Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inversion theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Integral functions of electron lateral distribution and their fluctuations in electron-photon cascades

Monte Carlo simulated lateral distribution functions for electrons of EPC developing in lead, at superhigh energies (.1-1 PeV) for depths t or = 60 c.u. delta t=1t. c.u. are presented. The higher moment characteristics, i.e., variation, asymmetry, excess, are presented along with analytical solutions for the same characteristics at fixed observation level calculated to theory approximations A and B by using numerical inversion of the Laplace transformation. The conclusion is made of a complex, usually non-Gaussian shape of the function of the particle number distribution within a circle of given radius at fixed depth.

Ivanenko, I. P.↗

The analysis and simulation of compressible turbulence

Compressible turbulent flows at low turbulent Mach numbers are considered. Contrary to the general belief that such flows are almost incompressible, (i.e., the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a non-dimensional time scale which is the inverse of the fluctuating Mach number. An asymptotic theory which enables one to obtain a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence.

Erlebacher, Gordon↗

Nonlinear development and secondary instability of Gortler vortices in hypersonic flows

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Goertler vortices is the temperature adjustment layer over which the basic state temperature decreases monotonically to its free stream value. Except for a special wall curvature distribution, the evolution of Goertler vortices trapped in the temperature adjustment layer will in general be strongly affected by the boundary layer growth through the O(M sup 3/2) curvature of the basic state, where M is the free stream Mach number. Only when the local wavenumber becomes as large as of order M sup 3/8, do nonparallel effects become negligible in the determination of stability properties. In the latter case, Goertler vortices will be trapped in a thin layer of O(epsilon sup 1/2) thickness which is embedded in the temperature adjustment layer; here epsilon is the inverse of the local wavenumber. A weakly nonlinear theory is presented in which the initial nonlinear development of Goertler vortices in the neighborhood of the neutral position is studied and two coupled evolution equations are derived. From these, it can be determined whether the vortices are decaying or growing depending on the sign of a constant which is related to wall curvature and the basic state temperature.

Fu, Yibin B.↗

The analysis and simulation of compressible turbulence

Compressible turbulent flows at low turbulent Mach numbers are considered. Contrary to the general belief that such flows are almost incompressible (i.e., the divergence of the velocity field remains small for all times), it is shown that even if the divergence of the initial velocity field is negligibly small, it can grow rapidly on a nondimensional time scale which is the inverse of the fluctuating Mach number. An asymptotic theory which enables one to obtain a description of the flow in terms of its divergence-free and vorticity-free components has been developed to solve the initial-value problem. As a result, the various types of low Mach number turbulent regimes have been classified with respect to the initial conditions. Formulae are derived that accurately predict the level of compressibility after the initial transients have disappeared. These results are verified by extensive direct numerical simulations of isotropic turbulence.

Erlebacher, Gordon↗

Initial value and two point boundary value solutions to the Clohessy-Wiltshire equations

The nonhomogeneous Clohessy-Wiltshire (C-W) equations are formulated and solved as an initial value problem in the form structure of linear systems theory. The state transition matrix (STM) and its inverse are obtained explicitly in both Newtonian and Hamiltonian form. It is shown that the STM for the C-2 equations possesses a special property making its inverse easily obtainable. Since solutions to the C-W equations are needed in two-point boundary value form to construct a good mission design tool for orbit transfer, the Lambert problem is solved in the context of the C-W equations.

Mullins, Larry D.↗

SAR terrain classifier and mapper of biophysical attributes

In preparation for the launch of SIR-C/X-SAR and design studies for future orbital SAR, a program has made considerable progress in the development of an SAR terrain classifier and algorithms for quantification of biophysical attributes. The goal of this program is to produce a generalized software package for terrain classification and estimation of biophysical attributes and to make this package available to the larger scientific community. The basic elements of the SAR (Synthetic Aperture Radar) terrain classifier are outlined. An SAR image is calibrated with respect to known system and processor gains and external targets (if available). A Level 1 classifier operates on the data to differentiate: urban features, surfaces and tall and short vegetation. Level 2 classifiers further subdivide these classes on the basis of structure. Finally, biophysical and geophysical inversions are applied to each class to estimate attributes of interest. The process used to develop the classifiers and inversions is shown. Radar scattering models developed from theory and from empirical data obtained by truck-mounted polarimeters and the JPL AirSAR are validated. The validated models are used in sensitivity studies to understand the roles of various scattering sources (i.e., surface trunk, branches, etc.) in determining net backscatter. Model simulations of sigma (sup o) as functions of the wave parameters (lambda, polarization and angle of incidence) and the geophysical and biophysical attributes are used to develop robust classifiers. The classifiers are validated using available AirSAR data sets. Specific estimators are developed for each class on the basis of the scattering models and empirical data sets. The candidate algorithms are tested with the AirSAR data sets. The attributes of interest include: total above ground biomass, woody biomass, soil moisture and soil roughness.

Ulaby, Fawwaz T.↗

On the perihelion precession as a Machian effect

A Lagrangian is constructed which gives Newtonian gravity in the lowest-order approximation in an isotropic universe and also predicts the correct advance of the perihelion with the proper choice of a constant governing the ratio of inertial to gravitational mass. The situation considered is that of a test particle orbiting a central body with external mass at rest and distributed isotropically at large distances from the central body. In the theory developed, the perihelion advance is due to a small contribution to the test-particle inertial mass by the central attracting body rather than to a failure of the inverse-square law of attraction. Some interesting Machian features of this theory are that: (1) the local value of the gravitational constant is determined by the mass distribution of the external matter; (2) the orbits are fixed, and the perihelion advances unambiguously with respect to the external-mass distribution; (3) there are no vestiges of absolute space; (4) the perihelion precession arises from the inertial interaction of the test particle with the central mass; (5) the local rest mass is really determined by the mass distribution of the rest of the universe; and (6) a limited form of the equivalence principle is inherent in one of the equations.

Eby, P. B.↗

Recent progress in the theory of bulk photovoltaic effect

The bulk photovoltaic effect (BPVE) occurs in solids with broken inversion symmetry and refers to DC generation due to uniform illumination, without the need of heterostructures or interfaces, a feature that is distinct from the traditional photovoltaic effect. Its existence has been demonstrated almost 50 years ago, but predictive theories only appeared in the last ten years, allowing for the identification of different mechanisms and the determination of their relative importance in real materials. It is now generally accepted that there is an intrinsic mechanism that is insensitive to scattering, called shift current, where first-principles calculations can now give highly accurate predictions. Another important but more extrinsic mechanism, called ballistic current, is also attracting a great deal of attention, but due to the complicated scattering processes, its numerical calculation for real materials is only made possible quite recently. In addition, an intrinsic ballistic current, usually referred to as injection current, will appear under circularly polarized light and has wide application in experiments. In this review, experiments that are pertinent to the theory development are reviewed, and a significant portion is devoted to discussing the recent progress in the theories of BPVE and their numerical implementations. As a demonstration of the capability of the newly developed theories, a brief review of the materials' design strategies enabled by the theory development is given. Finally, remaining questions in the BPVE field and possible future directions are discussed to inspire further investigations.

Dai, Zhenbang (ORCID:0000000333046008)↗

Backus-Gilbert theory and its application to retrieval of ozone and temperature profiles

The inversion method provides a quantitative evaluation of the trade-off between vertical resolution of a retrieved profile and formal root-mean-square (rms) error due to measurement noise propagation. The problem of retrieving the top-side ozone profile from backscattered ultraviolet (BUV) measurements is considered. For measurements of the type currently being obtained with the Nimbus 4 and AE-E BUV experiments, it is found that a vertical resolution of approximately 0.75 scale height can be achieved for a formal volume mixing ratio profile error of 10%. Other examples include treatments of the retrieval of temperature profiles from measurements in the 15 micron CO2 absorption band for both the terrestrial and Martian atmospheres. Finally, the method is applied to the problem of retrieving temperature profiles of the Jovian planets from measurements in the far infrared pressure induced H2 lines to be obtained from the Mariner Jupiter/Saturn fly-by missions.

Conrath, B. J.↗

The inverse problem for radiation scattering

A brief survey of recent theoretical progress on the inverse scattering problem for radiation scattering from reflective boundaries and variable indices of refraction. The theory of radiation scattering is concerned primarily with the far-field relations between incident and scattered radiation in the presence of a scattering object. The primary, or direct, problem of this theory is to develop quantitative information about these scattering relations from a knowledge of the scattering object. The secondary, or inverse, problem, on the other hand, is to determine the nature of the object from an analysis of the scattering relations.

Prosser, R. T.↗

A unified viscous theory of lift and drag of 2-D thin airfoils and 3-D thin wings

A unified viscous theory of 2-D thin airfoils and 3-D thin wings is developed with numerical examples. The viscous theory of the load distribution is unique and tends to the classical inviscid result with Kutta condition in the high Reynolds number limit. A new theory of 2-D section induced drag is introduced with specific applications to three cases of interest: (1) constant angle of attack; (2) parabolic camber; and (3) a flapped airfoil. The first case is also extended to a profiled leading edge foil. The well-known drag due to absence of leading edge suction is derived from the viscous theory. It is independent of Reynolds number for zero thickness and varies inversely with the square root of the Reynolds number based on the leading edge radius for profiled sections. The role of turbulence in the section induced drag problem is discussed. A theory of minimum section induced drag is derived and applied. For low Reynolds number the minimum drag load tends to the constant angle of attack solution and for high Reynolds number to an approximation of the parabolic camber solution. The parabolic camber section induced drag is about 4 percent greater than the ideal minimum at high Reynolds number. Two new concepts, the viscous induced drag angle and the viscous induced separation potential are introduced. The separation potential is calculated for three 2-D cases and for a 3-D rectangular wing. The potential is calculated with input from a standard doublet lattice wing code without recourse to any boundary layer calculations. Separation is indicated in regions where it is observed experimentally. The classical induced drag is recovered in the 3-D high Reynolds number limit with an additional contribution that is Reynold number dependent. The 3-D viscous theory of minimum induced drag yields an equation for the optimal spanwise and chordwise load distribution. The design of optimal wing tip planforms and camber distributions is possible with the viscous 3-D wing theory.

Yates, John E.↗

Discovery of a Wurtzite-like Cu 2 FeSnSe 4 Semiconductor Nanocrystal Polymorph and Implications for Related CuFeSe 2 Materials

I 2 -II-IV-VI 4 and I-III-VI 2 semiconductor nanocrystals have found applications in photovoltaics and other optoelectronic technologies because of their low toxicity and efficient light absorption into the near-infrared. Herein, we report the discovery of a metastable wurtzite-like polymorph of Cu 2 FeSnSe 4 , a member of the I 2 -II-IV-VI 4 family of semi-conductors containing only Earth-abundant metals. Density functional theory calculations on this metastable poly-morph of Cu 2 FeSnSe 4 indicate that it may be a superior semiconductor for solar energy and optoelectronics applications compared to the thermodynamically preferred stannite polymorph, since the former displays a sharper dispersion of energy levels near the conduction band minimum that can enhance electron mobility and suppress hot electron cooling. The experimental optical band gap was measured by the inverse logarithmic derivative method to be direct, in agreement with theory, and in the range of 1.48-1.59 eV. Mechanistic studies reveal that this metastable phase de-rives from intermediate Cu 3 Se 2 nanocrystals that serve as a structural template for the final hexagonal wurtzite-like product. We compare the chemistry of wurtzite-like Cu 2 FeSnSe 4 to the related CuFeSe 2 material system. Our experimental and computational comparisons between Cu 2 FeSnSe 4 and CuFeSe 2 help explain both the crystal chemistry of CuFeSe 2 that prevents it from forming wurtzite-like polymorphs and the essential role of Sn in stabilizing the metastable structure of Cu 2 FeSnSe 4 . Furthermore, this work provides insight into the importance of elemental composition when designing syntheses for metastable materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Coefficient-to-Basis Network: a fine-tunable operator learning framework for inverse problems with adaptive discretizations and theoretical guarantees

We propose a Coefficient-to-Basis Network (C2BNet), a novel framework for solving inverse problems within the operator learning paradigm. C2BNet efficiently adapts to different discretizations through fine-tuning, using a pre-trained model to significantly reduce computational cost while maintaining high accuracy. Unlike traditional approaches that require retraining from scratch for new discretizations, our method enables seamless adaptation without sacrificing predictive performance. Furthermore, we establish theoretical approximation and generalization error bounds for C2BNet by exploiting low-dimensional structures in the underlying datasets. Our analysis demonstrates that C2BNet adapts to low-dimensional structures without relying on explicit encoding mechanisms, highlighting its robustness and efficiency. To validate our theoretical findings, we conducted extensive numerical experiments that showcase the superior performance of C2BNet on several inverse problems. The results confirm that C2BNet effectively balances computational efficiency and accuracy, making it a promising tool to solve inverse problems in scientific computing and engineering applications.

97 MATHEMATICS AND COMPUTING↗

Topological magnons on the ferromagnetic zigzag lattice

Motivated by the experimental identification of magnetic compounds consisting of zigzag chains, we analyze the band structure topology of magnons in ferromagnets on a zigzag lattice. We account for the general lattice geometry by including spatially anisotropic Heisenberg exchange interactions and by Dzyaloshinskii-Moriya interaction on inversion asymmetric bonds. Within the linear spin-wave theory, we find two magnon branches, whose band structure topology (i.e., Chern numbers) we map out in a comprehensive phase diagram. Notably, besides topologically trivial and gapless phases, we identify topologically nontrivial phases that support chiral edge magnons. We show that these edge states are robust against elastic defect scattering.

Subramanian, Skandan [ORNL] (ORCID:000900087255487↗

Acoustic performance of inlet suppressors on an engine generating a single mode

Three single degree of freedom liners with different open area ratio face sheets were designed for a single spinning mode in order to evaluate an inlet suppressor design method based on mode cutoff ratio. This mode was generated by placing 41 rods in front of the 28 blade fan of a JT15D turbofan engine. At the liner design this near cutoff mode has a theoretical maximum attenuation of nearly 200 dB per L/D. The data show even higher attenuations at the design condition than predicted by the theory for dissipation of a single mode within the liner. This additional attenuation is large for high open area ratios and should be accounted for in the theory. The data show the additional attenuation to be inversely proportional to acoustic resistance. It was thought that the additional attenuation could be caused by reflection and modal scattering at the hard to soft wall interface. A reflection model was developed, and then modified to fit the data. This model was checked against independent (multiple pure tone) data with good agreement.

Heidelberg, L. J.↗

Acoustic performance of inlet suppressors on an engine generating a single mode

As part of a program to evaluate an inlet suppressor design method based on mode cutoff ratio, three single degree of freedom liners with different open area ratio face sheets were designed for a single spinning mode. This mode was generated by placing 41 rods in front of the 28 blade fan of a JT15D turbofan engine. At the liner design this near cutoff mode has a theoretical maximum attenuation of nearly 200 dB per L/D. The data show even higher attenuations at the design condition than predicted by the theory for dissipation of a single mode within the liner. This additional attenuation is large for high open area ratios and should be accounted for in the theory. The data shows the additional attenuation to be inversely proportional to acoustic resistance. It was thought that the additional attenuation could be caused by reflection and modal scattering at the hard to soft wall interface. A reflection model was developed, and then modified to fit the data. This model was checked against independent (multiple pure tone) data with good agreement.

Heidelberg, L. J.↗

Molecular-Weight-Dependent Infiltration and Adsorption of Polymers into Nanochannels

The mesoporous silica shell coating hydrogenolysis nano-catalysts alters the molecular weight distributions of cleaved polymer chains compared to catalysts without a shell. The shell, composed of radially aligned narrow cylindrical nanopores, reduces the formation of low-valued gaseous products and increases the median molecular weight of the product, thus enhancing the value of the products for polymer upcycling. Here, to understand the role of the mesoporous shell, we have studied the spatial distribution of polystyrene chains, used as a model polymer, in the nanochannels in both the melt phase and solution phase. In the melt, we observed from small-angle X-ray scattering experiments that the infiltration rate of the polymer into the nanochannels is inversely proportional to the molecular weight, which is consistent with theory. In theta solution experiments using UV–vis spectroscopy, we found that the shell significantly enhances polymer adsorption compared to nanoparticles without pores. In addition, the degree of polymer adsorption is not a monotonic function of molecular weight but initially increases with the molecular weight before eventually decreasing. The molecular weight for the peak adsorption increases with the pore diameter. This adsorption behavior is rationalized as resulting from a balance between the mixing entropy gain by surface adsorption and the conformational entropy penalty incurred by chains confined in the nanochannels. The spatial distribution of polymer chains in the nanochannels is visualized by energy-dispersive X-ray spectroscopy (EDX), and inverse Abel-transformed data reveals a less uniform polymer distribution along the primary pore axis for longer chains.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗