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At least 145 records · Page 8

Recommended Direct Simulation Monte Carlo Collision Model Parameters for Reacting Methane Flows

While hydrocarbon combustion and gas-surface interactions have been simulated for a variety of applications in continuum solvers, such processes have been rarely investigated in Direct Simulation Monte Carlo (DSMC). Thus Variable Hard/Soft Sphere (VHS/VSS)collision parameters are not available for most molecules of interest in the decomposition of methane, a significant pyrolysis gas product and potential atmospheric species for Titan re-entries. As these properties are essential for accurate modeling of gas transport and thermochemical effects, a method must be devised to compute them for use in DSMC. In this study, the methodology outlined in Stephani et al is utilized to compute the VHS/VSS parameters by fitting the Ω(1,1)and Ω(2,2) collision integrals [1]. These collision integrals are typically computed from intermolecular potentials and are used in CFD simulations to calculate transport properties such as viscosity, thermal conductivity, and diffusion. This approach ensures consistency between micro-scale collisions and macro-scale transport properties. To produce the necessary collision integrals needed for the fitting routine, we utilize the method described by Laricchiuta et al, where collision integrals are computed based on the constituent particles’ polarizability and effective electron number [2].Preliminary computations of pure-species Ω(1,1)and Ω(2,2)collision integrals produced from the coupled approach of Stephani et al and Laricchiuta et al for methane show good agreement with those computed via available ab-initio Potential Energy Surface Computations, as seen in Figure 1. Above 300K, no more than 12% deviation is observed between the two results over the temperature range of the fitted PES data [3].Current results of this study include full collision-specificVSS transport properties for a complex-species mixture involving major byproducts of pure methane decomposition. Targeted final results will include a comprehensive list of VSS parameters relevant toDSMC simulations of Titan atmospheric entry, based on the reduced kinetic model of Savajano et al [4].

M R Gosma↗

A Multimodel Investigation of Asian Summer Monsoon UTLS Transport Over the Western Pacific

The Asian summer monsoon (ASM) as a chemical transport system is investigated using a suite of models in preparation for an airborne field campaign over the Western Pacific. Results show that the dynamical process of anticyclone eddy shedding in the upper troposphere rapidly transports convectively uplifted Asian boundary layer air masses to the upper troposphere and lower stratosphere over the Western Pacific. The models show that the transported air masses contain significantly enhanced aerosol loading and a complex chemical mixture of trace gases that are relevant to ozone chemistry. The chemical forecast models consistently predict the occurrence of the shedding events, but the predicted concentrations of transported trace gases and aerosols often differ between models. The airborne measurements to be obtained in the field campaign are expected to help reduce the model uncertainties. Furthermore, the large-scale seasonal chemical structure of the monsoon system is obtained from modeled carbon monoxide, a tracer of the convective transport of pollutants, which provides a new perspective of the ASM circulation, complementing the dynamical characterization of the monsoon.

Laura L. Pan↗

The Photochemistry of Purine in Ice Analogs Relevant to Dense Interstellar Clouds

The aromatic nitrogen heterocyclic compound purine is the core structural framework of many important biomolecules, particularly nucleobases. Purine and purine derivatives have been observed in carbonaceous chondrites, and it has been hypothesized that the exogenous delivery of these compounds, along with many other biologically relevant compounds, may have played a role in the emergence of life. Numerous experiments in our laboratory have demonstrated that the nucleobases used by life to encode genetic material could have been produced abiotically under astrophysically relevant conditions. Specically, the UV photoprocessing of pyrimidine and purine in simple ices of astrophysical interest has resulted in the production of all five biological nucleobases, namely, uracil (RNA), cytosine (RNA and DNA), thymine (DNA), adenine (RNA and DNA), and guanine (RNA and DNA). Additionally, follow-up work has examined the photochemistry of pyrimidine in more complex astrophysical ice mixtures to better understand the formation of these compounds under realistic conditions. In this work, we examine the photochemistry of purine in more complex ices of astrophysical interest and compare our results with those from simpler ice mixtures. We also examine the effects of competing parallel synthesis of organic compounds in the ices (unrelated to purine). Finally, we discuss the astrophysical and astrobiological implications of our findings.

Molecular Processes↗

The Photochemistry of Purine in Ice Analogs Relevant to Dense Interstellar Clouds

The aromatic nitrogen heterocyclic compound purine is the core structural framework of many important biomolecules, particularly nucleobases. Purine and purine derivatives have been observed in carbonaceous chondrites, and it has been hypothesized that the exogenous delivery of these compounds, along with many other biologically relevant compounds, may have played a role in the emergence of life. Numerous experiments in our laboratory have demonstrated that the nucleobases used by life to encode genetic material could have been produced abiotically under astrophysically relevant conditions. Specifically, the UV photoprocessing of pyrimidine and purine in simple ices of astrophysical interest has resulted in the production of all five biological nucleobases, namely, uracil (RNA), cytosine (RNA and DNA), thymine (DNA), adenine (RNA and DNA), and guanine (RNA and DNA). Additionally, follow-up work has examined the photochemistry of pyrimidine in more complex astrophysical ice mixtures to better understand the formation of these compounds under realistic conditions. In this work, we examine the photochemistry of purine in more complex ices of astrophysical interest and compare our results with those from simpler ice mixtures. We also examine the effects of competing parallel synthesis of organic compounds in the ices (unrelated to purine). Finally, we discuss the astrophysical and astrobiological implications of our findings.

Astrobiology↗

Chemistry of the outer planets: Investigations of the chemical nature of the atmosphere of Titan

It is clear from the experiments that a variety of complex organic models can be produced by lightning in a Titan-like gas mixture. The dominant products were found to be acetylene and hydrogen cyanide, with smaller amounts of many other species. Any aerosol produced by lightning inititated process will consist of a complex mixture of organic compounds, many of which should easily be identified by pyrolytic gas chromatography. Work will continue to expand the data base of molecules produced by lightning and other processes in order to assist in the design of appropriate analytical instruments for the upcoming Saturn/Titan mission and any other planetary probes.

Scattergood, Thomas W.↗

Laboratory identification of the emission features near 3.5 microns in the pre-main sequence star HD 97048

This paper presents the results of a laboratory study of formaldehyde (H2CO) suspended in low temperature molecular matrices with compositions similar to what may be found in the 'dirty ice' mantles of grains. It is shown that the emission features near 3.5 microns in the pre-main-sequence star HD 97048 can be matched by a mixture of chemical complexes of H2CO with surrounding molecules in the grain. Furthermore, a discussion is presented of various possible excitation mechanisms for this emission. The conclusion is, that for the features near 3.5 microns in HD 97048, UV pumped IR fluorescence is the most likely mechanism.

Van Der Zwet, G. P.↗

Gas chromatography/ion mobility spectrometry as a hyphenated technique for improved explosives detection and analysis

Ion Mobility Spectrometry (IMS) is currently being successfully applied to the problem of on-line trace detection of plastic and other explosives in airports and other facilities. The methods of sample retrieval primarily consist of batch sampling for particulate residue on a filter card for introduction into the IMS. The sample is desorbed into the IMS using air as the carrier and negative ions of the explosives are detected, some as an adduct with a reagent ion such as Cl(-). Based on studies and tests conducted by different airport authorities, this method seems to work well for low vapor pressure explosives such as RDX and PETN, as well as TNT that are highly adsorptive and can be found in nanogram quantities on contaminated surfaces. Recently, the changing terrorist threat and the adoption of new marking agents for plastic explosives has meant that the sample introduction and analysis capabilities of the IMS must be enhanced in order to keep up with other detector developments. The IMS has sufficient analytical resolution for a few threat compounds but the IMS Plasmogram becomes increasingly more difficult to interpret when the sample mixture gets more complex.

Mercado, AL↗

Bright Points and Subflares in Ultraviolet Lines and X-Rays

We have analyzed an active region which was observed in H.alpha (Multichannel Subtractive Double Pass Spectrograph), in UV lines (SMM/UVSP), and in X-rays (SMM/HXIS). In this active region there were only a few subflares and many small bright points visible in UV and in X-rays. Using an extrapolation based on the Fourier transform, we have computed magnetic field lines connecting different photospheric magnetic polarities from ground-based magnetograms. Along the magnetic inversion lines we find two different zones: (1) a high-shear region (> 70 deg) where subflares occur, and (2) a low-shear region along the magnetic inversion line where UV bright points are observed. In these latter regions the magnetic topology is complex with a mixture of polarities. According to the velocity field observed in the Si IV lamda.1402 line and the extrapolation of the magnetic field, we notice that each UV bright point is consistent with emission from low-rising loops with downflows at both ends. We notice some hard X-ray emissions above the bright-point regions with temperatures up to 8 x 10(exp 6) K, which suggests some induced reconnection due to continuous emergence of new flux. This reconnection is also enhanced by neighboring subflares.

Rovira, M.↗

Application of High-Dimensional Fuzzy K-Means Cluster Analysis to CALIOP/CALIPSO Version 4.1 Cloud-Aerosol Discrimination

This study applies fuzzy k-means (FKM) cluster analyses to a subset of the parameters reported in the CALIPSO lidar level 2 data products in order to classify the layers detected as either clouds or aerosols. The results obtained are used to assess the reliability of the cloud–aerosol discrimination (CAD) scores reported in the version 4.1 release of the CALIPSO data products. FKM is an unsupervised learning algorithm, whereas the CALIPSO operational CAD algorithm (COCA) takes a highly supervised approach. Despite these substantial computational and architectural differences, our statistical analyses show that the FKM classifications agree with the COCA classifications for more than 94 % of the cases in the troposphere. This high degree of similarity is achieved because the lidar-measured signatures of the majority of the clouds and the aerosols are naturally distinct, and hence objective methods can independently and effectively separate the two classes in most cases. Classification differences most often occur in complex scenes (e.g., evaporating water cloud filaments embedded in dense aerosol) or when observing diffuse features that occur only intermittently (e.g., volcanic ash in the tropical tropopause layer). The two methods examined in this study establish overall classification correctness boundaries due to their differing algorithm uncertainties. In addition to comparing the outputs from the two algorithms, analysis of sampling, data training, performance measurements, fuzzy linear discriminants, defuzzification, error propagation, and key parameters in feature type discrimination with the FKM method are further discussed in order to better understand the utility and limits of the application of clustering algorithms to space lidar measurements. In general, we find that both FKM and COCA classification uncertainties are only minimally affected by noise in the CALIPSO measurements, though both algorithms can be challenged by especially complex scenes containing mixtures of discrete layer types. Our analysis results show that attenuated backscatter and color ratio are the driving factors that separate water clouds from aerosols; backscatter intensity, depolarization, and mid-layer altitude are most useful in discriminating between aerosols and ice clouds; and the joint distribution of backscatter intensity and depolarization ratio is critically important for distinguishing ice clouds from water clouds.

Zeng, Shan↗

Mineral Dust Optical Properties for Remote Sensing and Global Modeling: A Review

Dust plays a key role in many Earth system processes and is ubiquitous in the Martian atmosphere. Various intensive field campaigns, laboratory analyses, space-based remote sensing missions, and global modeling efforts aim to characterize dust optical properties. This is a bountiful time for dust scientists, and yet the interpretation of retrievals and comparison to models remains complicated by various conflicting assumptions that are part of each algorithm. For example, the conversion of satellite radiance measurements into products like aerosol optical depth for model evaluation depends upon aerosol properties like particle size and shape that are often prescribed and not part of the retrieval. Conversely, the model calculation of aerosol optical depth often uses different assumptions. The goal of this review is to first document algorithmic assumptions by various satellite retrieval products and models, and identify where there is consistency and where there are differences. In general, the differences documented in this paper reflect uncertainties resulting from incomplete observational characterization of dust aerosols and limitations in our understanding. Second, we note what observations might reduce uncertainties in our knowledge and bring greater consistency to retrievals and models, allowing for a more rigorous and harmonious comparison. The lack of comprehensive and realistic shape models for dust is an outstanding issue, such that closure between forward modeling from particle refractive index, shape, and size and observed optical properties cannot be achieved. Limitations in the computational methods that must be applied to model scattering from complex shapes also makes accurate optical modeling for dust challenging. Field observations indicate the persistence of coarse and giant dust particles at higher altitudes and farther downwind from their source than previously expected. Remote sensing retrieval algorithms based on observations at visible wavelengths have limited sensitivity to these particles and generally do not consider them, although a recent product based on longwave radiances is encouraging. Current measurements of the refractive index of bulk dust and fundamental dust minerology components such as hematite vary widely, inhibiting attempts to represent the variability in dust optical properties and forcing, as expected from different major dust source regions on Earth that have varying mineralogical composition. Some remote sensing retrieval algorithms allow for limited refractive index variability in their inversion solutions through mixing with other fine mode aerosol models, or optimizing the single scattering albedo, but Earth system models surveyed for this paper assume a globally uniform, size-invariant refractive index. Although no Martian dust samples have yet been returned to Earth, remote sensing observations indicate that Martian dust is globally homogenous in composition, and a single spectral refractive index assumption has been widely adopted to represent Martian dust. The lack of comprehensive, statistically representative measurements of dust particle microphysical properties (size distribution, morphology, complex index of refraction spectra, internal structure heterogeneity), and the resulting optical properties, limits our ability to verify the fidelity of these assumptions. A chain of measurements is needed, ranging from characterizing individual dust mineralogy components (e.g., pure hematite and goethite) to in situ sampling of complex atmospheric aerosol mixtures. Such results could be applied to both remote sensing retrievals that characterize the optical properties of the total aerosol burden in the atmosphere from total radiance measurements, and to global models that represent the total aerosol burden in the atmosphere by building it up from the balance of individual aerosol sources and sinks.

Aeolian dust↗

Radiation Shielding of Lunar Regolith/Polyethylene Composites and Lunar Regolith/Water Mixtures

Space radiation is a complex mixed field of ionizing radiation that can pose hazardous risks to sophisticated electronics and humans. Mission planning for lunar exploration and long duration habitat construction will face tremendous challenges of shielding against various types of space radiation in an attempt to minimize the detrimental effects it may have on materials, electronics, and humans. In late 2009, the Lunar Crater Observation and Sensing Satellite (LCROSS) discovered that water content in lunar regolith found in certain areas on the moon can be up to 5.6 +/-2.8 weight percent (wt%) [A. Colaprete, et. al., Science, Vol. 330, 463 (2010). ]. In this work, shielding studies were performed utilizing ultra high molecular weight polyethylene (UHMWPE) and aluminum, both being standard space shielding materials, simulated lunar regolith/ polyethylene composites, and simulated lunar regolith mixed with UHMWPE particles and water. Based on the LCROSS findings, radiation shielding experiments were conducted to test for shielding efficiency of regolith/UHMWPE/water mixtures with various percentages of water to compare relative shielding characteristics of these materials. One set of radiation studies were performed using the proton synchrotron at the Loma Linda Medical University where high energy protons similar to those found on the surface of the moon can be generated. A similar experimental protocol was also used at a high energy spalation neutron source at Los Alamos Neutron Science Center (LANSCE). These experiments studied the shielding efficiency against secondary neutrons, another major component of space radiation field. In both the proton and neutron studies, shielding efficiency was determined by utilizing a tissue equivalent proportional counter (TEPC) behind various thicknesses of shielding composite panels or mixture materials. Preliminary results from these studies indicated that adding 2 wt% water to regolith particles could increase shielding of the regolith materials by about 6%. The findings may be utilized to extend the possibilities of potential candidate materials for lunar habitat structures, will potentially impact the design criteria of future human bases on the moon, and provide some guidelines for future space mission planning with respect to radiation exposure and risks posed on astronauts.

Johnson, Quincy F.↗

The THS Experiment: Simulating Titans Atmospheric Chemistry at Low Temperature (200K)

In Titan's atmosphere, composed mainly of N2 (95-98%) and CH4 (2-5%), a complex chemistry occurs at low temperature, and leads to the production of heavy organic molecules and subsequently solid aerosols. Here, we used the Titan Haze Simulation (THS) experiment, an experimental setup developed at the NASA Ames COSmIC simulation facility to study Titan's atmospheric chemistry at low temperature. In the THS, the chemistry is simulated by plasma in the stream of a supersonic expansion. With this unique design, the gas is cooled to Titan-like temperature ( approximately 150K) before inducing the chemistry by plasma, and remains at low temperature in the plasma discharge (approximately 200K). Different N2-CH4-based gas mixtures can be injected in the plasma, with or without the addition of heavier precursors present as trace elements on Titan, in order to monitor the evolution of the chemical growth. Both the gas- and solid phase products resulting from the plasma-induced chemistry can be monitored and analyzed using a combination of complementary in situ and ex situ diagnostics. A recent mass spectrometry[1] study of the gas phase has demonstrated that the THS is a unique tool to probe the first and intermediate steps of Titan's atmospheric chemistry at Titan-like temperature. In particular, the mass spectra obtained in a N2-CH4-C2H2-C6H6 mixture are relevant for comparison to Cassini's CAPS-IBS instrument. The results of a complementary study of the solid phase are consistent with the chemical growth evolution observed in the gas phase. Grains and aggregates form in the gas phase and can be jet deposited on various substrates for ex situ analysis. Scanning Electron Microscopy images show that more complex mixtures produce larger aggregates. A mass spectrometry analysis of the solid phase has detected the presence of aminoacetonitrile, a precursor of glycine, in the THS aerosols. X-ray Absorption Near Edge Structure (XANES) measurements also show the presence of imine and nitrile functional groups, showing evidence of nitrogen chemistry. These complementary studies show the high potential of THS to better understand Titan's chemistry and the origin of aerosol formation.

Laboratory↗

Edible carbohydrates from formaldehyde in a spacecraft

The autocatalytic nature of the base catalyzed condensation of formaldehyde to formose sugars is eliminated by using as a cocatalyst, an aldose, or ketose having an alpha-hydrogen. This is more strongly complexed by base than is formaldehyde and the cocatalyst and sugar products accumulate as catalyst complexes instead of formaldehyde. Because of the presence of alpha-hydrogen atoms in cocatalysts and formose sugars, their removal by cross Cannizzaro reaction of complexed sugars does not occur, so the formose reaction behaves autocatalytically due to this accumulation. It is believed that a given catalytic formose complex is not a discrete complexed sugar, but rather, a scrambled dynamic mixture of sugars having weakened structures. The sugar complexes derive from a common salt-like formaldehyde complex, which, because of the absence of alpha-hydrogen, has a greater tendency to undergo Cannizzaro reaction, rather than formose condensation. Because of this, the Cannizzaro reaction can proceed without measurable formose condensation. The reverse is not possible.

Weiss, A. H.↗

Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction

Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.

Peter A Liever↗

Demonstration of Capability to Simulate Particle Irregular Shape and Poly-Disperse Mixtures Within Lunar Lander Plume-Surface Interaction

Plume-Surface Interaction (PSI) between lander engine plumes and regolith soil creates hazards in obscuration and contamination by particle clouds, high-energy ejecta streams, and landing area cratering damage. The MSFC Fluid Dynamics Branch is developing simulation tools to offer a predictive PSI capability to NASA customers such as the Human Lander System (HLS) and Commercial Lunar Payload Services (CLPS). The Gas-Granular Flow Solver (GGFS) is the main application tool for coupled gas-particle two-phase flow simulations to predict the range of PSI effects from onset of surface erosion to deep crater formation. GGFS features an Eulerian-Eulerian modeling approach, treating both gas and granular material as interacting continuum phases. Modeling the lunar regolith granular material fluidic characteristics poses special challenges due to complex particle shapes and mixture composition. The lunar regolith is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking jagged particle shapes. Eulerian granular material flow modeling requires closure formulations for the granular material constitutive models (stress, friction, collisional and kinetic energy dissipation, drag, etc.). While closure models for spherical particles are available from particle kinetic theory, closure models for realistic non-spherical particles must be extracted from unit physics Discrete Element Model (DEM) particle interaction simulations and provided in the form of tabular datasets. The effects of particle irregular shape (non-spherical shape factors, angular particle surface roughness, and interlocking features) are simulated by approximating the particle features in the form of grouped elemental spheres to form composite particles in the DEM simulations. The effects of the wide range of regolith mixture particle sizes and the strong effects of the presence of the small particle sizes results in high cohesion and low porosity of the regolith mixture. The range of particle sizes is simulated by binning the particle sizes into an appropriate finite number of particle-size species and solving the problem as a species mixture. Combining these two modeling approaches enables simulations to capture both, the contributions of the irregular particle shape and the particle size distribution. The integration and maturation of the DEM-based constitutive model database generation process and poly-disperse mixture binning approach into the GGFS simulation framework are proceeding under funding by the NASA Game Changing Development program. The status of current capabilities will be presented in comparisons of crater characteristics resulting for spherical and irregular shape particles, and for mono-, bi-, and tri-disperse mixture simulations of Apollo LM plume-surface interaction. The computational results confirm the significance of including the particle shape and mixture effects. Going forward plans for the full implementation of the general poly-disperse regolith modeling capability and maturation towards NASA project application readiness under the GCD program will be presented.

Peter A. Liever↗

A correlation study based on Al/Si X-ray fluorescence data from southwestern part of Mare Serenitatis

A correlation study based on Al/Si intensity ratios, broad-spectrum visible-albedo measurements, color-difference photography, color-ratio images, and spectral-reflectivity curves was undertaken to understand why the Tacquet Formation in southwestern Mare Serenitatis has unusually low visible albedos for the Al/Si intensity ratios measured by the Apollo 15 X-ray fluorescence experiment. The statistical analysis of the Al/Si data is described, general correlations among all the remote-sensing data are noted, and correlations in the area of the Tacquet Formation are examined. It is shown that the discrepancy between visible albedos and Al/Si intensities may be due primarily to the presence of unevenly deposited highland-type ejecta from Menaleus crater, although the possibility cannot be excluded that the Tacquet Formation is more complex than a simple mixture of highland and mare materials.

Andre, C. G.↗

Storage and retrieval of mass spectral information

Computer handling of mass spectra serves two main purposes: the interpretation of the occasional, problematic mass spectrum, and the identification of the large number of spectra generated in the gas-chromatographic-mass spectrometric (GC-MS) analysis of complex natural and synthetic mixtures. Methods available fall into the three categories of library search, artificial intelligence, and learning machine. Optional procedures for coding, abbreviating and filtering a library of spectra minimize time and storage requirements. Newer techniques make increasing use of probability and information theory in accessing files of mass spectral information.

Hohn, M. E.↗