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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Evolving MEMS Resonator Designs for Fabrication

Because of their small size and high reliability, microelectromechanical (MEMS) devices have the potential to revolution many areas of engineering. As with conventionally-sized engineering design, there is likely to be a demand for the automated design of MEMS devices. This paper describes our current status as we progress toward our ultimate goal of using an evolutionary algorithm and a generative representation to produce designs of a MEMS device and successfully demonstrate its transfer to an actual chip. To produce designs that are likely to transfer to reality, we present two ways to modify evaluation of designs. The first is to add location noise, differences between the actual dimensions of the design and the design blueprint, which is a technique we have used for our work in evolving antennas and robots. The second method is to add prestress to model the warping that occurs during the extreme heat of fabrication. In future we expect to fabricate and test some MEMS resonators that are evolved in this way.

Hornby, Gregory S.↗
NASA NTRS2010

Isolation of Resistance-Bearing Microorganisms

To better exploit the principles of gas transport and mass transport during the processes of cell seeding of 3D scaffolds and in vitro culture of 3D tissue engineered constructs, the oscillatory cell culture bioreactor provides a flow of cell suspensions and culture media directly through a porous 3D scaffold (during cell seeding) and a 3D construct (during subsequent cultivation) within a highly gas-permeable closed-loop tube. This design is simple, modular, and flexible, and its component parts are easy to assemble and operate, and are inexpensive. Chamber volume can be very low, but can be easily scaled up. This innovation is well suited to work with different biological specimens, particularly with cells having high oxygen requirements and/or shear sensitivity, and different scaffold structures and dimensions. The closed-loop changer is highly gas permeable to allow efficient gas exchange during the cell seeding/culturing process. A porous scaffold, which may be seeded with cells, is fixed by means of a scaffold holder to the chamber wall with scaffold/construct orientation with respect to the chamber determined by the geometry of the scaffold holder. A fluid, with/without biological specimens, is added to the chamber such that all, or most, of the air is displaced (i.e., with or without an enclosed air bubble). Motion is applied to the chamber within a controlled environment (e.g., oscillatory motion within a humidified 37 C incubator). Movement of the chamber induces relative motion of the scaffold/construct with respect to the fluid. In case the fluid is a cell suspension, cells will come into contact with the scaffold and eventually adhere to it. Alternatively, cells can be seeded on scaffolds by gel entrapment prior to bioreactor cultivation. Subsequently, the oscillatory cell culture bioreactor will provide efficient gas exchange (i.e., of oxygen and carbon dioxide, as required for viability of metabolically active cells) and controlled levels of fluid dynamic shear (i.e., as required for viability of shear-sensitive cells) to the developing engineered tissue construct. This bioreactor was recently utilized to show independent and interactive effects of a growth factor (IGF-I) and slow bidirectional perfusion on the survival, differentiation, and contractile performance of 3D tissue engineering cardiac constructs. The main application of this system is within the tissue engineering industry. The ideal final application is within the automated mass production of tissue- engineered constructs. Target industries could be both life sciences companies as well as bioreactor device producing companies.

Venkateswaran, Kasthuri, J.↗
NASA NTRS2010

Oscillating Cell Culture Bioreactor

To better exploit the principles of gas transport and mass transport during the processes of cell seeding of 3D scaffolds and in vitro culture of 3D tissue engineered constructs, the oscillatory cell culture bioreactor provides a flow of cell suspensions and culture media directly through a porous 3D scaffold (during cell seeding) and a 3D construct (during subsequent cultivation) within a highly gas-permeable closed-loop tube. This design is simple, modular, and flexible, and its component parts are easy to assemble and operate, and are inexpensive. Chamber volume can be very low, but can be easily scaled up. This innovation is well suited to work with different biological specimens, particularly with cells having high oxygen requirements and/or shear sensitivity, and different scaffold structures and dimensions. The closed-loop changer is highly gas permeable to allow efficient gas exchange during the cell seeding/culturing process. A porous scaffold, which may be seeded with cells, is fixed by means of a scaffold holder to the chamber wall with scaffold/construct orientation with respect to the chamber determined by the geometry of the scaffold holder. A fluid, with/without biological specimens, is added to the chamber such that all, or most, of the air is displaced (i.e., with or without an enclosed air bubble). Motion is applied to the chamber within a controlled environment (e.g., oscillatory motion within a humidified 37 C incubator). Movement of the chamber induces relative motion of the scaffold/construct with respect to the fluid. In case the fluid is a cell suspension, cells will come into contact with the scaffold and eventually adhere to it. Alternatively, cells can be seeded on scaffolds by gel entrapment prior to bioreactor cultivation. Subsequently, the oscillatory cell culture bioreactor will provide efficient gas exchange (i.e., of oxygen and carbon dioxide, as required for viability of metabolically active cells) and controlled levels of fluid dynamic shear (i.e., as required for viability of shear-sensitive cells) to the developing engineered tissue construct. This bioreactor was recently utilized to show independent and interactive effects of a growth factor (IGF-I) and slow bidirectional perfusion on the survival, differentiation, and contractile performance of 3D tissue engineering cardiac constructs. The main application of this system is within the tissue engineering industry. The ideal final application is within the automated mass production of tissue- engineered constructs. Target industries could be both life sciences companies as well as bioreactor device producing companies.

Freed, Lisa E.↗
NASA NTRS2017

The Effects of Normal Metal Stripes on TES Performance

Exploring the effects of size and geometry of normal metal features on the transition shapes and performance of transition-edge sensor microcalorimeters. The spectral resolution of transition-edge sensor (TES) microcalorimeters is very sensitive to the specific dependencies of the resistance R in the superconducting transition on the current I, magnetic field B, and temperature T. In particular, it has been shown that transitions that are very steep in (R,T) space lead to a significant noise term, in excess of conventional expectations. This so-called unexplained noise is known to be reduced by the addition of normal metal stripes across the TES perpendicular to the direction of current flow. These normal metal stripes have been shown to drastically alter the oscillatory patterns seen in measurements of the critical current as a function of magnetic field. However, there are many remaining questions about the exact impact of the stripes on current distributions within the TES, the Fraunhofer pattern and, therefore, the shape of the R(I, B, T) surface. Through measurements of the resistance under DC bias of TES devices of various sizes, with different stripe patterns and dimensions, we will discuss how these stripes can affect the R(I, B, T) surface. In addition, using measurements and analysis of the noise spectra of various devices we will present how these changes to the stripe pattern may affect the performance of the TES. In particular, we will discuss strategies to reduce the presence of localized discontinuities in the derivative of R, associated with increased noise, while maintaining the globally low levels of unexplained noise currently achieved with conventional metal stripe patterns. Implementing these strategies is a path towards producing large arrays with highly uniform transitions and high spectral resolution. These large uniform arrays will be required for future x-ray astronomy applications, such as the X-IFU on ATHENA.

TES↗
DOE OSTI2021

A Study on Computational Cost Reduction of Simulations of Phase-Change Material (PCM) Embedded Heat Exchangers

Thermal storage can be implemented using Phase-Change Materials (PCM), which absorb significant latent heat with a relatively small temperature change. PCM phase-change processes are transient and are driven by thermal diffusion and natural convection – the latter, especially for melting process. Modeling and simulation of PCM heat exchangers (HX’s) is typically computationally intensive due to the relatively complex time-dependent physics. Most of the PCM modeling work in the literature uses high-order modeling tools such as Computational Fluid Dynamics (CFD) and Lattice-Boltzmann Method (LBM). For design purposes, the existing PCM modeling approaches are not practical, limiting researchers in their ability to investigate new ideas and different PCM’s with faster turnarounds. This paper presents a study investigating the reduction of computational cost of PCM embedded HX’s CFD models by evaluating the feasibility of spatial reduction without losing accuracy. The analysis consists of comparing full and partial domain under full melting conditions. The subject of this study is a single straight tube with circular transverse fins in the vertical orientation, using PCM’s with 35oC nominal melting temperature. Different tube and fin dimensions are investigated. Results indicate that the reduced domain reproduces - in half the run time - the same behavior as the full domain since the buoyancy effects are localized and patterned. The outputs from the partial domain simulation were used to build a non-general correlation for the PCM heat transfer characteristics and demonstrated how it can be implemented in a Finite Control Volume Reduced Order Model (ROM). The ROM can accurately reproduce the CFD simulations at 4 to 5 orders of magnitude faster.

25 ENERGY STORAGE↗
DOE OSTI2024

Heat Transfer Experiments of Ribbed, Serpentine Cooling Passages with Supercritical CO2

The results of heat transfer experiments with supercritical CO2 (sCO2) to capture the performance of ribbed, serpentine cooling passages for Reynolds numbers in the range of 100,000 - 400,000 are presented. The oxy-combustion turbine operating in an Allam-Fetvedt cycle has a turbine inlet temperature exceeding 1100°C, necessitating internally cooled turbine blades due to material creep strength limits. Reynolds numbers for sCO2, with its combination of high fluid density and low viscosity, can be up to an order of magnitude higher than comparable internal cooling conditions for an air-breathing engine where the majority of experimental data exists. To improve the prediction of cooling performance through turbulated passages, a test rig was designed and constructed with interchangeable insert capability for operation in sCO2 with heat transfer from a heater outlet flow stream to a lower temperature recuperator outlet flow stream. The inserts included serpentine passage geometry with five passes, one of the inserts including chevron ribs and the other a plain wall. The multi-pass serpentine geometry allowed for the evaluation of the effects 180 deg. tip turns have on the return passage flow characteristics, as they can depart significantly from fully-developed flow characteristics. The test procedure included the use of a modified Wilson plot method, with hot flow stream conditions kept effectively constant so that monitored changes in the overall thermal resistance could be attributed to manipulations in cooling flow stream conditions. Conditions during testing consisted of test section pressures of approximately 180 bar, cooling flow stream temperature of 175°C and hot flow stream temperature of 410°C. Test points at discrete cool flow Reynolds numbers up to 400,000 demonstrated an expected trend of decreased fluid thermal resistance with increasing Reynolds number, while at comparable Reynolds number there was an exhibited lower thermal resistance and higher passage pressure drop for the ribbed insert compared to the plain-walled insert. Processing of test data included establishment of Nusselt number enhancement ratios, so that for different internal cooling passage dimensions in the actual turbine blade at comparable Reynolds number the ratio could be applied to predict cooling performance.

Marshall, Michael↗
NASA NTRS1990

Fractal image analysis - Application to the topography of Oregon and synthetic images.

Digitized topography for the state of Oregon has been used to obtain maps of fractal dimension and roughness amplitude. The roughness amplitude correlates well with variations in relief and is a promising parameter for the quantitative classification of landforms. The spatial variations in fractal dimension are low and show no clear correlation with different tectonic settings. For Oregon the mean fractal dimension from a two-dimensional spectral analysis is D = 2.586, and for a one-dimensional spectral analysis the mean fractal dimension is D = 1.487, which is close to the Brown noise value D = 1.5. Synthetic two-dimensional images have also been generated for a range of D values. For D = 2.6, the synthetic image has a mean one-dimensional spectral fractal dimension D = 1.58, which is consistent with the results for Oregon. This approach can be easily applied to any digitzed image that obeys fractal statistics.

Huang, Jie↗
NASA NTRS2008

Three-Dimensional Signatures of Intermittent Magnetic Reconnection in Global Simulations of Dayside Magnetosphere Dynamics

We performed high resolution global MHD simulations of THEMIS dayside crossings events in May -June 2007. We found that magnetopause surface is not in steady-state even during extended periods of steady solar wind conditions. The so-called tilted reconnection lines become unstable due to formation of pressure bubbles, strong core field flux tubes, vortices, and traveling magnetic field cavities. The topology of FTEs differ from that in two dimension cartoons representing obliquely oriented quasi-2D flux rope. The structure of FTE is changing at spatial scales of 1 -2 Re. Closely located space probes can observe completely different signatures. Branches of bent flux rope can move in opposite directions. THEMIS and Cluster observations are consistent with signatures predicted by simulations.

Kuznetsova, M.M.↗
NASA NTRSDate not supplied

Regional and Model-Specific Response Types in A Global Gridded Crop Model Ensemble

Crop models are often employed to project crop yields under changing conditions such as global warming and associated management change for adaptation. Multi-model ensembles are promoted to enhance the robustness of projections, but questions remain on what causes often large differences between projections of individual models. Global Gridded Crop Models (GGCMs) are especially exposed to this question when applied for assessing climate change impacts, adaptation, environmental impacts of agricultural production, because their results are used in downstream analyses, such as in integrated assessment or economic modeling for projecting future land-use change. Even though global gridded crop models are often based on detailed field-scale models or have implemented similar modeling principles in other ecosystem models, global-scale models are subject to substantial uncertainties from both model structure and parametrization as well as from calibration and input data quality. AgMIP’s Global Gridded Crop Model Intercomparison (GGCMI) has thus set out to intercompare GGCMs in order to evaluate model performance, describe model uncertainties, identify inconsistencies within the ensemble and underlying reasons, and to ultimately improve models and modeling capacities. In phase 2 of the GGCMI activities, 12 modeling groups followed a modeling protocol that asked for up to 1404 31-year global simulations at 0.5 arc-degree spatial resolution to assess models’ sensitivities to changes in carbon dioxide (C; 4 different levels) temperature (T; 7 different offset levels), water supply (W; 9 levels), and nitrogen (N; 3 levels), the so-called CTWN experiment (Franke et al. 2020; http://dx.doi.org/10.5194/gmd-13-2315-2020). We here present analyses of model response types using impact response surfaces along the C, T, W, and N dimensions, respectively and collectively. Doing so, we can understand differences in simulated responses per driver rather than aggregated changes in yields. We find that models’ sensitivities to the individual driver dimensions are substantially different and often more different across models than across regions. A cluster analysis finds regional and model-specific patterns. There is some agreement across models with respect to the spatial patterns of response types but strong differences in the distribution of response type clusters across models suggests that models need to undergo further scrutiny. We suggest establishing standards in model process evaluation not only against historical dynamics but also against dedicated experiments across the CTWN dimensions.

crop models↗
DOE OSTI2020

Dependence of Enstrophy Transport and Mixed Mass on Dimensionality and Initial Conditions in the Richtmyer–Meshkov Instability Induced Flows

Here we present a comparative study of the enstrophy budget and mixed mass between two- and three-dimensional flows induced by Richtmyer–Meshkov instability (RMI). Specifically, the individual contributions to the enstrophy budget due to the production from baroclinicity and from vortex stretching (which vanishes in two-dimensional (2D) flow) are delineated. This is enabled by a set of two- and three-dimensional computations at Atwood 0.5 having both narrow- and broad-band perturbations. A further three-dimensional (3D) computation is conducted at Atwood 0.9 using an identical narrowband perturbation to the Atwood 0.5 case to examine the sensitivity to density ratio. The mixed mass is also considered with the goal to obtain insight on how faithfully a simplified calculation performed in two dimensions can capture the mixed mass for an inertial confinement fusion (ICF) or other practical application. It is shown that the late time power law decay of variable density enstrophy is substantially different in two and three dimensions for the narrowband initial perturbation. The baroclinic production term is negligible in three dimensions (aside from the initial shock interaction), as vortex stretching is larger by two orders of magnitude. The lack of vortex stretching considerably reduces the decay rate in both narrowband and broadband perturbations in two dimensions. In terms of mixed mass, the lack of vortex stretching reduces the mixed mass in two dimensions compared to three in all cases. In the broadband cases, the spectral bandwidth in the 2D case is wider; hence, there is a longer time period of sustained linear growth which reduces the normalized mixed mass further.

42 ENGINEERING↗
DOE OSTI2024

Ultrahigh-resolution mass spectrometry data associated with the manuscript “A functional microbiome catalog crowdsourced from North American rivers"

This data package is associated with the publication “A functional microbiome catalog crowdsourced from North American rivers” submitted to Nature (Borton et al., 2024); (https://www.biorxiv.org/content/10.1101/2023.07.22.550117v1). Predicting elemental cycles and maintaining water quality under increasing anthropogenic influence requires understanding the spatial drivers of river microbiomes. However, the unifying microbial determinants governing river biogeochemistry are hindered by a lack of genome-resolved functional insights and sampling across multiple rivers. Here we employed a community science effort to accelerate the sampling of river microbiomes to create the Genome Resolved Open Watersheds database (GROWdb). GROWdb is a publicly available resource that paves the way for watershed predictive modeling and microbiome-based management practices. This resource profiled the identity, distribution, function, and expression of thousands of microbial genomes across rivers covering 90% of United States watersheds. We identified the most cosmopolitan microbiome members, while also revealing local drivers of strain endemism across ecological dimensions. We provide the first evidence that microbial functional trait expression followed the tenets of the River Continuum Concept, suggesting the structure and function of river microbiomes is predictable. The Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS) data were one of many different data types used in establishing the ecological dimensions along which different microbes were detected .This data package only contains the processed FTICR-MS data associated with this manuscript; all other data is accessible via Zenodo (https://zenodo.org/records/8173287), GitHub (https://github.com/jmikayla1991/Genome-Resolved-Open-Watersheds-database-GROWdb), KBase (https://doi.org/10.25982/109073.30/1895615), and NCBI via Bioproject PRJNA946291.This dataset consists of (1) a file-level metadata (flmd) file; (2) a data dictionary (dd) file; (3) a readme; (4) three Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS) processed data files (a ‘data’ file containing peak-by-sample observations, a ‘mol’ file containing peak metadata, and a transformation profile containing transformation-by-sample observations). All files are .csv or .pdf.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Universality of Rényi Entropy in Conformal Field Theory

We use the thermal effective theory to prove that, for the vacuum state in any conformal field theory in 𝑑 dimensions, the 𝑛th Rényi entropy 𝑆$^{(𝑛)}_{𝐴}$ behaves as 𝑆$^{(𝑛)}_{𝐴}$ = [𝑓⁡/(2⁢𝜋⁢𝑛) 𝑑−1 ]⁢[Area⁡(∂𝐴)/(𝑑−2)⁢𝜀 𝑑−2 ]⁢(1+𝑂⁡(𝑛)) in the 𝑛 → 0 limit when the boundary of the entanglement domain 𝐴 is spherical with the UV cutoff 𝜀. The theory dependence is encapsulated in the cosmological constant 𝑓 in the thermal effective action. Using this result, we estimate the density of states for large eigenvalues of the modular Hamiltonian for the domain 𝐴. In two dimensions, we can use the hot spot idea, which describes the effective action in the high-temperature limit when the temperature is position-dependent, to derive more powerful formulas valid for arbitrary positive 𝑛. We discuss the difference between two and higher dimensions and clarify the applicability of the hot spot idea. We also use the thermal effective theory to derive an analog of the Cardy formula for boundary operators in higher dimensions.

Conformal field theory↗
DOE OSTI2021

Fractal dimension of optical cirrus in Stripe82

ABSTRACT The geometric characteristics of dust clouds provide important information on the physical processes that structure such clouds. One of such characteristics is the 2D fractal dimension D of a cloud projected on to the sky plane. In previous studies, which were mostly based on infrared (IR) data, the fractal dimension of individual clouds was found to be in a range from 1.1 to 1.7 with a preferred value of 1.2–1.4. In this work, we use data from Stripe82 of the Sloan Digital Sky Survey to measure the fractal dimension of the cirrus clouds. This is done here for the first time for optical data with significantly better resolution as compared to IR data. To determine the fractal dimension, the perimeter-area method is employed. We also consider IR (IRAS and Herschel) counterparts of the corresponding optical fields to compare the results between the optical and IR. We find that the averaged fractal dimension across all clouds in the optical is $\langle D \rangle =1.69^{+0.05}_{-0.05}$ which is significantly larger than the fractal dimension of its IR counterparts $\langle D\rangle =1.38^{+0.07}_{-0.06}$. We examine several reasons for this discrepancy (choice of masking and minimal contour level, image and angular resolution, etc.) and find that for approximately half of our fields the different angular resolution (point spread function) of the optical and IR data can explain the difference between the corresponding fractal dimensions. For the other half of the fields, the fractal dimensions of the IR and visual data remain inconsistent, which can be associated with physical properties of the clouds, but further physical simulations are required to prove it.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Radiation-induced Alteration of Meta-chert

Concrete aggregate identified as “meta-chert” was irradiated with gamma-rays and neutrons. To identify the volume expansion of the aggregate under neutron irradiation, herein the following analyses were performed for pristine and irradiated α-quartz and meta-chert: X-ray diffraction (XRD)/Rietveld analysis, dimension change, water pycnometry, He-pycnometry, light optical microscopy (LOM), and scanning electron microscopy (SEM). From the difference of volume expansion observed from dimension change and water / helium pycnometry, the crack opening inside the aggregate subjected to irradiation was elucidated, and this was confirmed by LOM and SEM analysis. The crack contribution to the expansion of the aggregate was significant for neutron fluence > 6.99 × 1019 n/cm 2 , for E ≥ 0.01 MeV. Based on the XRD analysis, changes in lattice parameters were identified and the cell volume expansion was compared with the data by helium pycnometry. Based on the density change calculation and phase calculation data, the density of X-ray amorphous phase was consistent with that of expanded crystal α-quartz.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Fractal dimension analyses of lava surfaces and flow boundaries

An improved method of estimating fractal surface dimensions has been developed. The accuracy of this method is illustrated using artificially generated fractal surfaces. A slightly different from usual concept of linear dimension is developed, allowing a direct link between that and the corresponding surface dimension estimate. These methods are applied to a series of images of lava flows, representing a variety of physical and chemical conditions. These include lavas from California, Idaho, and Hawaii, as well as some extraterrestrial flows. The fractal surface dimension estimations are presented, as well as the fractal line dimensions where appropriate.

Cleghorn, Timothy F.↗
NASA NTRS1981

Space Shuttle Program: STS-1 Medical Report

The necessity for developing medical standards addressing individual classes of Shuttle crew positions is discussed. For the U.S. manned program the conclusion of the Apollo era heralded the end of water recovery operations and the introduction of land-based medical operations. This procedural change marked a significant departure from the accepted postflight medical recovery and evaluation techniques. All phases of the missions required careful re-evaluation, identification of potential impact on preexisting medical operational techniques, and development of new methodologies which were carefully evaluated and tested under simulated conditions. Significant coordination was required between the different teams involved in medical operations. Additional dimensions were added to the concepts of medical operations, by the introduction of different toxic substances utilized by the Space Transportation Systems especially during ground operations.

Source record↗
NASA NTRS2003

Classifying Urban Land Covers Using Local Indices of Spatial Complexity

The skewed statistical distributions of land cover types in complex, heterogeneous urban areas limits the effectiveness of traditional spectrally based maximum-likelihood classifiers. This work examines the utility of fractal dimension and Moran's I index of spatial autocorrelation in segmenting high-resolution panchromatic and lower-resolution multispectral imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze multi-temporal and multi-platform imagery of Atlanta, Georgia. In this example, land cover change trajectories from forest or grassland to built up land covers lead to decreased spatial autocorrelation. In lower resolution imagery such as Landsat MSS, the complex details of forested land covers and urbanized areas are smoothed, and texture-based change detection is less effective. Although segmentation of panchromatic images is possible using fractal dimension or Moran's I, widely differing land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification.

Arumugam, Mahesh↗
NASA NTRS1994

Dimensions and Fragmentation of the Nuclei of Comet Shoemaker-Levi 9

Central regions on the digital maps of 13 nuclear condensations of Comet Shoemaker-Levi 9, obtained with the Planetary Camera of the Hubble Space Telescope on January 27, March 30, and July 4, 1994, have been analyzed with the aim to identify the presence of distinct, major fragments in each condensation, to deconvolve their contributions to the signal that also includes the contribution from a surrounding cloud of dust (modeled as an extended source, using two different laws), to estimate the dimensions of the fragments and to study their temporal variations, and to determine the spatial distributions of the fragments as projected on to the plane of the sky. The deconvolution method applied is described and the results of the analysis are summarized, including the finding that sizable fragments did survive until the time of atmospheric entry. This result does not contradict evidence of the comet's continuing, apparently spontaneous fragmentation, which still went on long after the extremely close approach to Jupiter in July 1992 and which, because of the Jovian tidal effects, may have intensified in the final days before the crash on Jupiter. Since the developed approach is based on certain premises and involves approximations, the results should be viewed as preliminary and the problem should be the subject of further investigation.

Comet Shoemaker-Levi 9 Hubble Space Telescope come↗