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NASA NTRS1965

Theory of Intramolecular Relaxation Processes

A master equation is derived to describe internal relaxation processes in molecular systems with a relatively small number of degrees of freedom. It is an inhomogeneous equation, taking into account nondiagonal elements of the coarse‐grained density matrix which prove to be the most relevant ones for the problem under consideration. Various relaxational time scales, inherent in a molecular system, can thus be shown to exist. Relaxation mechanisms and equilibrium states on these time scales can be determined. The general character and different types of solutions of the master equation are investigated. The theory is applied to internal vibrational relaxation and intramolecular rearrangement (isomerization) reactions.

Hofacker, G. Ludwig↗

NASA NTRS1979

Ion velocity distributions in the high-latitude ionosphere

The theory and observations relating to ion velocity distributions in the high-latitude F region are reviewed. The review covers three basic aspects, including methods for calculating ion velocity distributions, experimental evidence for the existence of non-Maxwellian ion velocity distributions, and the ionospheric consequences of non-Maxwellian distributions. Specific topics covered include closed form solutions to Boltzmann's equation for a simple collision model, series solutions to the Boltzmann equation for more general collision models, retarding potential analyzer measurements, excitation of VLF electrostatic emissions, ion-neutral reaction rates, and transport effects.

St-Maurice, J.-P.↗

NASA NTRS2007

The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation

A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.

Campbell, Joel↗

DOE OSTI2024

Emergent Chern-Simons interactions in 3+1 dimensions

Parity-violating superconductors can support a low-dimension local interaction that becomes, upon condensation, a purely spatial Chern-Simons term. Solutions to the resulting generalized London equations can be obtained from solutions of the ordinary London equations with a complex penetration depth, and suggest several remarkable physical phenomena. The problem of flux exclusion by a sphere brings in an anapole moment, the problem of current-carrying wires brings in an azimuthal magnetic field, and the problem of vortices brings in currents along the vortices. We demonstrate that interactions of this kind, together with a conceptually related dimensionally reduced Chern-Simons interaction, can arise from physically plausible microscopic interactions. Published by the American Physical Society 2024

Materials Science↗

NASA NTRS1961

Method for Approximating the Vacuum Motions of Spinning Symmetrical Bodies with Nonconstant Spin Rates

A method for approximating the vacuum motions of spinning rigid symmetrical bodies with varying spin rates and inertias has been completed. The analysis includes the effects of time varying thrust misalignments, mass unbalance, and jet damping. Results are given in the form of equations for space referenced Euler angles, flight-path angles, body referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. The method consists of dividing the problem into intervals during which the time-dependent variables are assumed constant at their mean interval value. In order to check this procedure, solutions for various interval sizes are compared with solutions obtained with numerical methods. Although the method is somewhat lengthy for accurate hand computation in most cases, it is readily programed for machine solutions. Probably more important, the general solutions give insight into the separate effects of the variables and, in many cases, can be quickly used to determine the approximate ranges of the variables required for the desired solution to a given problem. In this respect, equations for determining maximum wobble have been derived for certain input conditions. The method has been shown to compare closely with the numerical solutions of two sample problems. The sample problems also illustrated the relatively large effect of pitch and yaw jet damping on body motions.

VACUUM↗

NASA NTRS2005

Data Assimilation and Data Fusion for Planetary Atmospheres

The overarching goal of this Cooperative Agreement was to develop a model and procedures for the data assimilation of planetary spacecraft atmospheric observations. Data assimilation - in its application to weather analysis and prediction - is the process of finding an initial state of the meteorological variables (winds, temperatures, pressures, etc.) of an atmosphere, which, when propagated forward in time using a deterministic general circulation model, reproduces all of the available observations over that time to within the measurement and computational errors. With this definition, data assimilation is seen to be a natural extension of well-known least-squares minimization techniques. The primary complication arises from the scale of the problem: For the Martian atmosphere with the available nadir-viewing Thermal Emission Spectrometer data from Mars Global Surveyor, approximately 1,000,000 individual measurements of channel radiances (in the 15-micrometer region, where these radiances relate directly to the surface and atmospheric temperature) were made per day. A suitable general circulation model for dealing with this data set has on the order of 20,000 independent variables. After some spatial and temporal averaging of the data - which provides a necessary statistical estimate of the representativeness of the measurements, a crucial issue in data assimilation - the problem reduces in scale to the solution of approximately 50,000 equations for the 20,000 variables.

Houben, Howard↗

NASA NTRSDate not supplied

A Reynolds-Averaged Navier-Stokes Perspective for the High Lift Common Research Model Using the LAVA Framework

An in-depth assessment of the High Lift-Common Research Model (HL-CRM) aerodynamic performance is made using a Reynolds-Averaged Navier-Stokes (RANS) methodology. Results presented here were produced in support of the 4th AIAA High Lift Prediction Workshop(HLPW-4), with additional simulation results and analysis used to support findings from the workshop. Mesh resolution, RANS closure models, and tunnel effects were among the sources of simulation sensitivity addressed, all in the pursuit of evaluating best-practice simulation methods for complex high-lift configurations. In general, free-air simulations using RANS yield accurate predictions of integrated loads in the pre-stall regime for the HL-CRM, while strong sensitivity to simulation method is observed near CLmax. Additionally, a study assessing changes in aerodynamic performance due to flap deflection angle indicated strong sensitivity to turbulence model closure and mesh resolution, particularly at the highest deflection setting. Several available corrections for the Spalart-Allmaras (SA) turbulence model were tested and generally introduced more error relative to the experiment in comparison to the baseline SA closure model. The Standard Menter Baseline Two-Equation (k-ωBSL) turbulence model was also explored, which arguably yielded results highly consistent with experiment, but at a substantially higher computational cost. Therefore, as a compromise between computational cost and accuracy, the baseline SA closure model was selected for additional HL-CRM studies that assess alternative solution methods. These strategies include “warm start” approaches, which initialize the simulation from a previously converged solution at a nearby angle of attack, unsteady calculations, and simulations that model the experimental wind tunnel. Results from these studies would reinforce the shortcomings of RANS in predicting aircraft performance at high-lift conditions, namely at high-αand highly loaded flap conditions, while also answering questions about appropriate modeling techniques to minimize the errors associated with RANS where possible

TTT↗

NASA NTRS1981

On the formation of protostellar disks

An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion of a rotating gas cloud. Streamline equations for the flow onto the disk are derived, including the special case where the disk is very thin. For the radial structure of the disk, detailed equations of conservation of mass, momentum, angular momentum, and energy are given. Exact solutions are found for the case of no internal viscosity. For the more general case where there is viscous stress, hypotheses are formulated with the objective of discovering the main qualitative characteristics of a turbulent system and to estimate the magnitude of the turbulent stress. Solutions are also found for boundary conditions, and the large and small viscosity limits. The relation of energy balance to disk thermal structure is detailed. Finally, trends in the collapse of the dust cloud are discussed in the light of the solutions given.

Cassen, P.↗

NASA NTRS2000

Magnetic Susceptibility Effects and Lorentz Damping in Diamagnetic Fluids

A great number of crystals (semi-conductor and protein) grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity and g-jitter. Both static and dynamic (rotating or travelling wave) magnetic fields can be used to reduce the effects of convection in materials processing. In semi-conductor melts, due to their relatively high electrical conductivity, the induced Lorentz force can be effectively used to curtail convective effects. In melts/solutions with reduced electrical conductivity, such as aqueous solutions used in solution crystal growth, protein crystal growth and/or model fluid experiments for simulating melt growth, however, the variation of the magnetic susceptibility with temperature and/or concentration can be utilized to better damp fluid convection than the Lorentz force method. This paper presents a comprehensive, comparative numerical study of the relative damping effects using static magnetic fields and gradients in a simple geometry subjected to a thermal gradient. The governing equations are formulated in general terms and then simplified for the numerical calculations. Operational regimes, based on the best damping technique for different melts/solutions are identified based on fluid properties. Comparisons are provided between the numerical results and available results from experiments in surveyed literature.

Ramachandran, Narayanan↗

NASA NTRS1981

A new payload integration method

This paper introduces a new payload integration method. The system equations of motion are derived in terms of interface-restrained booster and payload modes. These system equations are directly integrated, avoiding the solution of an expensive eigenvalue problem. A modified Newmark-Chan-Beta numerical scheme is used to perform this integration. Due to the unique form of the system equations it is possible to achieve significant savings. A similar savings is feasible for the computation of the internal loads. This new approach does not involve approximations. Although completely general, the presented technique is most effective when the number of interface degrees of freedom is relatively small. Both determinate and indeterminate interfaces are allowed.

Engels, R. C.↗

NASA NTRS1988

Inevitable inflation in Einstein-Cartan theory with improved energy-momentum tensor with spin

Generalized, or power-law, inflation is shown to necessarily exist for a simple, anisotropic, (Bianchi Type-1) cosmology in the Einstein-Cartan gravitational theory with the Ray-Smalley improved energy momentum tensor with spin. Formal solution of the EC field equations with the fluid equations of motion explicitly shows inflation caused by the RS spin angular kinetic energy density. Shear is not effective in preventing inflation in the ECRS model. The relation between fluid vorticity, torsion, reference axis rotation, and shear ellipsoid precession shows through clearly.

Fennelly, A. J.↗

NASA NTRS1991

Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

Walker, K. P.↗

NASA NTRS2016

A Nonlinear Modal Aeroelastic Solver for FUN3D

A nonlinear structural solver has been implemented internally within the NASA FUN3D computational fluid dynamics code, allowing for some new aeroelastic capabilities. Using a modal representation of the structure, a set of differential or differential-algebraic equations are derived for general thin structures with geometric nonlinearities. ODEPACK and LAPACK routines are linked with FUN3D, and the nonlinear equations are solved at each CFD time step. The existing predictor-corrector method is retained, whereby the structural solution is updated after mesh deformation. The nonlinear solver is validated using a test case for a flexible aeroshell at transonic, supersonic, and hypersonic flow conditions. Agreement with linear theory is seen for the static aeroelastic solutions at relatively low dynamic pressures, but structural nonlinearities limit deformation amplitudes at high dynamic pressures. No flutter was found at any of the tested trajectory points, though LCO may be possible in the transonic regime.

Goldman, Benjamin D.↗

NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗

DOE OSTI2024

Tunable noninteracting free-energy density functionals for high-energy-density physics applications

In this work, we introduce the concept of a tunable noninteracting free-energy density functional and present two examples realized: (i) via a simple one-parameter convex combination of two existing functionals and (ii) via the construction of a generalized gradient approximation (GGA) enhancement factor that contains one free parameter and is designed to satisfy a set of incorporated constraints. Functional (i), constructed as a combination of the local Thomas–Fermi and a pseudopotential-adapted GGA for the noninteracting free-energy, has already demonstrated its practical usability for establishing the high temperature end of the equation of state of deuterium [Phys. Rev. B 104, 144104 (2021)] and CHON resin [Phys. Rev. E 106, 045207 (2022)] for inertial confinement fusion applications. Hugoniot calculations for liquid deuterium are given as another example of how the application of computationally efficient orbital-free density functional theory (OF-DFT) can be utilized with the employment of the developed functionals. Once the functionals have been tuned such that the OF-DFT Hugoniot calculation matches the Kohn–Sham solution at some low-temperature point, agreement with the reference Kohn–Sham results for the rest of the high temperature Hugoniot path is very good with relative errors for compression and pressure on the order of 2% or less.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1983

Space radiation interaction mechanisms in materials

Models of charged-particle impact under conditions typical of the space environment are reported, with a focus on impact excitation and nuclear reactions, especially for heavy ions. Impact excitation is studied by using a global model for electronic excitation based on formal relations through the classical dielectric function to derive an approximation related to the local plasma (electron density distribution) within the atoms and molecules; and corrections to the model resulting from the nonfluid nature of this plasma are discussed. Nuclear reactions are studied by reducing quantum-mechanical treatment of this general N-body problem to an equivalent two-body problem that is solvable, and by comparing the results with experimental data. The equations for heavy-charged-particle transport are derived and solution techniques demonstrated. Finally, these methods of analysis are applied to study the change in the electrical properties of a GaAs semiconductor for photovoltaic applications; proton damage to GaAs crystals is found to arise from stable replacement defects and to be nonannealable, in contrast to electron-induced damage.

Wilson, J. W.↗

NASA NTRS1983

The attenuation of sound in a randomly lined duct

The kinetic theory of wave propagation in random media is applied to assess the relative merits of the peripherally segmented, axially segmented and 'checkerboard' configured acoustic duct treatments proposed by Mani (1976). It is argued that, in a first approximation, a multisegmented liner involving many discrete and distinct sections may be modelled as a liner whose impedance varies randomly with position. This results in a relatively simple analytical description of the acoustic properties of the liner in terms of a system of linear, first order ordinary differential equations, whose solution gives the distribution with axial distance of the acoustic modal intensities. The theory is expected to be valid provided that the variation in the impedance from segment to segment is small, so that the conclusions obtained here are of a preliminary nature, and must be regarded as giving a general indication of features which should be incorporated into the design of efficient acoustic liners. The principal such conclusion is that a checkerboard liner offers the best means of increasing the attenuation over and above that of a uniformly lined duct. On the other hand, only minimal gains are to be derived from the use of strictly peripherally segmented liners.

Howe, M. S.↗

NASA NTRS1987

Optimal time free nodal transfers between elliptical orbits

The paper presents the necessary conditions for the minimum fuel, time-free transfer between two noncoplanar elliptical orbits. It is shown that the solution is obtained by solving a system of three nonlinear equations for three unknowns. The case where the impulses are applied along the line of nodes is discussed. In general, this nodal transfer is nonoptimal, but the characteristic velocity for the best nodal transfer, called the minimizing nodal transfer, is reasonably close to the one for the optimal transfer for it to be useful as a substitute for a practical transfer. Furthermore, when the relative position of the two terminal orbits is varied, the two characteristic velocities, for the minimizing nodal transfer and the optimal transfer, exhibit the same trend in the sense that they pass through their maxima and minima at nearly the same relative position. This makes the set of explicit formulas for computing the minimizing nodal transfer, as presented in this paper, a useful tool for designing a minimum fuel transfer between several orbits.

Vinh, Nguyen X.↗