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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

A versatile system for processing geostationary satellite data with run-time visualization capability

To better predict global climate change, scientists are developing climate models that require interdisciplinary and collaborative efforts in their building. We are currently involved in several such projects but will briefly discuss activities in support of two such complementary projects: the Atmospheric Radiation Measurement (ARM) program of the Department of Energy and Sequoia 2000, a joint venture of the University of California, the private sector, and government agencies. Our contribution to the ARM program is to investigate the role of clouds on the top of the atmosphere and on surface radiance fields through the data analysis of surface and satellite observations and complex modeling of the interaction of radiation with clouds. One of our first ARM research activities involves the computation of the broadband shortwave surface irradiance from satellite observations. Geostationary satellite images centered over the first ARM observation site are received hourly over the Internet network and processed in real time to compute hourly and daily composite shortwave irradiance fields. The images and the results are transferred via a high-speed network to the Sequoia 2000 storage facility in Berkeley, where they are archived These satellite-derived results are compared with the surface observations to evaluate the accuracy of the satellite estimate and the spatial representation of the surface observations. In developing the software involved in calculating the surface shortwave irradiance, we have produced an environment whereby we can easily modify and monitor the data processing as required. Through the principles of modular programming, we have developed software that is easily modified as new algorithms for computation are developed or input data availability changes. In addition, the software was designed so that it could be run from an interactive, icon-driven, graphical interface, TCL-TK, developed by Sequoia 2000 participants. In this way, the data flow can be interactively assessed and altered as needed. In this environment, the intermediate data processing 'images' can be viewed, enabling the investigator to easily monitor the various data processing steps as they progress. Additionally, this environment allows the rapid testing of new processing modules and allows their effects to be visually compared with previous results.

Landsfeld, M.↗
NASA NTRS2014

The Prediction and Analysis of Jet Flows and Scattered Turbulent Mixing Noise About Flight Vehicle Airframes

Jet flows interacting with nearby surfaces exhibit a complex behavior in which acoustic and aerodynamic characteristics are altered. The physical understanding and prediction of these characteristics are essential to designing future low noise aircraft. A new approach is created for predicting scattered jet mixing noise that utilizes an acoustic analogy and steady Reynolds-averaged Navier-Stokes solutions. A tailored Green's function accounts for the propagation of mixing noise about the air-frame and is calculated numerically using a newly developed ray tracing method. The steady aerodynamic statistics, associated unsteady sound source, and acoustic intensity are examined as jet conditions are varied about a large at plate. A non-dimensional number is proposed to estimate the effect of the aerodynamic noise source relative to jet operating condition and airframe position. The steady Reynolds-averaged Navier-Stokes solutions, acoustic analogy, tailored Green's function, non- dimensional number, and predicted noise are validated with a wide variety of measurements. The combination of the developed theory, ray tracing method, and careful implementation in a stand-alone computer program result in an approach that is more first principles oriented than alternatives, computationally efficient, and captures the relevant physics of fluid-structure interaction.

Miller, Steven A.↗
NASA NTRS2014

The Prediction and Analysis of Jet Flows and Scattered Turbulent Mixing Noise about Flight Vehicle Airframes

Jet flows interacting with nearby surfaces exhibit a complex behavior in which acoustic and aerodynamic characteristics are altered. The physical understanding and prediction of these characteristics are essential to designing future low noise aircraft. A new approach is created for predicting scattered jet mixing noise that utilizes an acoustic analogy and steady Reynolds-averaged Navier-Stokes solutions. A tailored Green's function accounts for the propagation of mixing noise about the airframe and is calculated numerically using a newly developed ray tracing method. The steady aerodynamic statistics, associated unsteady sound source, and acoustic intensity are examined as jet conditions are varied about a large flat plate. A non-dimensional number is proposed to estimate the effect of the aerodynamic noise source relative to jet operating condition and airframe position.The steady Reynolds-averaged Navier-Stokes solutions, acoustic analogy, tailored Green's function, non-dimensional number, and predicted noise are validated with a wide variety of measurements. The combination of the developed theory, ray tracing method, and careful implementation in a stand-alone computer program result in an approach that is more first principles oriented than alternatives, computationally efficient, and captures the relevant physics of fluid-structure interaction.

Miller, Steven A. E.↗
NASA NTRSDate not supplied

Predicting Melt Properties Using Atomistic Simulations With A Highly Accurate Physically Informed Neural Network Interatomic Potential

The use of a recently developed machine learning (ML) interatomic potential for molecular dynamics simulations of aluminum melt properties will be presented. Such properties are critical for process modeling in additive manufacturing, including the melt pool size, solidification, and formation of solidification microstructures. Direct first-principles modeling of these processes is computationally prohibitive whereas simulations employing ML potentials combine the high accuracy of quantum-mechanical methods with high computational speeds. The physically-informed neural network (PINN) method used herein, integrates a high-dimensional regression implemented by an artificial neural network with a physics-based bond-order interatomic potential. PINN potentials can accurately reproduce many properties of aluminum in both crystalline-solid and liquid phases. We examine the accuracy of a PINN Al potential in predicting the density, self-diffusivity, viscosity, and the tension of the liquid surface and liquid-solid interfaces. Comparison with experimental data and ab initio molecular dynamics calculations shows very good agreement for all properties tested.

molecular dynamics↗
NASA NTRS2001

Doppler and Reflectivity Measurements at Two Closely-Spaced Frequencies

Spaceborne and airborne radars are limited with a respect to the mass and size of the instrument and the power available to operate it. As a consequence, dual-wavelength radars that require separate antennas and power amplifiers are expensive and often impractical. However, if the frequency difference can be reduced so that a single antenna and the same radio-frequency subsystem can be used for both frequencies, dual- wavelength Doppler measurements can be made with a radar of about the same size and mass as its single-frequency counterpart. In the first part of the paper we present calculations of the reflectivity factor differences as functions of the center frequency from 10 to 35 GHz and for frequency differences between -10% and 10% of the center frequency. The results indicate that differential-frequency operation at Ka-band frequencies (26.5 - 40 GHz) provides relatively strong differential signals if the frequencies can be separated by at least 5%. Unlike lower frequency operation, the differential signals at Ka-band (both reflectivity and Doppler) are directly related to the median mass diameter. An important feature of the differential mean Doppler is that it depends only on the drop-size dependent part of the radial velocity. In principle, the mean and mean differential Doppler data from a nadir-looking platform can be used to infer vertical air motion and characteristics of the particle size distribution. To test the instrument concept, the ER-2 Doppler radar was modified for differential frequency operation. Measurements by the modified radar, operating at frequencies of 9.1 GHz and 10 GHz, were made using an 8 degree zenith-pointing offset parabolic antenna. Simultaneous data were taken with an optical rain gauge and an impact disdrometer. Measured and DSD-estimated values of the differential dBZ mean Doppler are presented.

Meneghini, Robert↗
NASA NTRS2000

MHD Energy Bypass Scramjet Performance with Real Gas Effects

The theoretical performance of a scramjet propulsion system incorporating an magneto-hydro-dynamic (MHD) energy bypass scheme is calculated. The one-dimensional analysis developed earlier, in which the theoretical performance is calculated neglecting skin friction and using a sudden-freezing approximation for the nozzle flow, is modified to incorporate the method of Van Driest for turbulent skin friction and a finite-rate chemistry calculation in the nozzle. Unlike in the earlier design, in which four ramp compressions occurred in the pitch plane, in the present design the first two ramp compressions occur in the pitch plane and the next two compressions occur in the yaw plane. The results for the simplified design of a spaceliner show that (1) the present design produces higher specific impulses than the earlier design, (2) skin friction substantially reduces thrust and specific impulse, and (3) the specific impulse of the MHD-bypass system is still better than the non-MHD system and typical rocket over a narrow region of flight speeds and design parameters. Results suggest that the energy management with MHD principles offers the possibility of improving the performance of the scramjet. The technical issues needing further studies are identified.

Park, Chul↗
NASA NTRS1999

The Enigmatic Longevity of Granular Materials on Mars: The Case for Geologically Episodic Dune Formation

Martian sand dunes are concentrated in vast sand seas in the circumpolar belt of the planet's northern hemisphere, but they are also pervasive over the whole planet. Their occurrence is to be expected on a super-arid planetary surface subjected to boundary layer drag from a continually active atmosphere. Whilst their occurrence is to be expected, their survival is enigmatic. But the enigma only arises if the martian system is considered similar to Earth's --where sand is moved highly frequently, more or less on a seasonal basis. Experimentally it is readily demonstrated that active sand will soon wear down to small grains and eventually diminish to below the critical sand size required to sustain dune formation. According to conventional wisdom, sand moves at higher speeds on Mars than on Earth, and if it were to move as frequently as it does on Earth, then the dune-forming sand population should have long since disappeared, given the great longevity of the martian aeolian system (Sagan coined the term "kamikaze" grains to express this disappearance). No supply of sand could keep pace with this depletion, especially in light of the fact that Mars does not have very active weathering, nor significant crustal differentiation. On Earth, plate tectonics, magmatic activity, and general crustal differentiation over geological time have produced great concentrations of quartz crystals in the continental crustal masses. Not only are these quartz grains chemically and mechanically resilient, they are about the right size for being transported by either wind or water. Add to this, the geologically recent contribution of glacial grinding, and it is easy to see why there are dune field on Earth. So what are the martian dunes composed of, and how does the material survive the eons of attrition? In addition to experimental demonstrations of sand comminution in laboratory aeolian simulations, the problem can be approached from first principles. Sagan showed that by simple considerations of material strength versus mechanical work applied to the material, comminution to sub-sand size would be inevitable. Another semi-analytical approach might be taken by considering that the archetypal aeolian sand surface texture is an irregularly pitted ("frosted") surface composed of chipping hollows approximately 10 microns in diameter, 5 microns deep. Their volume = about 250 cubic microns, or about 1/25000 of the volume of a 100 micron diameter dune grain. Because a saltating grain always strikes another grain, then two surfaces are impacted. Thus each grain undergoes two impacts for every one saltation leap, when the impact statistics are considered for a closed dune system (it can be calculated that a grain can never undergo <1 impact, and never >2 per saltation leap). Hence, if we conservatively assume that there is damage to a grain each time it bounces, but with the minimum damage of only 2 microscopic craters per impact, then approximately 12,500 impacts are required to completely eliminate the grain. Of course, it would require only a fraction of this amount to reduce the grain to below sand size. A grain will make only several tens of saltation leaps on the stoss side of a dune before becoming buried on the lee slope. The dune then has to move its full length before the grain is exhumed again for abrasion. Even with this hiatus in transport, it is easy to see that terrestrial dunes need resupplying with sand in order to survive. In recent theoretical work it has been shown that martian aeolian transport may be initiated with high-speed grains, but this converts to a lower energy dynamic transport equilibrium in which a reptation population dominates grain transport (on Earth, at least half of the flux is by reptation and creep). On Mars, therefore, average grain speeds may be lower than those on Earth, or at least comparable. This would permit greater longevity for martian sands, but it would not go far enough to solve the survival problem. It may, however, explain why martian dunes are about the same size as terrestrial dunes. If martian saltation leaps were significantly longer than on Earth (as usually assumed), then a dune's lee slope would have to be correspondingly longer in order to trap the sand; this would scale up the whole dune structure. But with shorter trajectories in a reptation population, larger dunes would be unnecessary. Additional information is contained in the original.

Marshall, J.↗
NASA NTRS1999

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗
NASA NTRS2007

The Continuous Intercomparison of Radiation Codes (CIRC): Phase I Cases

CIRC aspires to be the successor to ICRCCM (Intercomparison of Radiation Codes in Climate Models). It is envisioned as an evolving and regularly updated reference source for GCM-type radiative transfer (RT) code evaluation with the principle goal to contribute in the improvement of RT parameterizations. CIRC is jointly endorsed by DOE's Atmospheric Radiation Measurement (ARM) program and the GEWEX Radiation Panel (GRP). CIRC's goal is to provide test cases for which GCM RT algorithms should be performing at their best, i.e, well characterized clear-sky and homogeneous, overcast cloudy cases. What distinguishes CIRC from previous intercomparisons is that its pool of cases is based on observed datasets. The bulk of atmospheric and surface input as well as radiative fluxes come from ARM observations as documented in the Broadband Heating Rate Profile (BBHRP) product. BBHRP also provides reference calculations from AER's RRTM RT algorithms that can be used to select the most optimal set of cases and to provide a first-order estimate of our ability to achieve radiative flux closure given the limitations in our knowledge of the atmospheric state.

Oreopoulos, Lazaros↗
NASA NTRS2016

Simulation of an Electromechanical Spin Motor System of a Control Moment Gyroscope

A two-phase brushless DC motor (BDCM) with pulse-width modulated (PWM) voltage drive is simulated to control the flywheel speed of a control moment gyroscope (CMG). An overview of a double-gimballed control moment gyroscope (DGCMG) assembly is presented along with the CMG torque effects on the spacecraft. The operating principles of a two-phase brushless DC motor are presented and the system's electro-mechanical equations of motion are developed for the root-mean-square (RMS) currents and wheel speed. It is shown that the system is an extremely "stiff" set of first-order equations for which an implicit Euler integrator is required for a stable solution. An adaptive proportional voltage controller is presented which adjusts the PWM voltages depending on several control modes for speed, current, and torque. The simulation results illustrate the interaction between the electrical system and the load dynamics and how these influence the overall performance of the system. As will be shown, the CMG spin motor model can directly provide electrical power use and thermal power output to spacecraft subsystems for effective (average) calculations of CMG power consumption.

Inampudi, Ravi↗
NASA NTRS1995

Electronic structure and the van Hove singularity scenario in high-T(sub c)H(g)Ba2CuO(4+delta) superconductors

The electronic structure and the hole concentrations in the high Tc superconductor HgBa2CuO(4+delta) (delta = O, 1) has been investigated by employing a first principles full potential self-consistent LMTO method with the local density functional theory. The scalar relativistic effects have been considered. The hole concentrations of the Cu-d and O-p(x,y) orbitals are seen to be larger for the HgBaCuO5 system than those of the HgBaCuO4 solid. However, the van Hove singularity (vHs) induced Cu-d and O-p peak which is seen to lie comparatively away and above the Fermi level in the delta = 1 system shifts towards the Fermi level in the delta = 0 system. Thus, the superconducting behavior appears to originate from the occurrence of the vHs peak at the Fermi level. The Fermi surface nesting area in the delta = 0 compound is seen to be larger than in the delta = 1 compound. The calculation reveals that the increase in pressure on the crystal enhances the hole concentrations but without showing any optimum value, On the other hand, the vHs peak approaches to-wards the Fermi level with pressure and crosses the Fermi surface near V/Vo approximately equals 0.625 (V and Vo are the crystal volumes at high and normal pressures, respectively). Our calculated value of the bulk modulus equal to 0.626 Mbar predicts the occurrence of this crossover at about 24 GPa which is in complete agreement with the experimental value. At this pressure the compound has maximum nesting area and self-doped behavior.

Agrawal, Bal K.↗
NASA NTRS1991

The detection of the electric field vertical distribution underneath thundercloud: Principle and applications

During the Florida 89 experiment at Kennedy Space Center, a new system was used in order to obtain the vertical distribution of the electric field underneath thunderstorms. It consists of a standard shutter field mill at ground level and five other field sensors suspended from a cable fastened to a tethered balloon located at an altitude of about 1000 meters. It also includes a reception station for telemetered information transmitted by sensors, a processing system in order to store data, and real time display on a screen to show the simultaneous field variations at each level along with the instantaneous electric field profile. The first results obtained show the great importance of the electric field vertical distribution. The field detected at a height of 600m reaches 65 kV/m while that at the surface does not exceed 5 kV/m. The field intensity in altitude is a better criterion for determining the right moment to launch a rocket devoted to flash triggering. Using Gauss's law, the simultaneous field variations at several levels are used in order to evaluate charge densities. Average values close to 1nC.m(-3) are calculated in layers up to 600 m. The calculation of different average charge densities leads to the characterization of the layer between cloud and ground just before the leader propagation in the case of cloud to ground flash.

Soula, Serge↗
NASA NTRS1991

Evaluation of dual flow thrust vectored nozzles with exhaust stream impingement

The main objective of this project was to predict the expansion wave/oblique shock wave structure in an under-expanded jet expanding from a convergent nozzle. The shock structure was predicted by combining the calculated curvature of the free pressure boundary with principles and governing equations relating to oblique shock wave and expansion wave interaction. The procedure was then continued until the shock pattern repeated itself. A mathematical model was then formulated and written in FORTRAN to calculate the oblique shock/expansion wave structure within the jet. In order to study shock waves in expanding jets, Schlieren photography, a form of flow visualization, was employed. Thirty-six Schlieren photographs of jets from both a straight and 15 degree nozzle were taken. An iterative procedure was developed to calculate the shock structure within the jet and predict the non-dimensional values of Prandtl primary wavelength (w/rn), distance to Mach Disc (Ld) and Mach Disc radius (rd). These values were then compared to measurements taken from Schlieren photographs and experimental results. The results agreed closely to measurements from Schlieren photographs and previously obtained data. This method provides excellent results for pressure ratios below that at which a Mach Disc first forms. Calculated values of non-dimensional distance to the Mach Disc (Ld) agreed closely to values measured from Schlieren photographs and published data. The calculated values of non-dimensional Mach Disc radius (rd), however, deviated from published data by as much as 25 percent at certain pressure ratios.

Carpenter, Thomas W.↗
NASA NTRS2000

Laser Lightcraft Performance

The purpose of this study is to establish the technical ground for modeling the physics of laser powered pulse detonation phenomenon. The principle of the laser power propulsion is that when high-powered laser is focused at a small area near the surface of a thruster, the intense energy causes the electrical breakdown of the working fluid (e.g. air) and forming high speed plasma (known as the inverse Bremsstrahlung, IB, effect). The intense heat and high pressure created in the plasma consequently causes the surrounding to heat up and expand until the thrust producing shock waves are formed. This complex process of gas ionization, increase in radiation absorption and the forming of plasma and shock waves will be investigated in the development of the present numerical model. In the first phase of this study, laser light focusing, radiation absorption and shock wave propagation over the entire pulsed cycle are modeled. The model geometry and test conditions of known benchmark experiments such as those in Myrabo's experiment will be employed in the numerical model validation simulations. The calculated performance data will be compared to the test data.

Chen, Yen-Sen↗
NASA NTRS1987

Atmospheric reentry of the in-core thermionic SP-100 reactor system

Presumed end-of-life atmospheric reentry of the GA SP-100 system was studied to assess dispersal feasibility and associated hazards. Reentry was studied by sequential use of an orbital trajectory and a heat analysis computer program. Two heating models were used. The first model assumed a thermal equilibrium condition between the stagnation point aerodynamic heating and the radiative cooling of the skin material surface. The second model allowed for infinite conductivity of the skin material. Four reentering configurations were studied representing stages of increased SP-100 breakup: (1) radiator, shield and reactor, (2) shield and reactor, (3) reactor with control drums, and (4) reactor without control drums. Each reentering configuration was started from a circular orbit at 116 km having an inertial velocity near Mach 25. The assumed failing criterion was the attainment of melting temperature of a critical system component. The reentry analysis revealed breakup of the vessel in the neighborhood of 61 km altitude and scattering of the fuel elements. Subsequent breakup of the fuel elements was not predicted. Oxidation of the niobium skin material was calculated to cause an increase in surface temperature of less than ten percent. The concept of thermite analogs for enhancing reactor reentry dispersal was assessed and found to be feasible in principle. A conservative worst-case hazards analysis was performed for radioactive and nonradioactive toxic SP-100 materials assumed to be dispersed during end-of-life reentry. The hazards associated with this phase of the SP-100 mission were calculated to be insignificant.

Stamatelatos, M. G.↗
NASA NTRS2011

Towards Autonomous Operation of Robonaut 2

The Robonaut 2 (R2) platform, as shown in Figure 1, was designed through a collaboration between NASA and General Motors to be a capable robotic assistant with the dexterity similar to a suited astronaut [1]. An R2 robot was sent to the International Space Station (ISS) in February 2011 and, in doing so, became the first humanoid robot in space. Its capabilities are presently being tested and expanded to increase its usefulness to the crew. Current work on R2 includes the addition of a mobility platform to allow the robot to complete tasks (such as cleaning, maintenance, or simple construction activities) both inside and outside of the ISS. To support these new activities, R2's software architecture is being developed to provide efficient ways of programming robust and autonomous behavior. In particular, a multi-tiered software architecture is proposed that combines principles of low-level feedback control with higher-level planners that accomplish behavioral goals at the task level given the run-time context, user constraints, the health of the system, and so on. The proposed architecture is shown in Figure 2. At the lowest-level, the resource level, there exists the various sensory and motor signals available to the system. The sensory signals for a robot such as R2 include multiple channels of force/torque data, joint or Cartesian positions calculated through the robot's proprioception, and signals derived from objects observable by its cameras.

Badger, Julia M.↗
NASA NTRS1993

Topographic mapping using a monopulse SAR system

Terrain height variations in mountainous areas cause two problems in the radiometric correction of SAR images: the first being that the wrong elevation angle may be used in correcting for the radiometric variation of the antenna pattern; the second that the local incidence angle used in correcting the projection of the pixel area from slant range to ground range coordinates may vary from that given by the flat earth assumption. We propose a novel design of a SAR system which exploits the monopulse principle to determine the elevation angle and thus the height at the different parts of the image. The key element of such a phase monopulse system is an antenna, which can be divided into a lower and upper half in elevation using a monopulse comparator. In addition to the usual sum pattern, the elevation difference pattern can be generated by a -pi phase shift on one half of the antenna. From the ratios of images radiometrically modulated by the difference and sum antenna pattern in cross-track direction, we can derive the appropriate elevation angle at any point in the image. Together with the slant range we can calculate the height of the platform above this point using information on the antenna pointing and the platform attitude. This operation, repeated at many locations throughout the image, allows us to build up a topographic map of the height of the aircraft above each location. Inversion of this map, using the precisely determined aircraft altitude and the accurate flight path, leads to the actual topography of the imaged surface. The precise elevation of one point in the image could also be used to convert the height map to a topographic map. In this paper, we present design considerations for a corresponding airborne SAR system in X-Band and give estimates of the error due to system noise and azimuth ambiguities as well as the expected performance and precision in topographic mapping.

Zink, M.↗
NASA NTRS1993

The quantum dynamics of electronically nonadiabatic chemical reactions

Considerable progress was achieved on the quantum mechanical treatment of electronically nonadiabatic collisions involving energy transfer and chemical reaction in the collision of an electronically excited atom with a molecule. In the first step, a new diabatic representation for the coupled potential energy surfaces was created. A two-state diabatic representation was developed which was designed to realistically reproduce the two lowest adiabatic states of the valence bond model and also to have the following three desirable features: (1) it is more economical to evaluate; (2) it is more portable; and (3) all spline fits are replaced by analytic functions. The new representation consists of a set of two coupled diabatic potential energy surfaces plus a coupling surface. It is suitable for dynamics calculations on both the electronic quenching and reaction processes in collisions of Na(3p2p) with H2. The new two-state representation was obtained by a three-step process from a modified eight-state diatomics-in-molecules (DIM) representation of Blais. The second step required the development of new dynamical methods. A formalism was developed for treating reactions with very general basis functions including electronically excited states. Our formalism is based on the generalized Newton, scattered wave, and outgoing wave variational principles that were used previously for reactive collisions on a single potential energy surface, and it incorporates three new features: (1) the basis functions include electronic degrees of freedom, as required to treat reactions involving electronic excitation and two or more coupled potential energy surfaces; (2) the primitive electronic basis is assumed to be diabatic, and it is not assumed that it diagonalizes the electronic Hamiltonian even asymptotically; and (3) contracted basis functions for vibrational-rotational-orbital degrees of freedom are included in a very general way, similar to previous prescriptions for locally adiabatic functions in various quantum scattering algorithms.

Truhlar, Donald G.↗