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Intermediate magnetostatic propagation mode for spin wave in axially magnetized rod containing turning point, including spin wave losses, explaining delay time
The vibrational energy of crystals is known to propagate in a fixed number of phonon branches allowed by symmetry. In the realm of nonlinear dynamics, however, additional nonlinear propagating modes are possible. Nonlinear propagating modes have unique properties that are important in many disciplines including optical communications, conducting polymers, biology, magnetism, and nuclear physics. Yet, despite the crucial importance of crystal lattice vibrations in fundamental and applied science, such additional propagating modes have not been observed in ordinary crystals. Here, we show that propagating modes exist beyond the phonons in fluorite-structured thoria, urania, and natural calcium fluoride using neutron scattering and first-principles calculations. These modes are observed at temperatures ranging from 5 K up to 1200 K, extend to frequencies 30–40% higher than the maximum phonon frequency, and travel at velocities comparable to or higher than the fastest phonon. The nonlinear origin of the modes is explained in part via perturbation theory, which approximately accounts for nonlinearity. Given that these modes are still clearly observed at 5 K, they are likely an inherent feature of the quantum ground state. The existence of these waves in three-dimensional crystals may have ramifications for material properties.
The question of the number of propagating modes within a small range of mode cut off ratio was raised. The population density of modes were shown to be greatest near cut off and least for the well propagating modes. It was shown that modes of nearly the same cut off ratio behave nearly the same in a sound absorbing duct as well as in the way they propagate to the far. Handling all of the propagating modes individually, they can be grouped into several cut off ratio ranges. It is important to know the modal density function to estimate acoustic power distribution.
Higher order mode propagation in a nonuniform circular duct without mean flow was investigated. An approximate wave equation is derived on the assumptions that the duct cross section varies slowly and that mode conversion is negligible. Exact closed form solutions are obtained for a particular class of converging-diverging circular duct which referred to as 'circular cosh duct.' Numerical results are presented in terms of the transmission loss for the various duct shapes and frequencies. The results are applicable to multimodal propagation, single mode propagation, and sound radiation from certain types of contoured inlet ducts, or of sound propagation in a converging-diverging duct of somewhat different shape from a cosh duct.
Often raised questions in duct sound propagation studies involve the total number of propagating modes, the number of propagating radial modes for a particular spinning lobe number, and the number of modes possible between two given values of cutoff ratio or eigenvalue. These questions can be answered approximately by using the modal distribution function which is the integral of the modal density function for ducts in a manner similar to that previously published for architectural acoustics. The modal density functions are derived for rectangular and circular ducts with a uniform steady flow. Results from this continuous theory are compared to the actual (discrete) modal distributions.
This paper presents an analytical investigation of higher order mode propagation in a nonuniform circular duct without mean flow. An approximate wave equation is derived on the assumptions that the duct cross section varies slowly and that mode conversion is negligible. Exact closed form solutions are obtained for a particular class of converging-diverging circular duct which is here referred to as 'circular cosh duct'. Numerical results are presentd in terms of the transmission loss for the various duct shapes and frequencies. The results are applicable to studies of multimodal propagation as well as single mode propagation. The results are also applicable to studies of sound radiation from certain types of contoured inlet ducts, or of sound propagation in a converging-diverging duct of somewhat different shape from a cosh duct.
Results are presented from a series of tests of radio bursts on the nightside of Venus (observed by an orbiting electric field detector on board the Pioneer Venus Orbiter), which were conducted as a search for the evidence of whistler mode propagation from lightning. Preliminary results suggest that there are at least two main categories of bursts: one that exhibits one or more properties consistent with whistler mode propagation from subionospheric lightning sources, and another that is not.
Dispersion equation for whistler mode propagation in warm plasma in parallel static fields, using Vlasov-Maxwell equation
Quantum structure in ferromagnetic metals dielectric function, noting anomalous helicon and magnon propagation modes in uniform magnetic field
We have observed a new temperature-entropy wave that propagates opposite to the direction of a steady heat flux Q when the helium column is heated from above. This propagating mode is due to non-linear thermo-conductance of the helium sample in the self-organized state. Such a mode had been predicted to exist on the self-organized heat transport state for Q less than about 100 nW/sq cm. We confirm that this mode exists in this regime. However, we also observe that it propagates even when the helium is pushed away from the self-organized heat transport state into the normal state.
Whistler mode propagation in presence of longitudinal static electric field in region of ionosphere where particle collisions influence ion motion
The time-dependent governing acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard-wall duct without flow and with spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the steady solutions of the acoustic field. The transient method did not converge to the steady-state solution for cutoff acoustic duct modes. This has implications as to its use in a variable-area duct, where modes may become cutoff in the smal-area portion of the duct. For single cutoff mode propagation the steady-state impedance boundary condition produced acoustic reflections during the initial transient that caused finite instabilities in the numerical calculations. The stability problem is resolved by reformulating the exit boundary condition. Example calculations show good agreement with exact analytical and numerical results for forcing frequencies above, below, and nearly at the cutoff frequency.
A previously reported closed form solution is expanded to determine effects of isentropic mean flow on mode propagation in a slowly converging-diverging duct, a circular cosh duct. On the assumption of uniform steady fluid density, the mean flow increases the power transmission coefficient. The increase is directly related to the increase of the cutoff ratio at the duct throat. With the negligible transverse gradients of the steady fluid variables, the conversion from one mode to another is negligible, and the power transmission coefficient remains unchanged with the mean flow direction reversed. With a proper choice of frequency parameter, many different modes can be made subject to a single value of the power transmission loss. A systematic method to include the effects of the gradients of the steady fluid variables is also described.
A previously reported closed form solution is expanded to determine effects of isentropic mean flow on mode propagation in a slowly converging-diverging duct - a circular cosh duct. On the assumption of uniform steady fluid density, the mean flow increases the power transmission coefficient. The increase is directly related to the increase of the cutoff ratio at the duct throat. With the negligible transverse gradients of the steady fluid variables, the conversion from one mode to another is negligible, and the power transmission coefficient remains unchanged with the mean flow direction reversed. With a proper choice of frequency parameter, many different modes can be made subject to a single value of the power transmission loss. The paper also describes a systematic method to include the effects of the gradients of the steady fluid variables.
The cutoff mode instability problem associated with a transient finite difference solution to the wave equation is explained. The steady-state impedance boundary condition is found to produce acoustic reflections during the initial transient, which cause finite instabilities in the cutoff modes. The stability problem is resolved by extending the duct length to prevent transient reflections. Numerical calculations are presented at forcing frequencies above, below, and nearly at the cutoff frequency, and exit impedance models are presented for use in the practical design of turbofan inlets.
The NASA Glenn Research Center's Advanced Noise Control Fan (ANCF) was developed in the early 1990s to provide a convenient test bed to measure and understand fan-generated acoustics, duct propagation, and radiation to the farfield. A series of tests were performed primarily for the use of code validation and tool validation. Rotating Rake mode measurements were acquired for parametric sets of: (i) mode blockage, (ii) liner insertion loss, (iii) short ducts, and (iv) mode reflection.
The NASA Glenn Research Center's Advanced Noise Control Fan (ANCF) was developed in the early 1990s to provide a convenient test bed to measure and understand fan-generated acoustics, duct propagation, and radiation to the farfield. A series of tests were performed primarily for the use of code validation and tool validation. Rotating Rake mode measurements were acquired for parametric sets of: (1) mode blockage, (2) liner insertion loss, (3) short ducts, and (4) mode reflection.
Previously cited in issue 07, p. 969, Accession no. A82-20290