Theoretical method for solution of aerodynamic forces on thin wings in nonuniform supersonic stream with an application to tail surfaces
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THEORIES - WINGS↗
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Twisting of thin walled columns perfectly restrained at one end
Proceeding from the basic assumptions of the Batho-Bredt theory on twisting failure of thin-walled columns, the discrepancies most frequently encountered are analyzed. A generalized approximate method is suggested for the determination of the disturbances in the stress condition of the column, induced by the constrained warping in one of the end sections.
Lazzarino, Lucio↗
Reexamination of hydrodynamic phonon transport in thin graphite
The recent hydrodynamic phonon transport theory for graphitic materials has been supported by the measurements of the second sound at temperatures up to about 100 K. When boundary scattering becomes comparable to momentum-conserving normal phonon scattering processes that are responsible for phonon hydrodynamics, Poiseuille phonon flow phenomena can emerge to give rise to unique size-dependent thermal conductivity in thin graphite. Here, we examine the thickness range for the Poiseuille phonon flow to become observable in thin graphite with the use of both deviational Monte Carlo simulation of the Peierls-Boltzmann transport equation and four-probe thermal transport measurements. As the basal-plane thermal conductivity calculated by prior first-principles theories saturates to the graphite value when the thickness is increased to five graphene layers, the phonon dispersion of graphite is used in the current calculations of thin graphite of micrometer thickness and a 23-layer thick ultrathin graphite (UTG) sample. The calculations show that diffuse surface scattering by surface defects can lead to Poiseuille phonon flow at 50 K in thin graphite with the thickness close to several micrometers but not in the 65 μm thin graphite and 23-layer UTG, where phonon scattering by the top and bottom surfaces become, respectively, much less and more frequent than the normal processes. In addition, the calculation results with the bulk graphite dispersion and diffuse surface scattering show decreased basal-plane thermal conductivity with decreasing thickness, opposite to recent thermocouple measurements of thin graphite samples. In comparison, the calculation results reveal that partially diffuse surface defect scattering can yield the four-probe measurement results of UTG samples, which are prepared here with an improved process to minimize surface contamination.
36 MATERIALS SCIENCE↗
A simple theory for the propagation of film detonations
Detonation propagation velocity through tubes with walls coated with thin fuel film, using turbulent boundary layer theory
Nicholls, J. A.↗
Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms
A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.
Prosser, W. H.↗
A linearized solution for time-dependent velocity potentials near three-dimensional wings at supersonic speeds
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SUPERSONIC↗
Theoretical and experimental investigations of collective microwave phenomena in solids
Methods of generating microwave shear waves efficiently were studied. A new technique of mode conversion from a longitudinal wave to a shear wave was investigated and virtually 100% conversion efficiency could be obtained. Several aspects of Gunn oscillators were studied. One involved the detailed study of domains in Gunn oscillators using long samples of bulk gallium arsenide. Several new techniques were devised for measuring the properties of the domains. A fundamental theory of the efficiency of a Gunn oscillator was worked out. A computer program was devised to study the transient effect of domains passing through Gunn diodes. Some of the first planar epitaxial Gunn oscillators were made using liquid epitaxial material grown by liquid phase techniques on semi-insulating substrate. A new theory which predicted the properties of RF signals propagating in a thin film layer of GaAs was developed. The theory of the operation of a traveling wave amplifier is described.
Kino, G. S.↗
Thickness and camber effects in slender wing theory
It is noted that the flow past thin slender wings with round leading edges can remain attached up to moderate values of angle of attack. In the low aspect ratio limit, the slender wing theory of Jones (1946) can therefore provide a simple analytical tool for studying this flow. First-order corrections to slender wing theory due to spanwise thickness and camber are developed. For wings of general planform, the validity and applicability of slender wing theory have recently been extended with the addition of chordwise and compressibility corrections by Levin and Seginer (1982). It is believed that similar corrections can be applied to the present results.
Plotkin, A.↗
Increasing the mobility and power-electronics figure of merit of AlGaN with atomically thin AlN/GaN digital-alloy superlattices
Alloy scattering in random AlGaN alloys drastically reduces the electron mobility and, therefore, the power-electronics figure of merit. As a result, Al compositions greater than 75% are required to obtain even a twofold increase in the Baliga figure of merit compared to GaN. However, beyond approximately 80% Al composition, donors in AlGaN undergo the DX transition, which makes impurity doping increasingly more difficult. Moreover, the contact resistance increases exponentially with the increase in Al content, and integration with dielectrics becomes difficult due to the upward shift of the conduction band. Atomically thin superlattices of AlN and GaN, also known as digital alloys, are known to grow experimentally under appropriate growth conditions. These chemically ordered nanostructures could offer significantly enhanced figure of merit compared to their random alloy counterparts due to the absence of alloy scattering, as well as better integration with contact metals and dielectrics. In this work, we investigate the electronic structure and phonon-limited electron mobility of atomically thin AlN/GaN digital-alloy superlattices using first-principles calculations based on density-functional and many-body perturbation theory. The bandgap of the atomically thin superlattices reaches 4.8 eV, and the in-plane (out-of-plane) mobility is 369 (452) cm 2 V -1 s -1 . Using the modified Baliga figure of merit that accounts for the dopant ionization energy, here we demonstrate that atomically thin AlN/GaN superlattices with a monolayer sublattice periodicity have the highest modified Baliga figure of merit among several technologically relevant ultra-wide bandgap materials, including random AlGaN, β-Ga 2 O 3 , cBN, and diamond.
36 MATERIALS SCIENCE↗
Analysis of the surface load and radiated sound of a vibrating airfoil with application to the experiment of Brooks
A method is developed for calculating the surface load and radiated sound from a vibrating surface in a compressible viscous fluid. The method is applied to a thin two-dimensional elliptic cross-section. For large values of the viscous diffusion parameter, the surface load tends to an elliptic distribution in agreement with the results of inviscid theory when edge pressure continuity is enforced. For thin surfaces, the surface load is insensitive to variations in the thickness ratio. A three-dimensional spectral technique is developed to calculate the inviscid surface load and radiated sound from a thin vibrating airfoil. The inviscid theory predicts the correct form of the far field sound pressure and its phase. The actual levels are somewhat sensitive to the choice of theoretical spanwise surface pressure mode but are in better agreement with the experiment than the surface pressure. The comparison of theoretical and experimental surface pressure indicates that the viscous theory, used to validate the inviscid theory, is either inadequate or there is a source of experimental error.
Yates, J. E.↗
Photoemission and dynamical mean field theory study of electronic correlations in a t 2 g 5 metal SrRhO 3 thin film
Perovskite rhodates are characterized by intermediate strengths of both electronic correlation as well as spin-orbit coupling (SOC) and usually behave as moderately correlated metals. A recent publication on epitaxial SrRhO 3 thin films reported a bad-metallic behavior and suggested the occurrence of antiferromagnetism below 100 K. In this work, we have further studied this SrRhO 3 thin film by hard x-ray photoemission spectroscopy and found a very small density of states (DOS) at the Fermi level $(E_F)$, which is consistent with the previously reported bad-metallic behavior. However, the absence of DOS persists up to room temperature, which contradicts the explanation of antiferromagnetic transition at ~100 K. We also employed electronic structure calculations within the framework of density functional theory and dynamical mean-field theory. In contrast to the photoemission results, our calculations indicate metallic behaviors of both bulk SrRhO 3 and the SrRhO 3 thin film, and a stronger correlation effect was observed in the thin film than that in the bulk. The calculated uniform magnetic susceptibility is substantially larger in the thin film than that in the bulk. We also investigated the role of SOC and found only a moderate modulation of the band structure. Hence SOC is not expected to significantly affect the electronic correlation in SrRhO 3 . Extrinsic effects of finite-thickness effects beyond our calculations and localization effects may play important roles to induce the negligible spectral weight at $(E_F)$.
36 MATERIALS SCIENCE↗
Multifractally-enhanced superconductivity in thin films
The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifractally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
An investigation of spray velocity resulting from high-velocity penetration of thin plates by disks
Analysis based on one-dimensional shock wave theory to study maximum velocity of spray emanating from rear surface of thin meteoroid bumper
SHOCK WAVE↗
Flutter analysis of composite box beams
The dynamic aeroelastic instability of flutter is an important factor in the design of modern high-speed, flexible aircraft. The current trend is toward the creative use of composites to delay flutter. To obtain an optimum design, we need an accurate as well as efficient model. As a first step towards this goal, flutter analysis is carried out for an unswept composite box beam using a linear structural model and Theodorsen's unsteady aerodynamic theory. Structurally, the wing was modeled as a thin-walled box-beam of rectangular cross section. Theodorsen's theory was used to get 2-D unsteady aerodynamic forces, which were integrated over the span. A free-vibration analysis is carried out. These fundamental modes are used to get the flutter solution using the V-g method. Future work is intended to build on this foundation.
Hodges, Dewey H.↗
A multi-dimensional Child–Langmuir law for any diode geometry
While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A closer look at how symmetry constraints and the spin–orbit coupling shape the electronic structure of Bi(111)
Abstract Fully relativistic density-functional-theory calculations of Bi(111) thin films are analyzed to revisit their two metallic surface-states branches. We first contrast these metallic branches with surface states arising at gaps in the valence band opened by the spin–orbit coupling (SOC). We find that the two metallic branches along Γ M ‾ do not overlap with the bulk band at the zone boundary,M. We show that the spin texture observed in such states cannot be traced to the lifting of Kramers’ degeneracy. Instead, we track them to the m j = ± 1 / 2 – m j = ± 3 / 2 SOC splitting, the potential anisotropy for in-plane and out-of-plane states, and the coupling between the opposite surfaces of a slab occurring nearM, which is driven by a spatial redistribution of the four metallic states composing the two metallic branches. Each of these branches appears to be non-degenerate at the tested surface, yet each is degenerate with another state of opposite spin at the other surface. Nevertheless, the four metallic states bear some contribution on both surfaces of the film because of their spatial redistribution nearM. The overlapping among these states nearM, afforded by their spatial redistribution on both surfaces, causes a hybridization that perpetuates the splitting between the two branches, makes the film’s electronic structure thickness dependent nearM, extinguishes the magnetic moment of the metallic states avoiding the magnetic-moment discontinuity atM, and denies the need or expectancy of the metallic branches becoming degenerate atM. We propose that theoppositespin polarization observed for the two metallic branches occurs because the surface atoms retain their covalent bonds and thus cannot afford magnetic polarization. We show that the Rashba-splitting of the metallic states for inversion-asymmetric films does not have a fixed magnitude but can be tuned by changing the perturbation breaking inversion symmetry.
Physics↗
Diffusion flame in homologous turbulent shear flows.
The simplifed statistical theory developed previously is employed to analyze the equilibrium and near-equilibrium combustion of initially unmixed reactants. It is found that the flame zone in the limit of large Damkohler numbers is very thick and is of the order of the local integral scale of turbulence. This is in contrast to the existing phenomenological theories which predict the infinitesimally thin flame sheet, in the same limit, as it is with the laminar diffusion flame. Qualitative agreements with the available experimental results are shown. It is found that singularities exist at the edges of the flame which are removed as Damkohler number is reduced. Also, it is found that the heat transfer may take place against the local mean temperature gradient in certain regions within the flame.
Chung, P. M.↗
Convergence of finite difference transient response computations for thin shells.
Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.
Sobel, L. H.↗