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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Recursive analytical solution describing artificial satellite motion perturbed by an arbitrary number of zonal terms

An analytical first order solution has been developed which describes the motion of an artificial satellite perturbed by an arbitrary number of zonal harmonics of the geopotential. A set of recursive relations for the solution, which was deduced from recursive relations of the geopotential, was derived. The method of solution is based on Von-Zeipel's technique applied to a canonical set of two-body elements in the extended phase space which incorporates the true anomaly as a canonical element. The elements are of Poincare type, that is, they are regular for vanishing eccentricities and inclinations. Numerical results show that this solution is accurate to within a few meters after 500 revolutions.

Mueller, A. C.↗
NASA NTRS1978

A singularity free analytical solution of artificial satellite motion with drag

An analytical satellite theory based on the regular, canonical Poincare-Similar (PS phi) elements is described along with an accurate density model which can be implemented into the drag theory. A computationally efficient manner in which to expand the equations of motion into a fourier series is discussed.

Mueller, A.↗
DOE OSTI2011

A Mathematical Method for Exact Analytical Solution of the Schroedinger Equation with Non-central Potential

In this paper, we have studied the Schroedinger equation with central and non-central potential. We have solved the Schroedinger equation in spherical coordinate analytically by using supersymmetric and shape invariance methods. Then we have found the radial and angular parts of wavefunction. Finally the energy eigenvalues of the Schroedinger equation with non-central potential are obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Analytical solutions of a fractional diffusion-advection equation for solar cosmic-ray transport

Motivated by recent applications of superdiffusive transport models to shock-accelerated particle distributions in the heliosphere, we analytically solve a one-dimensional fractional diffusion-advection equation for the particle density. We derive an exact Fourier transform solution, simplify it in a weak diffusion approximation, and compare the new solution with previously available analytical results and with a semi-numerical solution based on a Fourier series expansion. We apply the results to the problem of describing the transport of energetic particles, accelerated at a traveling heliospheric shock. Our analysis shows that significant errors may result from assuming an infinite initial distance between the shock and the observer. We argue that the shock travel time should be a parameter of a realistic superdiffusive transport model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes the rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.

36 MATERIALS SCIENCE↗
DOE OSTI2015

An analytical solution of the time-independent Schrödinger equation for the Woods-Saxon potential for arbitrary angular momentum l states

The Woods-Saxon potential is probably the most studied and widely used short range potential in all of nuclear physics. For the angular momentum l= 0 case, Flügge had devised a method to obtain an analytical expression for the bound state energies of the radial time-independent Schrödinger equation for a neutron confined in a Woods-Saxon potential well. In this study, we extend Flügge's method to solve the radial Schrödinger equation for a neutron within the Woods-Saxon potential and the centrifugal potential for arbitrary values of l. Here, the Pekeris method is used to deal with the centrifugal term. We obtain an analytical expression for the bound states, valid for arbitrary angular momentum, and show that our expression reduces to that of Flügge, which applies to the l= 0 case. The numerical computations performed also show very good agreement with our analytical expression.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Analytic Solutions in Nonlinear Massive Gravity

We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering general relativity below a Vainshtein radius given by (r{sub g}m{sup 2}){sup 1/3}, where m is the graviton mass and r{sub g} is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to de Sitter-Schwarzschild spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films

Cross-plane heat transport in thin films with thicknesses comparable to the phonon mean free paths is of both fundamental and practical interest for applications such as light-emitting diodes and quantum well lasers. However, physical insight is difficult to obtain for the cross-plane geometry due to the challenge of solving the Boltzmann equation in a finite domain. Here, we present a semi-analytical series expansion method to solve the transient, frequency-dependent Boltzmann transport equation that is valid from the diffusive to ballistic transport regimes and rigorously includes the frequency-dependence of phonon properties. Further, our method is more than three orders of magnitude faster than prior numerical methods and provides a simple analytical expression for the thermal conductivity as a function of film thickness. Our result enables a straightforward physical understanding of cross-plane heat conduction in thin films.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

The analytic solution for the power series expansion of Heun function

The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric {sub 2}F{sub 1}, {sub 1}F{sub 1} and {sub 0}F{sub 1} functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins. In this paper I will apply three term recurrence formula (Y.S. Choun, (arXiv:1303.0806), 2013) to the power series expansion in closed forms of Heun function (infinite series and polynomial) including all higher terms of A{sub n}’s. Section 3 contains my analysis on applying the power series expansions of Heun function to a recent paper (R.S. Maier, Math. Comp. 33 (2007) 811–843). Due to space restriction final equations for the 192 Heun functions are not included in the paper, but feel free to contact me for the final solutions. Section 4 contains two additional examples using the power series expansions of Heun function. This paper is 3rd out of 10 in series “Special functions and three term recurrence formula (3TRF)”. See Section 5 for all the papers in the series. The previous paper in series deals with three term recurrence formula (3TRF). The next paper in the series describes the integral forms of Heun function and its asymptotic behaviors analytically. -- Highlights: •Power series expansion for infinite series of Heun function using 3 term rec. form. •Power series for polynomial which makes B{sub n} term terminated of Heun function. •Applicable to areas such as the Teukolsky equation in Kerr–Newman–de Sitter geometries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Failed Radiatively Accelerated Dusty Outflow Model of the Broad Line Region in Active Galactic Nuclei. I. Analytical Solution

The physical origin of the broad line region in active galactic nuclei is still unclear despite many years of observational studies. The reason is that the region is unresolved, and the reverberation mapping results imply a complex velocity field. We adopt a theory-motivated approach to identify the principal mechanism responsible for this complex phenomenon. We consider the possibility that the role of dust is essential. We assume that the local radiation pressure acting on the dust in the accretion disk atmosphere launches the outflow of material, but higher above the disk the irradiation from the central parts causes dust evaporation and a subsequent fallback. This failed radiatively accelerated dusty outflow is expected to represent the material forming low ionization lines. In this paper we formulate simple analytical equations to describe the cloud motion, including the evaporation phase. The model is fully described just by the basic parameters of black hole mass, accretion rate, black hole spin, and viewing angle. We study how the spectral line generic profiles correspond to this dynamic. We show that the virial factor calculated from our model strongly depends on the black hole mass in the case of enhanced dust opacity, and thus it then correlates with the line width. This could explain why the virial factor measured in galaxies with pseudobulges differs from that obtained from objects with classical bulges, although the trend predicted by the current version of the model is opposite to the observed trend.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

ATMOSPHERIC CHEMISTRY FOR ASTROPHYSICISTS: A SELF-CONSISTENT FORMALISM AND ANALYTICAL SOLUTIONS FOR ARBITRARY C/O

We present a self-consistent formalism for computing and understanding the atmospheric chemistry of exoplanets from the viewpoint of an astrophysicist. Starting from the first law of thermodynamics, we demonstrate that the van’t Hoff equation (which describes the equilibrium constant), Arrhenius equation (which describes the rate coefficients), and procedures associated with the Gibbs free energy (minimization, rescaling) have a common physical and mathematical origin. We address an ambiguity associated with the equilibrium constant, which is used to relate the forward and reverse rate coefficients, and restate its two definitions. By necessity, one of the equilibrium constants must be dimensionless and equate to an exponential function involving the Gibbs free energy, while the other is a ratio of rate coefficients and must therefore possess physical units. We demonstrate that the Arrhenius equation takes on a functional form that is more general than previously stated without recourse to tagging on ad hoc functional forms. Finally, we derive analytical models of chemical systems, in equilibrium, with carbon, hydrogen, and oxygen. We include acetylene and are able to reproduce several key trends, versus temperature and carbon-to-oxygen ratio, published in the literature. The rich variety of behavior that mixing ratios exhibit as a function of the carbon-to-oxygen ratio is merely the outcome of stoichiometric book-keeping and not the direct consequence of temperature or pressure variations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Analytic solutions in the dyon black hole with a cosmic string: Scalar fields, Hawking radiation and energy flux

Charged massive scalar fields are considered in the gravitational and electromagnetic field produced by a dyonic black hole with a cosmic string along its axis of symmetry. Exact solutions of both angular and radial parts of the covariant Klein–Gordon equation in this background are obtained, and are given in terms of the confluent Heun functions. The role of the presence of the cosmic string in these solutions is showed up. From the radial solution, we obtain the exact wave solutions near the exterior horizon of the black hole, and discuss the Hawking radiation spectrum and the energy flux. -- Highlights: •A cosmic string is introduced along the axis of symmetry of the dyonic black hole. •The covariant Klein–Gordon equation for a charged massive scalar field in this background is analyzed. •Both angular and radial parts are transformed to a confluent Heun equation. •The resulting Hawking radiation spectrum and the energy flux are obtained.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

The combined approach to obtain approximate analytical solution of instability phenomenon arising in secondary oil recovery process

Instability phenomenon mainly occurs in secondary oil recovery process due to viscosity difference of water and oil. Mathematical modeling of this phenomenon yields the non-linear partial differential equation. The homotopy perturbation new integral transform method has been proposed to solve this non-linear partial differential equation subject to appropriate initial and boundary conditions. It is concluded that the saturation of injected water S{sub w}(X,T) is increasing during instability phenomenon, when length of fingers(perturbance) and time increases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

ANALYTIC SOLUTION FOR SELF-REGULATED COLLECTIVE ESCAPE OF COSMIC RAYS FROM THEIR ACCELERATION SITES

Supernova remnants (SNRs), as the major contributors to the galactic cosmic rays (CRs), are believed to maintain an average CR spectrum by diffusive shock acceleration regardless of the way they release CRs into the interstellar medium (ISM). However, the interaction of the CRs with nearby gas clouds crucially depends on the release mechanism. We call into question two aspects of a popular paradigm of the CR injection into the ISM, according to which they passively and isotropically diffuse in the prescribed magnetic fluctuations as test particles. First, we treat the escaping CR and the Alfven waves excited by them on an equal footing. Second, we adopt field-aligned CR escape outside the source, where the waves become weak. An exact analytic self-similar solution for a CR ''cloud'' released by a dimmed accelerator strongly deviates from the test-particle result. The normalized CR partial pressure may be approximated as P(p,z,t)=2[|z|{sup 5/3}+z{sub dif}{sup 5/3}(p,t)]{sup -3/5} exp[-z{sup 2}/4D{sub ISM}(p)t], where p is the momentum of CR particle, and z is directed along the field. The core of the cloud expands as z{sub dif}{proportional_to}{radical}(D{sub NL}(p)t) and decays in time as p{proportional_to}2z{sup -1}{sub dif}(t). The diffusion coefficient D{sub NL} is strongly suppressed compared to its background ISM value D{sub ISM}: D{sub NL} {approx} D{sub ISM}exp (- {Pi}) << D{sub ISM} for sufficiently high field-line-integrated CR partial pressure, {Pi}. When {Pi} >> 1, the CRs drive Alfven waves efficiently enough to build a transport barrier (p Almost-Equal-To 2/ Divides z Divides -{sup p}edestal{sup )} that strongly reduces the leakage. The solution has a spectral break at p = p{sub br}, where p{sub br} satisfies the equation D{sub NL}(p{sub br}) {approx_equal} z {sup 2}/t.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Analytical solutions to the free vibration of a double-walled carbon nanotube carrying a bacterium at its tip

We calculate the natural frequencies and mode shapes of a cantilevered double-walled carbon nanotube carrying a rigid body—representative of a bacterium or virus—at the tip of the outer nanotube. By idealizing the nanotubes as Bernoulli-Euler beams, we are able to obtain exact expressions for both the mode shapes and characteristic frequency equation. Separate analyses are performed for the special case of a concentrated tip mass and the more complicated situation where the tip body also exhibits inertia and mass center offset from the beam tip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Sum-Frequency Generation from a Thin Spherical Layer: I. Analytical Solution

In the tensor form, using the generalized Rayleigh–Gans–Debye approximation, the problem of the sum-frequency generation from a thin nonlinear layer deposited on a dielectric spherical particle placed in a dielectric medium is solved. The second-order nonlinear dielectric susceptibility tensor is chosen in a general form containing chiral components. In the vector and tensor forms, expressions are obtained that describe the spatial distribution of the sum-frequency radiation field generated by two plane electromagnetic elliptically polarized waves. Limiting expressions that describe the spatial distribution of the sum-frequency harmonic at small and large radii of the spherical layer are obtained. It is revealed that, at small radii of the spherical layer, the radiation due to the chiral anisotropy coefficients makes a dominant contribution to the generation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗