation) within the reactor. This has enabled timely assessment of the various measurement locations and detectors to identify the most effective and efficient safeguards approach for a specific MSR design. Lastly, the tool kit also simulates extracted samples that can be aged to a desired dose, enabling stakeholders to optimize a measurement plan to use sample analysis as an element within a broader material accountancy plan.
A MCNP study for a water-reflected sphere of plutonium metal water pseudo-solution was performed for a various ratios of {sup 238}Pu to {sup 239}Pu to develop minimum critical mass curves. The {sup 238}Pu atom percent (at. %) was varied from 35 to 100 percent. It was demonstrated that at {sup 238}Pu ratios of ≥ 65 at. % the high absorption cross section of {sup 238}Pu in the thermal energy region dominates the system reactivity for water moderated systems resulting in a minimum critical mass in the metal rather than solution regime. However, due to the lack of available benchmark experiments to validated use of the {sup 238}Pu cross-section data for quantities above gram-level, the models fell outside the area of applicability (AOA) of the Los Alamos National Laboratory's (LANL) Nuclear Criticality Safety Division's (NCSD) MCNP validation report. An additional of margin of subcriticality (MOS) is needed for {sup 238}Pu systems. This additional MOS will be dependent on the amount and significance of the {sup 238}Pu, which varies in the MCNP study. Whisper is a computational software package designed to assist with validation studies for MCNP. Whisper uses sensitivity/uncertainty (S/U) methods to select relevant benchmarks to a particular application model. Therefore, Whisper 1.0.0 was used on the curve minima in the solution regime for the 65 at. % {sup 238}Pu curve to estimate an appropriate additional margin of subcriticality and create a subcritical curve based on the suggested upper subcritical limits (USL)
The literature on stopping powers and ranges for proton and heavier ions is vast. It includes measurements, theory, evaluations and tabulations, and software programs and routines. Electronic stopping powers are typically calculated with either the Bethe-Bloch Equation or empirically derived functions, depending on the energy regime of the ion. Nuclear stopping powers are typically calculated using a theoretical approach. Ranges are commonly calculated numerically using path length integration, stopping power data and the continuous slowing down approximation. The Stopping and Ranges of Ions in Matter (SRIM) by Ziegler et al., which provides these and other capabilities, exemplifies the integration of highly-realistic theories, evaluated data, and radiation transport capabilities. In applications where speed and simplicity are paramount considerations, analytical calculations of range offer considerable advantages over numerical methods. Range has long been calculated analytically using a simple power law known as the range-energy relationship. This provides excellent accuracy over a surprisingly wide interval of ion species (e.g. protons, carbon), ion energies (e.g. 10-200 MeV/u), absorber compositions (e.g. plastic, water, metal), and thickness (e.g. 0.5-1 10 mm). The major limitation of formulas derived from a simple power law relation was their limited interval of applicability, 1.e., 10-200 MeV for protons in water. Thus, fora projectile in a stopping length target, such as a cancer patient, the simple power law model breaks down in the biologically important interval below 10 MeV. In current standard-of-care treatment planning, this is typically not a concern because the resulting range errors are less than 1 mm (and can be accounted for) and because biological effects are not calculated based on ion stopping power. However, there is considerable interest to perform multi-scale calculations of ion beams, e.g., at dimensions corresponding to cellular DNA, with ion energies below 10 MeV. Thus, there is an increasing need for new fast and simple formulae to calculate range and stopping power across a broader energy intervals of ion energy. It was not known if simple analytical equations would meet this need and, if so, the limits of their applicability. The aim of this work was to develop a simple, non-piecewise continuous model of total stopping power which could be analytically integrated to provide a simple formula for range. More specifically, we sought to develop a model to provide stopping powers with accuracy of better than 20% and range errors less than 1 mm for hydrogen, carbon, iron, and uranium projectile ions and target materials including water, carbon, aluminum, lead, copper, iron, gadolinium, and gold. (authors)
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The Dependency Analysis Project creates datasets from package management ecosystems to determine what package a file was likely installed by, and provides tools to recognize implicit dependencies when source code is available for a variety of language ecosystems. The overarching goal is to help answer the question: what software does a system use?
This 2018 progress report contains a list of Los Alamos National Laboratory's top innovations of the time, including: Inventing - Los Alamos National Laboratory has been inventing for the past 75 years to accomplish the difficult, the unexpected and at times, what seems impossible. The Feynman Center is rethinking roadmaps for patent and software strategies to enable Los Alamos to achieve greater impact of its innovations; Innovating - The US technology advantage in national security is dependent on continual innovation. Los Alamos’ immense contributions in leading edge science and technology research and development are directed into solving complex and forthcoming national security challenges. Check out the Technology Snapshot platform at https://techsnapshot.lanl.gov to explore Los Alamos’s technologies ready to be developed into disruptive applications; Disrupting - Known well for developing the first nuclear weapon, big and small science at Los Alamos is behind many other disruptive innovations. This year we are highlighting Los Alamos’s leadership in small modular nuclear reactor design and development, work on international nuclear safeguards electronics instrumentation, and first demonstrated deployment of non-destructive testing to measure corrosion in nuclear material storage containers; Partnering - Los Alamos science has assisted partners big and small with their toughest challenges, this year Los Alamos scientists assisted two New Mexico farm owners—Tim Seaman with Manzanar Los Silvestres apple orchard in Abiquiu and Christopher Bassett of Freshies of New Mexico in El Guique — protect their crops from frost.
The National Center for Atmospheric Research (NCAR) is pleased to have led a partnership to advance the state-of-the-science of solar power forecasting by designing, developing, building, deploying, testing, and assessing the SunCast™ Solar Power Forecasting System. The project has included cutting edge research, testing in several geographically- and climatologically-diverse high penetration solar utilities and Independent System Operators (ISOs), and wide dissemination of the research results to raise the bar on solar power forecasting technology. The partners include three other national laboratories, six universities, and industry partners. This public-private-academic team has worked in concert to perform use-inspired research to advance solar power forecasting through cutting-edge research to advance both the necessary forecasting technologies and the metrics for evaluating them. The project has culminated in a year-long, full-scale demonstration of provide irradiance and power forecasts to utilities and ISOs to use in their operations. The project focused on providing elements of a value chain, beginning with the weather that causes a deviation from clear sky irradiance and progresses through monitoring and observations, modeling, forecasting, dissemination and communication of the forecasts, interpretation of the forecast, and through decision-making, which produces outcomes that have an economic value. The system has been evaluated using metrics developed specifically for this project, which has provided rich information on model and system performance. Research was accomplished on the very short range (0-6 hours) Nowcasting system as well as on the longer term (6-72 hour) forecasting system. The shortest range forecasts are based on observations in the field. The shortest range system, built by Brookhaven National Laboratory (BNL) and based on Total Sky Imagers (TSIs) is TSICast, which operates on the shortest time scale with a latency of only a few minutes and forecasts that currently go out to about 15 min. This project has facilitated research in improving the hardware and software so that the new high definition cameras deployed at multiple nearby locations allow discernment of the clouds at varying levels and advection according to the winds observed at those levels. Improvements over “smart persistence” are about 29% for even these very short forecasts. StatCast is based on pyranometer data measured at the site as well as concurrent meteorological observations and forecasts. StatCast is based on regime-dependent artificial intelligence forecasting techniques and has been shown to improve on “smart persistence” forecasts by 15-50%. A second category of short-range forecasting systems employ satellite imagery and use that information to discern clouds and their motion, allowing them to project the clouds, and the resulting blockage of irradiance, in time. CIRACast (the system produced by the Cooperative Institute for Atmospheric Research [CIRA] at Colorado State University) was already one of the more advanced cloud motion systems, which is the reason that team was brought to this project. During the project timeframe, the CIRA team was able to advance cloud shadowing, parallax removal, and implementation of better advecting winds at different altitudes. CIRACast shows generally a 25-40% improvement over Smart Persistence between sunrise and approximately 1600 UTC (Coordinated Universal Time) . A second satellite-based system, MADCast (Multi-sensor Advective Diffusive foreCast system), assimilates data from multiple satellite imagers and profilers to assimilate a fully three-dimensional picture of the cloud into the dynamic core of WRF. During 2015, MADCast (provided at least 70% improvement over Smart Persistence, with most of that skill being derived during partly cloudy conditions. That allows advection of the clouds via the Weather Research and Forecasting (WRF) model dynamics directly. After WRF-Solar™ showed initial success, it was also deployed in nowcasting mode with coarser runs out to 6 hours made hourly. It provided improvements on the order of 50-60% over Smart Persistence for forecasts up to 1600 UTC. The advantages of WRF-Solar-Nowcasting and MADCast were then blended to develop the new MAD-WRF model that incorporates the most important features of each of those models, both assimilating satellite cloud fields and using WRF-So far physics to develop and dissipate clouds. MAE improvements for MAD-WRF for forecasts from 3-6 hours are improved over WRF-Solar-Now by 20%. While all the Nowcasting system components by themselves provide improvement over Smart Persistence, the largest benefit is derived when they are smartly blended together by the Nowcasting Integrator to produce an integrated forecast. The development of WRF-Solar™ under this project has provided the first numerical weather prediction (NWP) model specifically designed to meet the needs of irradiance forecasting. The first augmentation improved the solar tracking algorithm to account for deviations associated with the eccentricity of the Earth’s orbit and the obliquity of the Earth. Second, WRF-Solar™ added the direct normal irradiance (DNI) and diffuse (DIF) components from the radiation parameterization to the model output. Third, efficient parameterizations were implemented to either interpolate the irradiance in between calls to the expensive radiative transfer parameterization, or to use a fast radiative transfer code that avoids computing three-dimensional heating rates but provides the surface irradiance. Fourth, a new parameterization was developed to improve the representation of absorption and scattering of radiation by aerosols (aerosol direct effect). A fifth advance is that the aerosols now interact with the cloud microphysics, altering the cloud evolution and radiative properties, an effect that has been traditionally only implemented in atmospheric computationally costly chemistry models. A sixth development accounts for the feedbacks that sub-grid scale clouds produce in shortwave irradiance as implemented in a shallow cumulus parameterization Finally, WRF-Solar™ also allows assimilation of infrared irradiances from satellites to determine the three dimensional cloud field, allowing for an improved initialization of the cloud field that increases the performance of short-range forecasts. We find that WRF-Solar™ can improve clear sky irradiance prediction by 15-80% over a standard version of WRF, depending on location and cloud conditions. In a formal comparison to the NAM baseline, WRF-Solar™ showed improvements in the Day-Ahead forecast of 22-42%. The SunCast™ system requires substantial software engineering to blend all of the new model components as well as existing publically available NWP model runs. To do this we use an expert system for the Nowcasting blender and the Dynamic Integrated foreCast (DICast®) system for the NWP models. These two systems are then blended, we use an empirical power conversion method to convert the irradiance predictions to power, then apply an analog ensemble (AnEn) approach to further tune the forecast as well as to estimate its uncertainty. The AnEn module decreased RMSE (root mean squared error) by 17% over the blended SunCast™ power forecasts and provided skill in the probabilistic forecast with a Brier Skill Score of 0.55. In addition, we have also developed a Gridded Atmospheric Forecast System (GRAFS) in parallel, leveraging cost share funds. An economic evaluation based on Production Cost Modeling in the Public Service Company of Colorado showed that the observed 50% improvement in forecast accuracy will save their customers $819,200 with the projected MW deployment for 2024. Using econometrics, NCAR has scaled this savings to a national level and shown that an annual expected savings for this 50% forecast error reduction ranges from $11M in 2015 to $43M expected in 2040 with increased solar deployment. This amounts to a $455M discounted savings over the 26 year period of analysis.
As a consequence of thermal motion, inter-atomic distances in proteins fluctuate strongly around their average values, and hence, also interaction energies (i.e. the pair-potentials evaluated at the fluctuating distances) are not constant in time but exhibit pronounced fluctuations. These fluctuations cause that time-averaged interaction energies do generally not coincide with the energy values obtained by evaluating the pair-potentials at the average distances. More precisely, time-averaged interaction energies behave typically smoother in terms of the average distance than the corresponding pair-potentials. This averaging effect is referred to as the thermal smoothing effect. Here, we estimate the strength of the thermal smoothing effect on the Lennard-Jones pair-potential for globular proteins at ambient conditions using x-ray diffraction and simulation data of a representative set of proteins. For specific atom species, we find a significant smoothing effect where the time-averaged interaction energy of a single atom pair can differ by various tens of cal/mol from the Lennard-Jones potential at the average distance. Importantly, we observe a dependency of the effect on the local environment of the involved atoms. The effect is typically weaker for bulky backbone atoms in beta sheets than for side-chain atoms belonging to other secondary structure on the surface of the protein. The results of this work have important practical implications for protein software relying on free energy expressions. We show that the accuracy of free energy expressions can largely be increased by introducing environment specific Lennard-Jones parameters accounting for the fact that the typical thermal motion of protein atoms depends strongly on their local environment.
We have recently reported MZA, a new and simple mass spectrometry data structure based on the broadly supported HDF5 format and created to facilitate software development. While this format is inherently supportive of application development, the availability of a core library with standard mass spectrometry utilities greatly facilitates fast software development. Here, we present a Python library, mzapy, for efficient extraction and processing of mass spectrometry data in the MZA format. In addition to raw data extraction, mzapy contains supporting utilities enabling tasks including calibration, signal processing, peak finding, and generating plots. Being implemented in pure Python with minimal and largely standardized dependencies makes mzapy uniquely suited to application development in the multi-omics domain. The free and open source mzapy is built with extensibility in mind, and future development will support cloud computing and artificial intelligence/machine learning applications. The software source code is freely available at https://github.com/PNNL-m-q/mzapy.
Multi-heme cytochromes (MHCs), together with accessory proteins like porins and periplasmic cytochromes, enable microbes to transport electrons between the cytoplasmic membrane and extracellular substrates (e.g., minerals, electrodes, other cells). Extracellular electron transfer (EET) has been described in multiple systems; yet, the broad phylogenetic and mechanistic diversity of these pathways is less clear. One commonality in EET-capable systems is the involvement of MHCs, in the form of porin-cytochrome complexes, pili-like cytochrome polymers, and lipid-anchored extracellular cytochromes. Here, we put forth MHCscan—a software tool for identifying MHCs and identifying potential EET capability. Using MHCscan, we scanned ~60,000 bacterial and 2,000 archaeal assemblies, and identify a diversity of MHCs, many of which represent enzymes with no known function, and many found within organisms not previously known to be electroactive. In total, our scan identified ~1,400 unique enzymes, each encoding more than 10 heme-binding motifs. In our analysis, we also find evidence for modularity and flexibility in MHC-dependent EET pathways, and suggest that MHCs may be far more common than previously recognized, with many facets yet to be discovered. We present MHCscan as a lightweight and user-friendly software tool that is freely available: https://github.com/Arkadiy-Garber/MHCscan.
The contribution of radiative heat transfer (RHT) to convective heat transfer in a heated vertical pipe with laminar flow and constant wall temperature, for FLiBe molten salt, is investigated computationally. The combined effects of conduction in the fluid, forced convection, buoyancy, temperature-dependent physical properties, and thermal radiation are investigated. The P1 approximation is employed in the discretization of the Radiative Transfer Equation (RTE). The COMSOL Multiphysics software is used to generate the numerical solutions. The theoretical analysis developed here demonstrates that only for intermediate values of the optical thickness, i.e. τ D ~ O 1 , the participating media effects are expected to be important. This analysis is confirmed computationally and a value of τ D ≈ 4 is shown to lead to the highest increase in overall heat transfer behavior. Under forced convection, the Nusselt ratio N u total / N u no - rad reaches a peak value of 1.76 at τ D = 4 and z/D = 200 , and is less than 1.1 for τ D < 0 . 1 and τ D > 60 . Under aiding-flow mixed convection, N u total / N u no - rad reaches a peak of 1.34 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 4 and τ D > 36 . Under opposing-flow mixed convection, Nu total / Nu no - rad reaches a peak of 1.81 at τ D = 4 . 2 and is less than 1.1 for τ D < 0 . 2 and τ D > 50 . RHT effects on the overall heat transfer are most pronounced in opposing mixed convection, where N u total / N u no - rad is 2.26 observed at z/D = 50 . The sensitivity to wall emissivity is evaluated; in forced convection, the peak N u total / N u no - rad is 1.66 at ε = 0 (reflective wall) and 2.04 at ε = 1 (absorptive wall). Finally, the sensitivity to pipe diameter is also discussed. Overall, for a vertical heated tube, radiative heat transfer effects lead to enhancement of heat transfer by as high as a factor of two, and they depend on the optical thickness of the flow, mixed convection environment ( Gr / R e 2 and direction of flow relative to the gravitational force), surface emissivity, and entrance effects.
This software package provides functionality to fit piecewise cubic splines to model the relationship between a univariate X (independent variable) and a univariate Y (dependent variable). The output is akin to linear regression but has higher "capacity" in that it can learn more complicated relationships despite leveraging only a single predictor. It thus can learn very reasonable relationships between X and Y with minimal effort. The canonical intended use case is for predicting electric demand (Y) from temperature (X). There can be complicated, non-linear relationships between these two variables, but these can be reasonably approximated by the sum of: 1) an "aggregate" relationship between daily average temperature and daily average demand, and 2) intra-day patterns represented as hourly offsets from the daily average load. The spline functionality is used for learning a robust "aggregate" relationship without the inconvenience of manual feature engineering while still ensuring robust results. The model fitting workhorse is R's built-in smooth.spline. This package provides a suite of options for controlling how smooth.spline fits a spline to the data. In particular, it is designed to return a model with a single critical point (i.e., a single location along the domain/support where the first derivative is zero). This is to ensure that predicted changes in electric demand are always positive as temperatures become more extreme. This helps to prevent overfitting, particularly when the input data has few observations or has significant uncertainty from other sources.
Supercomputing centers are seeing increasing demand for user-defined software stacks (UDSS), instead of or in addition to the stack provided by the center. These UDSS support user needs such as complex dependencies or build requirements, externally required configurations, portability, and consistency. The challenge for centers is to provide these services in a usable manner while minimizing the risks: security, support burden, missing functionality, and performance. We present Charliecloud, which uses the Linux user and mount namespaces to run industry-standard Docker containers with no privileged operations or daemons on center resources. Our simple approach avoids most security risks while maintaining access to the performance and functionality already on offer, doing so in less than 500 lines of code. Charliecloud promises to bring an industry-standard UDSS user workflow to existing, minimally altered HPC resources.
In the 1984 martial arts drama film, The Karate Kid, a young Daniel LaRusso is unexpectedly placed in an adversarial environment unable to eYectively adapt to a series of new threats and limitations. Fortunately for the main character, once placed under the tutelage of a Mr. Miyagi, he finds resiliency not through the adoption of new tools, but a re-focused set of fundamentals. Much in the same way that Daniel learns waxing on and buYing oY car wax by hand has rewards for Karate, LANL is choosing the harder path of self-hosting Large Language Models (LLMs) for enterprise use instead of only relying on buying access to a hosted AI service like Azure’s OpenAI Application Programming Interface (API). We also are not willing to wait for software-as-a-service (SAAS) AI services to meet us where we need to be from a FedRAMP accreditation standpoint. Our operations regularly depend on access at CUI, UCNI, ITAR and other FIPS-199 moderate-impact data levels and hosting our own services gives us the right security and compliance posture to be useful across the broad range of our work at LANL. With the rise in threats to critical infrastructure, cloud service providers (CSPs), and supply chain attacks from both state and non-state actors, we are not placing the bet that SAAS hosted AI services will be available when we need them. Should a major event occur, we do not want our staY and operations left without a pathway for us to fix the problem and resume the use of AI tools.
Purpose: Microchambers demonstrate anomalous voltage-dependent polarity effects. Existing polarity and ion recombination correction factors do not account for these effects. As a result, many commercial microchamber models do not meet the specification of a reference-class ionization chamber as defined by the American Association of Physicists in Medicine. The purpose of this investigation is to determine the cause of these voltage-dependent polarity effects. Methods: A series of microchamber prototypes were produced to isolate the source of the voltage-dependent polarity effects. Parameters including ionization-chamber collecting-volume size, stem and cable irradiation, chamber assembly, contaminants, high-Z materials, and individual chamber components were investigated. Measurements were performed with electrodes coated with graphite to isolate electrode conductivity. Chamber response was measured as the potential bias of the guard electrode was altered with respect to the collecting electrode, through the integration of additional power supplies. Ionization chamber models were also simulated using COMSOL Multiphysics software to investigate the effect of a potential difference between electrodes on electric field lines and collecting volume definition. Results: Investigations with microchamber prototypes demonstrated that the significant source of the voltage-dependent polarity effects was a potential difference between the guard and collecting electrodes of the chambers. The voltage-dependent polarity effects for each prototype were primarily isolated to either the guard or collecting electrode. Polarity effects were reduced by coating the isolated electrode with a conductive layer of graphite. Polarity effects were increased by introducing a potential difference between the electrodes. COMSOL simulations further demonstrated that for a given potential difference between electrodes, the collecting volume of the chamber changed as the applied voltage was altered, producing voltage-dependent polarity effects in the chamber response. Ionization chamber measurements and COMSOL simulations demonstrated an inverse relationship between the chamber collecting volume size and the severity of voltage-dependent polarity effects on chamber response. The effect of a given potential difference on chamber polarity effects was roughly ten times greater for microchambers as compared to Farmer-type chambers. Stem and cable irradiations, chamber assembly, contaminants, and high-Z materials were not found to be a significant source of the voltage-dependent polarity effects. Conclusions: A potential difference between the guard and collecting electrodes was found to be the primary source of the voltage-dependent polarity effects demonstrated by microchambers. For a given potential difference between electrodes, the relative change in the collecting volume is smaller for larger-volume chambers, illustrating why these polarity effects are not seen in larger-volume chambers with similar guard and collecting electrode designs. Thus, for small-volume chambers, it is necessary to reduce the potential difference between the guard and collecting electrodes in order to reduce polarity effects for reference dosimetry measurements.
Studies generating transcriptomics, proteomics, lipidomics, and metabolomics (colloquially referred to as “omics”) data allow researchers to find biomarkers or molecular targets, or understand complex biological structures and functions by identifying changes in biomolecule abundance and expression between experimental conditions. Omics data is multi-dimensional and oftentimes summarization techniques such as principal component analysis (PCA) are used to identify high-level patterns in data. Though useful, these summaries don’t allow exploration of detailed patterns in omics data that may have biological relevance. The use of interactive HTML displays with plots allows researchers to interact with omics data at a detailed level, but building these displays requires significant coding expertise. To overcome this barrier, the software MODE was built to empower users to build their own interactive HTML displays to support scientific discovery. These displays are easily shareable, do not depend on a specific operating system, and allow users to effortlessly sort and filter plots by categorical or numerical variables. MODE allows users to build and share these displays with several options for plot design and meta selection. In conclusion, the MODE web application and its capabilities are presented and then demonstrated on lipidomics data from a leaf wounding study.
Physical optics simulations for beamlines and experiments are essential for the effective use of synchrotron light source facilities such as NSLS-II at BNL. The SRW software package supports such source-to-detector simulations for coherent X-ray scattering and imaging experiments through its Python interface and Sirepo browser-based graphical user interface. This allows one to define custom sample models, assess the feasibility of an experiment, and estimate most appropriate beamline settings before using valuable beamtime. We discuss the recent use of general-purpose GPU resources and coherent mode decomposition algorithms in SRW to accelerate physical optics simulations with partially coherent X-rays. To illustrate these new capabilities, we describe simulations of typical time series of partially coherent scattering images used in X-ray Photon Correlation Spectroscopy (XPCS) experiments; aiming to characterize the nanoscale dynamics of a disordered sample, representing a solution of nanoparticles undergoing Brownian diffusion.