Search NASASearch

SEARCH · Search NASA

Results for “Information theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

479 records · Page 11

PERSIANN-Unet: A Global Deep Learning Framework for Near-Real-Time Precipitation Estimation Using Infrared Data

Access to high-quality, high-resolution, near-real-time precipitation data is essential for hydrological and meteorological research and disaster mitigation. Traditional tools such as rain gauges and radar networks, though effective, have limitations, including sparse coverage in remote areas and high operational costs. Satellite data, with its global coverage and high spatial and temporal resolutions, mitigates limitations in coverage. Satellite precipitation products like Hydro Estimator (HE), Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) utilize both geosynchronous thermal infrared (IR) and passive microwave (PMW) data in their operation. PMW sensors offer detailed atmospheric profiles but suffer from higher latency, whereas IR sensors provide lower latency but only capture cloud-top information. Despite this constraint, IR data remains attractive for low-latency precipitation estimation. Recent advances in deep learning, particularly convolutional neural networks (CNNs), have further improved satellite precipitation retrievals. This study introduces PERSIANN-Unet (PUnet or PERSIANN V3), a quasi-global algorithm covering 60°N–60°S that combines IR data, monthly climatology, and the UNet architecture to produce half-hourly precipitation estimates at 0.04° resolution. The product is evaluated against HE, IMERG, and PDIR-Now for 2022–2023. Results show that PUnet closely matches its training target, IMERG V07 Final, at the global scale, and performance is further evaluated against Stage IV as a reference over CONUS. Training PUnet on IMERG (2016–2021) leverages a high-quality, integrated PMW IR-gauge precipitation product while developing an IR-based framework not reliant on PMW availability. By operating on a single global image, PUnet avoids tile partitioning and blending steps, reducing edge discontinuities, and produces more spatially consistent precipitation fields across hemispheres.

Phu Nguyen

Discrete Rotational Energy for Polyatomic Molecules in Direct Simulation Monte Carlo

The environments experienced by vehicles upon entry into planetary atmospheres generally result in severe aerothermodynamic loading. These flows are characterized by the formation of strong shock waves, behind which high temperatures and non-equilibrium environments are generated, and the accurate prediction of internal energy relaxation and chemical kinetics becomes important. This manuscript focuses on the internal relaxation of the rotational energy of polyatomic molecules. Previous work has described the implementation of a discrete rotational energy model for diatomic molecules (linear rotators). Later, Gimelshein et. al extended this model to include polyatomic molecular internal energies. However, they did not include details on how to generate the particles at equilibrium conditions and centrifugal distortion was not included in their model. The purpose of the present study is to extend the afore-mentioned models to the treatment of discrete rotational energy in polyatomic molecules with the addition of centrifugal distortion. An overview of the background theory needed for the implementation of the model will be given followed by the model itself and verification of the model. For example, sampled versus Boltzmann distributions are compared in Figure 1 for CH3 (oblate rotator – two quantum numbers) and examples of thermal relaxation behavior for linear and non-linear rotators are presented in Figure 2. In addition, comparisons of thermophysical properties will be presented, as well as examples of adiabatic relaxation and application to hypersonic flow.

Rarefied Gas Dynamics

Multireference diffusion Monte Carlo reaches 2D materials

Abstract Quantum confinement in 2D materials strongly enhances electronic correlation effects. Therefore, predicting the properties of these unique materials, with both a high level of accuracy and computational efficiency, without relying on adjustable parameters or functionals, remains an outstanding theoretical challenge. The majority of theoretical studies are based on the approximations of density functional theory (DFT). The reliability of DFT predictions are heavily dependent on the choice of an approximated exchange-correlation functional. Here, we estimate the magnitude of impact of correlation on the total energy for the quintessential 2D material, graphene, by performing and comparing state-of-the-art selected CI and quantum Monte Carlo extrapolated calculations for a single unit cell at the$$\Gamma$$point. We demonstrate that Self-Healing Diffusion Monte Carlo (SHDMC) obtains a very compact, but high-quality wavefunction for this system that lacks the strong basis set dependence displayed by state of the art quantum chemistry methods. The SHDMC wavefunction is of higher quality compared to that obtained from sCI, in the same orbital basis, while being$$\sim$$ 1000 times smaller in terms of determinant count compared to sCI. We also demonstrate that extrapolating SHDMC results to the infinite determinant limit compares extremely well with complete basis set extrapolated sCI. Our work paves the way for future validation of SHDMC applied to challenging 2D materials.

Science & Technology - Other Topics

Quantum graph models for transport in filamentary switching

The formation of metallic nanofilaments bridging two electrodes across an insulator is a mechanism for resistive switching. Examples of such phenomena include atomic synapses, which constitute a distinct class of memristive devices the behavior of which is closely tied to the properties of the filament. Until recently, experimental investigation of the low-temperature regime and quantum transport effects has been limited. However, with growing interest in understanding the true impacts of the filament on device conductance, comprehending quantum effects has become crucial for quantum neuromorphic hardware. Here, we discuss quantum transport resulting from filamentary switching in a narrow region where the continuous approximation of the contact is not valid, and only a few atoms are involved. In this scenario, the filament can be represented by a graph depicting the adjacency of atoms and the overlap between atomic orbitals. Using the theory of quantum graphs with locally diffusive node scattering, we calculate the scattering amplitude of charge carriers on this graph and explore the interplay between filamentary formation and quantum transport effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Mechanochemically responsive polymer enables shockwave visualization

Abstract Understanding the physical and chemical response of materials to impulsive deformation is crucial for applications ranging from soft robotic locomotion to space exploration to seismology. However, investigating material properties at extreme strain rates remains challenging due to temporal and spatial resolution limitations. Combining high-strain-rate testing with mechanochemistry encodes the molecular-level deformation within the material itself, thus enabling the direct quantification of the material response. Here, we demonstrate a mechanophore-functionalized block copolymer that self-reports energy dissipation mechanisms, such as bond rupture and acoustic wave dissipation, in response to high-strain-rate impacts. A microprojectile accelerated towards the polymer permanently deforms the material at a shallow depth. At intersonic velocities, the polymer reports significant subsurface energy absorption due to shockwave attenuation, a mechanism traditionally considered negligible compared to plasticity and not well explored in polymers. The acoustic wave velocity of the material is directly recovered from the mechanochemically-activated subsurface volume recorded in the material, which is validated by simulations, theory, and acoustic measurements. This integration of mechanochemistry with microballistic testing enables characterization of high-strain-rate mechanical properties and elucidates important insights applicable to nanomaterials, particle-reinforced composites, and biocompatible polymers.

Science & Technology - Other Topics

Elastic-plastic models for multi-site damage

This paper presents recent developments in advanced analysis methods for the computation of stress site damage. The method of solution is based on the p-version of the finite element method. Its implementation was designed to permit extraction of linear stress intensity factors using a superconvergent extraction method (known as the contour integral method) and evaluation of the J-integral following an elastic-plastic analysis. Coarse meshes are adequate for obtaining accurate results supported by p-convergence data. The elastic-plastic analysis is based on the deformation theory of plasticity and the von Mises yield criterion. The model problem consists of an aluminum plate with six equally spaced holes and a crack emanating from each hole. The cracks are of different sizes. The panel is subjected to a remote tensile load. Experimental results are available for the panel. The plasticity analysis provided the same limit load as the experimentally determined load. The results of elastic-plastic analysis were compared with the results of linear elastic analysis in an effort to evaluate how plastic zone sizes influence the crack growth rates. The onset of net-section yielding was determined also. The results show that crack growth rate is accelerated by the presence of adjacent damage, and the critical crack size is shorter when the effects of plasticity are taken into consideration. This work also addresses the effects of alternative stress-strain laws: The elastic-ideally-plastic material model is compared against the Ramberg-Osgood model.

Actis, Ricardo L.

Mechanistic origin of solvent-dependent thermal stability in sodiated Sn anodes for sodium-ion batteries

Understanding the thermal stability of high-energy density alloy anodes is critical for the safe deployment of sodium-ion batteries (SIBs). Here, accelerating rate calorimetry (ARC), post-mortem characterizations, and density functional theory (DFT) calculations are combined to understand the thermal reactivity of fully sodiated Sn, Sn-hard carbon (HC) blends, and HC anodes in carbonate- and ether-based electrolytes. ARC measurements show that propylene carbonate (PC) causes earlier self-heating rate (SHR) onset and higher reactivity than tetraethylene glycol dimethyl ether (TEGDME), indicating inferior thermal stability. Sodiated Sn exhibits better thermal stability than sodiated HC, while Sn-HC blends show intermediate behavior that improves with increasing Sn content. Post-ARC analyses reveal desodiation of Na15Sn4 to metallic Sn with particle coalescence, whereas Sn-HC blends and HC retain finer morphologies. PC promotes Sn oxidation to SnO, while TEGDME suppresses oxide formation; NaPF6-containing electrolytes additionally form NaF. DFT calculations show that PC adsorption lowers Na extraction energy and enhances interfacial electronic interactions, facilitating Na release and reductive decomposition. These results establish a direct correlation between solvent-dependent reaction pathways and thermal stability in SIB alloy anodes.

Accelerating rate calorimetry

A holistic platform for accelerating sorbent-based carbon capture

Abstract Reducing carbon dioxide (CO 2 ) emissions urgently requires the large-scale deployment of carbon-capture technologies. These technologies must separate CO 2 from various sources and deliver it to different sinks 1,2 . The quest for optimal solutions for specific source–sink pairs is a complex, multi-objective challenge involving multiple stakeholders and depends on social, economic and regional contexts. Currently, research follows a sequential approach: chemists focus on materials design 3 and engineers on optimizing processes 4,5 , which are then operated at a scale that impacts the economy and the environment. Assessing these impacts, such as the greenhouse gas emissions over the plant’s lifetime, is typically one of the final steps 6 . Here we introduce the PrISMa (Process-Informed design of tailor-made Sorbent Materials) platform, which integrates materials, process design, techno-economics and life-cycle assessment. We compare more than 60 case studies capturing CO 2 from various sources in 5 global regions using different technologies. The platform simultaneously informs various stakeholders about the cost-effectiveness of technologies, process configurations and locations, reveals the molecular characteristics of the top-performing sorbents, and provides insights on environmental impacts, co-benefits and trade-offs. By uniting stakeholders at an early research stage, PrISMa accelerates carbon-capture technology development during this critical period as we aim for a net-zero world.

Science & Technology - Other Topics

Uncertainty quantification for competing failure mechanisms in unidirectionally reinforced carbon–carbon composites

Microstructure-informed finite element models play a key role in the carbon–carbon composite design process. Variability in manufacturing process parameters and experimental limitations introduce model parameter uncertainty. This study quantifies the effect of model parameter uncertainty on transverse tensile fracture behavior and proposes a methodology to predict the failure mode based on competing microscale damage mechanisms. Finite element simulations incorporate fiber–matrix interface debonding with cohesive zones and matrix damage with a smeared crack band approach in a unidirectional carbon–carbon composite. Results from a variance-based global sensitivity analysis identifies interfacial and matrix damage parameters as the primary source of variability in fracture behavior. Sobol’ indices indicate that matrix and cohesive zone strengths contribute 94% of the variance in the effective ultimate stress. A local analysis elucidates the relationship between these constituent strength parameters and failure mode by estimating the probability of cohesive, matrix, and mixed-mode dominated failure. Based on the results for 4000 simulations, 93% exhibit mixed-mode or interfacial dominated failure, which underscores the crucial role of fiber–matrix interface debonding in the transverse tensile failure of carbon–carbon composites. These uncertainty quantification results facilitate more efficient model calibration and provide a framework for microstructure-informed failure predictions in the face of manufacturing-induced uncertainty.

36 MATERIALS SCIENCE

PROBABALISTIC RISK ANALYSIS AND THERMAL MARGIN PROCESS FOR AN INFLATABLE AEROSHELL

Atmospheric entry vehicle thermal protection systems (TPS) are margined due to the uncertainties that exist in entry aeroheating environments and the thermal response of the materials and structures. Traditional approaches typically over-margin TPS and offer very little insight into the risk of over-temperature during flight. A probabilistic margin process can be used to apply thermal margin to an aeroshell based on a rigorously calculated risk of failure. This probabilistic margin process allows engineers to make informed aeroshell design, entry-trajectory modifications, and risk trades while preventing excessive margin from being applied. This methodology can also be applied to other TPS applications, hot structures, and other engineering disciplines.

Steven A Tobin

Active Fluids Form System-Spanning Filamentary Networks

Recent experimental realizations of liquid-liquid phase separation of active liquid crystals have offered an insight into the interaction between phase separation, ubiquitous in soft matter and biology, and chaotic active flows. Here, in this Letter, we use continuum theory to examine phase separation of an active liquid crystal and a passive fluid and report two new results. First, we provide an analytical derivation of the activity-induced suppression of the phase boundary of the coexistence region—a result first reported in simulations and experiments. We show that the shift in the critical point is a result of the balance between self-stirring active flows and phase-separating diffusive fluxes. Second, we show that this same balance is responsible for dramatically changing the morphology of the phase separated state, resulting in the emergence of a new mixed active phase consisting of a dynamical filamentous active network that invades the entire system area, trapping droplets of passive material. This structure exists even for very low volume fractions of active material. Our work provides an important step towards the goal of understanding how to use activity as a new handle for sculpting interfaces.

active nematics

In‐Plane Anisotropy in van der Waals NiTeSe Ternary Alloy

Abstract The anisotropic properties of materials profoundly influence their electronic, magnetic, optical, and mechanical behaviors and are critical for a wide range of applications. In this study, the anisotropic characteristics of Ni‐based van der Waals materials, specifically NiTe 2 and its alloy NiTeSe, utilizing a combination of comprehensive scanning tunneling microscopy (STM), angle‐resolved photoemission spectroscopy (ARPES), and density functional theory (DFT) calculations, are explored. Unlike 1T‐NiTe 2 , which exhibits trigonal in‐plane symmetry, the substitution of Te with Se in NiTe 2 (resulting in the NiTeSe alloy) induces a pronounced in‐plane anisotropy. This anisotropy is clear in the STM topographs, which reveal a distinct linear order of charge distribution. Corroborating these observations, ARPES measurements and DFT calculations reveal an anisotropic Fermi surface centered at the point, which is notably elongated along the k y direction, leading to directional variations in in‐plane carrier velocities. Consequently, the Fermi velocity is highest along the k x direction where the linear charge distribution aligns in real space and is lowest along the k y direction. These findings offer valuable insights into the tunability of anisotropic properties in ternary transition metal dichalcogenide systems, highlighting their potential applications in the development of anisotropic electronic and optoelectronic devices.

Chemistry

SOLPS-ITER modeling of a dedicated divertor for negative triangularity operation on DIII-D

The design of a new dedicated divertor for negative triangularity (NT) operation on DIII-D with neutral baffles and pumping is informed by SOLPS-ITER transport modeling. This dedicated NT divertor is the latest step in a progression of NT shapes with various divertor characteristics explored on DIII-D, including NT shapes at reduced triangularity and a campaign with stronger shaping that included new armored components on the outboard side. SOLPS simulations played a key role in these divertor designs. Interpretive simulations, using cross-field diffusivities constrained by experimental data in the NT Shelf shape were used to inform the design of the 2023 armor campaign components. A similar procedure used armor campaign data to predict conditions for the dedicated NT divertor. The predictive simulations were used to assess the divertor fluxes, detachment threshold, pumped flux, and neutral leakage. For the dedicated NT divertor, SOLPS simulations and two-point-modeling were used to show the relative impact of magnetic topology (mainly longer connection length) and divertor closure on the divertor conditions relative to the armor campaign. It is predicted that the dedicated NT divertor reaches detachment (measured by target ion flux rollover) at a lower upstream density (≈(1.75−−2.4)×1⁢019m−3) as compared to the armor campaign shape. For the preliminary design geometry, divertor closure reduces the neutral leakage by ≈10%. Parametric optimization indicating further ≈20%–60% improvement in the leakage flux and recycled flux crossing the pump entrance is possible for relatively minor changes to the divertor and baffle layout.

Lore, Jeremy [ORNL] (ORCID:000000029192465X)

Performance Optimization for Lunar Extravehicular Activity Readiness (POLAR) Study: Methods Paper

To better understand which aspects of physical fitness may be most related to performance during Lunar surface operations and thereby help to inform the current NASA fitness standards, much can be learned from fields encompassing the “tactical athlete.” Other physically demanding professions such as law enforcement, military, or rescue professionals often require candidates to meet occupationally-relevant fitness standards. The determination of such standards is a multistep process, including both objective and subjective measures, to determine tasks essential to occupational performance and identify the minimal fitness profile needed to meet physical demands of the job. Notably, fitness is only one component which may contribute to the demands of astronaut selection, flight assignment, and occupational performance. Utilizing a framework to systematically determine which domains of fitness most contribute to relevant job tasks can aid in the refinement of current NASA-STD-3001 fitness standards. Therefore, NASA’s Exercise Physiology & Countermeasures Laboratory conducted the Performance Optimization for Lunar Extravehicular Activity Readiness (POLAR) study to identify and examine a comprehensive list of fitness tests (including NASA-STD-3001 assessments: 1-Repetition Maximum [1-RM] bench press and deadlift) and determine preliminary relationships between identified fitness parameters and novel Artemis-relevant tasks to help inform future investigations for the continued development of aerobic and muscular fitness standards for surface EVAs. This was accomplished through 1) a review of the literature relating fitness assessments to simulated or real EVA performance to identify fitness tests that are most correlated with simulated EVA task performance; 2) a task analysis following a modified framework for physical employment standards development to down select mission critical tasks; and 3) development and pilot testing of a novel, portable Artemis-relevant EVA task circuit to relate to a battery of fitness assessments. The current report describes the methodology used to complete the task analysis, EVA task circuit development, and the pilot study.

Nicole C Strock

Final Report: A Multi-Channel Fusion Product

The goal of this project was to measure charged fusion products from the d(d,p)t reaction in MAST-U plasmas as a function of time and position with good energy resolution using a system of up to six charged particle detectors. The data from this new diagnostic will make it possible to determine the neutral beam ion density profile as a function of R, z, and t with reduced model dependency and contribute new information to a global analysis of fast ion diagnostic data needed for the determination of the fast ion distribution function (velocity space tomography).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Measure sea level air pressure from space to improve knowledge and forecasting of the atmospheric state

Modern numerical weather prediction (NWP) and analysis models require globally-observed meteorological data including sea-level pressure (SLP) for accurate operations. Up until now, SLP has only been measured by in situ instruments from ships, buoys, and ocean platforms. These measurements are sparse with large gaps, leaving models starved of this critical information to constrain the atmospheric state. Recent advancements in differential absorption radar (DAR) provide a path to close this critical observation gap through spaceborne observations in the coming decade, improving the analysis models relied upon for atmospheric research and the weather forecasts depended upon daily for public safety and commerce.

Matthew L Walker McLinden

Water Observations of Flow/No-Flow for the East-Taylor Watershed, Colorado (June-July 2025 and 2026)

This dataset provides multi-year, ground-truth visual observations of surface water flow/no-flow conditions within the East-Taylor Watershed, Colorado, collected during June and July of 2025 and 2026. In June and July 2025, on-the-ground visual observations of flow/no-flow were collected as part of the Watershed Function Scientific Focus Area (SFA) and Rocky Mountain Biological Laboratory (RMBL) Colorado Headwaters Ecological Spectroscopy Study (CHESS) campaign (further details are provided within the CHESS Project Description). We obtained 377 water observations of flow/no-flow within the East-Taylor Watershed, Colorado. These ground-truth observations were collected to validate classification maps from remote sensing data and model results within the East-Taylor Watershed. In 2025, flow/no-flow measurements were collected using a field-based app for the CHESS Campaign (Zerion iForm). Within the field app, a water observation form was created to collect coordinates and metadata about the observation. Information collected for the water observation points included information about visually-assessed streamflow presence/absence (standard question obtained from Colorado State University’s StreamTracker project), flow estimate, stream or ponded area width, canopy cover, manganese films, iron seeps, and beaver activity. For 2025 water observations, this dataset contains: (1) a data file with the water observations and coordinates (2025_Water_Observations.csv); (2) a Keyhole Markup Language Zipped (KMZ) with the water observation locations and metadata (2025_Water_Observations_Locations.kmz); (3) photos (.jpg and .jpeg) of the water observation points, organized by location, contained within 2025_Water_Observations_FieldPhotographs.zip file; and (4) water observation protocols and figures (2025_Water_Observation_Protocols.pdf). In June and July 2026, on-the-ground visual observations of flow/no-flow were collected as part of the Watershed Function SFA project. We obtained 365 water observations of flow/no-flow within the East-Taylor Watershed, Colorado. The 2026 observations focused on collecting repeat measurements at the 2025 flow/no-flow observation locations conducted as part of the CHESS campaign. These ground-truth observations were collected to understand differences in flow/no-flow in 2026, given the unprecedented 2026 drought in Colorado. In 2026, flow/no-flow measurements were collected using ArcGIS (Geographic Information System) Survey123. Within the field app, a water observation form was created to collect coordinates and metadata about the observation. Information collected for the water observation points included repeat information from the 2025 water observation effort, including visually-assessed streamflow presence/absence (standard question obtained from Colorado State University’s StreamTracker project), flow estimate, stream or ponded area width, canopy cover, manganese films, iron seeps, beaver activity, and a new metadata component of estimated stream depth (for select locations). For 2026 water observations, this dataset contains: (1) a data file with the water observations and coordinates (2026_Water_Observations.csv); (2) a Keyhole Markup Language Zipped (KMZ) with the water observation locations and metadata (2026_Water_Observations_Locations.kmz); (3) photos (.jpg) of the water observation points, organized by location, contained within 2026_Water_Observations_FieldPhotographs.zip file; and (4) water observation protocols and figures (2026_Water_Observation_Protocols.pdf). For 2025 and 2026 water observations, this dataset contains: (1) a location metadata file (locations.csv); (6) a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and (7) a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type. CHESS Project Description: The Colorado Headwaters Ecological Spectroscopy Study (CHESS) comprised a multi-week airborne remote sensing and field observation campaign in the Upper Gunnison Basin, Colorado, conducted in June and July of 2025. Airborne remote sensing was conducted by the National Ecological Observatory Network Airborne Observation Platform (NEON AOP), concurrent with a field campaign run by the Rocky Mountain Biological Laboratory (RMBL), the Lawrence Berkeley National Laboratory (LBNL) and SLAC National Accelerator Laboratory Watershed Function Science Focus Area (SFA), and NASA-JPL (Jet Propulsion Laboratory) Earth Surface Mineral Dust Source Investigation (EMIT) program. Between June 10 and July 18, 2025, the NEON AOP flight team collected high-resolution aerial imaging spectroscopy and Light Detection and Ranging (LiDAR) data over three domains: the Upper East River (CRBU), Almont Triangle (ALMO), and the Upper Taylor Basin (UPTA). In coordination with the flights, a field campaign acquired ground-truth observations, including observations of vegetation composition, foliar traits, forest demography, and subsurface properties in 18 core sampling areas within the domains. Additional surface water observations were taken at over 380 point locations. All CHESS campaign datasets can be found within the CHESS ESS-DIVE data portal: https://data.ess-dive.lbl.gov/portals/chess. This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231. 2026-09-02: This dataset was updated to include 2026 water observation measurements. The 2025 observation files were also updated to ensure a consistent file naming convention across water observation years.

2018 NEON and 2025 CHESS Campaigns

Radioactivity of the Moon, Planets, and Meteorites

This paper reviews and summarizes analytical data for the content of natural radioactive elements in meteorites, eruptive terrestrial rocks, and also, in lunar samples returned by Apollo missions and the Luna series of automatic stations. The K-U systematics of samples analyzed in the laboratory are combined with data for orbital gamma-ray measurements for Mars (Mars 5) and with the results of direct gamma-ray measurements of the surface of Venus by the Venera 8 lander. Using information about the radioactivity of solar system bodies and evaluations of the content of K, U, and Th in the terrestrial planets, we examine certain aspects of the evolution of material in the protoplanetary gas-dust cloud and then in the planets of the solar system.

Yu A Surkov