Sum rule functions
Sum rule functions for expressions of atomic or molecular quantum mechanical properties
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Sum rule functions for expressions of atomic or molecular quantum mechanical properties
The stagnation-point convective heat transfer to an axisymmetric blunt body for arbitrary gases in chemical equilibrium was investigated. The gases considered were base gases of nitrogen, oxygen, hydrogen, helium, neon, argon, carbon dioxide, ammonia, and methane and 22 gas mixtures composed of the base gases. Enthalpies ranged from 2.3 to 116.2 MJ/kg, pressures ranged from 0.001 to 100 atmospheres, and the wall temperatures were 300 and 1111 K. A general equation for the stagnation-point convective heat transfer in base gases and gas mixtures was derived and is a function of the mass fraction, the molecular weight, and a transport parameter of the base gases. The relation compares well with present boundary-layer computer results and with other analytical and experimental results. In addition, the analysis verified that the convective heat transfer in gas mixtures can be determined from a summation relation involving the heat transfer coefficients of the base gases. The basic technique developed for the prediction of stagnation-point convective heating to an axisymmetric blunt body could be applied to other heat transfer problems.
Atmospheric structure of outer planets as determined by pressure, temperature, and accelerometers is reviewed and results obtained from the PAET earth entry are given. In order to describe atmospheric structure, entry is divided into two regimes, high and low speed. Acceleration is then measured: from these measurements density is determined as a function of time. The equations of motion are integrated to determine velocity, flight path angle, and altitude as a function of time. Density is then determined as a function of altitude from the previous determinations of density and altitude as a function of time. Hydrostatic equilibrium was assumed to determine pressure as a function of altitude. Finally the equation of space applied to determine temperature as a function of altitude, if the mean molecular weight is known. The mean molecular weight is obtained independently from either the low speed experiment or from the composition experiments.
The problem of detecting rocket plumes at thermospheric altitudes with satellite-borne submillimeter-wave radiometers is examined theoretically. To estimate the sizes of plume signatures contrasted against a 250-K earth background or in self-emission against the cold sky, a computer program has been developed to predict plume brightness temperatures and optical depths of rotational lines of plume molecular constituents (e.g., H2O) as a function of distance from the nozzle. The methods employed in the computations are described in general terms, and examples are presented to indicate that detectable H2O signatures extending to several thousand nozzle diameters should exist at plume altitudes above 250 km.
Ferredoxins are low-molecular-weight, nonheme, iron proteins which function as electron carriers in a wide variety of electron transport chains. Howard et al. (1983) have suggested that the amino end of Azotobacter vinelandii ferredoxin shows a greater similarity to the carboxyl end of ferredoxin from Chromatium vinosum and that their half-chain sequences are homologous when the half-chains of either species are considered in inverse order. Examination of this proposition has made it necessary to reevaluate previous conclusions concerning the evolution of bacterial ferredoxin. Attention is given to the properties of the bacterial ferredoxin sequences, and the evolution of the bacterial ferredoxins.
The nonlinearly viscoelastic response of an amorphous homopolymer is considered under aspects of time dependent free volume behavior. In contrast to linearly viscoelastic solids, this model couples shear and volume deformation through a shift function which influences the rate of molecular relaxation or creep. Sample computations produce all those qualitative features one observes normally in uniaxial tension including the rate dependent formation of a yield point as a consequence of the history of an imposed pressure.
We show that by a suitable change of variables, the derivatives of molecular integrals over Gaussian-type functions required for analytic energy derivatives can be evaluated with significantly less computational effort than current formulations. The reduction in effort increases with the order of differentiation.
Measurements were made of the flow of gases through various narrow channels a few microns wide at average pressures from 0.00003 to 40 cm. Hg. The flow rate, defined as the product of pressure and volume rate of flow at unit pressure difference, first decreased linearly with decrease in mean pressure in the channel, in agreement with laminar-flow theory, reached a minimum when the mean path length was approximately equal to the channel width, and then increased to a constant value. The product of flow rate and square root of molecular number was approximately the same function of mean path length for all gases for a given channel.
The order, conformations and dynamics of poly(oxyethylene) (POE) melts have been investigated through molecular dynamics simulations. The potential energy functions were determined from detailed ab initio electronic structure calculations of the conformational energies of the model molecules 1,2-dimethoxyethane (DME) and diethylether. The x-ray structure factor for POE from simulation will be compared to experiment. In terms of conformation, simulations reveal that chains are extended in the melt relative to isolated chains due to the presence of strong intermolecular O...H interactions, which occur at the expense of intramolecular O...H interactions. Conformational dynamics about the C-C bond were found to be significantly faster than in polymethylene, while conformational dynamics about the C-O bond even faster than the C-C dynamics. The faster local dynamics in POE relative to polymethylene is consistent with C-13 NMR spin-lattice relaxation experiments. Conformational transitions showed significant second-neighbor correlation, as was found for polymethylene. This correlation of transitions with C-C neighbors was found to be reduced relative to C-O neighbors. Dielectric relaxation from simulation will also be compared with experiment.
Sample return missions require chemical contamination to be minimized and potential sources of contamination to be documented and preserved for future use. Genesis focused on and successfully accomplished the following: - Early involvement provided input to mission design: a) cleanable materials and cleanable design; b) mission operation parameters to minimize contamination during flight. - Established contamination control authority at a high level and developed knowledge and respect for contamination control across all institutions at the working level. - Provided state-of-the-art spacecraft assembly cleanroom facilities for science canister assembly and function testing. Both particulate and airborne molecular contamination was minimized. - Using ultrapure water, cleaned spacecraft components to a very high level. Stainless steel components were cleaned to carbon monolayer levels (10 (sup 15) carbon atoms per square centimeter). - Established long-term curation facility Lessons learned and areas for improvement, include: - Bare aluminum is not a cleanable surface and should not be used for components requiring extreme levels of cleanliness. The problem is formation of oxides during rigorous cleaning. - Representative coupons of relevant spacecraft components (cut from the same block at the same time with identical surface finish and cleaning history) should be acquired, documented and preserved. Genesis experience suggests that creation of these coupons would be facilitated by specification on the engineering component drawings. - Component handling history is critical for interpretation of analytical results on returned samples. This set of relevant documents is not the same as typical documentation for one-way missions and does include data from several institutions, which need to be unified. Dedicated resources need to be provided for acquiring and archiving appropriate documents in one location with easy access for decades. - Dedicated, knowledgeable contamination control oversight should be provided at sites of fabrication and integration. Numerous excellent Genesis chemists and analytical facilities participated in the contamination oversight; however, additional oversight at fabrication sites would have been helpful.
Fractally branching vascular systems are a complex physiological requirement shared by humans with all higher terrestrial life forms, including other vertebrates, insects, and higher land plants. Vascular trees, networks, and tree-network composites are therefore mapped and quantified by the VESsel GENeration Analysis (VESGEN) software according to weighted physiological vascular rules that include vessel connectivity, tapering and bifurcational branching. According to fluid dynamics, successful vascular transport depends upon a complex distributed system of highly regulated laminar flow. VESGEN has elucidated changes in vascular patterning resulting from inflammatory, developmental and other signaling pathways within numerous tissues of major model organisms important for Space Biology, especially for rodents. Important early stage regenerative opportunities have been identified by VESGEN vascular analysis for visual impairments in the human retina, and is currently being used for research into astronaut visual and ocular disorders associated with long duration missions. The VESGEN 2D software is a mature, automated, widely published capability for which beta testing and public release by NASA is planned for the upcoming year. Early-stage capabilities for VESGEN 3D analysis are under development for the rodent retina and intestine as prototype tissues. A prototype VESGEN 2D Bioinformatics software capability has also been developed to associate phenotypic changes in molecular expression with vascular structure and function. By new VESGEN bioinformatic innovations, expression patterns of the genetic, transcriptional, protein and other markers for regulatory molecules such as vascular endothelial growth factor (VEGF) and their receptors, often indicators of tissue oxygenation status, are co-localized with alterations in vascular pattern. Biomarkers are therefore mapped and quantified as information dimensions directly correlated with the spatial dimensions of a vascular pattern. Further important technology innovations by NASA include substantial image segmentation advances for more automated binary extraction of the grayscale vascular patterns, together with informative associated image quality assessments. Vascular mapping and quantification capabilities for the rodent retina and intestine are illustrated for VESGEN 2D, along with technology status reports on VESGEN 3D and Bioinformatic capabilities. Research partially supported by Ames Center Innovation Awards.
Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^8 determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.
Over the past decade, NASA has invested in efforts to build predictive thermal protection system (TPS) material models from the micro-scale to the macro-scale. To complement the mission design cycle process and reduce the need for extensive testing, NASA is developing modeling and simulation tools that enable characterizing material properties and response to hot plasma experienced during atmospheric entry. Traditional material response and ablation modeling tools, such as the heritage code FIAT, and its multidimensional siblings, TITAN and 3dFIAT, are being complemented with newly developed software such as Icarus and PATO. Both of these programs are three-dimensional, finite-volume solvers that use unstructured meshes and 21st century programming paradigms to allow for efficient parallel simulations. FIAT and Icarus are also used for TPS sizing purposes. Today, these traditional tools are being supplemented with computational materials models at the atomistic level. The scales of interest range from computational chemistry (Density Functional Theory [DFT]), to atomistic simulations (Molecular Dynamics [MD]), to the microscale with the Porous Microstructure Analysis (PuMA) software that was recently awarded the 2022 NASA Software of the Year award. Finally, thermo-structural modeling is also of interest to the TPS Materials branch and done using commercial tools such as MSC MARC, MENTAT, NASTRAN and PATRAN. The present talk will also link the use of these computational tools to current NASA missions and projects associated with challenging and complex vehicles entries/reentries.
There exists a positive correlation between the pH of subcellular compartments and the median isoelectric point (pI) for the associated proteomes. Proteins in the human lysosome—a highly acidic compartment in the cell—have a median pI of ∼6.5, whereas proteins in the more basic mitochondria have a median pI of ∼8.0. Proposed mechanisms reflect potential adaptations to pH. For example, enzyme active site general acid/base residue pKs are likely evolved to match environmental pH. However, such effects would be limited to a few residues on specific proteins, and might not affect the proteome at large. A protein model that considers residue burial upon folding recapitulates the correlation between proteome pI and environmental pH. This correlation can be fully described by a neutral evolution process; no functional selection is included in the model. Proteins in acidic environments incur a lower energetic penalty for burying acidic residues than basic residues, resulting in a net accumulation of acidic residues in the protein core. The inverse is true under alkaline conditions. The pI distributions of subcellular proteomes are likely not a direct result of functional adaptations to pH, but a molecular spandrel stemming from marginal stability.
Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.
Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.
The Astrobiology Analytical Laboratory at GSFC has identified amino acids in meteorites and returned cometary samples by using liquid chromatography-electrospray ionization time-of-flight mass spectrometry (LCMS). These organic species are key markers for life, having the property of chirality that can be used to distinguish biological from non-biological amino acids. One of the critical components in the benchtop instrument is liquid chromatography (LC) analytical column. The commercial LC analytical column is an over- 250-mm-long and 4.6-mm-diameter stainless steel tube filled with functionized microbeads as stationary phase to separate the molecular species based on their chemistry. Miniaturization of this technique for spaceflight is compelling for future payloads for landed missions targeting astrobiology objectives. A commercial liquid chromatography analytical column consists of an inert cylindrical tube filled with a stationary phase, i.e., microbeads, that has been functionalized with a targeted chemistry. When analyte is sent through the column by a pressurized carrier fluid (typically a methanol/ water mixture), compounds are separated in time due to differences in chemical interactions with the stationary phase. Different species of analyte molecules will interact more strongly with the column chemistry, and will therefore take longer to traverse the column. In this way, the column will separate molecular species based on their chemistry. A lab-on-chip liquid analysis tool was developed. The microfluidic analytical column is capable of chromatographically separating biologically relevant classes of molecules based on their chemistry. For this analytical column, fabrication, low leak rate, and stationary phase incorporation of a serpentine microchannel were demonstrated that mimic the dimensions of a commercial LC column within a 5 10 1 mm chip. The microchannel in the chip has a 75- micrometer-diameter oval-shaped cross section. The serpentine microchannel has four different lengths: 40, 60, 80, and 100 mm. Functionized microbeads were filled inside the microchannel to separate molecular species based on their chemistry.
Approximation of scattering resonance energies and widths of ground state of molecular hydrogen from energy dependence of atomic collisional time delay functions