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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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Exact solutions to Brans-Dicke cosmologies in flat Friedmann universes.

The Brans-Dicke cosmological equations for flat Friedmann-type expanding universes are solved parametrically for time, density, expansion parameter, and scalar field. These results reduce to a previously obtained exact solution to the radiation cosmology. Although the scalar field may be undetectable at the present epoch, it is felt that, if it exists, it must play an important role as one approaches the initial singularity of the cosmology.

Morganstern, R. E.↗
NASA NTRS2004

An exact solution for the steady state phase distribution in an array of oscillators coupled on a hexagonal lattice

When electronic oscillators are coupled to nearest neighbors to form an array on a hexagonal lattice, the planar phase distributions desired for excitation of a phased array antenna are not steady state solutions of the governing non-linear equations describing the system. Thus the steady state phase distribution deviates from planar. It is shown to be possible to obtain an exact solution for the steady state phase distribution and thus determine the deviation from the desired planar distribution as a function of beam steering angle.

injection locking↗
NASA NTRS1983

Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.

Barnes, A.↗
NASA NTRS1998

Exact Solution to Stationary Onset of Convection Due to Surface Tension Variation in a Multicomponent Fluid Layer With Interfacial Deformation

Stationary onset of convection due to surface tension variation in an unbounded multicomponent fluid layer is considered. Surface deformation is included and general flux boundary conditions are imposed on the stratifying agencies (temperature/composition) disturbance equations. Exact solutions are obtained to the general N-component problem for both finite and infinitesimal wavenumbers. Long wavelength instability may coexist with a finite wavelength instability for certain sets of parameter values, often referred to as frontier points. For an impermeable/insulated upper boundary and a permeable/conductive lower boundary, frontier boundaries are computed in the space of Bond number, Bo, versus Crispation number, Cr, over the range 5 x 10(exp -7) less than or equal to Bo less than or equal to 1. The loci of frontier points in (Bo, Cr) space for different values of N, diffusivity ratios, and, Marangoni numbers, collapsed to a single curve in (Bo, D(dimensional variable)Cr) space, where D(dimensional variable) is a Marangoni number weighted diffusivity ratio.

Skarda, J. Raymond Lee↗
NASA NTRS2002

A review of some exact solutions to the planar equations of motion of a thrusting spacecraft

With the complexities in computing optimal low thrust trajectories, easily-computed, good sub-optimal trajectories provide both a practical alternative for mission designers and a starting point for optimisation. The present paper collects in one place for easy reference and comparison several exact solutions that have been obtained in the literature over the last few decades: the logarithmic spiral, Pinkham's variant thereof, Forbes spiral, the exponential sinusoid, the case of constant radial thrust, Markopoulos's Keplerian thrust arcs, Lawden's spiral, and the analogous Bishop and Azimov spiral.

low-thrust trajectories electric propulsion solar ↗
DOE OSTI2022

Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

In polar semiconductors and insulators, the Fröhlich interaction between electrons and long-wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearance of characteristic phonon sidebands in the spectral function, commonly dubbed “polaron satellites.” The simplest model that captures these effects is the Fröhlich model, whereby electrons in a parabolic band interact with a dispersionless longitudinal optical phonon. The Fröhlich model has been employed in a number of seminal papers, from early perturbation-theory approaches to modern diagrammatic Monte Carlo calculations. One limitation of this model is that it focuses on undoped systems, thus ignoring carrier screening and Pauli blocking effects that are present in real experiments on doped samples. Here, to overcome this limitation, we extend the Fröhlich model to the case of doped systems, and we provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. We perform the analysis using two approaches, namely, Dyson’s equation with the Fan-Migdal self-energy, and the second-order cumulant expansion. We find that these two approaches provide qualitatively different results. In particular, Dyson’s approach yields better quasiparticle masses and worse satellites, while the cumulant approach provides better satellite structures, at the price of worse quasiparticle masses. Both approaches yield an anomalous enhancement of the electron effective mass at finite doping levels, which in turn leads to a breakdown of the quasiparticle picture in a significant portion of the phase diagram.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS2004

Thermocapillary migration of a drop: an exact solution with Newtonian interfacial rheology and stretching/shrinkage of interfacial area elements for small Marangoni numbers

In this paper we analyze the effects of the following phenomena associated with the thermocapillary migration of a drop. The first is the influence of Newtonian surface rheology of the interface and the second is that of the energy changes associated with stretching and shrinkage of the interfacial area elements, when the drop is in motion. The former occurs because of dissipative processes in the interfacial region, such as when surfactant molecules are adsorbed at the interface in sufficient concentration. The interface is typically modeled in this instance by ascribing to it a surface viscosity. This is a different effect from that of interfacial tension gradients arising from surfactant concentration gradients. The stretching and shrinkage of interfacial area elements leads to changes in the internal energy of these elements that affects the transport of energy in the fluids adjoining the interface. When an element on the interface is stretched, its internal energy increases because of the increase in its area. This energy is supplied by the neighboring fluids that are cooled as a consequence. Conversely, when an element on the interface shrinks, the adjoining fluids are warmed. In the case of a moving drop, elements of interfacial area are stretched in the forward half of the drop, and are shrunk in the rear half. Consequently, the temperature variation on the surface of the drop and its migration speed are modified. The analysis of the motion of a drop including these effects was first performed by LeVan in 1981, in the limit when convective transport of momentum and energy are negligible. We extend the analysis of LeVan to include the convective transport of momentum by demonstrating that an exact solution of the momentum equation is obtained for an arbitrary value of the Reynolds number. This solution is then used to calculate the slightly deformed shape of the drop from a sphere.

Rheology/methods↗
NASA NTRS1988

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

Shebalin, John V.↗
DOE OSTI2023

Exact solutions for the electromagnetic fields of a flying focus

The intensity peak of a “flying” focus travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an accurate description of the electromagnetic fields. Here we present exact analytical solutions to Maxwell’s equations for the electromagnetic fields of a constant-velocity flying focus, generalized for arbitrary polarization and orbital angular momentum. Furthermore, the approach combines the complex source-point method, which transforms multipole solutions into beam-like solutions, with the Lorentz invariance of Maxwell’s equations. Propagating the fields backward in space reveals the space-time profile that an optical assembly must produce to realize these fields in the laboratory. Comparisons with simpler paraxial solutions provide conditions for their reliable use when modeling a flying focus.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Exact solution of the DeWitt-Brehme-Hobbs equation in copropagating electromagetic and gravitational waves

An accelerated charge interacts with its own electromagnetic field, a phenomenon known as electromagnetic radiation reaction. The DeWitt-Brehme-Hobbs (DWBH) equation describes the motion of a charged mass in the presence of combined electromagnetic and gravitational fields, taking into account electromagnetic radiation-reaction effects. Here, we find the first exact analytical solution of the DWBH equation in the case of a charged mass in the presence of copropagating and otherwise arbitrary electromagnetic and gravitational plane waves. As a consequence of the Penrose limit, the scenario considered here can be seen as a local limit around ultrarelativistic trajectories in a general curved spacetime. Finally, the paradigmatic example of an electromagnetic wave in the presence of a constant-amplitude gravitational wave is worked out explicitly and it is shown how the presence of the gravitational wave can qualitatively change electromagnetic radiation-reaction effects.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

Exact solutions for laminated composite cylindrical shells in cylindrical bending

Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.

Yuan, F. G.↗
NASA NTRS1992

Exact solution of a quantum forced time-dependent harmonic oscillator

The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.

Yeon, Kyu Hwang↗
DOE OSTI2025

Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping

The one-dimensional (1D) 𝐽 1 −𝐽 2 𝑞-state Potts model is solved exactly for arbitrary 𝑞 by analytically block-diagonalizing the original 𝑞 2 ×𝑞 2 transfer matrix into a simple 2 × 2 maximally symmetric subspace, based on using OpenAI's reasoning model o3-mini-high to exactly solve the 𝑞 = 3 case. Furthermore, by matching relevant subspaces, we map the Potts model onto a simpler effective 1D 𝑞-state Potts model, where 𝐽 2 acts as the nearest-neighbor interaction and 𝐽 1 as an effective magnetic field, nontrivially generalizing a 56-year-old theorem previously limited to the simplest case (𝑞 = 2, the Ising model). Our exact results provide insights to phenomena such as atomic or electronic order stacking in layered materials and the emergence of dome-shaped phases in complex phase diagrams. In conclusion, this work is anticipated to fuel both research in 1D frustrated magnets for recently discovered finite-temperature application potentials and the fast moving topic area of AI in science.

1-dimensional spin chains↗
DOE OSTI2023

Exact solution of the topological symplectic Kondo problem

The Kondo effect is an archetypical phenomenon in the physics of strongly correlated electron systems. Recent attention has focused on the application of Kondo physics to quantum information science by exploiting overscreened Kondo impurities with residual anyon-like impurity entropy. While this physics was proposed in the fine-tuned multi-channel Kondo setup or in the Majorana-based topological Kondo effect, we here study the Kondo effect with symplectic symmetry Sp(2k) and present details about the implementation which importantly only involves conventional s-wave superconductivity coupled to an array of resonant levels and neither requires perfect channel symmetry nor Majorana fermions. Here we carefully discuss the role of perturbations and show that a global Zeeman drives the system to a 2-channel SU(k) fixed point. Exact results for the residual entropy, specific heat and magnetization are derived using the thermodynamic Bethe Ansatz for Sp(2k). This solution not only proves the existence of a quantum critical ground state with anyon-like Hilbert space dimension, but also a particularly weak non-Fermi liquid behavior at criticality. We interpret the weakness of non-analyticities as a manifestation of suppressed density of states at the impurity causing only a very weak connection of putative anyons and conduction electrons. Given this weak connection, the simplicity of the design and the stability of the effect, we conjecture that the symplectic Kondo effect may be particularly suitable for quantum information applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1979

A numerical comparison with an exact solution for the transient response of a cylinder immersed in a fluid

The transient response of an elastic cylindrical shell immersed in an acoustic media that is engulfed by a plane wave is determined numerically. The method applies to the USA-STAGS code which utilizes the finite element method for the structural analysis and the doubly asymptotic approximation for the fluid-structure interaction. The calculations are compared to an exact analysis for two separate loading cases: a plane step wave and an exponentially decaying plane wave.

Giltrud, M. E.↗
DOE OSTI2021

Exact solution of two simple non-equilibrium electron-phonon and electron-electron coupled systems: The atomic limit of the Holstein-Hubbard model and the generalized Hatsugai-Komoto model

One of the challenges in many-body physics is determining the effects of phonons on strongly correlated electrons. The difficulty arises from strong correlations at differing energy scales—for band metals, Migdal-Eliashberg theory accurately determines electron-phonon coupling effects due to the absence of vertex corrections, but strongly correlated electrons require a more complex description, and the standard Migdal-Eliashberg approach does not necessarily apply. In this work, we solve for the atomic limit Green's function of the Holstein-Hubbard model with both time-dependent electron-electron and electron-phonon couplings. Then, we examine the photoemission spectra of this model in and out of equilibrium. Next, we use similar methods to exactly solve an extended version of the Hatsugai-Komoto model and examine its behavior in and out of equilibrium. These calculations lead us to propose using the first moment of the photoemission spectra to signal non-equilibrium changes in electron-electron and electron-phonon couplings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗