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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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The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.
An integral equation method for solving the full potential equation has been developed for arbitrary configurations in two- or three-dimensional transonic flows. This method is capable of capturing shocks using Murman-Cole type of finite difference scheme and is capable of predicting accurate and force-free wake shape as well. A rectangular grid combined with a technique of local grid refinement greatly improved the computational efficiency.
New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.
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The high-pressure equation of state (EOS) of energetic materials (EMs) is important for continuum and mesoscale models of detonation performance and initiation safety. Additionally, obtaining a high-fidelity EOS of the insensitive EM 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) has proven to be difficult because of challenges in experimental characterization at high pressures (HPs). In this work, powder X-ray diffraction patterns were fitted using the recently discovered monoclinic I2/a phase above 4 GPa, which shows that TATB is less compressible than when indexed with the triclinic $P\bar{1}$ phase. First-principles calculations were performed with Perdew–Burke–Ernzerhof (PBE) and PBE0 functionals including thermal effects using the $P\bar{1}$ phase. PBE0 improves the description of hydrogen bonding and thus predicts accurate planar a and b lattice parameters under ambient conditions. However, discrepancies in the predicted lattice parameters above 4–10 GPa compared with experimental measurements indexed with $P\bar{1}$ are further evidence of a structural modification at high pressure. Layer sliding defects are formed during molecular dynamics simulations, which induces an anharmonic effect on the thermal expansion of the c lattice parameter. In short, the results provide several insights into determining high-fidelity EOS parameters for TATB and other molecular crystals.
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We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.
Liapunov stability theory applied to class of partial differential equations, and generation of contraction groups related to equivalent norms
Dynamic equations for simulating multiple-bodied spacecraft configuration subjected to gravity gradient and disturbance torques and forces
Equations for active control system of generalized spacecraft simulation computer program
Boundary conditions for Tricomi equation in symmetric positive form, showing analytical and finite difference solutions
Biharmonic equation numerical solution by finite differences, discussing outer and inner iteration schemes
The glushko one equation model of turbulence is extended to compressible flows without boundary layer approximations.
The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.
In this paper, we present a tensorial derivation of the equations of motion of a formation consisting of N spacecraft each modeled as a rigid body.
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Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.