Uniform waveguides with arbitrary cross-section considered by the point-matching method.
Point-matching method, approximate technique for wave equations of uniform waveguides with very general cross sections
WAVEGUIDE↗
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Results for “wave equation”
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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Mode conversion and absorption of fast waves at high ion cyclotron harmonics in inhomogeneous magnetic fields
The propagation and absorption of high harmonic fast waves is of interest for non-inductive current drives in fusion experiments. The fast wave can be coupled with the ion Bernstein wave that propagates in the high magnetic field side of an ion cyclotron harmonic resonance layer. This coupling and the absorption are analyzed using the hot plasma dispersion relation and a wave equation that was converted from an approximate dispersion relation for the case where λ{sub i}=k{sub ⊥}{sup 2}ρ{sub i}{sup 2}/2≳1 (where k{sub ⊥} is the perpendicular wave number and ρ{sub i} is the ion Larmor radius). It is found that both reflection and conversion may occur near the harmonic resonance layer but that they decrease rapidly, giving rise to a sharp increase in the absorption as the parallel wave number increases.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Generalization of the nonstandard approach in the dynamic theory of diffraction for deformed crystals
The nonstandard theory of X-ray scattering in a deformed crystal has been generalized. The vector of atomic-plane displacement is introduced into the crystal polarizability model like in the generalized Takagi dynamic theory. The solution to the wave equation is sought for using the procedure of expanding the field amplitude and vector operators in the Fourier components of polarizability χ{sub H} in a series according to the multiscale method. It is shown that considering lattice strain generally calls for introducing various characteristic spatial regions for the diffraction equation, which is in complete agreement with the main concept of the multiscale method. A particular case of a strain field depending on one scale is considered. If a relative change in strain occurs at a length on the order of the extinction length, one can obtain equations generalizing the Takagi equations to the case of arbitrary diffraction geometries.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Wave kernels for the Dirac, Euler operators and the harmonic oscillator
Explicit solutions for the wave equations associated to the Dirac, Euler operators and the harmonic oscillator are given.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Analytical solutions of a generalized non-central potential in N-dimensions
We present that N-dimensional non-relativistic wave equation for the generalized non-central potential with arbitrary angular momentum is analytically solvable in the hyperspherical coordinates. Asymptotic iteration method as a different approach is applied to obtain N-dimensional energy eigenvalues and the corresponding eigenfunctions. In hyperspherical coordinates, the wave function solutions are obtained in terms of hypergeometric functions and Jacobi polynomials. The bound states of quantum systems under consideration for some special cases, such as Hartmann and Makarov potentials, have been discussed in N-dimensions.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Massive gravitational waves in Chern-Simons modified gravity
We consider the nondynamical Chern-Simons (nCS) modified gravity, which is regarded as a parity-odd theory of massive gravity in four dimensions. We first find polarization modes of gravitational waves for θ=x/μ in nCS modified gravity by using the Newman-Penrose formalism where the null complex tetrad is necessary to specify gravitational waves. We show that in the Newman–Penrose formalism, the number of polarization modes is one in addition to an unspecified Ψ{sub 4}, implying three degrees of freedom for θ=x/μ. This compares with two for a canonical embedding of θ=t/μ. Also, if one introduces the Ricci tensor formalism to describe a massive graviton arising from the nCS modified gravity, one finds one massive mode after making second-order wave equations, which is compared to five found from the parity-even Einstein–Weyl gravity.
79 ASTRONOMY AND ASTROPHYSICS↗
Radiation from current sources in an isotropic plasma.
Wave equations for disturbances in partly ionized gas due to current sources determined, using three-fluid model
THREE-FLUID MODEL↗
MO-F-CAMPUS-J-01: Acoustic Range Verification of Proton Beams: Simulation of Heterogeneity and Clinical Proton Pulses
Purpose: Through simulation, to assess acoustic-based range verification of proton beams (protoacoustics) under clinical conditions. Methods: Pressure waves generated by the energy deposition of a 150 MeV, 8 mm FWHM pulsed pencil proton beam were numerically simulated through two Methods: 1) For a homogeneous water medium, an analytical wave-equation solution was used to calculate the time-dependent pressure measured at detector points surrounding the proton Bragg peak. 2) For heterogeneity studies, a CT tissue image was used to calculate the proton dose deposition and define the acoustic properties of the voxels through which numerical pressure wave propagation was simulated with the k-Wave matlab toolbox. The simulations were used to assess the dependence of the acoustic amplitude and range-verification accuracy on proton pulse rise time and tissue heterogeneity. Results: As the proton pulse rise time is increased from 1 to 40 µs, the amplitude of the expected acoustic emission decreases (a 60% drop distal to the Bragg peak), the central frequency of the expected signal decreases (from 45 to 6 kHz), and the accuracy of the range-verification decreases (from <1 mm to 16 mm at 5 cm distal to the Bragg peak). For a 300 nA pulse, the expected pressure range is on the order of 0.1 Pa, which is observable with commercial detectors. For the heterogeneous medium, our test case shows that pressure waves emitted by an anterior pencil beam directed into the abdomen and detected posteriorly can determine the Bragg peak range to an accuracy of <2mm for a 1 µs proton pulse. Conclusion: For proton pulses with fast rise-times, protoacoustics is a promising potential method for monitoring penetration depth through heterogeneous tissue. The loss of range-verification accuracy with increasing rise-times, however, suggests the need for comparisons to modeling to improve accuracy for slower cyclotron proton sources.
07 ISOTOPE AND RADIATION SOURCES↗
Exact equations of state for nematics
We propose a novel approach to the solution of nematic Liquid Crystal models based on the derivation of a system of nonlinear wave equations for order parameters such that the occurrence of uniaxial and biaxial phase transitions can be interpreted as the propagation of a two-dimensional shock wave in the space of thermodynamic parameters. We obtain the exact equations of state for an integrable model of biaxial nematic liquid crystals and show that the classical transition from isotropic to uniaxial phase in absence of external fields is the result of a van der Waals type phase transition, where the jump in the order parameters is a classical shock generated from a gradient catastrophe at a non-zero isotropic field. The study of the equations of state provides the first analytical description of the rich structure of nematics phase diagrams in presence of external fields.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On the solution of the generalized wave and generalized sine-Gordon equations
The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.
Ablowitz, M. J.↗
Analytical Solutions to the Unsteady Response of an Isolated Finite Span Swept Airfoil to an Incident Gust and Unsteady Response of a Rectilinear Swept Cascade to an Incident Gust Problems
The solution to the problem of unsteady response of an isolated finite span swept airfoil to an incident gust is most conveniently obtained by introducing an acoustic velocity potential and eliminating all primitive variables from the governing equations. The end result is the convected wave equation for the acoustic velocity potential, phi. For the unsteady response of a rectilinear swept cascade to an incident gust problem, the governing equation and the imposed boundary conditions are the same as those for the isolated airfoil problem.
Envia, Edmane↗
Electromagnetoelastic Nano- and Microactuators for Mechatronic Systems
A generalized structural–parametric model of an electromagnetoelastic actuator is derived by solving the wave equation. Its transfer function is determined. The influence of geometric and physical parameters and the external load on its static and dynamic characteristics in the control system is established.
42 ENGINEERING↗
Exponential Runge-Kutta Parareal for non-diffusive equations
Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.
97 MATHEMATICS AND COMPUTING↗
A Contribution to the Theory of the Interaction of Transient Radiation of a Charged Particle with Periodically Modulated Anisotropic Magnetodielectric Filling of a Waveguide
Transient radiation of a charged particle in a waveguide with modulated anisotropic magnetodielectric filling is considered. It is assumed that the particle moves with a constant velocity perpendicularly to the axis of the waveguide the filling of which is periodically modulated by the harmonic law. Wave equations for the transverse electric (TE) and transverse magnetic (TM) fields in the waveguide have been obtained. Analytical expressions have been obtained for fields in the waveguide in the first approximation by small modulation indices of waveguide filling. Energies of transient radiation of a charged particle have been calculated in the region of weak (nonresonance) interaction between the radiation and modulation waves, in particular, in the case of a rectangular waveguide. It has been shown that radiation energies at the zero harmonic in the region of weak interaction do not depend on the modulation indices and are proportional to the modulation indices in the first power at the plus and minus first harmonics. The mechanism of the appearance of Cherenkov radiation has been analyzed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On the propagation of hypersonic solitons in a strained paramagnetic crystal
Nonlinear dynamics of a subnanosecond transverse elastic pulse in a low-temperature paramagnetic crystal placed into a magnetic field and statically strained in the same direction is investigated. Paramagnetic impurities implanted into the crystal have an effective spin of 3/2, and the pulse propagates at right angles to the magnetic field. In the general case, the structure of the pulse is such that the approximation of slowly varying envelopes, which is standard for quasi-monochromatic signals, is inapplicable. Under certain conditions, the pulse propagation in the 1D case is described by the Konno-Kameyama-Sanuki integrable wave equation for strain, which is transformed into the Hirota equation for the envelope of the given strain in the quasi-monochromatic limit. The effect of transverse perturbations on extremely short and quasi-monochromatic solitons is studied in detail. The conditions and features of self-focusing and defocusing of acoustic solitons in the form of extremely short pulses and envelope solitons are revealed. The propagation of an extremely short “half-wave” hypersonic pulse in the “acoustic bullet” regime in the medium with a quasiequilibrium population of quantum sublevels of effective spins is predicted.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Farfield viscous effects in nonlinear noise propagation
Discussion of the method of parametric differentiation in application to predictions of farfield noise propagation in both lossless and dissipative media. It is shown that, in the lossless medium, the governing equation, transformed to parameter space, reduces to a wave equation in the farfield. In the dissipative medium, the system of nonlinear partial differential equations, transformed to parameter space, reduces to a linear partial differential equation of the propagating type which contains a third-order derivative as well as the wave operator.
Harris, W. L., Sr.↗
Axisymmetric modes in magnetic flux tubes with internal and external magnetic twist
Observations suggest that twisted magnetic flux tubes are ubiquitous in the Sun's atmosphere. The main aim of this work is to advance the study of axisymmetric modes of magnetic flux tubes by modeling both twisted internal and external magnetic fields, when the magnetic twist is weak. In this work, we solve the derived wave equations numerically assuming that the twist outside the tube is inversely proportional to the distance from its boundary. We also study the case of a constant magnetic twist outside the tube and solve these equations analytically. We show that the solution for a constant twist outside the tube is a good approximation for the case where the magnetic twist is proportional to 1/r, namely, the error is in all cases less than 5.4%. The solution is in excellent agreement with solutions to simpler models of twisted magnetic flux tubes, i.e., without external magnetic twist. It is shown that axisymmetric Alfvén waves are naturally coupled with magnetic twist as the azimuthal component of the velocity perturbation is nonzero. We compared our theoretical results with observations and comment on what the Doppler signature of these modes is expected to be. Lastly, we argue that the character of axisymmetric waves in twisted magnetic flux tubes can lead to false positives in identifying observations with axisymmetric Alfvén waves.
79 ASTRONOMY AND ASTROPHYSICS↗
Linear confinement of spin-0 relativistic quantum particles in (1+2)-dimensions Gürses space–time
Highlights: •The relativistic wave equations with scalar potential are investigated in (1+2)-dimensional rotating space–time. •The bound state solutions are obtained. •The relativistic energy eigenvalues associated with different radial mode are discussed. -- Abstract: In this work, we investigate the linear confinement of spin- 0 relativistic quantum particle in the backgrounds of (1+2)-dimensions Gürses space–time (M. Gürses, Class. Quantum Grav. 11, 2585 (1994)). We solve the Klein–Gordon equation with a linear scalar potential in the considered framework, and evaluate the energy eigenvalues and corresponding eigenfunctions, in detail.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗